The Math Education Blog
I was happy to collaborate on this blog post with Dr. Stavroula Patsiomitou, a researcher at the Ministry of Education and Religious Affairs in Greece. Dr. Patsiomitou received her PhD from the University of Ioannina and has written extensively about the field of dynamic geometry environments, including Sketchpad and Web Sketchpad. Her textbook, Conceptual and...
In how many ways can you use dynamic geometry software to build a rhombus that stays a rhombus when its vertices are dragged? This challenge, a mainstay of Sketchpad workshops, invariably leads to great discussions because there are a multitude of ways to construct a rhombus, with each method highlighting different mathematical properties of the...
In Algebra 1, I was the king of solving for x. Algebraic manipulation was fun and satisfying, and I was good at it. But my confidence was shaken when I encountered a test question of the variety 4x + 5 = 4x – 3. After subtracting 4x from both sides, I was left with 5...
Below are some common methods that geometry curricula offer for constructing scaled polygons: To complement these standard approaches, I’d like to present a fourth option, one that allows students to form the original polygon and its dilated image simultaneously rather than starting with the preimage. In the Web Sketchpad model below (and here), begin by...
Pi Day 2022 is now over, but I’m still thinking about a tweet from 10-K Diver: Take two random numbers X and Y between 0 and 1. What is the probability that the integer nearest to X/Y is even? The answer—spoiler ahead—is (5 – π)/4. (You can run my Web Sketchpad simulation of the problem...
In a prior post, I shared some good news: The Connected Geometry high-school curriculum authored by Education Development Center (EDC) is now available for free. I could easily devote every future blog post to a tasty Connected Geometry morsel, but I’ll restrict myself to just a few. The investigation below, taken straight from the curriculum,...
In his article Simply Symmetric, Michael de Villiers observes that symmetry is a powerful but often overlooked tool for formulating proofs: Most primary geometry curricula around the world introduce the concept of line symmetry fairly early, and sometimes also that of rotational, translational and glide reflective symmetry. However, in high school and even college geometry...
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NCTM’s Virtual 2021 Annual Meeting ran from April 21 through May 1, and in Session 299 Daniel Scher, Karen Hollebrands, and I presented an on-demand video workshop to introduce Web Sketchpad (WSP). Even if you weren’t able to attend the conference, you can still take advantage of this workshop, and we will be glad to...
This post is a follow-up to Sarah Stephens’ guest post of a week ago, in which she described a lesson using embodied cognition to help students make sense of the interior angle sum theorem for triangles, not just as an abstract concept, but as a property grounded in their concrete physical experiences. The day before...
A game of enclosing sheep and wolves in fences helps children to develop their conceptual understanding of polygons.