How did you teach it?

The idea of MTT2K began when a group of preservice teachers could not wait until the end of a Khan Academy video to voice their concerns about the quality of its content. (You can learn more here.) Once the movement to critique Khan Academy videos gathered some momentum, it was suggested that teachers do more than nitpick (although, as this post explains, nitpicking is important). Consequently, a group of bloggers set out to make 101 alternative lessons.

Nine alternatives were scheduled as of today - the day before the MTT2K prize deadline. While this is less than we hoped for, it is a start. The energy behind projects like the mathtwitterblogosphere demonstrates how we all benefit when teachers make their own lessons available for others to use and improve on.

The lesson I want to share comes from that same day when the preservice teachers watched the Khan Academy video. We were focusing on NCTM's Communication Standard that day, and I wanted to share examples of people communicating the ideas associated with integer multiplication and division. Many of the area schools use PowerPoints in their math classrooms, so I wanted to model how I might use this medium to communicate my thinking.

The think-aloud focused on my approach to trying to understand some integer rules I memorized years ago. I used "I language" to remind the learners that I am making my thinking visible, not telling them what to do. Afterward, we debriefed about what they saw and heard and how what I shared might support their ability to understand the concept for themselves. (The demonstration is split into two parts because Jing only allows for 5 minute recordings.)

Part One

Part Two

Having watched this demonstration, how would you respond to these points:

• What did I do?
• What did I say?
• What did I think?
• Develop a consolidated recount regarding multiplication and division of integers.

And how might you improve on this demonstration?

When is it okay to use a calculator?

All too often, I run into teachers (both preservice and inservice) lamenting that kids are using calculators to compute something simple, like 6 x 7. These teachers express their frustration by threatening to not let kids use any calculators until the kids prove that they know their facts. And there will be no calculators for any simple computations. I understand this thinking but I am not sure it will achieve the desired result - wise calculator use (i.e. phronesis).

Problem is, if teachers are the ones deciding when their students can or cannot use calculators, then students are not able to practice this critical-thinking skill for themselves. Consequently, whenever a calculator is available in the future it can be used because that was what the students learned in school. As an alternative to controlling calculator use, I suggest a couple of activities that can help students to decide for themselves when it is appropriate to reach for the calculator.

The first activity comes from the article, John Henry - The Steel Driving Man. This article suggests several different experiments involving routines that can be completed by human or mechanical effort (eg: sharpening pencils). Students are asked to predict which method will take longer, gather data, and compare the results using box-plots. 

The experiment I am most interested in involves computing multiplication facts with and without a calculator. I give pairs of students four worksheets like the one shown below.

Each of the four worksheets is different. As one student completes the worksheet, the other one uses a stop watch to time the effort (errors add an extra five seconds to total time). This is repeated until each student completes two sheets - using the calculator for one but not the other. 

Classroom data are gathered and typically show that the students complete the worksheets quicker without a calculator. Discussing the results can provide students with an opportunity to reflect on whether or not it is efficient to use a calculator for basic facts. In the few cases when it is faster to use a calculator, the issue is usually that the student has a lot of wrong answers when computing without a calculator. Teachers must decide an appropriate course of action in these instances.

A second activity that I use to develop students' wise use of calculators involves a worksheet of multi-digit multiplication items. Instead of assigning the entire worksheet, I ask students to pick four items to compute without a calculator, four items to estimate, and four items to use a calculator on. The students are also expected to explain why they selected the approach to use with each item.

Calculator phronesis, the wise use of calculators, requires opportunities for students to experience activities that involve metacognitive aspects. We teachers will not always be there to guide students' choices, but this is not to suggest that we do not have a responsibility to help students to develop this ability. It is my hope that through these classroom experiences, students will be able to ask and answer for themselves the question, "When is it okay to use a calculator?"

What did you see/hear?

