tag:blogger.com,1999:blog-59578968128203413972024-02-06T21:07:17.402-08:00Delta ScapeA place to write my way to understanding about issues related to teaching and learning. (Because of my experience, my focus is on mathematics education.) Please join me as I explore the changing educational landscape.delta_dchttp://www.blogger.com/profile/18024582157985654525noreply@blogger.comBlogger283125tag:blogger.com,1999:blog-5957896812820341397.post-23532341394748000442023-02-11T08:09:00.000-08:002023-02-11T08:09:13.340-08:00Were you talkin' about me?<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggos2EWnxCgs3Npig8xKYnUdSk79vo_WZDpld9gUY9eciC5grHZwolMuog6YtxSODuSlbyuWonwUM2A54VBHWzsohZgEMXK8QSgfHQ7KCKceuIW3QppjtlIVoEbAtOwlUoF59DcETZ0POp_KtMrGIq_hCTQKkhl3pjLAxaEYpSOsEyxf8DVmnLQjMuHA/s498/ted-lasso.gif" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: verdana;"><img border="0" data-original-height="280" data-original-width="498" height="225" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggos2EWnxCgs3Npig8xKYnUdSk79vo_WZDpld9gUY9eciC5grHZwolMuog6YtxSODuSlbyuWonwUM2A54VBHWzsohZgEMXK8QSgfHQ7KCKceuIW3QppjtlIVoEbAtOwlUoF59DcETZ0POp_KtMrGIq_hCTQKkhl3pjLAxaEYpSOsEyxf8DVmnLQjMuHA/w400-h225/ted-lasso.gif" width="400" /></span></a></div><span style="font-family: verdana;"><br /></span><p style="text-align: justify;"><span style="font-family: verdana;">Yes, people might be talking about you, especially if you attend our live episode of the <a href="https://twitter.com/search?q=%23TeachingLikeTedLasso&src=hashtag_click&f=live" target="_blank">#TeachingLikeTedLasso</a> <a href="https://shows.acast.com/teaching-like-ted-lass">podcast</a> at GVSU's Math in Action <a href="https://www.gvsu.edu/mathinaction/" target="_blank">Conference</a> on February 25, 2023.</span></p><p style="text-align: justify;"><span style="font-family: verdana;">Here's the description of the live session:</span></p><p class="MsoNormal" style="margin: 0in; vertical-align: baseline;"></p><blockquote style="text-align: justify;"><span style="background-color: white; border: 1pt none windowtext; color: #242424; padding: 0in;"><span style="font-family: verdana;">We started the Teaching Like Ted Lasso Podcast because we BELIEVE in the rich connections we saw between teaching and the positive and popular Apple TV <a href="https://www.imdb.com/title/tt10986410/" target="_blank">show</a>. No knowledge of the show is required - just an interest in improving our teaching! CURIOUS? Then please join us for this live episode, where you are the special guests sharing what works for you.</span></span></blockquote><p><span style="font-family: verdana;"></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: verdana;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMzk2GvV8wqHiFX5M-aEO2Myl1leWkI3noo-SmbHgPMAIIyGLSReQ5zJ8S7B1FrVTtbDDuc61CfTEHZZUvW3Y2IUB21K_8hVGBBOAjwm0-MKhTSGghFNFY7VyLoIpTGhGK6ocmExYlIQzP5mPyEeGI3zM5V4QumaPnEOd5CqMXtDhGWalQPNiqTr7hZg/s1200/TLTL%20Themes.jpeg" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="1200" data-original-width="1200" height="189" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMzk2GvV8wqHiFX5M-aEO2Myl1leWkI3noo-SmbHgPMAIIyGLSReQ5zJ8S7B1FrVTtbDDuc61CfTEHZZUvW3Y2IUB21K_8hVGBBOAjwm0-MKhTSGghFNFY7VyLoIpTGhGK6ocmExYlIQzP5mPyEeGI3zM5V4QumaPnEOd5CqMXtDhGWalQPNiqTr7hZg/w189-h189/TLTL%20Themes.jpeg" width="189" /></a></span></div><span style="font-family: verdana;"><div style="text-align: justify;"><span style="font-family: verdana;">The <a href="https://play.acast.com/s/62f3ebde7f77c400141e89cb/62f545cb1a7cd400124cccc9" target="_blank">plan</a> for our 10 episode podcast is to attend to 10 major themes that connect the show and teaching. Thus far, we have explored five themes: <a href="https://play.acast.com/s/62f3ebde7f77c400141e89cb/63333b899b7a2e001397f986" target="_blank">Play</a>; <a href="https://play.acast.com/s/62f3ebde7f77c400141e89cb/635c6a513e31010011b6cae1" target="_blank">Curiosity</a>; <a href="https://play.acast.com/s/62f3ebde7f77c400141e89cb/63878039a5aab900119c32b5" target="_blank">Teamwork</a>; <a href="https://play.acast.com/s/62f3ebde7f77c400141e89cb/63af041df3911f0011f856a6" target="_blank">Vulnerability</a>; and <a href="https://play.acast.com/s/62f3ebde7f77c400141e89cb/63d98604e2a2f90010f81d72" target="_blank">Discourse</a>. Because we are at the halfway point, we see the live episode at Math in Action as a retrospective - a way to reflect on what we've learned and add voices to the conversation. Participants in our Math in Action session will have the opportunity to share with each other (and potentially the world) </span><span style="font-family: verdana;">how they see their teaching practice connecting to these themes</span><span style="font-family: verdana;">.</span></div></span><p></p><p style="text-align: justify;"><span style="font-family: verdana;">Even if you are not going to be in the Grand Rapids, Michigan area on the 25th of February, there are a couple of ways you can still participate. </span></p><p style="text-align: justify;"><span style="font-family: verdana;">Our session, like many others during the Math in Action Conference will be in a hybrid format. (The Conversations Among Colleagues Conference, focusing on teaching math, math education, and statistics in higher education, is taking place at the same time and also has hybrid session - two conferences for the price of one. You can see the schedules <a href="https://www.gvsu.edu/mathinaction/math-in-action-program-2023-16.htm" target="_blank">here</a> and <a href="https://www.gvsu.edu/mathinaction/cac-program-2023-18.htm" target="_blank">here</a>.) That means you can Zoom in from anywhere in the world to participate and share your ideas.</span></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGeRVIOLSpz7V4j7_hegZ88O946G1WMJ7byoITO-Vq4paMiqfjymRkV9EzxP1eQrsB0y-hjMSAkiQ2IDZIu5JFDbcjo70cLW9sbJ6r6u3UBsonPfp7v9jQSX0GG71DbMZK5p2PRs1gGAzhSED-B77UpmSsKoDXoGKhvBDbJj4RQzxit0M4uW5lLUgU-Q/s498/ted-lasso-how-about-that.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: verdana;"><img border="0" data-original-height="367" data-original-width="498" height="236" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGeRVIOLSpz7V4j7_hegZ88O946G1WMJ7byoITO-Vq4paMiqfjymRkV9EzxP1eQrsB0y-hjMSAkiQ2IDZIu5JFDbcjo70cLW9sbJ6r6u3UBsonPfp7v9jQSX0GG71DbMZK5p2PRs1gGAzhSED-B77UpmSsKoDXoGKhvBDbJj4RQzxit0M4uW5lLUgU-Q/s320/ted-lasso-how-about-that.gif" width="320" /></span></a></div><p style="text-align: justify;"><span style="font-family: verdana;">Or, if you are busy that day, make a short (five minutes or less) video recording of your answers to the following questions and send them to us at </span><span style="font-family: verdana;"><a href="mailto:teachingliketedlasso@gmail.com">teachingliketedlasso@gmail.com</a></span><span style="font-family: verdana;">: </span></p><p></p><p></p><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-family: verdana;">Who are you?</span></li><li style="text-align: justify;"><span style="font-family: verdana;">Where are you from?</span></li><li style="text-align: justify;"><span style="font-family: verdana;">What is your relationship to education? and</span></li><li style="text-align: justify;"><span style="font-family: verdana;">How do you apply [play, curiosity, teamwork, vulnerability, or discourse] in your teaching practice? </span></li></ul><span style="font-family: verdana;"><div style="text-align: justify;"><span style="font-family: verdana;">If you send the recording before February 25th, we might be able to share it during the session. Recordings sent before March 1, 2023 will be considered for the retrospective episode. We cannot guarantee that everyone's response will make the episode, but we will do our best. If your answers do make it onto the podcast, we will create for you one of these </span><span style="font-family: verdana;">handsome Teaching Like Ted Lasso trading cards. (So, you'll also want to send an action photo in your email - just in case).</span></div></span><p></p><span face="Verdana, sans-serif" style="color: #242424; font-family: verdana;"><o:p></o:p></span><p></p><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiATvgj6RcNIudCY78kKc80P9G4IdtuPdH0ffmQgj2aOORaMHJrRGH9Qzr5f3vA1BFUX3VhIQYk9kkkMvGMApesoJr84dOlW5bu_u9gr4hKNkVblySwhHD84zVi8sW-tuiqiLxKhpUPTAxP35nCtpt6hEP_X_DLW7aN0bNYqhmqF61Oivh75knBCKOaMQ/s1280/Vance.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: verdana;"><img border="0" data-original-height="1280" data-original-width="854" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiATvgj6RcNIudCY78kKc80P9G4IdtuPdH0ffmQgj2aOORaMHJrRGH9Qzr5f3vA1BFUX3VhIQYk9kkkMvGMApesoJr84dOlW5bu_u9gr4hKNkVblySwhHD84zVi8sW-tuiqiLxKhpUPTAxP35nCtpt6hEP_X_DLW7aN0bNYqhmqF61Oivh75knBCKOaMQ/w268-h400/Vance.jpg" width="268" /></span></a></div><div class="separator" style="clear: both; text-align: left;"><span style="font-family: verdana;"><br /></span></div><div class="separator" style="clear: both; text-align: justify;"><span style="font-family: verdana;">You can register for Math in Action <a href="https://www.gvsu.edu/mathinaction/mia-registration-4.htm" target="_blank">here</a>. Please send you video responses to <a href="mailto:teachingliketedlasso@gmail.com">teachingliketedlasso@gmail.com</a>. We are excited to add your voices to the Teaching Like Ted Lasso conversation.</span></div><div><span style="font-family: verdana;"><br /></span></div><span style="font-family: verdana;">PS: In-person participants might meet some of the stars of TLTL Theatre</span></div><div><span style="font-family: verdana;"><br /></span></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFRTZKT5L7GpdUzD1PgrDg2D4y_K45Q3g6cAuDmNzO4NECFFcPO8-CfWwvvr-vcGRLMWive2opiPYZ7QaqGE6eakJfTKuHUD_U5e768Od0zFzn8TDfwEr81I-OvU0MC7beVlWnms0-RSuZNd8s9_UOWXWE3CyfqFw9SjGVvxatwNIoETnVh1dYuJgxZA/s4032/Rebecca%20and%20Ted%20LR.HEIC" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="3024" data-original-width="4032" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFRTZKT5L7GpdUzD1PgrDg2D4y_K45Q3g6cAuDmNzO4NECFFcPO8-CfWwvvr-vcGRLMWive2opiPYZ7QaqGE6eakJfTKuHUD_U5e768Od0zFzn8TDfwEr81I-OvU0MC7beVlWnms0-RSuZNd8s9_UOWXWE3CyfqFw9SjGVvxatwNIoETnVh1dYuJgxZA/w400-h300/Rebecca%20and%20Ted%20LR.HEIC" width="400" /></a></div><br /><span style="font-family: verdana;"><br /></span></div><div><span style="font-family: verdana;">and experience the added bonus of biscuits!</span></div><div><span style="font-family: verdana;"><br /></span></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghFpJeEecb3H0uDiTAU9ifEckFGEUZvw2E1djQ0oww2xNF5uQKxJaHcEF8Wl6yHKR2IWUbzTCKg_nT7_RPSAsPRnew5yhS9yJKvRZg4eHzqCwXH7pFyVqBuTfiJ_gWWNdzudOqgnlO5dUrWFGuuuL7q1lKJAd6TJ_STm9trg_vZjwjkK9OtIC1mSWoXg/s275/Biscuits.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="257" data-original-width="275" height="374" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghFpJeEecb3H0uDiTAU9ifEckFGEUZvw2E1djQ0oww2xNF5uQKxJaHcEF8Wl6yHKR2IWUbzTCKg_nT7_RPSAsPRnew5yhS9yJKvRZg4eHzqCwXH7pFyVqBuTfiJ_gWWNdzudOqgnlO5dUrWFGuuuL7q1lKJAd6TJ_STm9trg_vZjwjkK9OtIC1mSWoXg/w400-h374/Biscuits.gif" width="400" /></a></div><br /><span style="font-family: verdana;"><br /></span><span style="font-family: verdana;"><br /></span></div>delta_dchttp://www.blogger.com/profile/18024582157985654525noreply@blogger.com0tag:blogger.com,1999:blog-5957896812820341397.post-24115887651930569532022-10-04T08:48:00.005-07:002022-10-04T09:01:06.800-07:00Whatcha been doing, Bobby Ewing?<p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span style="background-color: white; caret-color: rgb(13, 13, 13); text-size-adjust: auto;">My colleague and friend, <a href="http://mathhombre.blogspot.com/" target="_blank">John Golden</a>, and I </span><span style="background-color: white; caret-color: rgb(13, 13, 13); color: #0d0d0d; text-size-adjust: auto; white-space: pre-wrap;">watched the first two seasons of <a href="https://tv.apple.com/us/show/ted-lasso/umc.cmc.vtoh0mn0xn7t3c643xqonfzy?ign-itscg=MC_20000&ign-itsct=atvp_brand_omd&mttn3pid=Google%20AdWords&mttnagencyid=a5e&mttncc=US&mttnsiteid=143238&mttnsubad=OUS2019863_1-621472716635-c&mttnsubkw=105373391198__T5vZfnlx_&mttnsubplmnt=" target="_blank">Ted Lasso</a>, the Emmy Award Winning AppleTV+ series, and thought, "This has a lot of great lessons for educators." So, we're creating 10 episodes addressing major themes from the show that might support teachers in improving their professional practice. Each episode will include teaching and learning examples from the show, from the research, and from practice. If you're interested in this sort of thing, we ask that you become part of the Ted Ed community and share your ideas on Twitter at </span><span style="background-color: white; caret-color: rgb(13, 13, 13); color: #0d0d0d; text-size-adjust: auto; white-space: pre-wrap;">#<a href="https://twitter.com/hashtag/TeachingLikeTedLasso?src=hashtag_click&f=live" target="_blank">TeachingLikeTedLasso</a></span><span style="background-color: white; caret-color: rgb(13, 13, 13); color: #0d0d0d; text-size-adjust: auto; white-space: pre-wrap;">.</span></span></p><p><span style="font-family: verdana; font-size: medium;"><span style="background-color: white; caret-color: rgb(13, 13, 13); color: #0d0d0d; text-size-adjust: auto; white-space: pre-wrap;">Here's the video we put out that introduces the podcast:</span></span></p><p><span style="font-family: verdana; font-size: medium;"></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: verdana; font-size: medium;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/LPdrZ6V5Wlc" width="320" youtube-src-id="LPdrZ6V5Wlc"></iframe></span></div><p></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span style="color: #0d0d0d;"><span style="background-color: white; caret-color: rgb(13, 13, 13); white-space: pre-wrap;">Each episode we will be sharing scenes from the show, but, like Roy, we are really bad at impressions. So we've decided to have some fun with it.</span></span></span></p> <blockquote class="twitter-tweet"><p dir="ltr" lang="en">A sneak peak at the kind of content these <a href="https://twitter.com/TedLasso?ref_src=twsrc%5Etfw">@TedLasso</a> Little People will contribute to the <a href="https://twitter.com/hashtag/TeachingLikeTedLasso?src=hash&ref_src=twsrc%5Etfw">#TeachingLikeTedLasso</a> podcast. <a href="https://t.co/yxV2nOqDI6">pic.twitter.com/yxV2nOqDI6</a></p>— Teaching Like Ted Lasso (@LikeLasso) <a href="https://twitter.com/LikeLasso/status/1564417088298651653?ref_src=twsrc%5Etfw">August 30, 2022</a></blockquote><span style="font-family: verdana; font-size: medium;"><div style="text-align: justify;"><span style="background-color: white; caret-color: rgb(13, 13, 13); color: #0d0d0d; white-space: pre-wrap;">To make sure you don't miss any content, subscribe to our YouTube </span><a href="https://www.youtube.com/channel/UCGisypKl-TyaUTA-YYJH1iQ/null" style="caret-color: rgb(13, 13, 13); white-space: pre-wrap;" target="_blank">Channel</a><span style="background-color: white; caret-color: rgb(13, 13, 13); color: #0d0d0d; white-space: pre-wrap;"> or the audio version of the podcast</span></div></span><div> <script async="" charset="utf-8" src="https://platform.twitter.com/widgets.js"></script><iframe allow="autoplay" frameborder="0" height="110px" src="https://embed.acast.com/$/62f3ebde7f77c400141e89cb/the-introduction" width="100%"></iframe></div><div><span style="font-family: verdana; font-size: medium;"><span style="color: #0d0d0d;"><span style="background-color: white; caret-color: rgb(13, 13, 13); white-space: pre-wrap;">or both.</span></span></span></div><div><span style="font-family: verdana; font-size: medium;"><span style="color: #0d0d0d;"><span style="background-color: white; caret-color: rgb(13, 13, 13); white-space: pre-wrap;"><br /></span></span></span></div><div style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span style="color: #0d0d0d;"><span style="background-color: white; caret-color: rgb(13, 13, 13); white-space: pre-wrap;">Let us know what teaching and learning themes you see in the show by sharing them in the comments.</span></span></span></div><div><span style="font-family: verdana; font-size: medium;"><span style="color: #0d0d0d;"><span style="background-color: white; caret-color: rgb(13, 13, 13); white-space: pre-wrap;"><br /></span></span></span></div><div style="text-align: justify;"><span style="font-family: verdana; font-size: medium;"><span style="color: #0d0d0d;"><span style="background-color: white; caret-color: rgb(13, 13, 13); white-space: pre-wrap;">We appreciate you.</span></span></span></div><div><span style="font-family: verdana; font-size: medium;"><span style="color: #0d0d0d;"><span style="background-color: white; caret-color: rgb(13, 13, 13); white-space: pre-wrap;"><br /></span></span></span></div>delta_dchttp://www.blogger.com/profile/18024582157985654525noreply@blogger.com0tag:blogger.com,1999:blog-5957896812820341397.post-84026998733902647222021-08-10T11:40:00.000-07:002021-08-10T11:40:50.832-07:00How do you like your marshmallow?<p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiI_s9zXFxhGU0Be4MXEG7Ze344DKwPqowAEwphyphenhyphen1RFjlY0VB8pB8E2Wwt_Sl24er83gXQMmC_3EKqrWOHBbHXSdVb51TMCJajW3LXWhxgYVQqp2W-R7UhdaTzCMdZBSgCvDE71QViFj8fs/s720/IMG_2969.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="720" data-original-width="720" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiI_s9zXFxhGU0Be4MXEG7Ze344DKwPqowAEwphyphenhyphen1RFjlY0VB8pB8E2Wwt_Sl24er83gXQMmC_3EKqrWOHBbHXSdVb51TMCJajW3LXWhxgYVQqp2W-R7UhdaTzCMdZBSgCvDE71QViFj8fs/w200-h200/IMG_2969.jpg" width="200" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: justify;"><span style="font-family: verdana;">Today, I moderated a panel of early elementary educators who discussed the Values underlying Michigan's <i>Essential Instructional Practices in Early Mathematics </i>[<a href="https://www.gomaisa.org/downloads/gelndocs/early_math-prek-3_102219.pdf" target="_blank">PDF</a>]. </span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-family: verdana;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBAjH87liykd-EQ_Gk6iBu2I_C5pKeEql-f6saXyq43drgTfwx2_h24VMpeUB3gecK1eOnKrB7gCSQ9nIL-D7x4SkX-7AxDhsYZMgz2L998lpXKncdNsGo_BgpbZx2EyJBR6JXrr5CnGOM/s1216/Screen+Shot+2021-08-09+at+9.25.39+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1022" data-original-width="1216" height="336" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBAjH87liykd-EQ_Gk6iBu2I_C5pKeEql-f6saXyq43drgTfwx2_h24VMpeUB3gecK1eOnKrB7gCSQ9nIL-D7x4SkX-7AxDhsYZMgz2L998lpXKncdNsGo_BgpbZx2EyJBR6JXrr5CnGOM/w400-h336/Screen+Shot+2021-08-09+at+9.25.39+AM.png" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><span style="font-family: verdana;"><div style="text-align: justify;">The session began with my favorite ways to start a session/class: <b>While We Wait</b>. This is a nice way to give participants something to do while we wait for everyone to join the online space. It also provides an opportunity to get to know one another around a fun topic. Because today is National S'mores Day, I thought the following prompt was appropriate. (There's a whole <a href="https://nationaldaycalendar.com" target="_blank">calendar</a> of National Days.)</div></span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-family: verdana;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQJNXfTrk1LPT17tv-XB3yod5wEnK-dY7cDN6IGpbsrSBBP_f9XOQTivsZNknluU8xssDOe5G6HsIwR19YTehzWOcMkAR-LP3pAnww2_p_04e8gaQkqKOm7n435pH1omF9M8RYXIKvIl6Q/s1378/Screen+Shot+2021-08-10+at+2.17.17+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="776" data-original-width="1378" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQJNXfTrk1LPT17tv-XB3yod5wEnK-dY7cDN6IGpbsrSBBP_f9XOQTivsZNknluU8xssDOe5G6HsIwR19YTehzWOcMkAR-LP3pAnww2_p_04e8gaQkqKOm7n435pH1omF9M8RYXIKvIl6Q/w640-h360/Screen+Shot+2021-08-10+at+2.17.17+PM.png" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: justify;"><span style="font-family: verdana;">I also thought the question was a good metaphor for the session: how the Values ought to inform our teaching practice. By thinking about our desired marshmallow and the ways that impacts how we toast them, we could transition to how teaching early math might change to reflect our desired values.</span></div><div class="separator" style="clear: both; text-align: left;"><ul style="text-align: left;"><li style="text-align: justify;"><span style="font-family: verdana;">So, how do you like your marshmallows? </span></li><li style="text-align: justify;"><span style="font-family: verdana;">What do you do to get them toasted just right?</span></li><li style="text-align: justify;"><span style="font-family: verdana;">And how might the Values provided above change the way we teach math in the early grades?</span></li></ul><div style="text-align: justify;"><span style="font-family: verdana;">The comments are open.