Tag Archives: Pedagogy

Educational Technology, Geometry, Math Software

Pythagoras Plugged In

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The title of this post is a nod to the Sketchpad activity module Pythagoras Plugged In by Dan Bennett. Dan's book contains 18 visual, interactive proofs of the Pythagorean Theorem. And there are more:  The Pythagorean Proposition, published in 1928 by Elisha Scott Loomis, contains over 350 proofs, 255  of which are geometric. Wow! I revisited the … Continue Reading ››
Conferences, Educational Technology, Geometric Functions, Math Software

International Congress for Mathematics Education Part 2

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I began this post on Friday night in Hamburg Germany, near the end of ICME, the quadrennial international math-education conference that's been both exhilarating and exhausting. I’m now finishing it on the airplane headed back home. ICME-paper As interesting as many of the presentations have been, they've also been … Continue Reading ››
Conferences, Math Software, Professional Development

International Congress for Mathematics Education Part 1

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I'm currently attending the 13th International Congress on Mathematics Education (ICME) in Hamburg, Germany, with well over 1000 math educators from around the world. Professor Gabriele Kaiser opened the conference with a statement of solidarity with Turkish mathematics teachers and researchers who at the last minute were unable to attend due to newly imposed government … Continue Reading ››
Advanced Mathematics, Educational Technology, Math Software

A Mathematical Mystery Story with Web Sketchpad

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Several years ago, I wrote a blog post about the value that students derive from writing mathematics with Sketchpad. The post included an example of a simple Logo iteration, easily implemented in Sketchpad, that produces some very complex and interesting shapes depending on the values of several input parameters. In the … Continue Reading ››
Assessment, Educational Technology, Elementary Mathematics, Math Software

Bunny Times Brings Conceptual Understanding to Multiplication

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Four years ago, my colleague Scott Steketee and I set out to develop an interactive game to help students develop strategies for thinking about and solving multiplication problems. As we examined the existing apps on the market, we discovered that most focused on the drill aspect of learning one's multiplication facts. We set our goals higher. We … Continue Reading ››
Educational Technology, Geometry, Math Software

Putting the Power of a Point Theorem to Work

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The power of a point theorem is one of the more surprising results in elementary geometry. The theorem says that if two chords AB and CD of a circle intersect at point P, then the product AP · PB is equal to the product CP · PD. You can see an illustration of this theorem in the Web Sketchpad model below. Drag … Continue Reading ››
Assessment, Educational Technology, Geometric Functions, Geometry, Math Software

Dilation Games: Assessment That’s Fun

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March 2023 UPDATE: If the dilation games below whet your appetite for challenges based on transformations, check out these Reflection and Rotation games as well. What does dilation feel like? I recently had the opportunity to work with a group of students who were testing activities that treat geometric transformations as functions (what … Continue Reading ››
Educational Technology, Elementary Mathematics, Geometry, Math Software

Exploring Triangle Area with Custom-Built Tools

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With Web Sketchpad, it's easy to craft tools that are tailor made for the task at hand. I was reminded of this flexibility several weeks ago when creating an interactive model for the elementary curriculum Everyday Mathematics.

My goal was to design a lesson focusing on the triangle area formula, A … Continue Reading ››

Advanced Mathematics, Educational Technology, Real-World Math

WCYDWT: A Ball, a Trash Can, and Web Sketchpad

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Dan Meyer has posted a number of "What Can You Do With This?" activities on his blog. (Activities is probably too prescriptive a word; they're more in the nature of prompts for student thinking, noticing, and wondering.) One of the first was the image below, which he made by superimposing frames from a … Continue Reading ››