Last week, I attended the Michigan Reading Association's Annual Conference where I went to a session lead by Doug Fisher. He was presenting on Response to Intervention from a gradual release of responsibility perspective. It was the gradual release model that I was most interested in - especially since his book with Nancy Frey presents a slightly different version of this approach than the one I use. But I will leave that discussion for a later post. Today, I want to share my current thinking about what makes for an effective demonstration lesson (what Doug labels Purpose & Modeling).

From Doug Fisher's Michigan Reading Association Presentation

The demonstration I am sharing comes from a workshop for my Teaching and Learning Middle Grades Mathematics [TLMGM] course (a combination content and methods course that our secondary majors take prior to student teaching). This workshop focuses on comprehending the purpose behind a lesson that a teacher might encounter in an unfamiliar curriculum. Many of our student teachers find themselves using curricula that typically require a significant amount of professional development. Because our student teachers have not had this support, they sometime struggle to implement the lessons effectively. Therefore, I hope to share an approach I might use to better understand the rationale behind a lesson.

I used the ShowMe App to take a picture of a number string from a lesson found in the Context for Learning Mathematics series and then added my thinking. ShowMe records both my whiteboard annotations and voice to create a video that I can share with others.

A key piece to any demonstration is the debriefing: What did you see and what did you hear? This reflects Cambourne's perspective on who is ultimately responsible for learning: "Learners need to make their own decisions about when, how, and what 'bits' of information to learn in any learning task." By asking the learners what bits of information they attended to during the demonstration, the teacher is gathering important data that can inform future instruction (formative assessment). If the observers did not attend to something important presented in the demonstration, the teacher can highlight the missing points by saying, "I noticed that I was also..." The resulting list provides an anchor chart that learners can refer back to as they take more responsibility for employing the approach.

After I shared this demonstration with my learners in TLMGM, they noticed that I was trying to understand the string by:

• making connections between the expressions;
• considering different representations that might further my understanding;
• recognizing that computing the answers might help but wasn't enough;
• thinking about ways to put the expressions into a context; and
• analyzing my options before jumping into any plan.

Satisfied that they had attended to the major points of the demonstration, I provided them with further resources related to the Ratio Table unit and had them work collaboratively. They tried to look at the strings from the various angles in order to understand the purpose of the lessons.

During the workshop's reflection, I provided the opportunity for them to share what they had uncovered through Twitter. This provided everyone who wanted to contribute a voice and me with another artifact that I could use for formative assessment. Here is a sample of the discussion:

UPDATE 3/21/12
Reflecting back on this post, I have come to realize that if I were going to embrace the idea of "flipping" my class, this is what it would look like. I would use ShowMe to create demonstration lessons and have my learners watch them. When they finished, I would ask them to Tweet those things that they noticed in order to assess what they paid attention to and create an anchor chart for the class.

I know that my learners (college students) may differ from your's if you teach in a K12 school. But what do you think? Would this work for you?

Are we the first?

I admit it. I am a bit on the competitive side. But the question I tweeted to Dan Callahan about hosting a Twitter chat between two edcamps was also about gaining perspective. If it had been tried before, then I wanted to be able to build on previous successes and avoid prior pitfalls. Dan's response meant that we were on our own (and that we were first, but that's not what's really important here.)

The idea was the result of a Twitter conversation I had several months ago with Erin Ochoa. We were chatting about assessment and wishing that we could talk face-to-face about it at Edcamp Edmonton. It was then that I realized that Edcamp GR was being held the same day. Initially, we thought about a Skype session. I had seen it done at Edcamp Detroit and thought it went well (I wrote about it here) but wondered if we could get things started the same way Erin and I had begun our conversation - via Twitter. Therefore, we organized an "edchat" between the two edcamps around the following questions:

We worked out a schedule that took into account the two-hour difference between time zones. The first 10 minutes would be spent getting participants acquainted with Twitter, the next 30 minutes engaging in the Twitter chat, and the last 20 minutes Skyping, which would allow us to extend the conversation beyond 140 characters. So on November 5th, John Golden and I signed up to lead the following session:

It worked out well. I lead the conversation and highlighted some of the nuances of Twitter chats while John tweeted links supporting our discussions. You can see a transcript of the chat here. At about 12:40 pm EST, we Skyped between the sessions. Fortunately, Janet Bell, in Edmonton, took a picture and tweeted it:

Interestingly enough, the Skype conversation we engaged in was mostly about Twitter, not assessment. Participants wanted to talk about how we use it inside and outside the classroom. It was not what I expected (real learning rarely goes as planned) but I would say the first ever edcamp edchat was a success. But being first is not what is really important here. This is what is important:

Don't you get it?

or 

"What's not to like about the flipped classroom?"