</span></div></div><br /><span style="font-family: verdana;"><br /></span></div><br /> <p></p>delta_dchttp://www.blogger.com/profile/18024582157985654525noreply@blogger.com0tag:blogger.com,1999:blog-5957896812820341397.post-35627944588522016052021-07-23T11:00:00.003-07:002021-07-23T11:00:57.545-07:00What will you be teaching on October 20th?<p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJstxP7Dp96BsHhHXvDBevxGYtN0ktLomMTI1HnyguJK2_gkagnmz1vvZTHOhFtHi7DzLQXYPKyjQ6XOgOuDAsDB7c-XgPdk0ochRmBO-h41C6oRp3D-3fEr4-RsOYvYBxfNIIeVv_ch4p/" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" data-original-height="183" data-original-width="275" height="133" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJstxP7Dp96BsHhHXvDBevxGYtN0ktLomMTI1HnyguJK2_gkagnmz1vvZTHOhFtHi7DzLQXYPKyjQ6XOgOuDAsDB7c-XgPdk0ochRmBO-h41C6oRp3D-3fEr4-RsOYvYBxfNIIeVv_ch4p/w200-h133/Portable.jpg" width="200" /></a></div><span style="font-family: verdana;"><div style="text-align: justify;">My first real teaching job was at <a href="https://www.grantps.net" target="_blank">Grant</a> Middle School. I was hired on the Thursday before school started and began teaching the next Monday. I taught 8th grade math in a portable classroom (much like the one shown on the <a href="https://www.ramtechmodular.com/modular-school-buildings/modular-portable-classrooms/" target="_blank">right</a>) and coached the girls and boys basketball teams. It was wonderful but also stressful. I always felt like l was just a few lessons ahead of my students.</div></span><p></p><p style="text-align: justify;"><span style="font-family: verdana;">At the end of the school year, I vowed that I'd never be so disorganized in my teaching ever again. I spent the entire summer planning my lessons for the next year. I was assigned 8th grade math again and also an Algebra class. By the time school started, I could tell you exactly what I'd be doing during either class any day of the year.</span></p><p style="text-align: justify;"><span style="font-family: verdana;">It was my worst year of teaching. I had spent so much time focusing on the content that I had totally forgotten about the students. And I put so much effort into the plans that I was resistant to altering them. My students and I were all miserable.</span></p><p style="text-align: justify;"><span style="font-family: verdana;">I share this story with the teachers I work with as a cautionary tale. It's tempting to want to be totally prepared for every lesson. Unfortunately, it's impossible. It's better to have a lesson prototype in mind that can be altered in response to feedback from students. We use a version of this <a href="https://www.cultofpedagogy.com/one-sentence-lesson-plan/" target="_blank">One-Sentence Lesson Plan</a> as a framework for our prototypes for designing math adventures. The incompleteness leaves room for student-voice and student-choice during the lesson experiment.</span></p><p style="text-align: justify;"><span style="font-family: verdana;"></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: verdana;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghOS3B-9AQH4ksq-z6xoT-DQxipv827Tvnvh1KrA-YVuq9qXJNHRaD9KAeFJoP0fvet0Dsxv6HtJMcSGU_fGlqW6UVYOZpfSjaxSp33sCSH1U-hUXFRP1KuzLkS_gsi0QepqH8Monis7Ci/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="750" data-original-width="2000" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghOS3B-9AQH4ksq-z6xoT-DQxipv827Tvnvh1KrA-YVuq9qXJNHRaD9KAeFJoP0fvet0Dsxv6HtJMcSGU_fGlqW6UVYOZpfSjaxSp33sCSH1U-hUXFRP1KuzLkS_gsi0QepqH8Monis7Ci/w640-h240/OSLP.jpg" width="640" /></a></span></div><p></p><p style="text-align: justify;"><span style="font-family: verdana;">So, instead of spending the summer planning out every detail of the coming school year, please keep it simple and give yourself some time to recreate and </span><span style="font-family: verdana;">restore. Maybe you could explore some new places. This will hopefully re-energize you and allow you to be more responsive to the students in your classes.</span></p><p style="text-align: justify;"><span style="font-family: verdana;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5nLZDmy6iDrSkOvZlfxs9b6-L7rpz-j9wXKsupqqHwi6cC7V_a29WEe2h3R600_tsNKFEysQNoAzFlgbYqp9l5pmP8S3dpkdp6Y8C3pwGrEkBeG2EfVrrJVOSTHN6yw5ZVBcIhuXABzAm/" style="margin-left: auto; margin-right: auto;"><img alt="" data-original-height="768" data-original-width="1024" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5nLZDmy6iDrSkOvZlfxs9b6-L7rpz-j9wXKsupqqHwi6cC7V_a29WEe2h3R600_tsNKFEysQNoAzFlgbYqp9l5pmP8S3dpkdp6Y8C3pwGrEkBeG2EfVrrJVOSTHN6yw5ZVBcIhuXABzAm/" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="font-size: x-small;">Scampy McScamperson visits Devils Tower</span></td></tr></tbody></table><br /></span></p>delta_dchttp://www.blogger.com/profile/18024582157985654525noreply@blogger.com1tag:blogger.com,1999:blog-5957896812820341397.post-57423002858480272822021-06-30T06:31:00.004-07:002021-06-30T06:31:32.189-07:00What's the problem we're trying to solving in math education?<p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUY-Cag5Sf4rto28wK91i3L8RrC6JF_edIfdHoyovWIdgQvOOSHllbQywee666xcMTkhW_ZSkhbunMlxHhaEUrBRlxMRqwPTwspkFE9S3M5PwViaEu3qgJjMADur6JnQmOgmDz9yfBWb_H/s2048/IMG_3444.JPG" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="1536" data-original-width="2048" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUY-Cag5Sf4rto28wK91i3L8RrC6JF_edIfdHoyovWIdgQvOOSHllbQywee666xcMTkhW_ZSkhbunMlxHhaEUrBRlxMRqwPTwspkFE9S3M5PwViaEu3qgJjMADur6JnQmOgmDz9yfBWb_H/w200-h150/IMG_3444.JPG" width="200" /></a></div><span style="font-family: verdana; font-size: large;"><div style="text-align: justify;">The way we ask a question tends to frame our solution. This was one of the most long-lasting lessons that I learned at the d.school's week-long Teaching and Learning <a href="https://dschool.stanford.edu/university-innovation/vtls-july2021" target="_blank">Studio</a>. The activity we did early in the week to introduce this idea is one that I still do with teachers. I'll do my best to recreate that experience here.</div></span><p></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: large;">First, I need you to break into one of two groups. Each group will do a different task. Let's assign your task based on your birthdate. If the day of your birth is odd, then do the first task. If it is even, then do the second one. (e.g. I was born on the 29th, so I'd be in group one.)</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: large;">To begin, click on the appropriate link provided below. It will open up a copy of a Jamboard with the task's question. You can do your work on the Jamboard (it is yours to keep) or on a separate piece of paper.</span></p><p><span style="font-family: verdana; font-size: large;">Task <a href="https://jamboard.google.com/d/1dq6QGKvhTUFG-UPT1_bqsikWAJ6qaCpzRenZLWhhjeA/copy" target="_blank">One</a> (odd birthdates)</span></p><p><span style="font-family: verdana; font-size: large;">Task <a href="https://jamboard.google.com/d/1gTvblPaXoq62o96GiAKC26rI7Yv9x7mQZskw8BpyvsA/copy" target="_blank">Two</a> (even birthdates)</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: large;"><b>Don't read any farther until you've completed your task or you'll ruin the surprise.</b></span></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfisLu6tNGZIFcmBBCIXDyRBqg9J2oTXC5syZXO5QFajiUt24pFc4pA2SBLC-wt-H__xUGcyIsS95NUVldsrnMPjzfRc57aXVRjf4uZVqCfcZucnsHSdKbX-eFbI5AJ7C-61tX-o_DLbRM/s800/IMG_2902.JPG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="536" data-original-width="800" height="429" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfisLu6tNGZIFcmBBCIXDyRBqg9J2oTXC5syZXO5QFajiUt24pFc4pA2SBLC-wt-H__xUGcyIsS95NUVldsrnMPjzfRc57aXVRjf4uZVqCfcZucnsHSdKbX-eFbI5AJ7C-61tX-o_DLbRM/w640-h429/IMG_2902.JPG" width="640" /></a></div><p style="text-align: left;"><span style="font-family: verdana; font-size: large;">Once you've completed your task, click on the other task question and consider how that question might result in different solutions and why.</span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: large;">The first group often comes up with a variety of creative vases. Some have multiple openings at the top. Some hold the flowers sideways. However, because of the way the question is framed, they are all obviously vases.</span></p><p style="text-align: center;"><span style="font-size: large; margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2048" data-original-width="2048" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNYeK77UwAOQb3m0oHN-V9NuszaPHlqwqTJcN0j59Yq_xk70Rv5SpfujzeshXEdB8dKBe_prZF4l4bjfsyjFeR8OsG0x3LzkYt21m1eFkjPaJOKgSyql0iNZZnmebEy1mLrpVNrbWF2khD/w400-h400/IMG_9121.jpg" width="400" /></span></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: large;">Very few vases show up in the second group. Instead, flowers grow on the wall or hang from the ceiling. One participant had the flowers floating in a clear container with a fan at the bottom. Sure, it might not actually be feasible, but it is a much more creative way to start seeking solutions.</span></p><p style="text-align: justify;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7DtudKUp9KZ1sic0QLiDc3Ov6qPmkt0C-OE8o5PLv-BKYBkXyDgVFC8O1pbh1ngSxtp7Tr5jSA7ie6jJEybEPWvMrPqOiwssYEMv9mJU9zYPHz-MEg4rmoejfac4xq5ZaxDzfrTn_6i18/s1061/IMG_2904.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1061" data-original-width="1061" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7DtudKUp9KZ1sic0QLiDc3Ov6qPmkt0C-OE8o5PLv-BKYBkXyDgVFC8O1pbh1ngSxtp7Tr5jSA7ie6jJEybEPWvMrPqOiwssYEMv9mJU9zYPHz-MEg4rmoejfac4xq5ZaxDzfrTn_6i18/w400-h400/IMG_2904.jpg" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><div><span style="font-family: verdana; font-size: x-small;">IBM does a version of this activity in their </span></div><span style="font-family: verdana; font-size: x-small;"><a href="https://jchristyliu.com/blog/2019/3/14/ibm-enterprise-design-thinking-course" target="_blank">Enterprise Design Thinking Course</a><br /></span></td></tr></tbody></table></p><p style="text-align: justify;"><span style="text-align: left;"><span style="font-family: verdana; font-size: large;">I ask educators to do these tasks to highlight that most of our efforts to innovate in math classrooms amount to the first task. No matter what we do, we just end up with another vase. This is one reason why Kathy and I wrote <i>Designing Math Adventures</i> - because we want learners to experience something more than another math lesson.</span></span></p><p></p><p style="text-align: justify;"><span style="font-family: verdana; font-size: large;">So, what's the question you'll ask to frame your next school year? I'd like to collect them in the comments. Thanks for contributing to our creative problem-solving.</span></p>delta_dchttp://www.blogger.com/profile/18024582157985654525noreply@blogger.com0tag:blogger.com,1999:blog-5957896812820341397.post-7825377178293560352021-06-26T06:58:00.003-07:002021-06-26T07:02:25.997-07:00Why write Designing Math Adventures?<p></p><p style="text-align: justify;"><span style="font-family: verdana;">In planning the book, <i>Designing Math Adventures</i>, Kathy and I took Simon Sinek's <a href="https://youtu.be/fMOlfsR7SMQ" target="_blank">advice</a> and started by identifying our WHY: <b>to support educators' efforts to improve K-8 math learning</b>.</span></p><span style="font-family: verdana;"><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjoxA0D-ZwGfs5dyp8_KbSeO36QnSbRhIvMla8FrBfOPYbVJxcYl9sBxcdlx8SLgcDw4QQuNUe3lYCcoB3ow0G2Uv5Rx5i7YUD4CKLw3gaHF8l2ZtwQtWjF53aCFaaP2L8HYkM2RLRuy7E/s585/large_GC_slides_v1.4-585x439.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="439" data-original-width="585" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjoxA0D-ZwGfs5dyp8_KbSeO36QnSbRhIvMla8FrBfOPYbVJxcYl9sBxcdlx8SLgcDw4QQuNUe3lYCcoB3ow0G2Uv5Rx5i7YUD4CKLw3gaHF8l2ZtwQtWjF53aCFaaP2L8HYkM2RLRuy7E/w640-h480/large_GC_slides_v1.4-585x439.jpg" width="640" /></a></div><div style="text-align: center;"><span style="font-size: x-small;"><a href="https://sjef.nu/theory-of-change-and-the-golden-circle/" target="_blank">Golden Circle</a></span></div></div><p style="text-align: justify;"><span>Based on our interactions with thousands of teachers, we can confirm that Brené Brown is <a href="https://www.youtube.com/watch?v=w5TkA7d7eTw" target="_blank">right</a>. Most of us are doing the best we can under the circumstances. This doesn't mean there isn't room for improvement. We wrote this book to help teachers to make the subtle shifts necessary to change their current circumstances and improve the teaching and learning of math in their classrooms. </span></p></span><p style="text-align: justify;"><span style="font-family: verdana;"><span><span>HOW can teachers change their circumstances? Sometimes it's as simple as </span></span><span>doing more of what’s working and less of what’s not. The level of </span>intentionality we are talking about requires an honest examination of our teaching practice. This type of reflection isn't always easy.</span></p><p style="text-align: justify;"><span style="font-family: verdana;"><span>WHAT <i>Designing Math Adventures</i> offers is a design thinking <a href="https://innovatorscompass.org" target="_blank">tool</a> that supports teachers in creating meaningful math lessons. By considering five straightforward questions, teachers can write a lesson that responds to the mathematical brilliance of their students in thirty minutes or less. We know teachers are incredibly busy, so we want to ensure that the approach is both sustainable and satisfying.</span></span></p><div><p></p><p><span style="font-family: verdana;"><br /></span></p></div>delta_dchttp://www.blogger.com/profile/18024582157985654525noreply@blogger.com0tag:blogger.com,1999:blog-5957896812820341397.post-21147065256958910442021-06-23T06:45:00.000-07:002021-06-23T06:45:03.589-07:00Where have I been?<p style="text-align: justify;"><span style="font-family: verdana;">I haven't <a href="http://deltascape.blogspot.com/2018/09/how-might-we-deal-with-mismatch.html" target="_blank">posted</a> on this blog for nearly two years and nine months. It's not that I lost confidence in the power of blogging as a way to share and reflect on my thinking. I just got busy.</span></p><p style="text-align: justify;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfHzDI4eshp8E9NKdt9WMcWJh7mpDiuJeBBHKa9kfpjG8BOcfOmvI9jq4z-G5ZDzn90dN_L_H6TAPUxTaWgUTFCd4NpPrJa3oNOylZu8XCX6eXx5G_7bNdjQNR7m_3Soje3VfykeecaoHl/s2048/Laker+Life+Night.jpeg" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="1536" data-original-width="2048" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfHzDI4eshp8E9NKdt9WMcWJh7mpDiuJeBBHKa9kfpjG8BOcfOmvI9jq4z-G5ZDzn90dN_L_H6TAPUxTaWgUTFCd4NpPrJa3oNOylZu8XCX6eXx5G_7bNdjQNR7m_3Soje3VfykeecaoHl/w200-h150/Laker+Life+Night.jpeg" width="200" /></a></div><span style="font-family: verdana;"><div style="text-align: justify;">First, I took a position as director of the Design Thinking Academy [<a href="https://www.gvsu.edu/designthinking/" target="_blank">DTA</a>] at Grand Valley State University. The goal of the academy is to support the use of design thinking methods and mindsets across the campus community. My work entailed visiting classes, scheduling pop-up courses, facilitating semester-long design challenges, managing creativity kiosks, and organizing the GVSU Design Thinking Speaker Series.</div></span><div><span style="font-family: verdana; text-align: justify;"><br /></span></div><div><div style="text-align: left;"><span style="font-family: verdana; text-align: justify;">Ela Ben-Ur was our first speaker. She held a series of workshops where she introduced participants to a design thinking </span><a href="https://innovatorscompass.org" style="font-family: verdana; text-align: justify;" target="_blank">tool</a><span style="font-family: verdana; text-align: justify;"> she created - the Innovators' Compass.</span></div><p style="text-align: center;"><span style="font-family: verdana;"> <iframe allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" frameborder="0" height="315" src="https://www.youtube.com/embed/4-VkbQNxijw" title="YouTube video player" width="560"></iframe></span></p><p style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: verdana;">Ela Ben-Ur: </span><span style="font-family: verdana;"><i>Design Thinking and You</i> (GVSU DT Speaker Series)</span></span></p><p style="text-align: justify;"><span style="font-family: verdana;">I learned about Ela's work on this <a href="https://designthinking101.libsyn.com/the-innovators-compass-making-design-thinking-accessible-and-how-to-design-well-with-others-with-ela-ben-ur-dt101-e2" target="_blank">episode</a> of the Design Thinking 101 podcast.</span></p><p style="text-align: justify;"><span style="font-family: verdana;">This introduction to the Compass lead to the second project that has been occupying my time - writing a book. <a href="https://literacygurl.blogspot.com" target="_blank">Kathy</a> and I have been wanting to write about the Teaching & Learning Cycle for some time, but we always felt like something was lacking. When we learned about the Innovators' Compass and how it can help people to get unstuck or explore uncharted territory, we thought it would be a good resource for teachers engaging in the Cycle.</span></p><p style="text-align: justify;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCIovnzzWpIEbIvMC6VQMGRzgprRhwMd6OTZyL_tE_26FDFP1XYXs3346NaDdrWKVXCJOuhf41fUxVBQA6OTPBPB0PdaKdN-Bum7F9_Y5SYQsfOX9x2JsyFu_GckRZD34Xzwe8v9-7awG_/s1969/IC+DT+.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1969" data-original-width="1536" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCIovnzzWpIEbIvMC6VQMGRzgprRhwMd6OTZyL_tE_26FDFP1XYXs3346NaDdrWKVXCJOuhf41fUxVBQA6OTPBPB0PdaKdN-Bum7F9_Y5SYQsfOX9x2JsyFu_GckRZD34Xzwe8v9-7awG_/w501-h640/IC+DT+.jpg" width="501" /></a></div><span style="font-family: verdana;"><p style="text-align: center;"><span style="font-size: x-small;">Innovators' Compass - design thinking <a href="https://dschool.stanford.edu/resources/getting-started-with-design-thinking" target="_blank">cycle</a> (hexagons) - Teaching & Learning Cycle (purple)</span></p><p style="text-align: justify;">Now that a draft of the book is done (<a href="https://twitter.com/hashtag/DesigningMathAdventures?src=hashtag_click" target="_blank">#DesigningMathAdventures</a>) and sent to some publishers, I'm not as busy. Because I had set aside an hour each morning to engage in creative writing and didn't want to lose that momentum, I decided to fire up the old blog. I figured it would not only give me something to do while we <a href="https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwjE6JS15ajxAhXSvJ4KHQCLAQMQyCkwAHoECAIQAw&url=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DuMyCa35_mOg&usg=AOvVaw1UTN7_tFHsRFekfxKNEVWL" target="_blank">wait</a> to hear from the publishers but also allow me to share some parts from our writing that didn't make the latest cut.</p></span><p></p><p style="text-align: justify;"><span style="font-family: verdana;">Thanks for indulging me in this exercise of creativity. As always, if you have any questions, please post them below or reach out on Twitter (<a href="https://twitter.com/delta_dc">@delta_dc</a>). The comments are open.</span></p></div>delta_dchttp://www.blogger.com/profile/18024582157985654525noreply@blogger.com8tag:blogger.com,1999:blog-5957896812820341397.post-57392787766106716452018-09-27T12:33:00.000-07:002018-09-27T12:34:14.041-07:00How might we deal with the mismatch?<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhiks0hBiuaXWdp-x4tFfbiBKlGsdhKDvmDeRXFXUeSGN-rBq-678w3mkqzXGwAWgNAb71v7JhqVhw8Sxiss1Y9-2CboSEiA8LB798fhU1RqvbxwGbdpCv1bMqtRMDE25aXSpe1ErjmUvg6/s1600/Toyota+Lecture+Series+featuring+Kat+Holmes.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1600" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhiks0hBiuaXWdp-x4tFfbiBKlGsdhKDvmDeRXFXUeSGN-rBq-678w3mkqzXGwAWgNAb71v7JhqVhw8Sxiss1Y9-2CboSEiA8LB798fhU1RqvbxwGbdpCv1bMqtRMDE25aXSpe1ErjmUvg6/s200/Toyota+Lecture+Series+featuring+Kat+Holmes.jpg" width="200" /></a></div>
