Teaching the factoring of the sum of cubes and difference of cubes was not a priority for me in my teaching, and the topic does not seem to be part of the Common Core Standards. However, some people do have to include it in their classes, and as a result the subject occasionally comes up… Continue reading Sum and Difference of Cubes
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Wallpaper Symmetry Part 2
This post is a continuation of Wallpaper Symmetry Part 1, which you should read first. Both posts are companions to the Wallpapers Catalog on my website. --------------------------------------------------------------------- A long time ago, in my twenties, I attended a lecture about the mathematics of wallpaper designs. The presenter gave an overview of the entire proof that there are only… Continue reading Wallpaper Symmetry Part 2
Wallpaper Symmetry Part I
While sheltering in place, I decided to use some of my time to complete a project I had been contemplating for a long time: creating a catalog of the 17 wallpaper groups using pattern blocks. It is now live on my website: Wallpapers Catalog. The idea is to provide a bridge between schools, where pattern… Continue reading Wallpaper Symmetry Part I
User-Controlled GeoGebra Animation
Here is an animation I created in GeoGebra: As far as I can tell, WordPress only shows you the animation once, when you open this post. You can find the actual .ggb file, and an interactive applet in your browser here. (Links to related transformations applets are on this page.) The idea was to illustrate reflection in… Continue reading User-Controlled GeoGebra Animation
No One Way
My motto for this blog, and for my website, is “There is no one way”. It is a topic I have returned to many times, for example, in these posts: Catchphrases, where I mostly discuss the assorted slogans I have spouted over the years. How To, where I argue that there is no single “best way” to teach any… Continue reading No One Way
Minimum Polyomino Cover
When I taught elementary school (1971-1981 or so) I had more time for “enrichment”, which for me meant excursions off the beaten curricular path, especially into the world of recreational math. As a result, my first publications were largely about geometric puzzles. (Those books were assembled a few years later. More info about my books.) Anyway, one… Continue reading Minimum Polyomino Cover
Asilomar Report: Conic Sections
As my retirement starts to kick in, I no longer attend conferences — except for one: the annual meeting of the California Math Council (Northern Section.) Once again, I had a great day at Asilomar, a beautiful spot near Monterey, right on the Pacific Ocean. Here is my annual report. Conic Sections Figuring out an approach to… Continue reading Asilomar Report: Conic Sections
Towards Inquiry
When I was much younger, I was under the impression that anything students “discover”, they will remember. Over time, I realized that this is not really true. First of all, what I hope they discovered may not be what they actually understand. But also, it’s not clear to them what is important about their discovery,… Continue reading Towards Inquiry
Teaching the Distributive Property
A guest post by Rachel Chou I have been a classroom mathematics teacher for 20 years. I have heard students use the phrase “the distributive property” more times than I can count. Many of them misunderstand what “the distributive property” even is. But maybe I think that because I don’t really know what “the distributive property”… Continue reading Teaching the Distributive Property
Freakonomics Radio on Math Curriculum
Every now and then, an academic decides they’re qualified to fundamentally rethink math education, and to share their brilliant solution with the world. That is already problematic when the academic is a mathematician or a math education researcher, but it is even worse when it is someone whose only connection to K-12 math education is that… Continue reading Freakonomics Radio on Math Curriculum