I get it. Believe me, I get it. I understand why teachers like me are so enamored with the latest instructional craze. I saw it last night reading the Tweets from an #edchat on flipped classrooms. The attraction for me is that I get to have my cake and eat it too.

The model is based on the idea that teachers can flip the traditional way things are done in the classroom. Whole-class instruction, in the form of lectures or demonstrations or whatever, is now done after class. The application of what was taught, often thought of as homework, is done in class. Technology can support this shift but I am told it is unnecessary.

I like the idea that class time becomes more collaborative in this model. Instead of spending time disseminating information, the teacher can connect with learners one-on-one or in small groups. This offers teachers an opportunity to assess learners' progress in ways that are impossible during whole-class instruction. When learners struggle with a problem, they are not on their own (which is what typically happens when the same problem is assigned as homework). The teacher or their peers are available to support them through their struggles. Essentially, this represents a much more relationship-orientated approach of educating learners.

Outside of class, learners are assigned podcasts, videos, reading, or some other resources that prepares them for the next day's problems the way whole-class instruction used to prepare them for homework. Although technology is not required, it often comes up as a way to replace a lecture. I like the idea that learners might be given some choice as to when, where, and how they watch a lecture/demonstration of the content or skill being covered. I also like the idea that I can create the perfect talk. There will be no more forgetting my place, misspeaking, or being interrupted for a bathroom pass.

This flipped classroom model is a dream come true for teachers like me. It increases the amount of time I can spend working directly with learners without having to give up covering or controlling the content (and doing it perfectly, I might add). But I have spent the last twenty years of my professional (and personal) life working at moving beyond being a teacher like me.

As I see it, the flipped classroom tugs at both my instincts as a learner and my experiences as a student. The learner likes the collaborative approach that views learning from a social constructivist perspective. It fits with what I have learned about natural learning. I embrace this aspect and hope other teachers will as well. It is what the student in me likes - consumption, control, and perfectionism - that causes me concern. My successful experiences in the traditional school setting makes this attractive to me, especially since it "addresses" shortcomings like the ever increasing amount of material to cover and the need to differentiate instruction. But I do not believe that I can have it both ways - satisfying my learner and my student. While others may be able to walk this fine line, I have found that I always end up erring on the side of consumption, control, and perfectionism.

So I get it. I just don't want it - at least not all of it. I will take what works for my learners and leave the rest. And I trust all of you to do the same.

What is an EdCamp? Part III

Before this year, I had never heard of EdCamp, and then I got onto Twitter and began seeing tweets about it all the time. People raved about the experience and what they were learning at these unconferences. Was this a fad or would this be a transformative moment in education? I had to see for myself. Fortunately, Wayne State was scheduled to host an EdCamp - not exactly close, but close enough for me to check it out. Reflecting back over the EdCamp Detroit experience (the sessions I attended and the session I facilitated) I can see how it has helped me to refine my vision of 21st century education.

The two main points I wanted to address in my session were: (1) how isolation is destroying our education system; and (2) how technology can help us to break this isolation and connect. These were based on my view of education occurring in silos. Teachers isolated in their classrooms. Schools unaware of what was happening across their district. District disconnected from one another. Universities and K12 schools fighting over curriculum, methods, and resources. I thought that the answer was a lab school. In particular, a virtual lab school that would make use of the available technology to connect teacher educators, inservice teachers, preservice teachers, and K12 learners.