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<span style="font-family: "verdana" , sans-serif;">Last week I heard Kat Holmes </span><a href="https://designcore.org/eventbrite-event/toyota-lecture-series-kat-holmes-on-how-inclusion-shapes-design/" style="font-family: Verdana, sans-serif;" target="_blank">talk</a><span style="font-family: "verdana" , sans-serif;"> about her new book, </span><i style="font-family: Verdana, sans-serif;"><a href="https://mismatch.design/" target="_blank">Mismatch</a></i><span style="font-family: "verdana" , sans-serif;">. I learned </span><span style="font-family: "verdana" , sans-serif;">how designing for "</span><a href="https://www.thestar.com/news/insight/2016/01/16/when-us-air-force-discovered-the-flaw-of-averages.html" style="font-family: Verdana, sans-serif;" target="_blank">normal</a><span style="font-family: "verdana" , sans-serif;">" can miss the mark. As a result, many of us encounter mismatched experiences in our physical and virtual spaces. Effectively dealing with these mismatches requires inclusive design principles: </span><span style="font-family: "verdana" , sans-serif;">1) recognizing exclusion; 2) learning from diversity; and 3) solving for one - extending to many. In order to illustrate the second principle, Kat introduced us to </span><a href="https://www.youtube.com/watch?v=0BGwinfgdIg&feature=youtu.be" style="font-family: Verdana, sans-serif;" target="_blank">Victor Pineda</a><span style="font-family: "verdana" , sans-serif;"> who made the following point:</span></div>
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<span style="font-family: "times" , "times new roman" , serif;">There's a triangle of three different things that have to come together to really unlock human accomplishments for people with disabilities. And those involve assistive technology, personal assistance—somebody that's aware, understanding how to support </span><span style="font-family: "times" , "times new roman" , serif; font-size: 12pt;">you, and three is coping strategies. And so these three things sort of create a variety of tools.</span></blockquote>
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<span style="font-family: "verdana" , sans-serif;">Of course, I started connecting these ideas to teaching.</span><br />
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<span style="font-family: "verdana" , sans-serif;">A curriculum is often designed for the normal/average student.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6zXEN3RkCl4XmvxphpwP7YFUVyo24axyRNW95I-dkE-VK-sNt2CJQFR406ppEzlb-MlzCvRrzcn3lF8IumDvVGqbsETI3YBbjU5RGJ4mUmZNCq62yX5GlcIFXi4wm3zuGsyY_KsPEIygT/s1600/Normal.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="220" data-original-width="984" height="71" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6zXEN3RkCl4XmvxphpwP7YFUVyo24axyRNW95I-dkE-VK-sNt2CJQFR406ppEzlb-MlzCvRrzcn3lF8IumDvVGqbsETI3YBbjU5RGJ4mUmZNCq62yX5GlcIFXi4wm3zuGsyY_KsPEIygT/s320/Normal.jpeg" width="320" /></a></div>
<span style="font-family: "verdana" , sans-serif;">In reality, a student and the curriculum are typically mismatched.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfq04JWmrh4iDKH0nr87rVhUKTG4_F7nNRlE_N3UO0YrDIZtr-DlsFr9nR6zYY12jTcfuRFU5Hci0Gv4-d_DccfdGQefktBu_rA2ACcah0EdkLtgpXhIDvQ09B-o6fsBb-KLVh_WBZ70rX/s1600/Mismatch.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="478" data-original-width="1310" height="145" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfq04JWmrh4iDKH0nr87rVhUKTG4_F7nNRlE_N3UO0YrDIZtr-DlsFr9nR6zYY12jTcfuRFU5Hci0Gv4-d_DccfdGQefktBu_rA2ACcah0EdkLtgpXhIDvQ09B-o6fsBb-KLVh_WBZ70rX/s400/Mismatch.jpeg" width="400" /></a></div>
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<span style="font-family: "verdana" , sans-serif;">To help the student to connect with the curriculum and be a contributor, the teacher might need to offer personal assistance, assistive technology, and/or coping strategies. And we can ask the student (learning from diversity, or as Dr. Emdin <a href="http://www.ascd.org/publications/educational-leadership/sept16/vol74/num01/Seven-Cs-for-Effective-Teaching.aspx" target="_blank">writes</a> - co-teaching) to participate in the design.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjft0mijEHoBmdu8MFXIQcYqClZXdZL8pz-oSPr4ejGi45TysfhOoc7Rfmhz03J6bofi-J-urP__SDEIq5RyXhdcX2w9J9FLBv6XjCLIjXiQ-cp3o0KBAE1mS8Qn4rcepvQLOWpaK_FjkFZ/s1600/Unlock+Potential.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="442" data-original-width="1294" height="218" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjft0mijEHoBmdu8MFXIQcYqClZXdZL8pz-oSPr4ejGi45TysfhOoc7Rfmhz03J6bofi-J-urP__SDEIq5RyXhdcX2w9J9FLBv6XjCLIjXiQ-cp3o0KBAE1mS8Qn4rcepvQLOWpaK_FjkFZ/s640/Unlock+Potential.jpeg" width="640" /></a></div>
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<span style="font-family: "verdana" , sans-serif;">Having planned for one student, the teacher must consider how to extend the design to many students.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZunhY4SavHjwg3O1SvCEyLIfULdqqczRKB3lZnLswBYbQKOj90cUsxCmMfBAOg7okssxeDDKRK3L52pLgkFlnmSxCGnTbFmZgr8fBRJ93CiApdiafmW1nfnx2h4FwqCl-QbMnMghJLk1U/s1600/Extend.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="684" data-original-width="1276" height="342" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZunhY4SavHjwg3O1SvCEyLIfULdqqczRKB3lZnLswBYbQKOj90cUsxCmMfBAOg7okssxeDDKRK3L52pLgkFlnmSxCGnTbFmZgr8fBRJ93CiApdiafmW1nfnx2h4FwqCl-QbMnMghJLk1U/s640/Extend.jpeg" width="640" /></a></div>
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<span style="font-family: "verdana" , sans-serif;">After Kat's talk, I had the opportunity to watch a student-teacher deal with the mismatch between her students' experiences solving problems involving scientific notation [<a href="http://www.corestandards.org/Math/Content/8/EE/A/4/" target="_blank">8.EE.A.4</a>] and the curriculum used in her school. We talked about using a <a href="https://deltascape.blogspot.com/2016/01/where-was-i-using-process-standards.html" target="_blank">think-aloud</a> (personal assistance) to create an <a href="https://deltascape.blogspot.com/2011/10/now-what-part-ii.html" target="_blank">anchor chart</a> (assistive technology) that students could refer to (coping strategy) while solving 8.EE.A.4 problems. </span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitQKQU_RlGwJVjJvS5R6hOlCyrr9oimi7kmwKCKchPNEtJ5Fjz9ous-VZeJYkMJ7bPExJ0DYIOo1J3O_MID0wK04NRJdZ8oSQhL5nMpO7jssmLdBl-K1nsvLJc7KyBYEVVrvwIiktlDBar/s1600/IMG_5905.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitQKQU_RlGwJVjJvS5R6hOlCyrr9oimi7kmwKCKchPNEtJ5Fjz9ous-VZeJYkMJ7bPExJ0DYIOo1J3O_MID0wK04NRJdZ8oSQhL5nMpO7jssmLdBl-K1nsvLJc7KyBYEVVrvwIiktlDBar/s200/IMG_5905.jpg" width="150" /></a><span style="font-family: "verdana" , sans-serif;">In the next lesson, she tried these ideas out. The lesson started with her making her thinking visible </span><span style="font-family: "verdana" , sans-serif; text-align: justify;">while solving an 8.EE.A.4 problem</span><span style="font-family: "verdana" , sans-serif;">. Next, she asked students what they noticed in her thinking and added it to an anchor chat. She happened to put the anchor chart in the back of the room so it was obvious later in the lesson how many of the students were using this tool as they turned in their seats to see it. Because of her efforts, students were able to successfully connect to the curriculum.</span></div>
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<span style="font-family: "verdana" , sans-serif;">I'm still processing a lot of this and would appreciate you sharing your thoughts in the comments.</span><br />
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<span style="font-family: "verdana" , sans-serif; font-size: x-small;">[This blog post was written with the help of the <a href="http://innovatorscompass.org/resources/" target="_blank">Innovators' Compass</a>. Check out my <a href="https://icompass.me/compass/view/8f82b5f5" target="_blank">planning</a>.]</span></div>
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delta_dchttp://www.blogger.com/profile/18024582157985654525noreply@blogger.com3tag:blogger.com,1999:blog-5957896812820341397.post-9872372347017583002017-12-14T12:26:00.001-08:002018-08-28T05:05:17.150-07:00And then what did you do?<span style="font-family: "verdana" , sans-serif;">In my experience, middle school students are often reluctant to try a problem they don't already know how to solve and uninterested in using alternative solution methods once they have one that works. Some middle school math teachers I worked with this week have found the same thing. So we considered how we might use techniques from improv to help students get started on a problem and possibly explore an approach they might not normally use. Improv techniques like the "Yes, And..." activity.</span><br />
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<iframe allow="encrypted-media" allowfullscreen="" frameborder="0" gesture="media" height="315" src="https://www.youtube.com/embed/Qe2a3ppacUk" width="560"></iframe></div>
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<span style="font-family: "verdana" , sans-serif;">We decided to play it using this situation from <i>Context for Learning Mathematics</i> [<a href="https://www.heinemann.com/contextsforlearning/" target="_blank">CFLM</a>] and a couple of starting choices.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiifdHW7GpEzvMXc698cCrtWBqEpAtpDcJLCxYktPFoZ1zA8AwLeU153N_LFc5w65lEZPuUnKQRYBZkmhZGwuKpY6yzDHK-XJerofO3138sYTf2e3Kl-F22aYxPKA8N7jJ7FkdoN5O3wq1S/s1600/Turkey+Cost+Problem.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="346" data-original-width="466" height="473" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiifdHW7GpEzvMXc698cCrtWBqEpAtpDcJLCxYktPFoZ1zA8AwLeU153N_LFc5w65lEZPuUnKQRYBZkmhZGwuKpY6yzDHK-XJerofO3138sYTf2e3Kl-F22aYxPKA8N7jJ7FkdoN5O3wq1S/s640/Turkey+Cost+Problem.jpg" width="640" /></a></div>
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<span style="font-family: "verdana" , sans-serif;"><b>Starting Steps:</b></span></div>
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<span style="font-family: "verdana" , sans-serif;"><b>1) First, I split up the dollar and the 25 cents and multiplied the dollar by 24.</b></span></div>
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<span style="font-family: "verdana" , sans-serif;"><b>2) First I doubled $1.25 and got $2.50.</b></span></div>
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<span style="font-family: "verdana" , sans-serif;">We would make teams of three. Two people would engage in the "Yes, And..." activity while the third kept "numeric notes" that could be referred to after the activity. </span></div>
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<span style="font-family: "verdana" , sans-serif;">Here's how it might work:</span></div>
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<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2xvuKnYTLgWAnQhKCKvXo9BDHNX9-tJGGrVIjCkmE46HAGYmHxtO1oH50nJ8SFsQgPz0fGzB7K_tX0QekYX6HCuT3o1_PL1vOKgpnieupLJC83Fy7o1EmyhAZ-U7MTeiaeLRcEM_UVUE6/s1600/IMG_4915.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1148" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2xvuKnYTLgWAnQhKCKvXo9BDHNX9-tJGGrVIjCkmE46HAGYmHxtO1oH50nJ8SFsQgPz0fGzB7K_tX0QekYX6HCuT3o1_PL1vOKgpnieupLJC83Fy7o1EmyhAZ-U7MTeiaeLRcEM_UVUE6/s320/IMG_4915.jpg" width="229" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Numeric Notes</td></tr>
</tbody></table>
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<b><span style="font-size: x-small;"><span style="font-family: "verdana" , sans-serif;">First, </span><span style="font-family: "verdana" , sans-serif;">I split up the dollar and the 25 cents and multiplied the dollar by 24.</span></span></b></div>
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<b><span style="font-family: "verdana" , sans-serif;"><span style="font-size: x-small;"><br /></span></span></b></div>
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<span style="font-family: "verdana" , sans-serif;"><span style="font-size: x-small;">Yes, and then I added back the 25 cents and got $24.25.</span></span></div>
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<span style="font-family: "verdana" , sans-serif;"><span style="font-size: x-small;"><br /></span></span></div>
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<span style="font-family: "verdana" , sans-serif;"><b><span style="font-size: x-small;">Yes, and then I remembered there were 23 more quarters that I need add.</span></b></span></div>
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<span style="font-family: "verdana" , sans-serif;"><b><span style="font-size: x-small;"><br /></span></b></span></div>
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<span style="font-family: "verdana" , sans-serif; font-size: x-small;">Yes, and I don't know what 23x.25 is so I did a quarter plus a quarter is a half dollar instead.</span></div>
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<span style="font-family: "verdana" , sans-serif; font-size: x-small;"><br /></span></div>
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<span style="font-family: "verdana" , sans-serif; font-size: x-small;"><b>Yes, and that reminded me that there are four quarters in a dollar.</b></span></div>
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<span style="font-family: "verdana" , sans-serif; font-size: x-small;"><b><br /></b></span></div>
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<span style="font-family: "verdana" , sans-serif; font-size: x-small;">Yes, and that made me wonder about how many dollars there are in 24 quarters.</span></div>
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<span style="font-family: "verdana" , sans-serif; font-size: x-small;"><br /></span></div>
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<span style="font-family: "verdana" , sans-serif; font-size: x-small;"><b>Yes, and I divided 24 by 4 and got 6.</b></span></div>
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<span style="font-family: "verdana" , sans-serif; font-size: x-small;"><b><br /></b></span></div>
<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif; font-size: x-small;">Yes, and that means 24 times .25 is 6 dollars.</span></div>
<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif; font-size: x-small;"><br /></span></div>
<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif; font-size: x-small;"><b>Yes, and then I added 6 dollars to the original 24 dollars.</b></span></div>
<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif; font-size: x-small;"><br /></span></div>
<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif; font-size: x-small;">Yes, and that means the total cost of the turkey is $30.</span></div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span></div>
<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif;">Afterwards, the students reflect on the activity. This is an opportunity to observe their own thinking: what they did; why they did it; and how else they might have navigated the situation. I have done something <a href="http://deltascape.blogspot.com/2016/05/how-does-mathematician-see-world.html" target="_blank">similar</a> with my college students, who finish up by writing a <a href="http://deltascape.blogspot.com/2011/10/metacognitive-memoirs-what-are-they.html" target="_blank">Metacognive Memoir</a> about their experience.</span></div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span></div>
delta_dchttp://www.blogger.com/profile/18024582157985654525noreply@blogger.com0tag:blogger.com,1999:blog-5957896812820341397.post-75293728993552643072017-11-17T13:22:00.001-08:002017-11-17T13:22:53.746-08:00What is Fluency in Math?<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif;">When I was a junior in college, several of my friends spent a semester studying in </span><a href="http://pepperdineheidelberg.com/" style="font-family: Verdana, sans-serif;" target="_blank">Heidelberg</a><span style="font-family: "verdana" , sans-serif;">, Germany. I decided against going because knowing German or being willing to learn it was a prerequisite for the program. One of my friends, Scott, thought this was funny because the only German he knew/learned was, "</span><span style="font-family: "verdana" , sans-serif;">Bitte, haben Sie einen Plattenspieler?" which </span><a href="https://translate.google.com/#de/en/Bitte%2C%20haben%20Sie%20einen%20Plattenspieler%3F" style="font-family: Verdana, sans-serif;" target="_blank">translates</a><span style="font-family: "verdana" , sans-serif;"> to "Please, do you have a turntable?" I thought this was pretty funny, too, and I liked the way it sounded, so I also memorized the question. Clearly, this didn't make me or Scott fluent in German. In fact, unless I'm talking to some hipster familiar with record players, my question probably doesn't even make any sense to him or her anymore. </span><span style="font-family: "verdana" , sans-serif;">I often share this memory when a discussion about fluency in math turns toward the necessity to be fast and accurate with facts or some procedure. While speed and accuracy might result from fluency, speed is neither a requirement of nor a support for fluency. </span><br />
<span style="font-family: "verdana" , sans-serif;"><br /></span>
<span style="font-family: "verdana" , sans-serif;">Consider the actors playing Klingons on </span><i style="font-family: verdana, sans-serif;"><a href="http://www.cbs.com/shows/star-trek-discovery/" target="_blank">Star Trek: Discovery</a>:</i><span style="font-family: "verdana" , sans-serif;"> they correctly deliver their lines without any pause. Are they fluent in the Klingon language?</span></div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span></div>
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<iframe allowfullscreen="" frameborder="0" height="315" src="https://www.youtube.com/embed/bQF4dXX7zpE" width="560"></iframe></div>
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<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif;">Perhaps (some Trekkies are), but more likely they are professionals that have <b>memorized</b> a script. They are not responding to something said by another Klingon actor, and I doubt many of them would be able to improvise new dialog. </span></div>
<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif;"><br /></span></div>
<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif;">Is Siri fluent in mathematics? She is certainly fast and accurate.</span></div>
<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif;"><br /></span></div>
<div style="text-align: center;">
<iframe allowfullscreen="" frameborder="0" height="315" src="https://www.youtube.com/embed/ULa8U_DYc20" width="560"></iframe></div>
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<br /></div>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;">But ask her <i>how</i> she arrived at her answer, and she is at a lost.</span></div>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;"><br /></span></div>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;">What does it mean to be fluent? Fluent speakers demonstrate flexibility in their language usage - the ability to play with words and use figurative phrases. Certainly, there is also a need to know the words and grammar associated with the language. However, this alone isn't enough to be fluent in the language.</span></div>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;"><br /></span></div>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;">And, in my opinion, knowing alone is not enough to be fluent in math, either - no matter how quickly you can arrive at the answer.</span></div>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;"><br /></span></div>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;">So, how am I wrong? I'm looking for pushback before I tell this story again. Make some comments and make me smart.</span></div>
delta_dchttp://www.blogger.com/profile/18024582157985654525noreply@blogger.com3tag:blogger.com,1999:blog-5957896812820341397.post-62536865815295696162017-11-12T18:39:00.001-08:002017-11-12T18:39:49.073-08:00Should there be guns in schools?<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;">I intend to share this letter with my governor and as a letter to the editor. I would appreciate your feedback in the comments. Thank you in advance.</span></div>
<span style="font-family: Verdana, sans-serif;"><br /></span>
<div style="text-align: center;">
<span style="font-family: Verdana, sans-serif;">=====</span></div>
<span style="font-family: Verdana, sans-serif;"><br /></span>
<span style="font-family: Verdana, sans-serif;">Dear Governor Snyder,</span><br />
<span style="font-family: Verdana, sans-serif;"><br /></span>
<span style="font-family: Verdana, sans-serif;">
