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 ››

# Tag Archives: Dynamic Geometry

# Revisiting the Isosceles Triangle Challenge

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 ››

# A Geometry Challenge from Japan

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 ››

# Creating Animated Factorization Diagrams

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, … Continue Reading ››

# The Varied Paths to Constructing a Square

Using dynamic geometry software, a student can draw what looks like a square by eyeballing the locations of the vertices. However, the quadrilateral will not stay a square when its vertices are dragged. Building a "real" square requires that it stay a square when any of its parts are dragged. This is only possible by baking … Continue Reading ››

# Stars, Polygons, and Multiples

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 ››

# International Congress for Mathematics Education Part 2

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.
As interesting as many of the presentations have been, they've also been … Continue Reading ››

# International Congress for Mathematics Education Part 1

I'm currently attending the 13

^{th}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 ››# Estimating Angle Measurement

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, we focus on angle-as-turn. Given an angle, students enter an estimate … Continue Reading ››

# A Compendium of Elementary Web Sketchpad Activities

Below is a complete list of all the interactive elementary-themed activities we've offered on our Sine of the Times blog. Most of these activities grew out of the work that we did during our NSF-funded Dynamic Number project.
The list includes links to our original blog posts as well as links that take you directly … Continue Reading ››