What I learned at EdCamp Detroit was that my vision was too limited. While a lab school would be nice, it did not go far enough.  My vision changed because of what I saw there. I smiled as other session facilitators discussed web resources I had been using myself. Hundreds of miles apart and we had shared an educational experience. I watched as one of my sessions Skyped in with another session at EdCamp Boston. When Nick Provenzano (AKA @TheNerdyTeacher) began to describe an internet project he had used, the teachers in Boston screamed (actually screamed like Nick was some rock star) because they were familiar with his work. Mostly, I was amazed as these teachers referencing the online work of people I respect and follow on Twitter. People like Dan Meyer, Eric Marcos, Alan November, and Derek Muller.


Reflecting on all this has helped me to realize that a lab school might be thinking too small. What I really want is a virtual one-room schoolhouse. A place where it is safe to explore ideas with other like-mined learners. A system that expects success through collaboration and support. A learning environment where the more experienced mentor those with less experience. A school where we share common knowledge instead of isolating it based on subject or grade-level.

So, are EdCamps a fad or a transformative moment in education? I think they are an opportunity. We have worked in silos for far too long. It is time to breakdown the barriers that separate us and work together to educate all learners. EdCamp has the potential to move us toward this goal. 


See for yourself at the nearest EdCamp. Or you can start your own. I know that I will be at EdCamp Grand Rapids on November 5, 2011. I hope to see you there - maybe over Skype.

What is an EdCamp? Part II

In my previous post, I offered an overview of my experience at EdCamp Detroit. Well, it did not provide the entire experience. I still need to share my presentation and the wrap-up of the unconference - that is the purpose of this post.

I called my presentation, Collaboration between College and K12 Classrooms: Win-Win-Win-Win. It was essentially based on two of my prior blog posts: one dealing with using technology to support distance learning and my dream to reclaim assessment from politicians and testing companies. Earlier EdCamp Detroit sessions on technology and collaboration also gave me some resources. Mostly, though, I wanted to listen to the participants' experiences and ideas about ways to consolidate our efforts to improve education.

Consequently, my PowerPoint was fairly bland. The version provided here includes backchannel comments from Kristen Fontichiaro (@activelearning) who tweeted much of the session. I am grateful for her contribution.

After my initial remarks, I opened up the conversation to the participants. Some of the College-K12 collaboration experiences included: Preservice teachers acting as substitute teachers and an Autism Center in Novi partnering with a local university. Kristen also made us aware that the University of Michigan is already exploring a lab school.

The new ideas generated were wide ranging. A member of the local college faculty suggested that her students could hold extracurricular classes to address K12 students' interests. A high school social studies teacher thought that it would be helpful for college students to describe the process for entering and succeeding in college to potential first-generation college attendees. Participants also suggested using Skype as a way to provide homework support, using college students to staff existing projects like Destination Imagination, and teaming college students with National Honor Society students in mentoring younger students.

I am sure there were other ideas that I missed (always the problem with making a list). Several times I found myself so engaged with the conversation that I forgot to take notes. I would ask that you please add any other suggestions in the comments.

While these ideas were amazing, it was the connections that I made that I found most meaningful. I now have contacts across the state. Tech-savy contacts that I will tap this coming fall when I have 60 preservice teachers in need of experience working with real K12 learners. I went from my session to wrap-up filled with ideas and hope.

EdCamp Detroit ended with a summary of the day, another brief Skype session with Dan Callahan at EdCamp Boston, and door prizes. What sticks with me most is a question asked by Nick Provenzano: "What if your next Professional Development day was an EdCamp?" Well? What if...

What is an EdCamp? Part I

EdCamp Detroit was an eye-opening experience. A perk of being a university professor is attending a lot of conferences (NCTM and TEDxGrandRapids to name two recent ones). I had never been to an unconference, however, and was looking forward to checking out this new approach to improving teaching.

The first thing to know about EdCamps is that there are no prearranged speakers. Participants arrive and encounter instructions like those shown below. EdCamp Detroit had 32 slots available spread equally between four one-hour sessions. To my amazement (since we always struggle to find enough K12 teachers to present at Math in Action) these slots began to fill rather quickly.