</span>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;">On November 8th, the Michigan Senate passed legislation (<a href="http://www.legislature.mi.gov/(S(5t0mmxhpsi4bctjthbqmcmaw))/mileg.aspx?page=getObject&objectName=2017-SB-0584" target="_blank">584</a>, <a href="https://www.legislature.mi.gov/(S(kkryjo5ae3ie33k30lfrmtqf))/mileg.aspx?page=getobject&objectname=2017-SB-0585" target="_blank">585</a>, and <a href="http://www.legislature.mi.gov/(S(b25es5n5c5wjocki0datixem))/mileg.aspx?page=GetObject&objectname=2017-SB-0586" target="_blank">586</a>) allowing individuals with concealed weapons permits to request permission to carry guns in schools (and other previously gun-free zones) with extra training. <span style="letter-spacing: 0.07999999821186066px; word-spacing: 0.4000000059604645px;">“[A gun-free zone is] a target-rich environment for people that don’t abide by the law, and people should have the ability to protect themselves, wherever they are,” <a href="http://michiganradio.org/post/senate-adopts-bill-allow-concealed-weapons-gun-free-zones" target="_blank">explained</a> State Senate Majority Leader (and my senator) Arlan Meekhof. This follows the narrative often accompanying such legislation: the only thing that stops a bad guy with a gun is a good guy with a gun. </span></span><br />
<span style="font-family: Verdana, sans-serif;"><span style="letter-spacing: 0.07999999821186066px; word-spacing: 0.4000000059604645px;"><br /></span></span></div>
<span style="font-family: Verdana, sans-serif;">
</span>
<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif;"><span style="font-family: Verdana, sans-serif; letter-spacing: 0.07999999821186066px; word-spacing: 0.4000000059604645px;"><span style="font-family: verdana, sans-serif;">I understand why this is a compelling story; it makes us feel safe, empowered, and may even touch on our dreams of being a hero. There's even a recent </span><a href="http://www.foxnews.com/us/2017/11/08/texas-church-shooting-not-first-time-good-guy-with-gun-takes-down-mass-shooter.html" style="font-family: verdana, sans-serif;" target="_blank">example</a><span style="font-family: verdana, sans-serif;"> of a good guy with a gun helping to stop a bad guy. But law enforcement officials, like the Houston Police Department, want you to consider a different story when involved in an active shooter event: <b>run</b> first; <b>hide</b> if you can't run; and <b>fight</b> only as a last resort.</span></span></span></div>
<span style="font-family: "verdana" , sans-serif;"><span style="letter-spacing: 0.07999999821186066px; word-spacing: 0.4000000059604645px;"></span></span><br />
<div style="text-align: center;">
<iframe allowfullscreen="" frameborder="0" height="315" src="https://www.youtube.com/embed/5VcSwejU2D0" width="560"></iframe></div>
<br />
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;">Why would the police discourage you from being a hero? A couple of storylines come to mind:</span></div>
<ul>
<li style="text-align: justify;"><span style="font-family: Verdana, sans-serif;">Good guy with a gun shoots an <a href="http://westwing.wikia.com/wiki/War_Crimes" target="_blank">innocent</a> student or teacher while trying to stop a bad guy (with or without a gun); and</span></li>
<li style="text-align: justify;"><span style="font-family: Verdana, sans-serif;">Good guy with a gun shoots some other good guy with a gun after <a href="http://www.slate.com/articles/health_and_science/human_nature/2011/01/friendly_firearms.html" target="_blank">misidentifying</a> him as a bad guy with a gun.</span></li>
</ul>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;"><span style="font-family: Verdana, sans-serif;">We must also consider that confronting an active shooter isn't the only story that can be told around a good guy with a gun in a school. In fact</span>, the good guy with a gun is unlikely to actually encounter an active shooter in a Michigan school given current statistics. So what other stories might we tell that involve a good guy, a gun, and a school - minus a bad guy?</span></div>
<ul>
<li style="text-align: justify;"><span style="font-family: Verdana, sans-serif;">Good guy with a gun gets angry about something and shoots the student, teacher, administrator, or parent that made him <a href="http://www.star-telegram.com/news/local/community/arlington/article162871748.html" target="_blank">angry</a>;</span></li>
<li style="text-align: justify;"><span style="font-family: Verdana, sans-serif;">Child finds good guy's gun <a href="http://www.abc15.com/news/region-southeast-valley/chandler/gun-found-on-campus-at-hamilton-high-school-friday" target="_blank">carelessly</a> left laying around and shoots self or another child; and</span></li>
<li style="text-align: justify;"><span style="font-family: Verdana, sans-serif;">Child finds good guy's gun carefully <a href="http://woodtv.com/2017/08/28/5-year-old-boy-finds-gun-shoots-himself-in-hand/" target="_blank">hidden</a> away and shoots self or another child.</span></li>
</ul>
<div>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;">I get why we would rather not consider these tragic storylines. Most everyone would prefer the happy ending associated with "good guy with a gun stops bad guy with a gun." But just because you like one ending better than the other doesn't make it more likely to happen - especially when you compare the <a href="https://www.usatoday.com/story/news/nation/2016/12/09/new-cdc-data-understate-accidental-shooting-deaths-kids/95209084/" target="_blank">hundreds</a> of children accidentally shot each year with the handful of heroes.</span></div>
</div>
<div>
<span style="font-family: Verdana, sans-serif;"><br /></span></div>
<div>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;">We ought not be making laws based on Hollywood happy endings. Instead, we need to consider the reality and the possible unintended consequences that occur when a gun is added to any situation. If we truly want to use "common sense" when addressing gun violence, just remember that no one ever got shot in a place without guns.</span></div>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;"><br /></span></div>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;">Should these bills reach your desk, please exercise your veto. Do not put our children at risk just so a few people can dream of being a hero.</span></div>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;"><br /></span></div>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;">Sincerely,</span></div>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;">David Coffey</span></div>
</div>
delta_dchttp://www.blogger.com/profile/18024582157985654525noreply@blogger.com0tag:blogger.com,1999:blog-5957896812820341397.post-57911867588832160852017-11-11T10:59:00.001-08:002017-11-11T10:59:22.351-08:00What does this mean?<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;">The other day I was working with some high school students on problems like this one:</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxm65wbQL0NqREE3JpxaNtUEnpsCht0OV_o9llETVtjxbXvalTRh5lKwgehI1anli9mJytS0fdMvci_x9WZ8ZSF7Lm-PzNYbguasmrVNmzAiLOAxR4Cy0Dfz9FoUkTQ2j9FXtuF4YC1_vB/s1600/Calculate+and+Simplify.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="108" data-original-width="586" height="58" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxm65wbQL0NqREE3JpxaNtUEnpsCht0OV_o9llETVtjxbXvalTRh5lKwgehI1anli9mJytS0fdMvci_x9WZ8ZSF7Lm-PzNYbguasmrVNmzAiLOAxR4Cy0Dfz9FoUkTQ2j9FXtuF4YC1_vB/s320/Calculate+and+Simplify.jpg" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgE-DWfsT3MqWjpXHvnojRBRMnCBO1IN_ZlOHkxm716cwcvYdvQcHn4yu0IXL3w5Ci_b8FhUXD2hROA2Atxd330ZifCd8IMKfpv7bPi2MGMxqsHiRNXRJa86P_FIg__oatBQufEWHdVqsgh/s1600/Square+root+of+1+over+64.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="198" data-original-width="174" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgE-DWfsT3MqWjpXHvnojRBRMnCBO1IN_ZlOHkxm716cwcvYdvQcHn4yu0IXL3w5Ci_b8FhUXD2hROA2Atxd330ZifCd8IMKfpv7bPi2MGMxqsHiRNXRJa86P_FIg__oatBQufEWHdVqsgh/s200/Square+root+of+1+over+64.jpg" width="175" /></a></div>
<div class="separator" style="clear: both; text-align: justify;">
<span style="font-family: Verdana, sans-serif;">I asked what I thought was a pretty straightforward question, "What does this mean?" [SPOILER: it wasn't as straightforward as I thought.]</span></div>
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<span style="font-family: Verdana, sans-serif;"><br /></span></div>
<div class="separator" style="clear: both; text-align: justify;">
<span style="font-family: Verdana, sans-serif;">One student said/asked something like, "Split the square root? Make it the square root of one over the square root of 64?" (Seriously, these were implicit questions asking, "Is this where I start?") </span></div>
<div class="separator" style="clear: both; text-align: justify;">
<span style="font-family: Verdana, sans-serif;"><span style="color: red;"><b>STRIKE ONE!</b></span></span></div>
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<span style="font-family: Verdana, sans-serif;"><br /></span></div>
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<span style="font-family: Verdana, sans-serif;">I responded, pointing emphatically at the problem, "But what does this <i>mean</i>? How would you say it in words?"</span></div>
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<span style="font-family: Verdana, sans-serif;"><br /></span></div>
<div class="separator" style="clear: both; text-align: justify;">
<span style="font-family: Verdana, sans-serif;">The other student interjected, "The square root of 1 over 64." And then asked, "We should rationalize the denominator, right?" </span></div>
<div class="separator" style="clear: both; text-align: justify;">
<b style="color: red; font-family: Verdana, sans-serif;">STRIKE TWO!</b></div>
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<span style="font-family: Verdana, sans-serif;"><br /></span></div>
<div class="separator" style="clear: both; text-align: justify;">
<span style="font-family: Verdana, sans-serif;">I tried again, "You're focusing on what you would <i>do</i>. I want to know what you <i>understand</i> about square root problems. What if it was the square root of sixty-four, then what would the problem be asking you to <i>find</i>?"</span></div>
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<span style="font-family: Verdana, sans-serif;"><br /></span></div>
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<span style="font-family: Verdana, sans-serif;">The first student, clearly getting frustrated, "I'd take a half of 64." </span></div>
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<span style="font-family: Verdana, sans-serif;"><span style="color: red;"><b>STRIKE THREE! YOU'RE OUT, COFFEY!</b></span></span></div>
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<span style="font-family: Verdana, sans-serif;"><br /></span></div>
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<span style="font-family: Verdana, sans-serif;">I didn't see any point to continuing to frustrate them or me with more questions. So instead, I tried to model my thinking about solving problems involving radicals.</span></div>
<blockquote class="tr_bq">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8UVoMiHnkvPX1_hOi9Edy2EWGRW-tvc41zn5O4S7RNhF0X0o1YSjKRoRbiCFIufuFfU8ib-ximJEOGEPdexDF0WiebJrBmHkZtOLgTXAkapvuyW_2I5Sn_91koki1DmveyOkCRoW-nWP4/s1600/IMG_4722.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="1334" data-original-width="750" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8UVoMiHnkvPX1_hOi9Edy2EWGRW-tvc41zn5O4S7RNhF0X0o1YSjKRoRbiCFIufuFfU8ib-ximJEOGEPdexDF0WiebJrBmHkZtOLgTXAkapvuyW_2I5Sn_91koki1DmveyOkCRoW-nWP4/s320/IMG_4722.jpg" width="177" /></a><span style="font-family: Verdana, sans-serif;"><div style="text-align: justify;">
When I was a kid, I used to bring a four-function calculator with me on long road trips (like the one shown here). There was no square root button on the calculator, so I would play <i>What's the Square Root</i> by typing in a guess, pressing the multiplication button and then equals, and use the result to see how I might need to adjust my guess. It was hours of fun! </div>
</span></blockquote>
<blockquote class="tr_bq" style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;">If my question was, "What's the square root of two?" then I was essentially asking, "What number multiplied by itself is two?" So when I ask what this (again, emphatically point at the original problem) <i>means</i>, I'm thinking about playing the game and trying to determine what factor squared gives <i>this</i> (more pointing) product, the number inside the radical.</span></blockquote>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;">I went back to our simpler problem, "So this is asking me, 'What factor squared equals sixty-four." They both answered eight.</span></div>
<span style="font-family: Verdana, sans-serif;"><br /></span>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;">Then we went back to the original. "What does this mean?"</span></div>
<span style="font-family: Verdana, sans-serif;"><br /></span>
<span style="font-family: Verdana, sans-serif;">They said, "What number times itself gives one over sixty-four?"</span><br />
<span style="font-family: Verdana, sans-serif;"><br /></span>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;">"Yes, What factor squared is one-sixty-fourth? </span><span style="font-family: Verdana, sans-serif;">Now that we <i>understand</i>," I said, "we can begin thinking about what to </span><i style="font-family: Verdana, sans-serif;">do</i><span style="font-family: Verdana, sans-serif;">."</span></div>
<span style="font-family: Verdana, sans-serif;"><br /></span>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;">It's troubling to me that so many years after </span><span style="background-color: white; color: #333333; font-size: 14.850000381469727px; text-align: justify;"><span style="font-family: Verdana, sans-serif;">Pólya</span></span><span style="font-family: Verdana, sans-serif;"> wrote <i><a href="https://notendur.hi.is/hei2/teaching/Polya_HowToSolveIt.pdf" target="_blank">How To Solve It</a></i>, that students race past the first phase of the problem solving process - Understanding the Problem.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXjHRoiwYPZnQzgnuh2TqG1BIVT2pHzDzCeB_YI6PJdyUi3TNML1tNBvw3NVXYb1m-Sl7cXnIK0nPReJdjn2GfjQjAMErZAOrYoj7WGq4Z6v8CUTY-6c7WFeDLHR-sHkWT2vL_UlgFFEzY/s1600/how-to-solve-it_Polya.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1236" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXjHRoiwYPZnQzgnuh2TqG1BIVT2pHzDzCeB_YI6PJdyUi3TNML1tNBvw3NVXYb1m-Sl7cXnIK0nPReJdjn2GfjQjAMErZAOrYoj7WGq4Z6v8CUTY-6c7WFeDLHR-sHkWT2vL_UlgFFEzY/s400/how-to-solve-it_Polya.jpg" width="308" /></a></div>
<span style="font-family: Verdana, sans-serif;">Why is that? It can't be that we are focusing on the procedures and not the concepts. No, it can't be that, can it?</span><br />
<span style="font-family: Verdana, sans-serif;"><br /></span>
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<span style="font-family: Verdana, sans-serif;"><br /></span>delta_dchttp://www.blogger.com/profile/18024582157985654525noreply@blogger.com0tag:blogger.com,1999:blog-5957896812820341397.post-91303314416211815542017-09-12T14:00:00.001-07:002017-09-12T14:01:56.812-07:00What's your vision?<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif;">From <i><a href="http://stuff.samassaveneessa.info/docs/BlackElkSpeaks.pdf" target="_blank">Black Elk Speaks</a></i></span></div>
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<span style="font-family: "verdana" , sans-serif;">After the long winter of waiting, it was my first duty to go out lamenting. So after the first
rain storm I began to get ready.</span></blockquote>
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<span style="font-family: "verdana" , sans-serif;">I recently heard <a href="http://www.kentdobson.com/" target="_blank">Kent Dobson</a> talk about this idea of "lamenting" - what is often thought of as a "vision quest." [I apologize in advance if I get some of the details wrong in this post. A lot of what I'm writing is a combination of my memory of and the connections made during his talk. Please let me know in the comments if anything needs correcting.] </span></div>
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<span style="font-family: "verdana" , sans-serif;">In the Lakota tradition, when a seeker comes of age, he or she goes off with an elder to "<a href="http://aktalakota.stjo.org/site/News2?page=NewsArticle&id=8672" target="_blank">cry for a vision</a>." After some preparation, the seeker is left alone to lament the current state of the community and seek answers in the form of a vision. From time to time, the elder looks in on the lamenting to advise and support the seeker. When the lamenting is complete, the seeker returns to the community and shares the vision. This is an important rite for the community because without new ideas, a community withers and dies.</span></div>
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<span style="font-family: "verdana" , sans-serif;">As I begin a new year of supervising student teaching, I want this ritual to inform my work. I hope to play the role of the elder supporting coming-of-age teachers as they experience (and lament) the current circumstances in math education and seek new answers. I will listen to those answers and take them seriously because in many ways our profession is withering. And I will help the student teachers to share their visions with the larger math education community, so that these seekers might contribute to the development of our profession.</span></div>
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<span style="font-family: "verdana" , sans-serif;">Thank you in advance for welcoming these seekers and helping to interpret and implement their visions.</span></div>
delta_dchttp://www.blogger.com/profile/18024582157985654525noreply@blogger.com1tag:blogger.com,1999:blog-5957896812820341397.post-57673163078048309332017-06-05T07:47:00.001-07:002017-06-05T07:47:46.228-07:00What needs changing?<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif;">The Michigan Department of Education is considering changes to Michigan teacher certification and asking for <a href="http://www.michigan.gov/documents/mde/Proposed_Ed_Cert_565023_7.pdf" target="_blank">feedback</a>. Here is more information about their proposed certification structure.</span></div>
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<span style="font-family: Verdana, sans-serif;">Feedback is due today. (Sorry, I'm still a bit of a procrastinator.) However, if you consider yourself as having any stake in education, I encourage you to complete the <a href="https://mde.qualtrics.com/jfe/form/SV_9QxvRNEjWgoSF0h" target="_blank">survey</a>, as soon as possible. It'll take maybe 45 minutes to watch the video and answer some questions.</span></div>
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<span style="font-family: Verdana, sans-serif;">For what it's worth, here's my response. (And, yes, I know I am biased.)</span><br />
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My issue with the structure being proposed is that it seems
to presume that new teachers ought to be completely prepared upon
certification. Even if we focused on giving specific grade-level certification,
there is no way to address all the issues (textbooks, culture, community,
resources, …) new teachers might encounter across the state (or country).
Furthermore, this structure will limit the options available to teachers and
potentially restrict administrators' ability to fill positions. I can imagine
school districts asking for waivers to put PK-3 certified teachers in 4th grade
because of a lack of options - a teacher that may have no training at that
level.</blockquote>
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I encourage that the state look at the Grand Valley State University
teacher certification <a href="https://www.gvsu.edu/coe/undergraduate/" target="_blank">program</a> as a model. We support the development of
teacher-leaders in content areas by requiring even pre-service elementary
teachers to get a subject major. Local districts regularly call us looking for
recent majors because they know they will be content experts who can also
integrate other subjects into their practice.</blockquote>
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Also, the MDE needs to rethink professional development for
inservice teachers. Because no teacher is truly finished learning, we must
return to a robust professional development process that helps teachers build
on current education experiences to deepen their pedagogical content knowledge
in all discipline they might be teaching. Such a system is especially important
now because we have so many new, inexperienced teachers entering the
profession.</blockquote>
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This professional development ought to be in partnership
with accredited bodies responsible for initial teacher certification. These
institutions are aware of the training new teachers bring to the profession and
can provide meaningful experiences that can expand teachers’ current abilities.
