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.
Tag Archives: Geometry
Protect the Sheep
A game of enclosing sheep and wolves in fences helps children to develop their conceptual understanding of polygons.
The Perimeter Problem
At a recent meeting of mathematics content coaches (many from the organization Reimagined) we investigated the following problem: What is the perimeter of the polygon below?
It appears at first that there isn't enough information to solve the problem. Indeed, the lengths of only three of the polygon's … Continue Reading ››
Pythagoras Plugged In
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 ››
A Mathematical Mystery Story with Web Sketchpad
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 ››
Exploring Tessellations with Web Sketchpad
Metamorphosis is a New York-based company that offers professional content coaching to transform the mindset and practice of both teachers and administrators. I recently had the pleasure to collaborate with Metamorphosis staff members Toni Cameron and Kara Levin as well as mathematics coach Ariel Dlugasch from P.S. 276 in a coaching learning community that brought … Continue Reading ››
Dilation Games: Assessment That’s Fun
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 ››
Constructing an Ellipse with Web Sketchpad Tools
In a prior blog post, I described the pins-and-string approach to drawing an ellipse: Press two pins into a corkboard, place a loop of string around the pins, pull the string tight with a pencil, and trace the pencil tip's path as you pull the pencil around the taut string. Guaranteeing that the traced … Continue Reading ››
Hello Spring!
Today's blog post features a sketch from Anna Nguyen, who's a 9th grade student. Anna observes, "Math is one of my favorite subjects. I'm not a genius or the smartest in my class, but I do enjoy dealing with letters and numbers, which is also why I like chemistry. I think GSP is the most … Continue Reading ››
Constructing Morley Triangles
By Adrienne Barrett
This post is by guest blogger Adrienne Barrett, who's a senior mathematics and education dual major at Rowan University. She is currently student teaching and upon graduation in May, she hopes to find a full-time position teaching high-school mathematics. She's always loved math, and studying it in college has given her … Continue Reading ››