A Stop Along the Path to Growing Thinking Students

After the life-changing events of 2020 (loss of loved ones, raging pandemic, and racial reckoning, to name a few), I set a goal for this school year to become a transformational math teacher (read more in my July blog). I realized business as usual would no longer work, and that change could start with me. Transformational math teaching, as I define it, is math taught in such a way that it can change students’ lives for the better. Rather than regurgitate math procedures, I knew my students needed to be able to think and reason deeply enough to tackle any problem thrown at them in math, or even life.

Therefore, closely following Peter Liljedahl’s (2020) “Building Thinking Classrooms”, I set up whiteboards on walls all around my room and began using rich tasks to engage students in problem solving. Rich math tasks are accessible, often real-life problems which have multiple entry points, that students can utilize a range of strategies to solve. Rich tasks remove the focus on the “answer” and emphasize instead the process of solving. For example, one rich math task we did in class, called the Tax Collector, was adapted from Liljedahl’s text (2020, see p.107):

I have 12 envelopes numbered 1 to 12. Each contains the same number of dollars as the number on the envelope. When you take an envelope, the tax collector gets the remaining envelopes whose number is a factor of the envelopes you took.

The tax collector must always be able to take at least 1 envelope.

You must keep taking envelopes until you can no longer take one, the tax collector gets whatever is left.

What is the greatest amount of money you can get?

Hint: Have someone in your group play the role of the tax collector.

Here are photos of students working on the task and photos of one group’s work:

student's working at a whiteboard
math promblem work on a whiteboard
One of the most exhilarating experiences of my teaching career came when I was able to stand in the middle of my classroom and see student work and working students all around me!

One of the most exhilarating experiences of my teaching career came when I was able to stand in the middle of my classroom and see student work and working students all around me! While there have been many challenges, such as dealing with off-task behavior, consistently planning meaningful tasks, and teaching students what it means to work in teams, I’ve actually heard students say, “My brain hurts!” And, “You must think I’m smart.” As I stumble along making even more mistakes than my students with this “new” style of teaching, is it enough to really be transformational? Only time will tell. Stay tuned! Scroll down or use this link to watch a video about resources I used to developed this approach.