This post is part of the Virtual Conference of Mathematical Flavors, and is part of a group thinking about different cultures within mathematics, and how those relate to teaching. Our group draws its initial inspiration from writing by mathematicians that describe different camps and cultures — from problem solvers and theorists, musicians and artists, explorers, alchemists and wrestlers, to “makers of patterns.” Are each of these cultures represented in the math curriculum? Do different teachers emphasize different aspects of mathematics? Are all of these ways of thinking about math useful when thinking about teaching, or are some of them harmful? These are the sorts of questions our group is asking.
Here’s a thought experiment:
I wonder what math class might look like if our most important goal was to help young people love solving problems.
Literacy teachers have lots of goals, but I would wager most would tell you that above all they want their students to love reading. English classrooms are often filled with books, teachers are knowledgeable about the interests of their students and suggest books appropriately, and teachers work to build a love of reading in every student.
Is math just different?
But problems don’t seem to be our paradigm for a successful math class. If a student or group of students does well, we’re more likely to have them start learning the next year’s math than embrace the depth and complexity of non-curricular problems that student might enjoy exploring. Imagine if a student was a great reader and someone said, “hey, you’re going to do To Kill a Mockingbird in English class next year, why don’t you just get ahead and read it now,” rather than prompting the student to explore books that they’re interested in.
Sam Shah’s prompt for this conference was:
How does your class move the needle on what your kids think about the doing of math, or what counts as math, or what math feels like, or who can do math?
I want to move the needle on my students’ love of problems. This piece is more aspirational than anything — I don’t know that I do a particularly great job of fostering a love of problems in my class. But it’s something I care about, and something I am working to get better at. Here are some questions I have about helping students to love solving problems:
- I’ve observed that students are much more likely to enjoy solving problems when I find that “just right” task. How can I better do that for all students, while still valuing a social and collaborative classroom?
- The resources I referenced above are pretty abstract and logic-oriented, in the vein of many publications on problems and puzzles. How can I broaden my conception of “problem” to include problems about solving practical challenges that humans face and help math feel relevant to more students?
- A human can become pretty literate (after an initial period of learning to read) by just reading lots of books. Is something similar possible in learning math — could someone learn by just solving lots problems?
- To what extent do the goals of helping students to love solving problems, and helping students to learn required content, work in opposition or in parallel?