I’m a long-time user of interactive geometry software, of which the dominant instance these days is GeoGebra. Here are some ways it’s enhanced my teaching over the years. Most obviously, it provides an environment for students to explore geometry and geometric construction. I’ve written much about it on this blog, and shared some curriculum on… Continue reading Making a GeoGebra Slide Show

# Tag: Technology

## Asilomar report, 2021

I attended the California Math Council North’s conference in Asilomar last weekend. Because of Covid, it was a dramatically smaller conference than usual. As a consequence, there were fewer sessions to choose from, and probably a smaller turnout for many of them. Here is my nearly annual report. Python Turtle Ned Diamond presented the Python… Continue reading Asilomar report, 2021

## Fraction Rectangles

This is a sequel to my last post (Seeing is Believing?), addressing the same issue from a different point of view. Fractions, of course, are difficult. When teaching 4th and 5th grade in the 1970's I struggled with this, and came up with a powerful learning tool: fraction rectangles. The idea is that it is… Continue reading Fraction Rectangles

## Seeing is Believing?

“Proofs Without Words” are proofs based on a visual representation of a theorem which provides a convincing argument about its validity without the need for any accompanying text. The genre has been much enriched by the increased availability of computer animation. This is of course relevant to math education: many of the concepts we teach can be illustrated visually, including with… Continue reading Seeing is Believing?

## 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

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

## Virtual Manipulatives: Part 1

Learning Tools In 1981, after ten years in K-5, I switched to teaching high school math. In some ways, this felt like starting a whole new career: the math was more involved, the relationship with students less like parenting, and tradition weighed a lot more heavily on the profession. Still, in other ways, teaching is… Continue reading Virtual Manipulatives: Part 1

## 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

## 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