The Math Education Blog
Ah geometry, how you suffer from a lack of attention in the elementary grades! Rare is the curriculum that doesn’t stuff geometry into its final chapter, waiting patiently in line behind number and operation. But the one geometry topic that does command attention is classifying two-dimensional shapes into categories based on their properties. To quote...
This past semester, I taught a geometry course for teachers at City College here in New York. As you might expect, Sketchpad figured heavily in the course contents. But unlike other semesters when desktop Sketchpad was my tool of choice, this time, I took the plunge and limited myself to Web Sketchpad. Web Sketchpad kept...
This post, inspired by the work of Al Cuoco, uses Web Sketchpad to explore a transformations approach to complex numbers.
Given two segments and their midpoints, what quadrilaterals can you build using the segments as the diagonals of the quadrilateral?
This post examines the connections between origami and geometry in the context of a new book written by Daniel Scher and Marc Kirschenbaum.
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 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,...
It’s that time of year when we start seeing “best of” lists for books, movies, music and the like. In that spirit, but stretching way beyond the past year, some of my favorite geometry textbooks include Geometry: Seeing, Doing, Understanding (Harold Jacobs), Discovering Geometry (Michael Serra), and Geometry: A Transformation Approach (Coxford & Usiskin). There’s...
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...
In a prior blog post, I presented an uncommon method for solving the well-known Burning Tent problem. My solution, modeled on the approach in the Connected Geometry curriculum, used a dynamic ellipse to pinpoint the optimal solution. Now, I’d like to offer a related problem from Connected Geometry where the pedagogical benefit of using an...