In 2020, I wrote No One Way, a blog post which I used to explain my website’s motto (“There is no one way.”) I argued that it is the math itself that demands that we approach important topics in multiple ways. As it turns out, this is a favorite topic of mine: in 2016, I… Continue reading No Best Way

# Tag: Geometry

## Geometric Puzzles Unit

The Geometric Puzzles home page on my website contains many links, and it is organized reasonably well. Still, someone who is not familiar with all these puzzles may need help in turning them into a curriculum unit. This is what I hope to do in this post. (I will try to not duplicate the overview of… Continue reading Geometric Puzzles Unit

## Transformational Geometry for Teachers

I taught geometry for decades, starting in the 1980’s, and loved it. I’m reasonably good at manipulating algebraic symbols, but I don’t especially enjoy it. In contrast, I am happy to spend plenty of time on visual puzzles, and I am enthusiastic about sharing that passion with colleagues and with students. Early in my high… Continue reading Transformational Geometry for Teachers

## Tiling in GeoGebra

In my last two posts, I promoted the idea of using tiling (tessellation) as an interesting context in geometry class, especially for the introduction of some basic ideas of transformational geometry. One reason this works is the connection with art, including the abstract patterns in Islamic art and the mind-bending creations of M.C. Escher. John Golden is a connoisseur of… Continue reading Tiling in GeoGebra

## Tiling and Transformations

In my last post, I argued that tiling is a good topic to include in a geometry program. Students find it engaging: on the one hand, it connects with art and culture; on the other hand, it provides a context for student creativity. At the same time, it presents many connections with the geometry curriculum in middle school and high… Continue reading Tiling and Transformations

## Tiling

Covering the plane with an unlimited supply of identical tiles is called tiling the plane, or tessellation. Over the years, I’ve developed a number of classroom activities about tiling. You can find links to those on the Tiling home page on my website. In a conversation with a teacher a few months ago, I realized… Continue reading Tiling

## Virtual Manipulatives: Part 2

In the previous post, I discussed virtual manipulatives in general, and a particular implementation for algebra, using a Google Drawings representation of the Lab Gear. In this post, I will explore GeoGebra as a platform for virtual manipulatives. Pattern Blocks Virtual pattern blocks are not hard to find on the Web. One good implementation is on the Math… Continue reading Virtual Manipulatives: Part 2

## 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