The experiences would be the result of the institutions and inservice teachers collaborating
on areas needing improvement.</blockquote>
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In my discipline, we often hold up Dr. Deborah Ball (former
dean of the University of Michigan’s School of Education) as the model
elementary math teacher. However, we fail to recognize that Dr. Ball rose to
this level after identifying this as an area of weakness in her teaching – after
being a certified, inservice teacher (see p. <a href="https://www.stcloudstate.edu/tpi/initiative/documents/preparation/Building%20a%20Better%20Teacher.pdf" target="_blank">9</a>). She decided to do something about it by
going back to school and learning more about the subject and its teaching. We
need to allow all inservice teachers to follow the path from awareness to
adjustment without fear of being labeled unprepared or ineffective. </blockquote>
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While teacher preparation institution must make changes to
better prepare teacher-leaders, teacher certification is not the primary
problem. A lack of opportunities for meaningful professional development is the
issue. Changing teacher certification to try to address a broken inservice
support system focuses our efforts in the wrong direction and may do further
damage to education in Michigan.</blockquote>
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<span style="font-family: Verdana, sans-serif;">Thank you, in advance, for your attention to this issue.</span></div>
delta_dchttp://www.blogger.com/profile/18024582157985654525noreply@blogger.com0tag:blogger.com,1999:blog-5957896812820341397.post-67151143499461347642017-05-09T12:15:00.000-07:002017-05-09T12:43:44.576-07:00Wanna Play?<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif;">Grand Valley's <a href="http://www.gvsu.edu/clas/" target="_blank">College of Liberal Arts and Sciences</a> has a policy that all courses must meet and have a culminating experience during finals week. Typically, I try to do something other than a traditional exam during these meetings. Most of my students are preservice teachers, and I want to offer them an alternative way to "show what they know" and reflect on the semester; this often entails <a href="http://deltascape.blogspot.com/2011/12/what-did-we-learn.html" target="_blank">presentations</a>. But this year we decided to throw a party.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihvItFMhLfuva_Opob0iAI0B500Ps5WzkAELI374poFmfLASiGinNurkWecFrWk3ckHP0w19-9ajNtS6CQ_QvGNwfdggO8MlPS5JxLPuY1OYuInuF7EWjSYw5IYkZQY8MCTfKoAYGIjJaS/s1600/IMG_2980.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="251" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihvItFMhLfuva_Opob0iAI0B500Ps5WzkAELI374poFmfLASiGinNurkWecFrWk3ckHP0w19-9ajNtS6CQ_QvGNwfdggO8MlPS5JxLPuY1OYuInuF7EWjSYw5IYkZQY8MCTfKoAYGIjJaS/s320/IMG_2980.jpg" width="320" /></a><span style="font-family: "verdana" , sans-serif;">I got the idea when I attended a</span><span style="font-family: "verdana" , sans-serif;"> </span><span style="font-family: "verdana" , sans-serif;">session at the </span><span style="font-family: "verdana" , sans-serif;">NCTM <a href="http://www.nctm.org/2017SanAntonio/" target="_blank">2017</a> Annual Meeting and Exposition that was </span><span style="font-family: "verdana" , sans-serif;">led by Kassia Omohundro <a href="https://twitter.com/kassiaowedekind" target="_blank">Wedekind</a> and Mary Beth <a href="https://twitter.com/mbdillane" target="_blank">Dillane</a> - "</span><i style="font-family: Verdana, sans-serif;">We are Mathematicians": Building Mathematical Communities Based in Sense Making, Agency, and Joy</i><span style="font-family: "verdana" , sans-serif;">. During the session, they talked about kids at their school hosting a math party for their peer, teachers, and parents. At the party, the kids shared some of their favorite math activities. I decided this would be a great way to wrap up the semester.</span></div>
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<span style="font-family: "verdana" , sans-serif;">We started the celebration with a popular party game: The Marshmallow Challenge.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWNLMN3W-8fS9EY8boUSfYeGTXTvXXk_R2ltJfvMIsoRQPIukJJkF1wuTqy9zlbFOXMu8XeHLgI2tRYP4iphGftNtkXdk2-RjMD3ATW08X264wMCgkLqzR23q4D1weQkH1NCXFLool4o2a/s1600/C-VttHQWsAA5X3s.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWNLMN3W-8fS9EY8boUSfYeGTXTvXXk_R2ltJfvMIsoRQPIukJJkF1wuTqy9zlbFOXMu8XeHLgI2tRYP4iphGftNtkXdk2-RjMD3ATW08X264wMCgkLqzR23q4D1weQkH1NCXFLool4o2a/s320/C-VttHQWsAA5X3s.jpg" width="240" /></a></div>
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<span style="font-family: "verdana" , sans-serif;">Then the pre-service elementary teachers started developing their <b>Math Teaching Vision Boards</b>. I got the idea from this <a href="https://www.podomatic.com/podcasts/mathed/episodes/2017-03-17T08_50_54-07_00" target="_blank">podcast</a> that discusses the role instructional vision has on math teachers' instructional practice.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg82YDhH3Yt0zEjlX_lMm3x-xh50CKNHgvNWsy1sN_aGArx68YQ7LLCk0SdawHNSg6zRZsly-6N59KLpG5KN2VAfxJdMiR4wh-uXPLcyyOveW0SeTDA1tsmomtBMpskplIOZzMJNn1ywv9R/s1600/IMG_3170.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg82YDhH3Yt0zEjlX_lMm3x-xh50CKNHgvNWsy1sN_aGArx68YQ7LLCk0SdawHNSg6zRZsly-6N59KLpG5KN2VAfxJdMiR4wh-uXPLcyyOveW0SeTDA1tsmomtBMpskplIOZzMJNn1ywv9R/s320/IMG_3170.jpg" width="320" /></a></div>
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<span style="font-family: "verdana" , sans-serif;">After about 20 minutes, we were ready to share our visions. We didn't have peers, teachers, or parents at our party, so we set up a series of viewing venues arranged by group.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRFVPU6_jFC22-RigXMYmbexYW459TTGzHjUFKLZy4_mf9x-kjSb0RdKAnup4iVb-HaE2lFYpfbqHMD9w6mYbg6JOcjSJg6_tWmCqukfS_AdY2Y936qU4BHywHDuPU_1DxQRAiERituwlN/s1600/IMG_3182.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRFVPU6_jFC22-RigXMYmbexYW459TTGzHjUFKLZy4_mf9x-kjSb0RdKAnup4iVb-HaE2lFYpfbqHMD9w6mYbg6JOcjSJg6_tWmCqukfS_AdY2Y936qU4BHywHDuPU_1DxQRAiERituwlN/s320/IMG_3182.jpg" width="320" /></a></div>
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<span style="font-family: "verdana" , sans-serif;">The sharing looked a like this:</span></div>
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<iframe allowfullscreen="" frameborder="0" height="315" src="https://www.youtube.com/embed/PvIiHc7-EQ0" width="560"></iframe></div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">At the end of the party, the preservice teachers gave me some feedback. <a href="https://twitter.com/Cooper___Payton" target="_blank">One</a> said, "That was 2 hours of reflection disguised as fun."</span></div>
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<span style="font-family: "verdana" , sans-serif;">Another complained that they didn't get to go to the viewing parties of their table-mates. I told them that was too bad but maybe they could connect with those peers after class to talk about their visions. Then I wondered out loud, "Do you think I did that on purpose?"</span></div>
delta_dchttp://www.blogger.com/profile/18024582157985654525noreply@blogger.com0tag:blogger.com,1999:blog-5957896812820341397.post-78308522888542879662017-02-26T09:21:00.000-08:002017-02-26T09:54:10.296-08:00What's your next move?<div style="text-align: center;">
<span style="font-family: "verdana" , sans-serif;">Our presentation from <a href="http://www.gvsu.edu/mathinaction/" target="_blank">Math in Action</a> 2017</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsLIR9ii-kQsjEQubSkCO9H3f-1cbk3EFfIDFvUTPYfOC1CUus0Tx3bc8JlyrNEBUN9e0qesWN7ZXXSYmbI_jPqaynZKP8VRO6dnrwdgCCLl-yjreLj_R5L0IUEkWHN7r1iadP5SQs8dry/s1600/Engaging+Students+in+Meaningful+Math+using+Games.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="224" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsLIR9ii-kQsjEQubSkCO9H3f-1cbk3EFfIDFvUTPYfOC1CUus0Tx3bc8JlyrNEBUN9e0qesWN7ZXXSYmbI_jPqaynZKP8VRO6dnrwdgCCLl-yjreLj_R5L0IUEkWHN7r1iadP5SQs8dry/s320/Engaging+Students+in+Meaningful+Math+using+Games.jpg" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYKg8COmyIq1MOkc-mQpyFncuQIlv6hqtNqGOzMR71uePfu9WNEgywTQo0GuvasDtZSoLNtQ__mWVuTNUuItE1LI52BbSNWc0I6NUlPqiJRV-CiN0tzQP4zFU9Kt-vF4IQLFvzKGGb-i7f/s1600/Games.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYKg8COmyIq1MOkc-mQpyFncuQIlv6hqtNqGOzMR71uePfu9WNEgywTQo0GuvasDtZSoLNtQ__mWVuTNUuItE1LI52BbSNWc0I6NUlPqiJRV-CiN0tzQP4zFU9Kt-vF4IQLFvzKGGb-i7f/s200/Games.jpg" width="200" /></a></div>
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<b style="font-family: Verdana, sans-serif;">Description</b><span style="font-family: "verdana" , sans-serif;">: </span></div>
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<span style="font-family: "verdana" , sans-serif;">Games are an effective
way
to engage students in learning. Participants will experience how to support the
development of pre-adolescent mathematicians through purposeful play. [Grades 3-5]</span><!--EndFragment--></div>
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<span style="font-family: "verdana" , sans-serif;">Consider what you think it means to effectively teach mathematics. Now take the Simile <a href="http://deltascape.blogspot.com/search/label/Simile%20Survey" target="_blank">Survey</a> provided below. What are the characteristics of your simile selection that relate to good mathematics teaching?</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjS2w937uB4J-N9TKVEtHkIHhikhWrNPf-MtuQkZaxuKJu0UAyzlqqfdNb_aZaoYYjtEGh3LbmFNAjD4BOKdqFwD9pHFZAFBgTl7CnTWUMjlFTnYCahjKC4IPixK1FPRzEtsdxoaITF4MMy/s1600/Simile+Survey.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="264" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjS2w937uB4J-N9TKVEtHkIHhikhWrNPf-MtuQkZaxuKJu0UAyzlqqfdNb_aZaoYYjtEGh3LbmFNAjD4BOKdqFwD9pHFZAFBgTl7CnTWUMjlFTnYCahjKC4IPixK1FPRzEtsdxoaITF4MMy/s640/Simile+Survey.jpg" width="640" /></a></div>
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<span style="font-family: "verdana" , sans-serif;">A while back, <a href="http://go.sdsu.edu/education/edl/fisher.aspx" target="_blank">Dr. Doug Fisher</a> introduced me to another teaching simile: Teaching is like being an expert commentator. During the lesson, the teacher highlights important aspects of the "routine" that the student might otherwise overlook. In cases where the action moves too quick, the teacher might need to "rewind and show it in slow motion" in order to clarify some move. <a href="http://www.nbcolympics.com/video/olympic-trials-gabby-douglas-competes-uneven-bars" target="_blank">Here</a> is an example from the 2016 U.S. Olympic Trials that demonstrates these characteristics. So what does this look like in math class?</span></div>
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<span style="font-family: "verdana" , sans-serif;">Imagine we are in a 3rd-grade class playing BINGO. If the students are fluent in reading number symbols, there's not much to the game. So let's <a href="http://deltascape.blogspot.com/2015/11/how-do-you-play-bi-n-bi.html" target="_blank">break it</a> - add another dimension by allowing players to decompose the number that's <a href="https://www.random.org/" target="_blank">called</a>.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihd1m1KQZ_37TIP9LzXqkRlz0RdJuW25xzJEU_P63JWg3gF9WZzgAW_eiqDQovjoEHAK1b3F1Pshf71_RfnmFFOAK27CX0c1Cu0VKWrPZcpqIeqjIwdJjGhVKahXOR2vox7ShTvpqa3AC8/s1600/Breaking+BINGO.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihd1m1KQZ_37TIP9LzXqkRlz0RdJuW25xzJEU_P63JWg3gF9WZzgAW_eiqDQovjoEHAK1b3F1Pshf71_RfnmFFOAK27CX0c1Cu0VKWrPZcpqIeqjIwdJjGhVKahXOR2vox7ShTvpqa3AC8/s640/Breaking+BINGO.jpg" width="640" /></a></div>
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<span style="font-family: "verdana" , sans-serif;">If you were in a 5th-grade class, they might ask why they can't decompose </span><span style="font-family: "verdana" , sans-serif;">the called number into more than two addends ... or use operations other than addition. Then the challenge might be, "Can I get a BINGO with just one number called?"</span></div>
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<span style="font-family: "verdana" , sans-serif;">After (or during the game), what sorts of things would you want the students to notice? What would you highlight and maybe have to slow down? It depends on the game and our players.</span></div>
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<ul>
<li style="text-align: justify;"><span style="font-family: "verdana" , sans-serif;">If I was playing the regular game of BINGO with young kids still struggling with number recognition, I might be sure to call "thirteen" and highlight ways to tell the difference between 13 and 31.</span></li>
<li style="text-align: justify;"><span style="font-family: "verdana" , sans-serif;">If we are decomposing, I might want kids to recognize that 38 can be decomposed into 30+8 or 31+7 and highlight the concept of compensation.</span></li>
<li style="text-align: justify;"><span style="font-family: "verdana" , sans-serif;">For 5th graders, I might show how "thirteen" can be written as 13+8/(9-7)-4 and highlight an important property of zero in our number system. [To demonstrate another important property of zero, ask students if they could cover the entire board if "thirteen" was called.]</span></li>
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<span style="font-family: "verdana" , sans-serif;">It is important that teachers have the opportunity to play games before using them with their students. That way the teachers can consider possible modifications (ways to "break" the game) that would meet their students' needs. It also gives them experience playing the games that can lead to insights into important mathematical aspects encountered while playing that the teachers might want to highlight for their students.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8gVc3dE5UjNJk56bzERD87vgtm0OHnvEJFzY-rO8jc69q9kuj6IfAKWHdeLryC7bRt-8a2s8sPHO9NSwfDzbw4_1vlVAZ54WLlSCifgkEdrAuMZ7F1VOBe1flQ-5jqFzh38CeVrXeuTmW/s1600/IMG_2665.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="193" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8gVc3dE5UjNJk56bzERD87vgtm0OHnvEJFzY-rO8jc69q9kuj6IfAKWHdeLryC7bRt-8a2s8sPHO9NSwfDzbw4_1vlVAZ54WLlSCifgkEdrAuMZ7F1VOBe1flQ-5jqFzh38CeVrXeuTmW/s200/IMG_2665.jpg" width="200" /></a><span style="font-family: "verdana" , sans-serif;"></span></div>
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<span style="font-family: "verdana" , sans-serif;"><b>Game Centers </b></span></div>
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<b style="font-family: Verdana, sans-serif;">Number and Operations - Fractions </b></div>
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<b style="font-family: Verdana, sans-serif;">Grades 3-5 </b></div>
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<ul>
<li><a href="http://urmath.weebly.com/station-5--go-fish.html" style="font-family: Verdana, sans-serif; text-align: left; text-indent: -0.49in;" target="_blank">Fraction Go Fish</a> </li>
<li><span style="font-family: "verdana" , sans-serif; text-align: left; text-indent: -0.49in;">Fraction Memory [</span><span style="font-family: "verdana" , sans-serif; text-align: left; text-indent: -0.49in;"><a href="http://urmath.weebly.com/uploads/1/5/5/8/15580012/fractionmemorymatch.pdf" target="_blank">pdf</a></span><span style="font-family: "verdana" , sans-serif; text-align: left; text-indent: -0.49in;">] </span></li>
<li><span style="font-family: "verdana" , sans-serif; text-align: left; text-indent: -0.49in;">Cookie Fractions [</span><span style="font-family: "verdana" , sans-serif; text-align: left; text-indent: -0.49in;"><a href="http://www.ecac-parentcenter.org/wp-content/uploads/2016/03/Family-Math-Night-to-Go-.pdf" target="_blank">page36</a></span><span style="font-family: "verdana" , sans-serif; text-align: left; text-indent: -0.49in;">]</span></li>
<li><a href="http://mathhombre.blogspot.com/2010/05/decimal-point-pickle.html" style="font-family: Verdana, sans-serif; text-align: left; text-indent: -0.49in;" target="_blank">DecimalPickle</a><span style="font-family: "verdana" , sans-serif; text-align: left; text-indent: -0.49in;"> </span></li>
<li><span style="font-family: "verdana" , sans-serif; text-align: left; text-indent: -0.49in;">Pattern
</span><span style="font-family: "verdana" , sans-serif; text-align: left; text-indent: -0.49in;">Block Fraction </span><span style="font-family: "verdana" , sans-serif; text-align: left; text-indent: -0.49in;"><a href="http://www.doe.virginia.gov/testing/solsearch/sol/math/4/mess_4-2ab_2.pdf" target="_blank">Game</a></span></li>
<li><span style="font-family: "verdana" , sans-serif; text-align: left; text-indent: -0.49in;">Fraction Track [</span><span style="font-family: "verdana" , sans-serif; text-align: left; text-indent: -0.49in;"><a href="http://illuminations.nctm.org/Activity.aspx?id=4148" target="_blank">app</a></span><span style="font-family: "verdana" , sans-serif; text-align: left; text-indent: -0.49in;">]</span></li>
</ul>
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<span style="font-family: "verdana" , sans-serif;">=====</span></div>
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<span style="font-family: "verdana" , sans-serif;">Other Game Resources</span></div>
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<li><span style="font-family: "verdana" , sans-serif; text-indent: 0in;">Adventures </span><span style="font-family: "verdana" , sans-serif; text-indent: 0in;">with
Mathematics [</span><span style="font-family: "verdana" , sans-serif; text-indent: 0in;"><a href="https://www.mictm.org/index.php/mctm-publications/adventures-with-math/157-adventures-with-mathematics-series" target="_blank">MCTM</a></span><span style="font-family: "verdana" , sans-serif; text-indent: 0in;">]</span></li>
<li><a href="http://mathforum.org/blogs/max/games-with-fraction-strips-and-fraction-cards/" style="text-indent: 0in;" target="_blank"><span style="font-family: "verdana" , sans-serif;">Gameswith Fraction Strips and Fraction Cards</span></a></li>
<li><span style="font-family: "verdana" , sans-serif; text-indent: 0in;">Rational Number Resources [</span><span style="font-family: "verdana" , sans-serif; text-indent: 0in;"><a href="http://nrich.maths.org/public/leg.php?code=19&cl=2&cldcmpid=1249" target="_blank">NRICH</a></span><span style="font-family: "verdana" , sans-serif; text-indent: 0in;">]</span></li>
<li><span style="font-family: "verdana" , sans-serif; font-style: italic; text-indent: 0in;">Investigations</span><span style="font-family: "verdana" , sans-serif; text-indent: 0in;">
</span><span style="font-family: "verdana" , sans-serif; text-indent: 0in;"><a href="http://www.swsd.k12.wa.us/Page/220" target="_blank">Games</a></span></li>
</ul>
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<span style="font-family: "verdana" , sans-serif;">After playing the games, we reflect on our experiences using Math Teacher Chair:</span></div>
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<li><span style="font-family: "verdana" , sans-serif; text-indent: 0in;">What games did you play?</span></li>
<li><span style="font-family: "verdana" , sans-serif; text-indent: 0in;">So what mathematical ideas would you want to highlight?</span></li>
<li><span style="font-family: "verdana" , sans-serif; text-indent: 0in;">Now what would you do to break the game or slow down the play so students would benefit mathematically from playing?</span></li>
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<span style="font-family: "verdana" , sans-serif;">Thanks for your participation. You can reach us using the following contact information. </span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinCESdgMEXEJKn5nSADFsyjlLTNDzPEC0an0z_yANfdauiBEt_OE5QiTM2sdOj6h5AqGC48o-XEq3mAGpPhpbV9AQ7d4dOTytk1IntGc_z2LPnKsHXNZnra_2A1aPxbnsYaw1Sf30prG9F/s1600/contact+info.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="257" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinCESdgMEXEJKn5nSADFsyjlLTNDzPEC0an0z_yANfdauiBEt_OE5QiTM2sdOj6h5AqGC48o-XEq3mAGpPhpbV9AQ7d4dOTytk1IntGc_z2LPnKsHXNZnra_2A1aPxbnsYaw1Sf30prG9F/s400/contact+info.jpg" width="400" /></a><span style="font-family: "verdana" , sans-serif; text-indent: 0in;"></span></div>
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<span style="font-family: "verdana" , sans-serif; text-indent: 0in;"><span style="text-indent: 0in;">"Rocket science is child's play
compared to understanding child's play."</span></span></div>
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<span style="font-family: "verdana" , sans-serif; text-indent: 0in;"><span style="text-indent: 0in;">~ Unknown</span></span></div>
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<span style="font-family: "verdana" , sans-serif;">If you are attending the upcoming 2017 </span><a href="http://www.nctm.org/Conferences-and-Professional-Development/Annual-Meeting-and-Exposition/" style="font-family: Verdana, sans-serif;" target="_blank">NCTM</a><span style="font-family: "verdana" , sans-serif;"> Annual Meeting and Exposition in San Antonio, we will be presenting this session again. </span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgug4PNH2zDJpv3ud7_tW5kwZ8GHD4xoD_UljjhOB4tt4azkDQ3USdZGLfthqJKZn53flQ5PiFQoHfe4kZzGZwmWRm6WyGS4O31NUHv-btfN8LEMvFOZA08DPpiy0eUv0N8xwUf2AA6VR9D/s1600/NCTM.tiff" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="110" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgug4PNH2zDJpv3ud7_tW5kwZ8GHD4xoD_UljjhOB4tt4azkDQ3USdZGLfthqJKZn53flQ5PiFQoHfe4kZzGZwmWRm6WyGS4O31NUHv-btfN8LEMvFOZA08DPpiy0eUv0N8xwUf2AA6VR9D/s640/NCTM.tiff" width="640" /></a></div>
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<span style="font-family: "verdana" , sans-serif;">We promise it will be better next time thanks to the feedback you've provided on your session evaluations (or in the comments below).</span></div>
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delta_dchttp://www.blogger.com/profile/18024582157985654525noreply@blogger.com0tag:blogger.com,1999:blog-5957896812820341397.post-40228596802118919462017-02-10T13:03:00.003-08:002017-02-10T13:03:54.221-08:00Can we have five more minutes?<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRHupW45ax8FwNZyxvr8opewQWfzFqWM8pan9vZEdzUhyphenhyphen5DmUhZjH6d_ZzN-kOFZxVaDSWVbTE5VxFGM7KOKSzQY8uWeOl8wNhkJC2S5i8Ot1mejbNuUW2qSHC9WA0ddXUncRVvjZF77G2/s1600/Concept+Map.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRHupW45ax8FwNZyxvr8opewQWfzFqWM8pan9vZEdzUhyphenhyphen5DmUhZjH6d_ZzN-kOFZxVaDSWVbTE5VxFGM7KOKSzQY8uWeOl8wNhkJC2S5i8Ot1mejbNuUW2qSHC9WA0ddXUncRVvjZF77G2/s320/Concept+Map.jpg" width="245" /></a></div>
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<span style="font-family: Verdana, sans-serif;">Excuse the pun, but it was like clockwork. I would assign a group project (something like making a concept map), give them 20 minutes, and set the classroom timer. The timer would go off and nearly all the groups would ask for more time - usually about five minutes. It got to the point where I would just add five minutes into the plan but then they'd still want more time. </span></div>
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<span style="font-family: Verdana, sans-serif;">It wasn't as if they hadn't been working the entire time; they were just really invested in getting it perfect. Even the smallest detail, like the use of colors, had to be debated. I explained that these details didn't matter as much as the connections they were making, but somewhere they got the notion that the presentation of their ideas was paramount.</span></div>
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<span style="font-family: Verdana, sans-serif;">Then I was introduced to Design Thinking and the principles of <i>bias to action</i> and <i>prototyping to a solution</i>. I decided to apply these principles to the problem of students attempting to create the perfect poster. I went back to giving groups only twenty minutes but I broke it up into smaller intervals - each with a defined purpose.</span></div>
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<span style="font-family: Verdana, sans-serif;">First three minutes: organize the concepts in a way that reflects how you see them related and glue them on the paper.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8Kpz54kaEOPQYw1y-sBx8k4lfiODRWx8ivmIeVuMBtHITHoZebA5qLq6UMGWhixFGHwJakEcFLgg7tGj0-IqpKam8WqhIRC6-61gBeZmjOp369VGTVhIRajzhXG9qaBAcyuVeKVAXd9lv/s1600/Concepts.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8Kpz54kaEOPQYw1y-sBx8k4lfiODRWx8ivmIeVuMBtHITHoZebA5qLq6UMGWhixFGHwJakEcFLgg7tGj0-IqpKam8WqhIRC6-61gBeZmjOp369VGTVhIRajzhXG9qaBAcyuVeKVAXd9lv/s320/Concepts.jpg" width="320" /></a></div>
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<span style="font-family: Verdana, sans-serif;">I knew if I simply moved on to the next phase nothing would change; they would get stuck in the same old debates. Therefore, I had the groups rotate clockwise around the room. They were now looking at another group's vision of how the concepts might be arranged. </span></div>
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<span style="font-family: Verdana, sans-serif;">Next three minutes: consider the previous group's arrangement, talk through what the arrangement might represent, and add connections (nothing more).</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMYuN5W4DDYTFCW0_vxVgNGxKBlJaT3tdOQWYW-ESwP9Y6seSR__NApb_eu3eLmj4lbRpnIU8A6uCQcIkd_pgInqJJakIkwmmpUgL0Yz2M6Mm3Mwjo3XKs_68aFRcdAQf19bEk-2ykxuXO/s1600/Connections.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="291" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMYuN5W4DDYTFCW0_vxVgNGxKBlJaT3tdOQWYW-ESwP9Y6seSR__NApb_eu3eLmj4lbRpnIU8A6uCQcIkd_pgInqJJakIkwmmpUgL0Yz2M6Mm3Mwjo3XKs_68aFRcdAQf19bEk-2ykxuXO/s320/Connections.jpg" width="320" /></a></div>
