Tag Archives: Dynamic Geometry

Educational Technology, Geometry, Math Software

Digging Deep Into Varignon’s Theorem

1 Comment
In the interactive Web Sketchpad model below (and here on its own page), ABCD is an arbitrary quadrilateral whose midpoints form quadrilateral EFGH. Drag any vertex of ABCD. What do you notice about EFGH? The midpoint quadrilateral theorem, attributed to the French mathematician Pierre Varignon, is relatively new in the canon of geometry theorems, dating to 1731. Mathematics … Continue Reading ››
Conferences, Educational Technology, Geometry, Math Software

Function Dances at NCTM

Leave a comment
At the 2017 NCTM Annual Meeting I was invited to do a short Wednesday-afternoon presentation on Function Dances in the NCTM Networking Lounge. (Here's the handout from the presentation.) The idea of function dances is to get students (or in this case teachers) moving around, acting as the independent and dependent … Continue Reading ››
Educational Technology, Geometry, Math Software

Revisiting the Isosceles Triangle Challenge

Leave a comment
In my last post, I presented a lovely geometry problem from Japan that was ideally suited to a dynamic geometry approach. Below is a new problem whose construction is nearly identical to the original one. The text says, "Five isosceles triangles have their bases on one line, and there are 10 rhombi. One length of the rhombus … Continue Reading ››
Educational Technology, Geometry, Math Software

A Geometry Challenge from Japan

2 Comments
Here is a wonderful geometry problem from Japan: The five triangles below are all isosceles. The quadrilaterals are all rhombi. The shaded quadrilateral is a square. What is the area of the square? I wondered at first whether the English translation of the problem was correct because with so many side … Continue Reading ››
Elementary Mathematics, Geometry, Math Software, Professional Development

Creating Animated Factorization Diagrams

Leave a comment
Last year, I had the pleasure of co-organizing a geometry-focused coaching collaborative led by Metamorphosis, a New York-based organization that offers professional content coaching to transform the mindset and practices of teachers and administrators. I had so much fun that I decided to do it again! My workshop partners were Metamorphosis staffers Toni Cameron, Ariel Dlugasch, and … Continue Reading ››
Educational Technology, Geometry

The Varied Paths to Constructing a Square

Leave a comment
Using dynamic geometry software, students can use a Segment tool to draw what looks like a square by eyeballing the locations of the vertices. However, the resulting quadrilateral will not stay a square when its vertices are dragged. Building an “UnMessUpAble” square requires that the quadrilateral stay a square when any of its parts are … Continue Reading ››
Educational Technology, Elementary Mathematics, Math Software

Stars, Polygons, and Multiples

2 Comments
I've always found my collaborations with teachers to be a great inspiration for curriculum development, and that was especially true of my work with Wendy Lovetro, an elementary-school teacher in Brooklyn, NY. Wendy coordinated an after-school math club at her school, and I used the setting as an opportunity to develop and field test Sketchpad activities for the … Continue Reading ››
Conferences, Educational Technology, Geometric Functions, Math Software

International Congress for Mathematics Education Part 2

1 Comment
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

Leave a comment
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 ››
Educational Technology, Elementary Mathematics, Geometry, Math Software

Estimating Angle Measurement

Leave a comment
Angles are a thorny concept to teach because of the fundamentally different ways in which they can be used and understood. In the article What's Your Angle on Angles?, the authors divide the concept of angle into three main groups: angle-as-figure, angle-as-wedge, and angle-as-turn. In the Web Sketchpad game below (and here), we focus on angle-as-turn. Given an … Continue Reading ››