In most math curricula, students work on a single topic at a time. (When I taught elementary school, decades ago, I noticed that if we’re working on subtraction, it must be November! But the same applies at all grade levels.) The idea is that is that by really focusing on the topic, you are helping students really… Continue reading Spiraling Out of Control?
I have written quite a few posts in which I argued that extending student exposure to mathematical concepts is one key to reaching the whole range of students. This is based on the simple observation that students learn math at different rates, and that extending exposure by making simple changes to our routines can benefit… Continue reading More on Extending Exposure
It is not uncommon to read articles about math education in the mainstream press, arguing that students must master basic skills before they can develop conceptual understanding. And moreover, that the road to such mastery is teacher explanation followed by repetitive drill. These essays frequently argue that it’s like learning to play the piano: you must… Continue reading Understanding "understanding"
I’m done with my summer workshops, and I hope to resume blogging when the inspiration strikes. Today, a brief post about catchphrases, one per paragraph. (And no, this is not because this word has six consecutive consonants, which may well be a record.) I started thinking about this topic when I learned that Annie Fetter's catchphrase “What do… Continue reading Catchphrases
I'll be traveling a lot this month. Here's the plan, should you want to say hello.New York City April 5, 4:30pm: I will present Geometric Puzzles at the Museum of Math Teachers’ Circle. Geometric puzzles are accessible to solvers of all ages, but they can also challenge even the most tenacious of solvers. Join math education author… Continue reading April Travels, May Webinar, Summer Workshops
In my last post, I offered guidelines for sequencing math curriculum. The response I got on Twitter (and in one comment to the post) was quite positive. However, one point I made triggered some disagreement:Start with definitions? No! Most students find it difficult to understand a definition for something they have no experience with. It is more effective to start… Continue reading Vocabulary
In my last post, I argued that, as teachers and math education leaders in a school or district, we need to free ourselves from the sequencing preordained by the textbook, and instead pay attention to what actually works with our students. In this post, I will present some general guidelines for sequencing topics, and some… Continue reading Sequencing
Alison Blank makes good points in her interesting presentation: "Math is not linear", where she encourages us to make connections, go on tangents, preview future topics and review past ones. In short, we should not be trapped in the inflexible sequence suggested by textbooks and school culture. In a recent blog post, Jim Tanton makes… Continue reading Mind Maps
In my previous post, I listed questions to use in class discussions, or in conversation with a student or a group of students. Today, I'll discuss how to handle wrong answers. This is complicated and there is no single correct answer for all situations. I'll start by clarifying my goals:broad participation by students in the… Continue reading Handling Wrong Answers
On the first weekend of December, the California Math Council held its annual meeting in Asilomar for the 60th time. (I attended for the 33rd time, and presented roughly the same talk I had presented in 1984.) Over the decades, the "must-attend" presenters have changed. Two of my favorites back in the day were Harold… Continue reading Any Questions?