I have given plenty of talks, but I will admit that this format intimidated me a little - maybe because I had not done my typical preparation. After overhearing one of the organizers encouraging another participant to put an idea up on the board, I decided to take a risk. I selected a time slot at the end of the day and a topic that I thought would allow participants to be actively engaged. Most people feel like their brains are full at the end of a conference and I wanted to provide an opportunity for them to release that pressure by reflecting on what they learned. There will be more on my presentation later, but first I want to provide an overview of the EdCamp Detroit experience.

I chose sections that I thought I could incorporate into my final session. The first was called "The Flipped Classroom and Screencasting." Dan Spencer shared his ideas for using available technology to enhance learning and referenced examples like Khan Academy and MathTrain TV. Steve Dickie led the next session on "Pseudoteaching." He referenced blogs by Frank Noschese and Derek Muller (which actually questions some of the assumptions made by Khan Academy). In the third session, Mike Kaechele led a discussion about "Collaboration Across Classrooms." This included a Skype session with a group at EdCamp Boston (led by Marialice Curran) which allowed participants to share their experiences and see the power of this resource in action.

@TheNerdyTeacher shares with participants at EdCamp Boston

Very little of this was new to me. Again, I have more time than your typical K12 teacher to explore emerging educational approaches, ideas, and resources. Still, I was energized by these sessions because of the involvement of the participants. EdCamp presenters expect everyone to get involved and in most cases participants oblige. I left Mike's session excited to see what would develop in mine.

To be continued...

How can I use technology to make my thinking visible?

Last week I attended the NCTM 2011 Annual Meeting and Exposition in Indianapolis. Whenever I attend conferences of this size I always like to choose some theme in order to select sessions that work together. This year, I decided to focus on ways to use technology to make thinking visible. The idea of using think alouds to model mathematical practices is a major goal of my Teaching and Learning Middle Grades Mathematics (MTH 329) course but it has been hard to put into practice because of our lack of experience. The NCTM Conference provided me with more experiences to share with my teachers in training.

The first session that I attended was Using Technology to Transform Students' Problem-Solving Experiences and Perspectives. The presentation was true to the title with many good examples used by the presenters in their classrooms. (I will try to post about these in more detail later.) What I found most interesting was the idea of using the green screen feature in Photo Booth to embed learners into their problem-solving efforts.

I decided to try this for myself, and the result is provided below. Unfortunately, for some reason, my work in the background kept fading in and out. This was especially bad whenever I moved my arms to gesture at particular points. That is why I used my eyes and head to focus the viewer's attention in the video:

In the second session, Using Screen-Capture Movies to Assess Quadrilateral Constructions in Sketchpad, presenters showed how they used Geometer's Sketchpad and Jing to share learners' efforts to explore quadrilateral properties. This session was especially appropriate since I assigned my MTH 329 class a Shape Maker Lab before I left for the conference. The final unit of the course is on teaching geometry and now I had another way to make my thinking visible in this content area.

The Jing software only allows for five minutes of video so it took several tries to get my timing down. I like that this feature forces the person doing the think aloud to consolidate his or her thinking to a reasonable length, but it does require some planning and practice. Using Sketchpad's redo command helped to make the initial construction go more quickly. I did the construction and then undid it without Jing running. And then I hit "redo" multiple times while Jing was recording until the initial construction was complete. Only the dynamic exploration at the end was completely "live" during the video:

Given that these think alouds using technology are my first attempts, I am happy with the results. However, I know that with more experience and support they can be improved. In fact, that is what we will be considering in MTH 329 tomorrow - glows and grows for these reasoning recounts. As always, your comments are welcome as well.

How did my teaching go today?

I am willing to acknowledge that I may be wrong about this (which is one reason I am writing about it) but I think the experiment of using Twitter in a college classroom went well today. The other reason I am writing this is because we teachers often spend too much time beating ourselves up over flaws in our lessons. We have just as much, if not more, to learn from examining successes.

