Tuesday, August 10, 2021

How do you like your marshmallow?


Today, I moderated a panel of early elementary educators who discussed the Values underlying Michigan's Essential Instructional Practices in Early Mathematics [PDF]. 


The session began with my favorite ways to start a session/class: While We Wait. 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 calendar of National Days.)


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.
  • So, how do you like your marshmallows? 
  • What do you do to get them toasted just right?
  • And how might the Values provided above change the way we teach math in the early grades?
The comments are open.



 

Friday, July 23, 2021

What will you be teaching on October 20th?

My first real teaching job was at Grant 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 right) 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.

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.

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.

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 One-Sentence Lesson Plan as a framework for our prototypes for designing math adventures. The incompleteness leaves room for student-voice and student-choice during the lesson experiment.

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 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.

Scampy McScamperson visits Devils Tower

Wednesday, June 30, 2021

What's the problem we're trying to solving in math education?

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 Studio. 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.

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.)

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.

Task One (odd birthdates)

Task Two (even birthdates)

Don't read any farther until you've completed your task or you'll ruin the surprise.

Once you've completed your task, click on the other task question and consider how that question might result in different solutions and why.

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.

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.

IBM does a version of this activity in their
Enterprise Design Thinking Course

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 Designing Math Adventures - because we want learners to experience something more than another math lesson.

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.

Saturday, June 26, 2021

Why write Designing Math Adventures?

In planning the book, Designing Math Adventures, Kathy and I took Simon Sinek's advice and started by identifying our WHY: to support educators' efforts to improve K-8 math learning.

Based on our interactions with thousands of teachers, we can confirm that BrenĂ© Brown is right. 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. 

HOW can teachers change their circumstances? Sometimes it's as simple as doing more of what’s working and less of what’s not. The level of intentionality we are talking about requires an honest examination of our teaching practice. This type of reflection isn't always easy.

WHAT Designing Math Adventures offers is a design thinking tool 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.


Wednesday, June 23, 2021

Where have I been?

I haven't posted 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.

First, I took a position as director of the Design Thinking Academy [DTA] 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.

Ela Ben-Ur was our first speaker. She held a series of workshops where she introduced participants to a design thinking tool she created - the Innovators' Compass.

Ela Ben-Ur: Design Thinking and You (GVSU DT Speaker Series)

I learned about Ela's work on this episode of the Design Thinking 101 podcast.

This introduction to the Compass lead to the second project that has been occupying my time - writing a book. Kathy 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.

Innovators' Compass - design thinking cycle (hexagons) - Teaching & Learning Cycle (purple)

Now that a draft of the book is done (#DesigningMathAdventures) 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 wait to hear from the publishers but also allow me to share some parts from our writing that didn't make the latest cut.

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 (@delta_dc). The comments are open.

Thursday, September 27, 2018

How might we deal with the mismatch?

Last week I heard Kat Holmes talk about her new book, Mismatch. I learned how designing for "normal" 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: 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 Victor Pineda who made the following point:

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 you, and three is coping strategies. And so these three things sort of create a variety of tools.
Of course, I started connecting these ideas to teaching.

A curriculum is often designed for the normal/average student.
In reality, a student and the curriculum are typically mismatched.
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 writes - co-teaching) to participate in the design.


Having planned for one student, the teacher must consider how to extend the design to many students.


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 [8.EE.A.4] and the curriculum used in her school. We talked about using a think-aloud (personal assistance) to create an anchor chart (assistive technology) that students could refer to (coping strategy) while solving 8.EE.A.4 problems. 


In the next lesson, she tried these ideas out. The lesson started with her making her thinking visible while solving an 8.EE.A.4 problem. 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.



I'm still processing a lot of this and would appreciate you sharing your thoughts in the comments.


[This blog post was written with the help of the Innovators' Compass. Check out my planning.]

Thursday, December 14, 2017

And then what did you do?

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.


We decided to play it using this situation from Context for Learning Mathematics [CFLM] and a couple of starting choices.


Starting Steps:
1) First, I split up the dollar and the 25 cents and multiplied the dollar by 24.

2) First I doubled $1.25 and got $2.50.

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. 

Here's how it might work:

Numeric Notes
First, I split up the dollar and the 25 cents and multiplied the dollar by 24.

Yes, and then I added back the 25 cents and got $24.25.

Yes, and then I remembered there were 23 more quarters that I need add.

Yes, and I don't know what 23x.25 is so I did a quarter plus a quarter is a half dollar instead.

Yes, and that reminded me that there are four quarters in a dollar.

Yes, and that made me wonder about how many dollars there are in 24 quarters.

Yes, and I divided 24 by 4 and got 6.

Yes, and that means 24 times .25 is 6 dollars.

Yes, and then I added 6 dollars to the original 24 dollars.

Yes, and that means the total cost of the turkey is $30.

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 similar with my college students, who finish up by writing a Metacognive Memoir about their experience.

TEDxGrandValley