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<span style="font-family: Verdana, sans-serif;">During this time, I kept reminding them that the previous group had only spent three minutes coming up with the configuration of concepts upon which they were working. There was nothing they could do to ruin it. This was simply a prototype and they had limited time to add their contributions. After three minutes, they rotated clockwise to a new group's poster.</span></div>
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<span style="font-family: Verdana, sans-serif;">Third interval of three minutes: consider the work of the previous groups, talk through what the work represents, and add descriptions to the connections.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjthnZKg1uxR6o5sYrwmCN9AJmqYDHf1eWg-RQ5bsRcxkPueSHHKVKCA-inVfHb078TwC_N4WBNM8nG3Dv4gdGY9umKElCm0S7Ci2jcCJ0QDYbwm_LtpGI469bem70Rcp8X2P8NSnZ2Woi0/s1600/Descriptions.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjthnZKg1uxR6o5sYrwmCN9AJmqYDHf1eWg-RQ5bsRcxkPueSHHKVKCA-inVfHb078TwC_N4WBNM8nG3Dv4gdGY9umKElCm0S7Ci2jcCJ0QDYbwm_LtpGI469bem70Rcp8X2P8NSnZ2Woi0/s320/Descriptions.jpg" width="320" /></a></div>
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<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;">I reminded them that only six minutes of work had gone into poster. The previous groups didn't really have anything invested in what was already done. So they shouldn't worry about doing anything that might change the poster. I even encouraged them to add new connections if they thought it made sense. </span><span style="font-family: Verdana, sans-serif;">After three minutes, they rotated clockwise to another new poster.</span></div>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;"><br /></span></div>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;">Fourth, fifth, and sixth intervals of three minutes: repeated the previous intervals - add more concepts, add more connections, and add more descriptions.</span></div>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlBuRG7emXcdsy0eWtZ0i4yuX-8zT2p_t0bQ9oeXJWm1wywa5_QWlHq7LvjM_lPVgqjfIJdTze2SK6nI62715OxchSYwVX-m5ciSjI-bVwD62J3DreUN9H57FxSo-SevSw9qb07tpxsgJW/s1600/Repeat.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="202" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlBuRG7emXcdsy0eWtZ0i4yuX-8zT2p_t0bQ9oeXJWm1wywa5_QWlHq7LvjM_lPVgqjfIJdTze2SK6nI62715OxchSYwVX-m5ciSjI-bVwD62J3DreUN9H57FxSo-SevSw9qb07tpxsgJW/s320/Repeat.jpg" width="320" /></a></div>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;"><br /></span></div>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;">Each time, I repeated the mantra: "The other groups only spent three minutes on the poster. You can't ruin it. Just get to work." </span></div>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;"><br /></span></div>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;">After 18 minutes, each group returned to their original poster. There were some audible gasps and laughs. Rarely had the poster turned out as expected but each group could infer the intent behind the decisions other groups had made. They spent the last two minutes creating an artist statement for their concept map - something they thought an observer ought to notice.</span></div>
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<span style="font-family: Verdana, sans-serif;"><br /></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0C23Wxh7yjZk0huDi5jLz5hyX1A8aDbSlASPGrHdZE5h_jVjffHt82-5N-F6ca2pAW3H9DFjerZxIJcLKKIM8mPeYmcyNnjP3tA5EWSCz_ifBDO8jGzjcJdrAGfZAdUujOEOeaWkCxOrF/s1600/Artist+Statement.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="199" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0C23Wxh7yjZk0huDi5jLz5hyX1A8aDbSlASPGrHdZE5h_jVjffHt82-5N-F6ca2pAW3H9DFjerZxIJcLKKIM8mPeYmcyNnjP3tA5EWSCz_ifBDO8jGzjcJdrAGfZAdUujOEOeaWkCxOrF/s320/Artist+Statement.jpg" width="320" /></a></div>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;"><br /></span></div>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;">None of the groups asked for more time. They were satisfied that the posters were prototypes - works in progress that allowed viewers to add their own perspective. We used the "extra" five minutes to do a gallery walk and see how <b>our</b> work turned out.</span></div>
<div style="text-align: justify;">
<span style="font-family: Verdana, sans-serif;"><br /></span></div>
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delta_dchttp://www.blogger.com/profile/18024582157985654525noreply@blogger.com4tag:blogger.com,1999:blog-5957896812820341397.post-20451451076123188392016-12-01T11:27:00.002-08:002017-02-20T14:40:02.141-08:00What's the deal?<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif;">Over the past two years, <a href="https://twitter.com/hashtag/m323?f=tweets&vertical=default&src=hash" target="_blank">#M323</a> teacher-leaders have designed several centers associated with Common Core State Standard <a href="http://www.corestandards.org/Math/Content/6/SP/A/3/" target="_blank">6.SPA.3</a>. Below is one of my favorites, which I am attempting to revise for my <a href="https://twitter.com/search?f=tweets&vertical=default&q=%23m22106&src=typd" target="_blank">#M221</a> pre-service teachers. Any feedback you are willing to provide would be appreciated.</span></div>
<span style="font-family: "verdana" , sans-serif;"><br /></span>
<span style="font-family: "verdana" , sans-serif;">=====</span><br />
<div style="text-align: center;">
<span style="font-family: "verdana" , sans-serif; font-size: x-large;"><b>Data Set Deal</b></span></div>
<div style="text-align: center;">
<span style="font-family: "verdana" , sans-serif;">Rules</span></div>
<div class="MsoNormal">
</div>
<ul>
<li><span style="font-family: "times" , "times new roman" , serif;">Remove all the face cards and Jokers from a deck of cards;</span></li>
<li><span style="font-family: "times" , "times new roman" , serif;">Deal out five cards, face down, to each player;</span></li>
</ul>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1WECtlBkFxiyhoKYug1yrIj4HO_Pcq3aRKiAZoy78HQvVXjdqt3oRpWhle9Hk1zwoaxVp9c7yqgS9MP7MCA1DXn9m2VJ0nZKmFTBSjoZrx3s1DR9KtNUB9pXr0TbldWQZcGa7_7s7Bc-z/s1600/1.tiff" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="105" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1WECtlBkFxiyhoKYug1yrIj4HO_Pcq3aRKiAZoy78HQvVXjdqt3oRpWhle9Hk1zwoaxVp9c7yqgS9MP7MCA1DXn9m2VJ0nZKmFTBSjoZrx3s1DR9KtNUB9pXr0TbldWQZcGa7_7s7Bc-z/s640/1.tiff" width="640" /></a></div>
<ul>
<li><span style="font-family: "times" , "times new roman" , serif;">Turn over exactly three cards;</span></li>
<li><span style="font-family: "times" , "times new roman" , serif;">Determine the mode (color), median (number), and range
(number) of the three cards;</span></li>
<li><span style="font-family: "times" , "times new roman" , serif;">Other players check to see that your answers are correct [1
point per correct answer];</span></li>
<li><span style="font-family: "times" , "times new roman" , serif;">Predict the mode (color), median (number), and range
(number) of all five cards;</span></li>
</ul>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmdU9j9ukAicKEHXls1rcaPaeulyrejbuxFJpYdiZNLUG1HEQMZMzoCk2roCCxsuid5-DCIAOxuSb7iw9OL7XeMVMmuPvEJ-dS7MjCECzkKpFAEO5tvay_RkP2OSM0nJfHbZ1GmpTCWZhz/s1600/3.tiff" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="106" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmdU9j9ukAicKEHXls1rcaPaeulyrejbuxFJpYdiZNLUG1HEQMZMzoCk2roCCxsuid5-DCIAOxuSb7iw9OL7XeMVMmuPvEJ-dS7MjCECzkKpFAEO5tvay_RkP2OSM0nJfHbZ1GmpTCWZhz/s640/3.tiff" width="640" /></a></div>
<ul>
<li><span style="font-family: "times" , "times new roman" , serif;">Turn over another card;</span></li>
<li><span style="font-family: "times" , "times new roman" , serif;">Determine the mode (color), median (number), and range (number) of the four cards;</span></li>
<li><span style="font-family: "times" , "times new roman" , serif;">Other players check to see that your answers are correct [1
point per correct answer];</span></li>
<li><span style="font-family: "times" , "times new roman" , serif;">Predict the mode (color), median (number), and range
(number) of all five cards;</span></li>
</ul>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHYfBXFb6kfo2lymw2D61bBk1Iyg83YsTXJ3BCdQ806PbY4KZ1e3-IIkjWMwBJitHDV4MRoP-TrzB5hkMkpItogtJ6_5dYSfJB8COg7UCSJc9LF-iZRtihwv_Dz2Adgx51qpo3eO5-aD7E/s1600/7.tiff" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="108" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHYfBXFb6kfo2lymw2D61bBk1Iyg83YsTXJ3BCdQ806PbY4KZ1e3-IIkjWMwBJitHDV4MRoP-TrzB5hkMkpItogtJ6_5dYSfJB8COg7UCSJc9LF-iZRtihwv_Dz2Adgx51qpo3eO5-aD7E/s640/7.tiff" width="640" /></a></div>
<ul>
<li><span style="font-family: "times" , "times new roman" , serif;">Turn over the last card;</span></li>
<li><span style="font-family: "times" , "times new roman" , serif;">Determine the mode (color), median (number), and range
(number) of all five cards;</span></li>
<li><span style="font-family: "times" , "times new roman" , serif;">Other players check to see that your answers are correct [1
point per correct answer];</span></li>
</ul>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOEVAqsfT3ansTGJmiA2pED1zYp15t195p36sR2xRZYVK5OVi9itzytLpPFgBzrfloPKiAWt955aihQBBxeuTOWZD__e5NyVPZoQGnX9l3DIi_o80us8odl8qAbNaoWkzmB6zVlyBtMs38/s1600/11.tiff" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="120" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOEVAqsfT3ansTGJmiA2pED1zYp15t195p36sR2xRZYVK5OVi9itzytLpPFgBzrfloPKiAWt955aihQBBxeuTOWZD__e5NyVPZoQGnX9l3DIi_o80us8odl8qAbNaoWkzmB6zVlyBtMs38/s640/11.tiff" width="640" /></a></div>
<ul>
<li><span style="font-family: "times" , "times new roman" , serif;">Check to see which of your predictions were correct [2 points
per correct answer]; and</span></li>
</ul>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi68VM0rSrap1CwooM-XRkRAdPZnraxW_n_KaFcsc0gA6p80oGGeTU98J7g6NPSW5308Dq55ZhsbdHqQgR8Qo39KFDlVqodse2zYpXgBGxMaMD-7ECJ27YrkzVNpzfRCPLhH6isLYwp2xb0/s1600/14.tiff" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="124" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi68VM0rSrap1CwooM-XRkRAdPZnraxW_n_KaFcsc0gA6p80oGGeTU98J7g6NPSW5308Dq55ZhsbdHqQgR8Qo39KFDlVqodse2zYpXgBGxMaMD-7ECJ27YrkzVNpzfRCPLhH6isLYwp2xb0/s640/14.tiff" width="640" /></a></div>
<ul>
<li><span style="font-family: "times" , "times new roman" , serif;">The winner is the first one to 21 points.</span></li>
</ul>
<br />
<div style="text-align: left;">
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text Indent 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text Indent 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Block Text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Hyperlink"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="FollowedHyperlink"/>
<w:LsdException Locked="false" Priority="22" QFormat="true" Name="Strong"/>
<w:LsdException Locked="false" Priority="20" QFormat="true" Name="Emphasis"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Document Map"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Plain Text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="E-mail Signature"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Top of Form"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Bottom of Form"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Normal (Web)"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Acronym"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Address"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Cite"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Code"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Definition"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Keyboard"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Preformatted"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Sample"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Typewriter"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Variable"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Normal Table"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="annotation subject"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="No List"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Outline List 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Outline List 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Outline List 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Simple 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Simple 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Simple 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Classic 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Classic 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Classic 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Classic 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Colorful 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Colorful 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Colorful 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 6"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 7"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 8"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 6"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 7"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 8"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table 3D effects 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table 3D effects 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table 3D effects 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Contemporary"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Elegant"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Professional"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Subtle 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Subtle 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Web 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Web 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Web 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Balloon Text"/>
<w:LsdException Locked="false" Priority="39" Name="Table Grid"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Theme"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Note Level 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Note Level 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Note Level 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Note Level 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Note Level 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Note Level 6"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Note Level 7"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Note Level 8"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Note Level 9"/>
<w:LsdException Locked="false" SemiHidden="true" Name="Placeholder Text"/>
<w:LsdException Locked="false" Priority="1" QFormat="true" Name="No Spacing"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading"/>
<w:LsdException Locked="false" Priority="61" Name="Light List"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 1"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 1"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 1"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 1"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 1"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 1"/>
<w:LsdException Locked="false" SemiHidden="true" Name="Revision"/>
<w:LsdException Locked="false" Priority="34" QFormat="true"
Name="List Paragraph"/>
<w:LsdException Locked="false" Priority="29" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" QFormat="true"
Name="Intense Quote"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 1"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 1"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 1"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 1"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 1"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 1"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 1"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 1"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 2"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 2"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 2"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 2"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 2"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 2"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 2"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 2"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 2"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 2"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 2"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 2"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 2"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 2"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 3"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 3"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 3"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 3"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 3"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 3"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 3"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 3"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 3"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 3"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 3"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 3"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 3"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 4"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 4"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 4"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 4"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 4"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 4"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 4"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 4"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 4"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 4"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 4"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 4"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 4"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 4"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 5"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 5"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 5"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 5"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 5"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 5"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 5"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 5"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 5"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 5"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 5"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 5"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 5"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 5"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 6"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 6"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 6"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 6"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 6"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 6"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 6"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 6"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 6"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 6"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 6"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" QFormat="true"
Name="Subtle Emphasis"/>
<w:LsdException Locked="false" Priority="21" QFormat="true"
Name="Intense Emphasis"/>
<w:LsdException Locked="false" Priority="31" QFormat="true"
Name="Subtle Reference"/>
<w:LsdException Locked="false" Priority="32" QFormat="true"
Name="Intense Reference"/>
<w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" SemiHidden="true"
UnhideWhenUsed="true" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/>
<w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/>
<w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
<w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
<w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/>
<w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
<w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/>
<w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark"/>
<w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful"/>
<w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 1"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 1"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 1"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 1"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 1"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 1"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 1"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 2"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 2"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 2"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 2"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 2"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 2"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 2"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 3"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 3"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 3"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 3"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 3"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 3"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 3"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 4"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 4"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 4"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 4"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 4"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 4"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 4"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 5"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 5"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 5"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 5"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 5"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 5"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 5"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 6"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 6"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 6"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 6"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 6"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 6"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 6"/>
<w:LsdException Locked="false" Priority="46" Name="List Table 1 Light"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark"/>
<w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful"/>
<w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful"/>
<w:LsdException Locked="false" Priority="46"
Name="List Table 1 Light Accent 1"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 1"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 1"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 1"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 1"/>
<w:LsdException Locked="false" Priority="51"
Name="List Table 6 Colorful Accent 1"/>
<w:LsdException Locked="false" Priority="52"
Name="List Table 7 Colorful Accent 1"/>
<w:LsdException Locked="false" Priority="46"
Name="List Table 1 Light Accent 2"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 2"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 2"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 2"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 2"/>
<w:LsdException Locked="false" Priority="51"
Name="List Table 6 Colorful Accent 2"/>
<w:LsdException Locked="false" Priority="52"
Name="List Table 7 Colorful Accent 2"/>
<w:LsdException Locked="false" Priority="46"
Name="List Table 1 Light Accent 3"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 3"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 3"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 3"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 3"/>
<w:LsdException Locked="false" Priority="51"
Name="List Table 6 Colorful Accent 3"/>
<w:LsdException Locked="false" Priority="52"
Name="List Table 7 Colorful Accent 3"/>
<w:LsdException Locked="false" Priority="46"
Name="List Table 1 Light Accent 4"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 4"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 4"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 4"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 4"/>
<w:LsdException Locked="false" Priority="51"
Name="List Table 6 Colorful Accent 4"/>
<w:LsdException Locked="false" Priority="52"
Name="List Table 7 Colorful Accent 4"/>
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<div style="text-align: center;">
<span style="font-family: "verdana" , sans-serif;">Score Sheet</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWtg9d9v9ul4IXsPAsZrVBuvowTu1FIEEKA9DtSnjmEUp83nvn41qUHO7Pzm6umEokX9aQrk87CRIlaZOl4zBUkhbQMb8PBNocWelQ8b_FZ-EnLZTM0mlAl9eiu9S5e16Mkrn6ucFjl3FC/s1600/Data+Set+Deal+Score+Sheet.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWtg9d9v9ul4IXsPAsZrVBuvowTu1FIEEKA9DtSnjmEUp83nvn41qUHO7Pzm6umEokX9aQrk87CRIlaZOl4zBUkhbQMb8PBNocWelQ8b_FZ-EnLZTM0mlAl9eiu9S5e16Mkrn6ucFjl3FC/s640/Data+Set+Deal+Score+Sheet.jpg" width="494" /></a></div>
