This is connected educator month so I’m going to share my story of how I connected with an educator online and used his ideas in my classroom. Get this: that teacher works in THE SAME BUILDING as I do, but I had no idea what he was up to in English class, or how it could translate to Mathematics. I took my ideas from his website, and then had my own personal in-house professional development workshop, where he spent 15 minutes talking me through the concept so I could put it into action.

What was the concept? Visible Thinking. You can look at amazing examples of student work creating visual maps in English literature at his website, comicsineducation.com. I was fascinated with the student work on his site, so I asked if we could find a way to apply that to math… specifically, to Calculus.

Stop laughing! Look at this:

Calculus is many things: for some of you, it is the beginning of all great knowledge in the Scientific tradition; for others, it was the course that sent them on a track into other (non-math) fields; and for others, it was a necessary hurdle in pursuing other goals. It is also highly visual, conceptual, and * connected*. Calculus is the course where students begin to see all their other math knowledge and skills converge, where they must finally draw upon concepts they learned years before (fractions! exponents! trigonometry! algebra!), and bring them together in solving new problems. There are many stories within Calculus, but none as interesting to me as the stories going on inside my students’ minds as they learn.

And so, at the end of the first unit on derivatives, when my students had dutifully learned all the rules and (hopefully) internalized the big concepts, I had them create a visual narrative of their problem-solving process. In order to get them started, I showed them examples – I created one myself and had Dr. D. of Comics in Education create one as well (because aren’t all English teachers also Math nerds? This one is… follow him on twitter at @GlenDowney)

The results surprised me. In fact, I enjoyed creating my own example so much that I didn’t want to stop! My students were given 40 minutes to work on theirs, and begged to use the entire 80 minute period. They spent those 80 minutes engaged in mapping a solution to ONE single math problem! In tech circles this exercise could be called a “brain dump”, as I asked for them to show me their inner monologue as they solved the problem. What thoughts went through their minds? What connections were they making? Is there humor in that thought process? Confusion? Does it get resolved? The answers are evident in their work, and I am thrilled with the results.

In terms of logistics, I started by showing the classic animated TED talk that RSAnimate did with Sir Ken Robinson’s speech on Changing Paradigms in Education. We talked about the power of the visual component, then I gave them a choice of 3 problems. Each student chose one, and created a visual map of their solution path. We listened to good music, we talked about mathematics, they collaborated a bit and helped each other where necessary. It was one of my favorite lessons of the year, and I hope to find more meaningful chances to repeat the activity.

Many thanks to Dr. Downey for the ideas and the inspiration, and to my students who have agreed to display their work in this post!

It’s wonderful to see math cross into art, and to have what is abstract become visible. I’m sure some students saw a glimmer of hope in math that they had never experienced before. Keep crossing those boundaries!

Ruth,

What a great example of making thinking visible! It’s also a great tool for “observing” student thinking. I’m going to share this with my math teachers too!

Great to see you yesterday – thanks for the inspiration behind the social piece of Cohort 21 this year!

garth.

I have loved this idea and will definitely try this in my class. I think its a neat idea that ties in math and art in a creative way. Its great to keep the engagement process and keep the students involved.

For students who really connected with this method, I have started having them do at least one homework problem this way. It helps them solidify their understanding for the new concepts and connect to their existing knowledge, and then they can work through the remaining problems with much greater ease.

I still want to use it more as an in-class activity, but I at least now know that I have to use it at least once at the start of each year. That way I can identify those students who learn best this way, and keep them using it throughout the year.