TPACK Framework

My idea started last week after listening to Dr. Punya Mishra talk about the intersection between technology, pedagogy, and content knowledge (TPACK) at the GVSU 2011 Technology Symposium (connect to his talk here). We have used Twitter with our teacher assistants (TAs), mostly outside the seminar, as a means to monitor what is happening in their placement, communicate information to them, and model how social networks can be used to develop professional learning networks (PLN). But Dr. Mishra got me to thinking about how to use Twitter IN the classroom in meaningful ways.

The goal for the experimental lesson was to consider ways to improve teaching by focusing on engagement. This reflects two elements of the seminar’s content knowledge (the content being promising practices that support TAs’ efforts to improve their teaching).  The first is the text we use in the class, The Teaching Gap. We like the book’s message that change takes time and commitment, and teachers should be at the center of this development. We also focus on Action Plans as a professional development approach that supports teachers in identifying and addressing teaching challenges.

Here is where the pedagogical piece intersects. We know learners need to have a purpose in order for an activity to be meaningful. Therefore, I told the TAs to imagine that a colleague had developed an Action Plan asking for support in writing plans that would engage more learners. (An improvement would be to have a mock Action Plan – I just can’t help seeing what is missing). It was their job to watch his instruction and offer him, or his representatives, feedback after the lesson. The other pedagogical intersection was that the lesson was a video of one of the American lessons described in The Teaching Gap. Thus, it was a connection to the known – a pedagogical imperative if learning is going to occur.

The technology overlapped the content knowledge and the pedagogy in two ways. We accessed the video via the internet and used Twitter to take notes on our observations, questions, and ideas during the lesson. We chose an unused hashtag, #e3pd (ed 331 planning dialogue – shortened to make it easier to tweet), and then projected the video and the Twitter stream on a split screen.

Split Screen Reenactment

As the TAs tweeted, I noticed that some were not showing up on the list. I soon realized that because they had protected accounts their tweets were on my personal stream but not in the list. I quickly began quoting and retweeting but it became obvious that I was not going to be able to keep it up throughout the lesson. This is another thing to think about for next time.

Once I stopped retweeting I began noticing trends in the Twitter stream. The TAs were identifying some of the same actions and offering the same advice. Many of these were issues and ideas that we had discussed throughout the semester. They also began communicating to one another (and me) in pure backchannel fashion. And there was a record of it for us to look at later. If you had been in the seminar, you would have seen me smiling.

The lesson ended and the TAs immediately wanted to offer the teacher feedback. I told them he was unavailable but three of his representatives would be meeting with individual groups. As luck would have it, these TAs meet with me prior to seminar to discuss planning engaging lessons. I coached them ahead of time to be open to ideas but to push back with some of the constraints we had discussed earlier (time, classroom management, culture, …). One of the groups welcomed a representative saying, “Oh, you must be Mr. J’s student teacher.” I will stow this nice touch away for next time as well.

I walked around eavesdropping on these dialogues. It was great to hear the TAs offer ideas and support their point with successes from their own experience. One representative/student teacher took copious notes as she listened to her colleagues’ suggestions. (I need to remember to get a copy of those notes to see exactly what she wrote.) The reflection for the activity was for TA’s to tweet one final subtle shift that the teacher might consider incorporating into his planning to improve engagement.

The last piece of business was to get feedback about the experience. A couple TAs said they had been skeptical about tweeting during a video but they were now sold. Tweeting allowed them to remain engaged in an otherwise non-engaging lesson by bring their thinking to the surface. (Fostering metacognition is another example of how the lesson landed in the TPACK framework’s center.) We discussed trying the same approach while watching a German or Japanese lesson. They also appreciated that there was a record of their thoughts available to examine latter.

John gathered the tweets in Twapper Keeper and we may do an analysis at some point. What I observed in real time reminded me of the work Deb Roy shared in the second part of his TED Talk.  You can watch it here.

Looking back on the experiment, I remain pleased with the outcome. There are certainly things to improve, and I wonder if it will be as meaningful the second time.  Was it the novelty that made it so engaging?  How can I maintain this TPACK momentum?

Now that you have heard my story, I would be interested in your perspective.