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<span style="font-family: "verdana" , sans-serif;">=====</span></div>
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<span style="font-family: "verdana" , sans-serif;">Please leave any questions or suggestions in the comments. Thanks!</span></div>
delta_dchttp://www.blogger.com/profile/18024582157985654525noreply@blogger.com2tag:blogger.com,1999:blog-5957896812820341397.post-85271326897852063152016-11-25T14:52:00.001-08:002016-11-25T14:53:01.110-08:00We're really going to get to do it, aren't we?<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif;">One of the projects the pre-service elementary teachers (math majors) that I teach worked on this semester was designing a 4th-grade statistics lesson to address <a href="http://www.corestandards.org/Math/Content/4/MD/B/4/" target="_blank">4.MD.B.4</a>.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHwVRB3nZhNkz1vTfOWhz8KnionTNbL7ODlkpQ1DZGVe44yuwOOyWJszylGE6PXYyNzYxrfHSz_Za0L4-egT4k5hPXv_GK9m-DCm-FkWB6gX2ehqPy9M_6EmlpZ4F7I7HtnkI99tKEhEgr/s1600/4MDB4.tiff" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="107" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHwVRB3nZhNkz1vTfOWhz8KnionTNbL7ODlkpQ1DZGVe44yuwOOyWJszylGE6PXYyNzYxrfHSz_Za0L4-egT4k5hPXv_GK9m-DCm-FkWB6gX2ehqPy9M_6EmlpZ4F7I7HtnkI99tKEhEgr/s640/4MDB4.tiff" width="640" /></a></div>
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<span style="font-family: "verdana" , sans-serif;">The teachers went through a <a href="http://dschool.stanford.edu/dgift/" target="_blank">design cycle</a> to make the lesson. They ... </span></div>
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<ul>
<li><span style="font-family: "verdana" , sans-serif;">Built <b>empathy</b> by observing two fourth-grade classes;</span></li>
<li><span style="font-family: "verdana" , sans-serif;"><b>Defined</b> the problem by developing a <a href="https://joeyaquino.wordpress.com/2012/06/04/define-pt-2-of-my-stanford-design-thinking-crash-course/" target="_blank">User/Needs/Insight</a> statement;</span></li>
<li><span style="font-family: "verdana" , sans-serif;"><b>Brainstormed</b> a variety of possible activities;</span></li>
<li><span style="font-family: "verdana" , sans-serif;">Developed a <b>prototype</b> SAFARI Lesson;</span></li>
</ul>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_2_InzZKBq50N2QFcaAwk8xXV5Uw-D3Pd9j0ylA_5LYeg-iMuyKQweP-9Pb_tKRVqrodh0UCXOlHHNH6mRnjcvEAEMt0Y3E0aov_OrGrUEqbx-aAb6EYF-iq2taxXQ3ws7rUvOBeIBB5E/s1600/SAFARI+4MDB4+%25281%2529.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="140" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_2_InzZKBq50N2QFcaAwk8xXV5Uw-D3Pd9j0ylA_5LYeg-iMuyKQweP-9Pb_tKRVqrodh0UCXOlHHNH6mRnjcvEAEMt0Y3E0aov_OrGrUEqbx-aAb6EYF-iq2taxXQ3ws7rUvOBeIBB5E/s320/SAFARI+4MDB4+%25281%2529.jpg" width="320" /></a></div>
<ul>
<li><span style="font-family: "verdana" , sans-serif;"><b>Tested</b> the lesson by sharing it with the classroom teacher; and</span></li>
<li><span style="font-family: "verdana" , sans-serif;"><b>Revised</b> it based on her feedback.</span></li>
</ul>
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<span style="font-family: "verdana" , sans-serif;">Three teachers co-taught the lesson in two different fourth-grade STEM classes. They made adjustment between the lessons based on what worked and what didn't. Afterwards, they reflected on the experience and shared the lesson with me. The lesson was so cool, I decided to make a few adjustments and use it in another class for pre-service elementary teachers (mostly non-math majors) that I teach. Here is the SAFARI Lesson that I taught.</span></div>
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<span style="font-family: "verdana" , sans-serif;"><i>Schema Activation</i> - Prediction</span></div>
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<span style="font-family: "verdana" , sans-serif;">Directions: "You have two sticky notes. On the green sticky, I want you to predict the number of seconds you think it would take you to write the alphabet from A to Z. On the purple sticky, I want you to predict how long it would take you to write the alphabet in reverse order from Z to A. You have a quarter of a minute. Go!"</span></div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span></div>
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<span style="font-family: "verdana" , sans-serif;"><i>Focus</i> - <a href="http://www.corestandards.org/Math/Content/5/MD/B/2/" target="_blank">5.MD.B.2</a></span></div>
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<span style="font-family: "verdana" , sans-serif;">Share lesson target: "We are going to make line plots to display data sets of measurements in fractions of a unit."</span></div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span></div>
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<span style="font-family: "verdana" , sans-serif;">[Anticipated learner responses are in brackets.]</span></div>
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<span style="font-family: "verdana" , sans-serif;">"Who thinks they can write the alphabet forward the fastest? [13 seconds or 2 letters per second] Who thinks they will take the most time to write the alphabet forward? [52 seconds or 1 letter every 2 seconds] Alright, let's get up and stand in order from fastest predicted time to slowest predicted time."</span></div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span></div>
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<span style="font-family: "verdana" , sans-serif;">Learners order themselves</span></div>
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<span style="font-family: "verdana" , sans-serif;">"As I listened in, it became apparent that several of you made similar predictions. It would be interesting to see how the predictions cluster. But we could potentially have a lot of unique guesses. In order to gather those guesses, let's round our predictions to the nearest quarter-of-a-minute. For example, Sam <a href="https://twitter.com/ottensam/status/798619921911451649" target="_blank">guessed</a> 20 seconds forward and 55 seconds backwards. He would round to 1/4 of a minute for forward and one minute, four-fourths, backwards. Work with your neighbors to round your predictions to the nearest quarter-of-a-minute and then post them on the board - forward at the front and backwards at the back."</span></div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span></div>
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<span style="font-family: "verdana" , sans-serif;">Learners post rounded predictions</span></div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span></div>
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<span style="font-family: "verdana" , sans-serif;">"What do you notice about the data sets?" [The writing in reverse predictions are "higher" and more spread out than the forward predictions.] </span></div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span></div>
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<span style="font-family: "verdana" , sans-serif;">"Why?" [We are familiar with writing the alphabet forwards so we think we can do it faster and know more what to expect.]</span></div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span></div>
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<span style="font-family: "verdana" , sans-serif;"><i>Activity</i> - Writing the Alphabet in Reverse Order</span></div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span></div>
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<span style="font-family: "verdana" , sans-serif;">Directions: "I am going to give you three pieces of paper."</span></div>
<blockquote class="tr_bq" style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif;">At this point in my lesson, one of the pre-service teachers asked, "We're really going to get to do it, aren't we? We're really going to find out how long it takes us to write the alphabet from Z to A? Is it weird that I am so excited about this?" I reassured her that it wasn't weird - that my other pre-service teachers had designed a pretty cool lesson.</span></blockquote>
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<span style="font-family: "verdana" , sans-serif;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghtx9a__Xi11WuRZqlNoi9usOM1JoUSDhenHcIpi6wJ23apTT0RBpLQgE3Sn5jojHZb_YTBa51Bg4SV2kJdtUR3GVLxeZ2A0oOcqC_yoFKspKsCbopoSZUGXjhenZhdnjkq71QYsybqV2w/s1600/ABC+Blocks.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="130" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghtx9a__Xi11WuRZqlNoi9usOM1JoUSDhenHcIpi6wJ23apTT0RBpLQgE3Sn5jojHZb_YTBa51Bg4SV2kJdtUR3GVLxeZ2A0oOcqC_yoFKspKsCbopoSZUGXjhenZhdnjkq71QYsybqV2w/s200/ABC+Blocks.jpg" style="cursor: move;" width="200" /></a>Directions continued: "You have a choice. On the yellow paper, you may write the alphabet forward on one side and use it to help you to write it from Z to A on the other side. You'll see the second sheet has the alphabet already on the back in the form of classic blocks, like the ones my grandson plays with. If you choose that one, you will incur a 1/2 minute penalty, which means you will add 30 seconds to your time. The last piece is simply scrap paper; use it if you want to try to write the alphabet from Z to A without any other support.</span></div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span>
<span style="font-family: "verdana" , sans-serif;">"A few more things: </span><br />
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<ul>
<li style="text-align: justify;"><span style="font-family: "verdana" , sans-serif;">You must start at Z and write the letters in reverse order to A. You can't cheat and start at A on the right-side of your paper. </span></li>
<li style="text-align: justify;"><span style="font-family: "verdana" , sans-serif;">The letters must be legible. Your table-mates will decide if they can read your letters, and you will earn a 5 second penalty for each letter they can't read.</span></li>
<li style="text-align: justify;"><span style="font-family: "verdana" , sans-serif;">When you finish, check the timer on the front board, record your time, and round it to the nearest quarter-of-a-minute.</span></li>
</ul>
<blockquote class="tr_bq" style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif;">At this point, a student rose his hand to ask a question. The girl who was so excited blurted out, "I just want to get started!" The other student asked if the letters had to be upper or lower case. I said it didn't matter to me.</span></blockquote>
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<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif;">Set the online <a href="http://www.online-stopwatch.com/" target="_blank">stopwatch</a> and say, "Go!"</span></div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span></div>
<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif;">When everyone is finish, have learners trade papers check letters for legibility.</span></div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span></div>
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<span style="font-family: "verdana" , sans-serif;"><i>Reflection</i> - Noticing and Naming</span></div>
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<span style="font-family: "verdana" , sans-serif;">Directions: "If you used the yellow paper (wrote A to Z on the back), write your result, to the nearest quarter-of-a-minute, on the yellow sticky note. If you used the blocks, and added 30 seconds to your time, write your rounded result on the blue sticky note. If you did it without any support, write your rounded result on the pink sticky note. Your rounded results go on the line plot on the back board underneath your predictions."</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSx3PTAEoszgFAXaG0vrlIbpAhTgTWd1A0eR3rkDKpDuEpfIWLOEuyTcMJx2DQHr4LdpxbuR_wgqTwnZrNUl3aCGJ6B8j5LZBT0aaapbXwFwN7rxg4j3QNFznh2OjwV7HQNuSDPQO4aD_3/s1600/IMG_2231.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="214" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSx3PTAEoszgFAXaG0vrlIbpAhTgTWd1A0eR3rkDKpDuEpfIWLOEuyTcMJx2DQHr4LdpxbuR_wgqTwnZrNUl3aCGJ6B8j5LZBT0aaapbXwFwN7rxg4j3QNFznh2OjwV7HQNuSDPQO4aD_3/s640/IMG_2231.jpg" width="640" /></a></div>
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<span style="font-family: "verdana" , sans-serif;">"What do you notice?" [Look for opportunities to introduce terminology related to measures of center and spread, like median, mode, and range]</span></div>
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<span style="font-family: "verdana" , sans-serif;"><i>I want to ...</i> - Choice</span></div>
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<span style="font-family: "verdana" , sans-serif;">Directions: "What do you want to do now? Here are some ideas:</span></div>
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<ul>
<li><span style="font-family: "verdana" , sans-serif;">Try it again using a different level of support and add it to the line plot;</span></li>
<li><span style="font-family: "verdana" , sans-serif;">See if there is a difference between writing in upper and lower case;</span></li>
<li><span style="font-family: "verdana" , sans-serif;">Try it forward and compare it with your prediction;</span></li>
<li><span style="font-family: "verdana" , sans-serif;">Gather more data from your friends and family over Thanksgiving;</span></li>
<li><span style="font-family: "verdana" , sans-serif;">Consider other activities that ask people to do familiar things in unfamiliar ways and what the data might show; or</span></li>
<li><span style="font-family: "verdana" , sans-serif;">Come up with your own idea to extend your learning."</span></li>
</ul>
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<span style="font-family: "verdana" , sans-serif;"><br /></span></div>
delta_dchttp://www.blogger.com/profile/18024582157985654525noreply@blogger.com0tag:blogger.com,1999:blog-5957896812820341397.post-19707241780711667752016-11-23T14:10:00.001-08:002016-11-25T14:54:39.142-08:00What's the hurry?<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif;">The moment you (some of you) have been waiting for [insert <a href="https://www.youtube.com/watch?v=itAOGRiYRLI" target="_blank">drumroll</a>] ... the Carousel Lesson Design process. Previously, we learned about SAFARI <a href="http://deltascape.blogspot.com/2016/11/wanna-go-on-sa-f-r-i.html" target="_blank">lessons</a> and <a href="http://deltascape.blogspot.com/2016/11/where-are-we-in-sa-f-r-i.html" target="_blank">prototyping</a>. In this post, I share how to encourage teachers to embrace creativity and connectivity while collaborating on a week long unit design.</span></div>
<span style="font-family: "verdana" , sans-serif;"><br /></span>
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<div style="text-align: left;">
<span style="font-family: "verdana" , sans-serif;">First, you need some ingredients. It's best if you have: </span></div>
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGLlYlhxDXvQe30bp27rI6TPR_FsX-tfAEZdTG9vYFKPtI2Awh3d9bAb0tPighco406zj4ATkMEte_EW7tV82XJD64cSboBquryAkdbnvCbCbFKdg92IFXM-uPHJCrC2S82wvn1lMK2IZe/s1600/Shape+of+the+Data.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="120" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGLlYlhxDXvQe30bp27rI6TPR_FsX-tfAEZdTG9vYFKPtI2Awh3d9bAb0tPighco406zj4ATkMEte_EW7tV82XJD64cSboBquryAkdbnvCbCbFKdg92IFXM-uPHJCrC2S82wvn1lMK2IZe/s200/Shape+of+the+Data.jpg" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="https://investigations.terc.edu/" target="_blank">Investigations Curriculum</a></td></tr>
</tbody></table>
<span style="font-family: "verdana" , sans-serif;"></span><br />
<ul>
<li style="text-align: left;"><span style="font-family: "verdana" , sans-serif;">5 willing teachers;</span></li>
<li style="text-align: left;"><span style="font-family: "verdana" , sans-serif;">1 set of <a href="http://www.corestandards.org/Math/Content/4/MD/" target="_blank">targets</a>;</span></li>
<li style="text-align: left;"><span style="font-family: "verdana" , sans-serif;">1 rich curriculum;</span></li>
<li style="text-align: left;"><span style="font-family: "verdana" , sans-serif;">5 pieces of easel paper;</span></li>
<li style="text-align: left;"><span style="font-family: "verdana" , sans-serif;">Various scented (<a href="http://www.mrsketch.com/" target="_blank">optional</a>), colored markers;</span></li>
<li style="text-align: left;"><span style="font-family: "verdana" , sans-serif;">Multiple sticky notes;</span></li>
<li style="text-align: left;"><span style="font-family: "verdana" , sans-serif;">1 lesson design framework; and</span></li>
<li style="text-align: left;"><span style="font-family: "verdana" , sans-serif;">1 <a href="http://www.online-stopwatch.com/countdown-timer/" target="_blank">timer</a></span></li>
</ul>
<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif;">Each teacher is assigned one of five sequential lessons and given 5 minutes (no more, no less) to look through the lesson in order to determine what is important. At the end of this time, they use another 2 minutes to set up the SAFARI lesson framework on their easel paper and write down some of the most important ideas from the lesson they were assigned.</span></div>
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<span style="font-family: "verdana" , sans-serif;">After 2 minutes the teachers rotate (like a Carousel) to the next lesson. Day 1 goes to Day 2 ... and Day 5 goes to Day 1. They use what they know from their own lesson and the important points the previous teacher wrote down to inform them about the lesson. They also have exactly 2 minutes to add to the lesson. I am constantly reminding them, "Don't worry about designing it perfectly. You don't even know for sure what the lesson is about. Don't worry about offending the teacher that started the lesson. They spent all of 2 minutes on it so far."</span></div>
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<span style="font-family: "verdana" , sans-serif;">The teachers aren't always crazy about the artificial time crunch. However, it helps to contribute to their creativity (think <a href="http://www.macgyvermath.com/" target="_blank">MacGyverMath</a>) while ensuring progress. It keeps them from letting their perfectionism get in the way.</span></div>
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<span style="font-family: "verdana" , sans-serif;">Rotate! And repeat ... three more times (Note: only two interactions shown below) at 2 minutes a piece.</span></div>
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<span style="font-family: "verdana" , sans-serif;">The teachers are now back at their original lessons. They take 1 minute to read through what has been added to their initial ideas. The sticky notes are used to identify questions for the author or indicate likes (thumbs up). The teachers can also continue to add new ideas based on what they have seen in the other lessons. After 1 minute the teachers rotate again and again and again and again and again. At each lesson they answer questions, add stickies, or contribute ideas.</span></div>
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<span style="font-family: "verdana" , sans-serif;">At the end, the teachers have spent 20 minutes to design a five-day unit.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguR4syUD1nbxCKH6OKbAcexnVluc-PWB9K7GjPGSBL-4cdUMtcDeT6xiYicySNwmCqbw2GNhNXKloGphcsOzASlwcrUS0lXLY96zXXv7AmIHFgqibAc5jdb1Yq42bL_HFBNj1l1uEsQGNk/s1600/Final+Results.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguR4syUD1nbxCKH6OKbAcexnVluc-PWB9K7GjPGSBL-4cdUMtcDeT6xiYicySNwmCqbw2GNhNXKloGphcsOzASlwcrUS0lXLY96zXXv7AmIHFgqibAc5jdb1Yq42bL_HFBNj1l1uEsQGNk/s400/Final+Results.jpg" width="400" /></a></div>
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<span style="font-family: "verdana" , sans-serif;">Yes, there is still some work to do to sift out the essential elements of the lesson. These will be written in the SAFARI format and then shared with their peers for feedback. Finally, the lessons are tested out in the classroom. The <a href="http://deltascape.blogspot.com/2016/11/were-really-going-to-get-to-do-it-arent_5.html" target="_blank">next post</a> is about one of those lessons.</span></div>
delta_dchttp://www.blogger.com/profile/18024582157985654525noreply@blogger.com0tag:blogger.com,1999:blog-5957896812820341397.post-69530771442637581922016-11-22T13:10:00.001-08:002016-11-25T13:17:51.758-08:00Where are we in the SA F A R I?<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif;">I might have gotten a bit ahead of myself in the last <a href="http://deltascape.blogspot.com/2016/11/wanna-go-on-sa-f-r-i.html" target="_blank">post</a> (or perhaps I am building suspense - you decide). Before I introduce you to the Carousel Lesson Design process, let me explain a bit more about the SAFARI prototypes. This should put the framework into a clearer context.</span></div>
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<span style="font-family: "verdana" , sans-serif;">As I said, SAFARI is based on an instructional approach called the <a href="http://blog.stenhouse.com/archives/2013/06/20/blogstitute-week-1-debbie-miller-on-letting-kids-dig-in/" target="_blank">workshop model</a>. SAFARI is an acronym for </span><span style="font-family: "verdana" , sans-serif;">the components of the model</span><span style="font-family: "verdana" , sans-serif;"> [Schema Activation, Focus, Activity, Reflection, and "I want to ..."], and in Swahili it means journey. So in designing a lesson, we are thinking about it as a journey from the known to the new.</span></div>
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<span style="font-family: "verdana" , sans-serif;">One thing that design thinking has shown me, is that this journey also reflects the <b>flair</b> and <b>focus</b> necessary for innovative thinking.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWSc6_TOvv0ZHA3tUc6oNhYSK-SlCS7Uh7CrJgNPEYU8RPXekucMJuirXtcHACpwIVeP4NCDD3iX0Mk-cICSbOYJ4w_V-XWfGMVK_CFVatBMBIUEGkwKDsLncHkKns5dpYUyoCgIzQaTM0/s1600/SAFARI+Lesson+Prototyping.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="309" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWSc6_TOvv0ZHA3tUc6oNhYSK-SlCS7Uh7CrJgNPEYU8RPXekucMJuirXtcHACpwIVeP4NCDD3iX0Mk-cICSbOYJ4w_V-XWfGMVK_CFVatBMBIUEGkwKDsLncHkKns5dpYUyoCgIzQaTM0/s400/SAFARI+Lesson+Prototyping.jpg" width="400" /></a></div>
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<span style="font-family: "verdana" , sans-serif;">The <i>Schema Activation</i> begins with a flair. Sometimes referred to as the anticipatory set, it ought to be an open-ended invitation for everyone to join the journey. Next, the lesson quite literally <i>Focuses</i> the learners' attention on what to look for during the journey; this might be a "think aloud" in typical workshop lessons. Entering the A<i>ctivity</i> portion, the lesson once again flairs - allowing each learner room to roam. Here you might encounter what Dr. Jo Boaler refers to as a "low floor, high ceiling" <a href="https://www.youcubed.org/grade/low-floor-high-ceiling/" target="_blank">task</a>. After a set amount of time exploring, we refocus by <i>Reflecting</i> on what was important during the activity. We should not wait until everyone is finished before making time to consolidate our thinking. In fact, we want students to cry out for more time; it's what <a href="http://www.heinemann.com/products/E00323.aspx" target="_blank">Ellin Keene</a> calls fostering learning lust. Finally, we ask learners to consider what comes next by brainstorming <i>"I want to ..." </i>statements related to the lesson. Perhaps they want to spend more time exploring the task they didn't finish. This represents the final flair until tomorrow when the journey starts all over again.</span></div>
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<span style="font-family: "verdana" , sans-serif;">After explaining the components to my teachers, I give them 10 minutes to develop three different SAFARI lessons related to some topic.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5RteSnLsCM6ZIVtLQ86ZIk2TJ-pfczrUNfcAhQopradfs-A0XWbCAGWvYkB8lxIoFfCeNtQXlVaYH9eRoMSvg9F3aS9Tlg3THfwUh3lEpGva67fMrbn8jyJOrAEfh3WzAvEAwcRpf5ywv/s1600/SAFARI+Lesson+Prototyping.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="492" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5RteSnLsCM6ZIVtLQ86ZIk2TJ-pfczrUNfcAhQopradfs-A0XWbCAGWvYkB8lxIoFfCeNtQXlVaYH9eRoMSvg9F3aS9Tlg3THfwUh3lEpGva67fMrbn8jyJOrAEfh3WzAvEAwcRpf5ywv/s640/SAFARI+Lesson+Prototyping.jpg" width="640" /></a></div>
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<span style="font-family: "verdana" , sans-serif;">At the end of the 10 minutes, I ask the teachers to share their prototypes with a peer for feedback. The teachers are often resistant to share unfinished products because of the implicit need for perfection usually associated with typical lesson plans. I remind them, however, that they had, on average, three-and-a-third minutes on each prototype. So no one expects their lessons to be perfect.</span></div>
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<span style="font-family: "verdana" , sans-serif;">Afterwards, the teachers express appreciation for the process. Not only have they outlined three possible lessons that they could use in their classrooms, but because the lessons were <i>incomplete</i> their peers were able to add innovative ideas in the blank-spaces. "I wouldn' have thought of doing it that way," one teacher admitted. She continued, "And if I had created a full-blown lesson plan, I don't think [the other teacher] would have been able to see and share this amazing idea."</span></div>
