As math teachers, we all have seen the power of a well structured and timed question. Never has that been more true or more surprising as in my class last week. We were starting a new unit intended to expand our understanding of functional relationships. A few weeks prior, our team of eighth grade math teachers met and planned an introduction to this unit. We piloted it in a colleague’s classroom and then committed to trying it in our own rooms. The basis for this lesson was a website, http://www.visualpatterns.org/. We chose a few patterns and created a lesson focused on two learning targets. I understand how productive struggle makes me a better mathematician and I understand how visual patterns help me to make predictions and write rules.
To be totally honest, I am not a visual person. It is a running joke when I draw on the board. So, I approached this lesson with a touch a trepidation. I “drew” a pattern on the board, asked open ended questions and had students continue the pattern forward. We discussed what we noticed and how we could use what we notice to predict further steps in the pattern. Then I asked, “How could you write a rule that would tell us the total number of blocks in the pattern for any step?” I sat back and observed the struggle.
All of this gets us to the moment that I am still smiling about a week later. Students struggled and then came to the board to write their rules. My first volunteer came up and described his ideas in words. We struggled together to write his ideas down mathematically. Once we had it the way he wanted it, we plugged in the numbers and checked his work. Finally, came my non-visual leap of faith. I asked him where he saw the parts of his rule in the visual. Now, this was a risk for me, because I do not easily see where these two different representations match up, ever. I love numbers, but visual things hate me.
My leap of faith worked. My student helped me see where each part of his equation was represented, as did the next student I asked, and the next. As students explained their thinking, other students agreed, shared other versions and gained different understandings. I can’t wait to pick up where we left off last week. I have a new question in my arsenal, and a new understanding of how patterns can help even me make predictions and write rules. I will continue to ask, “Where do you see this in that?”