I wanted to find an image that tried to give the best representation of mathematical habitats in schools — colorful birds, some similarity of a natural environment, etc. But, in the end, there were cages. There was a boundary. There were limits.
Most of our classrooms in terms of mathematics are nicely curated zoo cages. We call them grade levels. One of the worst things that happened in mathematics was the belief that some topics were relegated to certain grade bands. Then, to create a curriculum that has the pressure to differentiate material in terms of “age appropriateness” for 12 years.
Welcome to the mathematical zoo.
Fractions are taught before integers. Algebra is generally siloed in upper middle school/high school. Number theory is a branch of mathematics. In schools, the mathematical tree is absent of that.
But, year after year, decade after decade, the false partitioning of many math topics and the occlusion of others, have made teachers become so fixated on the micro-management of this zoo. What should I teach in Grade 5? How do you teach______ in Grade 6? Teachers never built this zoo. And yet, they have been asked to be the chief custodians.
Teachers and students deserve better than these mathematical cages.
One of the best litmus tests of the culture of math teaching is to tell a teacher there will be no textbook this year for your course. For many — no fault of their own — this will be a source of anxiety. It should be the other way around. It should give you freedom. Which means it should give your students freedom.
The ONLY reason I took a job to teach remotely in these anxious times was that this was the first time in my entire career I was given an opportunity to teach ANYTHING I want to 4th to 6th graders. Anything. No marking. No grading. No homework. Just sharing any idea of mathematics that I thought would fascinate these kids. My meat and potatoes was arithmetic and algebra.
And, it’s all been playfully messy.
In order to get to the abstraction of algebra, I spent a lot of time with concrete numbers. I wanted students to feel comfortable with them. All algebra rules were created TOGETHER with numbers. I didn’t write any rules of algebra on the board.
I have one more week before it all ends. I will my students and my freedom to teach mathematics like this immensely. When I quit teaching, leaving behind a great salary/summers/benefits, I did so because I realized I was teaching in a zoo.
For me, this was not how it was going to end. I had lost my energy and soul.
Teaching this year with the freedom I never had — to put into practice — and see my students always smiling and laughing in the streams with the awe and wonder of mathematics has been one of the highlights in my career.
I finally found freedom with mathematics.