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<span style="font-family: "verdana" , sans-serif;">It's a good reminder that the creative process is often about finding and cultivating the cracks that allow new ideas to grow. So how does this get any better? Here's what you've been waiting for - the Carousel Lesson Design ... in the <a href="http://deltascape.blogspot.com/2016/11/the-moment-you-some-of-you-have-been.html" target="_blank">next post</a>.</span></div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span>delta_dchttp://www.blogger.com/profile/18024582157985654525noreply@blogger.com0tag:blogger.com,1999:blog-5957896812820341397.post-70890848484941573312016-11-21T14:56:00.002-08:002016-11-22T13:10:37.910-08:00Wanna go on a SA F A R I?<span style="font-family: "verdana" , sans-serif;"></span><br />
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<span style="font-family: "verdana" , sans-serif;">Recently, I have been considering how to apply principles from Design Thinking to education. For example, I think creating lesson prototypes instead of lesson plans can help teachers in several ways. </span></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaLqu4EbRxznbx6KFWYOzlRHO0X8K0JSqy4DZQ9QeRLTemj8TuC4oB8m1q_mkKmigd87AKLG3ljJ4KY42beEuNc_1EkPOVn91DAL41GCVvWBxQHiUJM9389GDl_aOJ_HaM7v_N9Lfp0Hv9/s1600/design-thinking-2.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaLqu4EbRxznbx6KFWYOzlRHO0X8K0JSqy4DZQ9QeRLTemj8TuC4oB8m1q_mkKmigd87AKLG3ljJ4KY42beEuNc_1EkPOVn91DAL41GCVvWBxQHiUJM9389GDl_aOJ_HaM7v_N9Lfp0Hv9/s320/design-thinking-2.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="http://dschool.stanford.edu/" target="_blank">d.school</a></td></tr>
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<li><span style="font-family: "verdana" , sans-serif;">We make prototypes faster than plans, which means more time for other teachery-things; </span></li>
<li><span style="font-family: "verdana" , sans-serif;">Because less time is spent developing a lesson prototype, the teacher is usually less invested in sticking to it when things go poorly;</span></li>
<li><span style="font-family: "verdana" , sans-serif;">Multiple prototypes are often made, so if the teacher wants to shift gears, there's another idea available; and </span></li>
<li><span style="font-family: "verdana" , sans-serif;">A prototype has more blank-space (less teacher control), which leaves more room for interesting interpretations of the lesson by students.</span></li>
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<span style="font-family: "verdana" , sans-serif;">When it came time to develop a framework for the lesson prototype, I returned to a familiar instructional approach: Math Workshop. I wrote about this approach with some GVSU math colleagues in a <i>Mathematics in the Middle School</i> <a href="http://www.nctm.org/Publications/mathematics-teaching-in-middle-school/2013/Vol19/Issue2/Teaching-with-the-Mathematical-Practices-in-Mind/" target="_blank">article</a>. Table 1 from the article, shown below, gives a good overview of the Math Workshop Model that we use.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwWuJe4RJEAyddZjRW6iN6bH9nZkp7okt8AQZSvHBGGCExKI1l2Rc8T3ZYGM_m3ioBEVrKRI0-TJCh7lmsnHmkSASX-TjGZkU7aqrQ38JwvuxjqUYE0SjTI85sDK2J6QNTc4OJYNpgFlfC/s1600/Math+Workshop+Table+1.tiff" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwWuJe4RJEAyddZjRW6iN6bH9nZkp7okt8AQZSvHBGGCExKI1l2Rc8T3ZYGM_m3ioBEVrKRI0-TJCh7lmsnHmkSASX-TjGZkU7aqrQ38JwvuxjqUYE0SjTI85sDK2J6QNTc4OJYNpgFlfC/s400/Math+Workshop+Table+1.tiff" width="388" /></a></div>
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<span style="font-family: "verdana" , sans-serif;">I tend to use "Schema activation" instead of "Making connections" for the first part of the lesson because of its use in reading workshop - where I was introduced to the approach.</span></div>
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<span style="font-family: "verdana" , sans-serif;">Last year, I shared this method with <a href="https://twitter.com/KristinFrang" target="_blank">Kristin Frang</a>. We were working on a project that required designing lessons. I wrote the framework on the board using only the initials:</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYgZ0LhCK6inQFmwx0D3ZMfndIjzXEmtNPny0YEnMyP6b9eM8xwQm0J82tLn9MXUDBdBX7psPFw-nmR9CXNHaFWQXUUS08m6KIvBS_jor5ntw6CdBL1zuR5Y-iXQi_2DPEUoisEJNbdxcM/s1600/SAFAR.tiff" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYgZ0LhCK6inQFmwx0D3ZMfndIjzXEmtNPny0YEnMyP6b9eM8xwQm0J82tLn9MXUDBdBX7psPFw-nmR9CXNHaFWQXUUS08m6KIvBS_jor5ntw6CdBL1zuR5Y-iXQi_2DPEUoisEJNbdxcM/s1600/SAFAR.tiff" /></a></div>
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<span style="font-family: "verdana" , sans-serif;">Kristin said, "If only you had an "I" it could be safari."</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbltqSqAi53U3Eg4V3qvT8ygD5ou8I-lpOJuGgavHfjeufJzPHYL1NQD8Oa3eGyB5Bbwl8rRysE4FY8dxfMsALOnc5F4QvR1w-gnHilBerIuZfD0vCGF5WDMhQz8MgZB0iAUt24B0-wJym/s1600/Safari+.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbltqSqAi53U3Eg4V3qvT8ygD5ou8I-lpOJuGgavHfjeufJzPHYL1NQD8Oa3eGyB5Bbwl8rRysE4FY8dxfMsALOnc5F4QvR1w-gnHilBerIuZfD0vCGF5WDMhQz8MgZB0iAUt24B0-wJym/s200/Safari+.jpg" width="200" /></a><span style="font-family: "verdana" , sans-serif;">Having been on an actual safari (and being a bit obsessive about acronyms), I couldn't believe I had never seen this before. All the framework needed was an "I" to complete the word, safari. </span><span style="font-family: "verdana" , sans-serif;"><br /></span></div>
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<span style="font-family: "verdana" , sans-serif;">The "I" became "I want to ..." as a way to recognize the importance of students making their own choice about what to explore in their learning journey. And that's the coolest thing about SAFARI lesson design - in Swahili, safari literally means travel or journey.</span></div>
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<span style="font-family: "verdana" , sans-serif;">With the framework developed, the next thing to do was create a process for using the framework to design the lesson prototypes. I wanted to stay true to Design Thinking and use a process that would foster innovation. So in the next <a href="http://deltascape.blogspot.com/2016/11/where-are-we-in-sa-f-r-i.html" target="_blank">post</a>, we will explore Carousel Lesson Design.</span></div>
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delta_dchttp://www.blogger.com/profile/18024582157985654525noreply@blogger.com0tag:blogger.com,1999:blog-5957896812820341397.post-53289575873307486232016-09-23T12:05:00.000-07:002016-09-25T13:19:05.588-07:00Should I keep these math flashcards?<div style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif;"><b>I am working on a project with Alyssa Boike called <a href="http://www.macgyvermath.com/blog" target="_blank">MacGyver Math</a>. Before I impose my kind of crazy on that site, however, I want to write a prototype post. Here it goes...</b></span></div>
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<span style="font-family: "georgia" , "times new roman" , serif;">Dear MacGyver Math,</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmfPszqBqR-Z67aE3P5fNI0GbPXcVpNBnzuWYPDz3TUxD_P8D9_yplL92EOyXC2h-ioe1MkzFqrtG704G8v06kVSJIQ2qEzT6yJ6M7dD_TETjXcEYaBudaoWY1CRLKuvYudiCawdE9RR0D/s1600/IMG_1937.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmfPszqBqR-Z67aE3P5fNI0GbPXcVpNBnzuWYPDz3TUxD_P8D9_yplL92EOyXC2h-ioe1MkzFqrtG704G8v06kVSJIQ2qEzT6yJ6M7dD_TETjXcEYaBudaoWY1CRLKuvYudiCawdE9RR0D/s200/IMG_1937.jpg" width="200" /></a><span style="font-family: "georgia" , "times new roman" , serif;"></span></div>
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<span style="font-family: "georgia" , "times new roman" , serif;">I am a new second-grade teacher. Over the summer I went through some of the boxes the previous teacher left in my classroom and found a bunch of math flashcards. It's my understanding that addition, subtraction, multiplication, and division flashcards are bad because they reinforce the belief that being good at math means being fast. And who can forget those awful <a href="http://www.educationworld.com/a_lesson/00-2/lp2113.shtml" target="_blank">Around the World</a> games in math class where one person dominated while the rest of us just sat there?</span></div>
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<span style="font-family: "georgia" , "times new roman" , serif;">So, should I keep the flashcards or throw them away?</span></div>
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<span style="font-family: "georgia" , "times new roman" , serif;">Sincerely,</span></div>
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<span style="font-family: "georgia" , "times new roman" , serif;">Enlightened Elementary Educator in Elmira</span></div>
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<span style="font-family: "georgia" , "times new roman" , serif;">***</span></div>
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<span style="font-family: "trebuchet ms" , sans-serif;">Dear Enlightened,</span></div>
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<span style="font-family: "trebuchet ms" , sans-serif;">Thanks for your letter. It reminded me of one of my favorite Macgyver quotes. </span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhD3gs8pPGX0wF1kEFPMblXbUm4ywicZ1capTmg3R-Wv-g-Cr0QZhe5GbDxqkCgSqSj_JEF5U2SFOORU-btiagAd-1zPzmdBzAXsp-D2lp8T5wzwIMgc9CTzjzTDm5jaj8fh9YVPSSG3PRE/s1600/Broken.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhD3gs8pPGX0wF1kEFPMblXbUm4ywicZ1capTmg3R-Wv-g-Cr0QZhe5GbDxqkCgSqSj_JEF5U2SFOORU-btiagAd-1zPzmdBzAXsp-D2lp8T5wzwIMgc9CTzjzTDm5jaj8fh9YVPSSG3PRE/s1600/Broken.jpg" /></a></div>
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<span style="font-family: "trebuchet ms" , sans-serif;">While you might not want to use the flashcards to reinforce false beliefs about doing math, they might serve other purposes.</span></div>
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<span style="font-family: "trebuchet ms" , sans-serif;">For example:</span></div>
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<span style="font-family: "trebuchet ms" , sans-serif;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGtEtOK8KhI5JhhOMJb6CBzZeXoR14IvY4raZEb1gV_fbeIFGQm3UXZyLKVBICG2JwysTUAOKWXRgkY4VYJ3WzwlBYDnnWVAerakL4J95xV4QRylkVqkGFpmlaS9LxhNe8yBdNCn7w7kPM/s1600/Sorting.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGtEtOK8KhI5JhhOMJb6CBzZeXoR14IvY4raZEb1gV_fbeIFGQm3UXZyLKVBICG2JwysTUAOKWXRgkY4VYJ3WzwlBYDnnWVAerakL4J95xV4QRylkVqkGFpmlaS9LxhNe8yBdNCn7w7kPM/s1600/Sorting.jpg" /></a><span style="font-family: "trebuchet ms" , sans-serif;"><br /></span></span></div>
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<span style="font-family: "trebuchet ms" , sans-serif;">We could ask our students to sort the flashcards; "Which facts do you know and which facts are you still learning?" Then we could see if there are any known facts that they could use to help them learn the unknown facts.</span></div>
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<span style="font-family: "trebuchet ms" , sans-serif;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhhk7_D3nrebvdVTgTrYp9lSHDOlOezpr8LedcXMot87wxVyUBwRiKBAuwIy1O4xE2NEvu6jGh8s6xgNCd6Kf9B9i1tc4AnLjVIAp9-DONJx09Cs45xB_GdGOalaQ29FpKR8RmKHdR92x42/s1600/Graphing.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhhk7_D3nrebvdVTgTrYp9lSHDOlOezpr8LedcXMot87wxVyUBwRiKBAuwIy1O4xE2NEvu6jGh8s6xgNCd6Kf9B9i1tc4AnLjVIAp9-DONJx09Cs45xB_GdGOalaQ29FpKR8RmKHdR92x42/s1600/Graphing.jpg" /></a><span style="font-family: "trebuchet ms" , sans-serif;"><br /></span></span></div>
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<span style="font-family: "trebuchet ms" , sans-serif;">Students could use an interesting/appropriate subset of flashcards to create a real graph of the answers. They could analyze the graph looking for patterns, making conjectures, and testing the conjectures. Like, "I think that if we keep sorting out our flashcards, 27 will show up the most because that's the largest product in our set of cards."</span></div>
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<span style="font-family: "trebuchet ms" , sans-serif;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwXsArh9iS1yKl_alsslYJ66mdoylKjx7dJzxXLTD3ptx1oeAVTujvCeZNi6OGo7l6ovYKyumnwj9gPKjlqlcsTd06jgnY0pwJO4rkyS4GHGJGIDjCPHiaFG55wKkDmRFLzKqEt_wCKU2X/s1600/WODB.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwXsArh9iS1yKl_alsslYJ66mdoylKjx7dJzxXLTD3ptx1oeAVTujvCeZNi6OGo7l6ovYKyumnwj9gPKjlqlcsTd06jgnY0pwJO4rkyS4GHGJGIDjCPHiaFG55wKkDmRFLzKqEt_wCKU2X/s1600/WODB.jpg" /></a></span></div>
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<span style="font-family: "trebuchet ms" , sans-serif;">We could use the flashcards to create Which One Doesn't Belong [WODB] scenarios. Or have students create their own WODB to challenge their peers. (See the WODB <a href="http://wodb.ca/" target="_blank">blog</a> and the <a href="https://www.stenhouse.com/content/which-one-doesnt-belong" target="_blank">book</a> by Christopher Danielson for more information about this instructional approach.)</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9DIJN5n96nlCjnP1XningWkzKF7gW56DDr7tcOCDcGJE9apm991bqXXuDmC-JkL8ipH87mCDTTQZ70IddtdnO1AffSFQ9Jmgvj5fVNACM4TxjXJffgZ1kldBcBDdjrGSONI-IRv5i0w5K/s1600/Fish.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9DIJN5n96nlCjnP1XningWkzKF7gW56DDr7tcOCDcGJE9apm991bqXXuDmC-JkL8ipH87mCDTTQZ70IddtdnO1AffSFQ9Jmgvj5fVNACM4TxjXJffgZ1kldBcBDdjrGSONI-IRv5i0w5K/s1600/Fish.jpg" /></a><span style="font-family: "trebuchet ms" , sans-serif;"><br /></span></div>
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<span style="font-family: "trebuchet ms" , sans-serif;">Finally, if we want to play a game that's not Around the World, maybe we play Go Fish. (Make up your own rules depending on what you want student to experience. Or better yet, maybe have them make the rules if you want to encourage them to play with math.)</span></div>
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<span style="font-family: "trebuchet ms" , sans-serif;">What do you think, regular (irregular, and new) MacGyver Math readers? How might Enlightened Elementary Educator in Elmira step back and take a look at what she's got (flashcards) in a totally different way? As always, leave your suggestions in the comments.</span></div>
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<span style="font-family: "trebuchet ms" , sans-serif;">Thanks,</span></div>
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<span style="font-family: "trebuchet ms" , sans-serif;">MacGyver Math</span></div>
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<span style="font-family: "verdana" , sans-serif;"><b>If you have suggestions for Enlightened in Elmira regarding using flashcards in novel ways, please address your comments to her. If you want to comment on this MacGyver Math format, please direct your comments to Dave. Either way, thanks for your participation.</b></span></div>
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delta_dchttp://www.blogger.com/profile/18024582157985654525noreply@blogger.com1tag:blogger.com,1999:blog-5957896812820341397.post-78039729782208734652016-05-05T11:52:00.002-07:002016-05-05T11:52:36.946-07:00How does a mathematician see the world?<blockquote class="tr_bq" style="text-align: justify;">
<span style="font-family: "verdana" , sans-serif;">And how does a math teacher help learners to see the world through a mathematician's eyes?</span></blockquote>
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<span style="font-family: "verdana" , sans-serif;">This was a major challenge during the past semester in my Intermediate Algebra sections. Many of the students came to class expecting me to show them a procedure that they would practice until test time - when they would reproduce the procedure and promptly forget it. Nearly all of the students had seen the Intermediate Algebra content in high school (linear, quadratic, and exponential functions) but it hadn't stuck.</span><br />
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<span style="font-family: verdana, sans-serif;">This was the problem. They had </span><i style="font-family: verdana, sans-serif;"><b>seen</b></i><span style="font-family: verdana, sans-serif;"> the content. Now it was time for them to use it to </span><b style="font-family: verdana, sans-serif;"><i>see</i></b><span style="font-family: verdana, sans-serif;"> the world. So I shared pictures and videos and asked them to look at them through a mathematical lens.</span></div>
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<span style="font-family: "verdana" , sans-serif;">At one point, a student said, "Just once, I wish I could see the world through your eyes." Exactly! Unfortunately, they were often so afraid of making a mistake, of breaking the mathematical glasses, that they were not willing to even put them on. They did not know how to be playful with the math we were exploring.</span></div>
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<span style="font-family: "verdana" , sans-serif;">So I introduced them to <b>Yes, And ...</b>; this is a problem finding activity that I developed using a well-know improv <a href="http://plays.about.com/od/improvgames/qt/YesAnd.htm" target="_blank">game</a> where participants accept and build on the ideas of their partners. Here are the instructions for my version:</span></div>
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<li style="text-align: justify;"><span style="font-family: "verdana" , sans-serif;">Provide a mathematical context (often pictures or videos) but without any identified problem;</span></li>
<li style="text-align: justify;"><span style="font-family: "verdana" , sans-serif;">Pair up the students and find a fun way to identify Student A;</span></li>
<li style="text-align: justify;"><span style="font-family: "verdana" , sans-serif;">Student A picks one of the contexts and <i>finds</i> a problem to solve;</span></li>
<li style="text-align: justify;"><span style="font-family: "verdana" , sans-serif;">For one minute (this is usually enough time to get started without completely solving the problem), Student A talks through his or her thinking while Student B writes as much as possible down on a piece of paper;</span></li>
<li style="text-align: justify;"><span style="font-family: "verdana" , sans-serif;">After one minute, the students switch roles. I say, "Yes, and ...," to signal the switch and to emphasize that Student B ought to build on the work that was already done.</span></li>
<li style="text-align: justify;"><span style="font-family: "verdana" , sans-serif;">Student B thinks out loud for one minute while Student A records the thinking on the same paper.</span></li>
<li style="text-align: justify;"><span style="font-family: "verdana" , sans-serif;">After one minute, I say, "Yes, and ...," and the roles reverse again.</span></li>
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<span style="font-family: "verdana" , sans-serif;"><b>Yes, And ...</b> can go on as long as the teacher wants. I found six minutes (three rounds) to be about right the first time we played the game. One student submitted this to demonstrate her engagement with the task.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxFeiXf6DB4zGiNxqFyb8vP8uUUyQKiyr5yD-uaCT4oV-8ih28sYdXlIK-5hEKW2tOlWOskvU46uClFsIm3N7tiaHTyUqERBS5YOfqtuLFxE56SI7m-Vxw_ylMsJJ2SspRh-Ay1tG2wyrq/s1600/Yes+and+Michelle+Smith+EE3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxFeiXf6DB4zGiNxqFyb8vP8uUUyQKiyr5yD-uaCT4oV-8ih28sYdXlIK-5hEKW2tOlWOskvU46uClFsIm3N7tiaHTyUqERBS5YOfqtuLFxE56SI7m-Vxw_ylMsJJ2SspRh-Ay1tG2wyrq/s400/Yes+and+Michelle+Smith+EE3.jpg" width="300" /></a></div>
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<span style="font-family: "verdana" , sans-serif;">I cannot claim for certain that <b>Yes, And ...</b> changed my students' view of mathematics or helped them to see the world through a mathematical lens. What I know is that for six minutes they played with math. It's a start.</span><br />
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delta_dchttp://www.blogger.com/profile/18024582157985654525noreply@blogger.com1tag:blogger.com,1999:blog-5957896812820341397.post-16373157471845785282016-05-03T12:47:00.001-07:002016-05-05T09:29:27.675-07:00Isn't it great to be a teacher?<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCB66bN_3c9C-5j_F3hAaoXNVSw5maMyrYUWVeQ3MSkRr4njoRgtQZCeBzS1MM-O7WUh20-oQHn34ZQUOE7yNkl7qHaO37mwTWUC40jiPEezBkPdqKEFhKy1j6orDWRkgGz8HstWubfywp/s1600/Teacher.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="293" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCB66bN_3c9C-5j_F3hAaoXNVSw5maMyrYUWVeQ3MSkRr4njoRgtQZCeBzS1MM-O7WUh20-oQHn34ZQUOE7yNkl7qHaO37mwTWUC40jiPEezBkPdqKEFhKy1j6orDWRkgGz8HstWubfywp/s400/Teacher.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">from <a href="http://perceptionvsfact.com/13to">http://perceptionvsfact.com/13to</a> </td></tr>
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<span style="font-family: "verdana" , sans-serif;">Yes, it is great to be a teacher. However, unless you are a teacher or know one very well, it's probably not for the reasons you think. The one example that I am constantly having to explain to people is the whole misunderstanding about the <i>summer pay</i> thing.</span></div>
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<span style="font-family: "verdana" , sans-serif;">"Isn't it great to be a teacher and have a paid summer vacation every year?" asks a person I just met when she/he finds out I am a teacher. </span></div>
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<span style="font-family: "verdana" , sans-serif;">I explain that the money I get paid is deferred from what I earn during the school year. Much like a pension or Social Security, it helps me make it through a time I would not normally be earning a salary. Also, it helps most districts to spread payments out over the year. Win-win, right?</span></div>
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<span style="font-family: "verdana" , sans-serif;">But what happens if the district is in financial trouble and runs out of money before paying the deferred salary to teachers? This is not a hypothetical question. It is happening right now in <a href="http://michiganradio.org/post/detroit-schools-closed-second-straight-day-state-republicans-blast-teacher-sickouts#stream/0" target="_blank">Detroit</a>. And state politicians are having a hard time understanding why the teachers are worried about their <i>summer pay</i>.</span></div>
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<span style="font-family: "verdana" , sans-serif;">Let's do the math. Imagine a Detroit teacher works for 9 months, September to May, for $36,000 (These are rough estimates. I am simplifying the problem to make it easier to follow.) The teacher can take the payment across 9 months, $4,000 per month, or 12 months, $3,000 per month. If a teacher in Detroit chose to spread her pay over 12 months and the district runs out of money at the end of June, then she will receive 10 months of pay or $30,000 of the $36,000 she earned. This translates to 7 1/2 months of teaching or through the middle of last month (April). In other words, if the legislature does not come through with the necessary funds, Detroit teachers have already worked for roughly 10 days for free. </span></div>
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<span style="font-family: "verdana" , sans-serif;">The governor's office tells teachers not to worry - that a $715 million aid package is moving through the legislation. Unfortunately, according to the <i><a href="http://www.nytimes.com/2016/05/03/us/teacher-protest-shuts-almost-all-detroit-public-schools.html?_r=0" target="_blank">New York Times</a></i>: </span></div>
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<span style="background-color: white; color: #333333; font-family: "georgia" , "times new roman" , "times" , serif; font-size: 17px;">A year ago, Mr. Snyder, a Republican, proposed a $715 million aid package for the Detroit district, but </span><a href="http://www.detroitnews.com/story/news/local/detroit-city/2016/04/18/detroit-school-rescue-hinges-charter-school-rules/83172258/" style="color: #326891; font-family: georgia, 'times new roman', times, serif; font-size: 17px; text-align: start;">it has been bogged down</a><span style="background-color: white; color: #333333; font-family: "georgia" , "times new roman" , "times" , serif; font-size: 17px;"> in the Republican-controlled Legislature.</span></blockquote>
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<span style="font-family: "verdana" , sans-serif;">No wonder Detroit teachers feel too sick to go to school.</span></div>
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<span style="font-family: "verdana" , sans-serif;">Oh, Happy Teacher Appreciation Day!</span><br />
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<span style="font-family: "verdana" , sans-serif;"><b>Update [5/4/2016]</b>: I was a bit off with my estimation of connivence, but it was close.</span><br />
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<span style="font-family: Verdana, sans-serif;"><b>Update [5/5/2016]</b>: Michigan House approves $500 million funding plan for Detroit Public Schools - but there are <a href="http://www.clickondetroit.com/news/vote-for-dps-bailout-expected-in-lansing" target="_blank">concerns</a>.</span></div>
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delta_dchttp://www.blogger.com/profile/18024582157985654525noreply@blogger.com0