A colleague passed along an article from The Economist, "America's Maths Wars" (https://www.economist.com/united-states/2021/11/06/americas-maths-wars) that discussed how teaching math in the U.S. has become a political issue: "Conservatives typically campaign for classical maths: a focus on algorithms (a set of rules to be followed), memorising (of times tables and algorithmic processes) and teacher-led instruction. ... Progressives typically favour a conceptual approach to maths based on problem-solving and gaining number-sense, with less emphasis on algorithms and memorizing."
The more I read and think about how we learn math, the more annoyed I get by articles like this (and there have been many!), and those that espouse the "best practices" of one side or the other. The argument that learning math is about the basics versus about conceptual thinking is an old and dusty one, and at the moment, I believe neither side is valid.
People argue that math, like reading, is fundamental, so we need to make sure every student learns it. I don’t disagree with this, but how we teach reading is also hotly debated (https://www.washingtonpost.com/education/2019/03/27/case-why-both-sides-reading-wars-debate-are-wrong-proposed-solution/). I wonder if the perceived importance of math and reading inclines people to think of them as part of the zero-sum "pool of power" and less thoughtful about how to teach them?
I think that math (and perhaps reading?) should be taught more like we teach art, music, or creative writing. In these subjects, we encourage students to get messy and draw/play/write what they know, provide tips and critique on their work, teach basic principles of structure, suggest edits based on historical/cultural norms (hopefully a variety of them), and how to break those norms effectively. And many students find joy in these subjects, and many students who don’t pursue them as careers still continue to draw, play, or write into adulthood.
Teaching math as SOMETHING YOU MUST KNOW AND HERE’S HOW TO LEARN IT misses the point. It loses sight of the fact that there is joy in math, and helping students to get messy and use what they know, providing feedback, and teaching the history and basic structures of the subject are all important parts of the learning process.
The “conservative” idea about “teach the basics” is good: learning a basic addition algorithm is good, but needs to be connected to students’ experiences instead of valued as an isolated skill. If we only focus on the “basics” we suck the joy out of and ignore the students’ connections to the subject.
Likewise, the “progressive” idea about “teach concepts” is good: seeing how the basic addition algorithm and all sorts of methods work are good, but need to be connected to students’ experiences and thinking instead of scatter-shotted without providing focus. If we only focus on the “concepts” we ignore any procedural fluency.
Art, music, and creative writing teachers know how to teach the basics of their fields and provide feedback that values the student’s contribution. They teach some basic techniques and encourage their students to practice those and to indulge their curiosity and imagination. They critique work (including their own), identifying good and interesting ideas and suggesting changes to make the work better. They recognize that not all students will pursue careers in these fields, but help students appreciate and find joy in the work.
The back-and-forth arguments about "best practices" for math education miss the mark, in that they both make assumptions about how ALL students learn math. I learned many years ago that successful teachers build up a repertoire of strategies that they can match to their students, content, and context.* It's not about one way being right and the other wrong. Teaching math is about figuring out when to teach the algorithm and when to let students explore; who needs clear and actionable feedback and who needs to just know if the work is right or wrong; and how to demonstrate perseverance and express joy in the messy, creative, and sometimes straightforward work of doing math.
I agree that math is something you should know, but ignoring the students’ and our own ideas and experiences in order to adhere to a “conservative” or “progressive” curriculum is not the way to help students know it. Do we need to teach basic techniques and have students practice them? Of course. Do we need to encourage students to indulge their curiosity and imagination? Certainly. Let’s also learn to critique their work (and our own) effectively, to identify the good and interesting ideas, and to suggest ways to make improvements. We need to help students appreciate and find joy in math, even if it’s not part of their career plans.
(*I was lucky enough to learn from Jon Saphier and his book The Successful Teacher about repertoire and matching many years ago. I still refer to the book for guidance when I start to feel frustrated about some aspect of my teaching.)
