Category Archives: Math Software

Function Dances at NCTM

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 ››

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 ››

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 ››

Raz’s Magic Multiplying Machine

Here is a question you don't hear very often: What does it feel like to experience multiplication in our bodies? It's a strange question because our typical exposure to multiplication is numerical. I give you two numbers—say, 3 and 5—and you tell me their product, 15. But multiplication need need not be so static and concrete. Back … Continue Reading ››

Pythagoras Plugged In

If there were an award for 'Mathematical Theorem Most Amenable to a Visual Proof,'  the Pythagorean Theorem would surely win. 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 … 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. ICME-paper 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 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 ››

Developing Arithmetic Fluency Through “Drill and Thrill”

In a previous post, I described the game Chisla, an app that succeeds in making basic arithmetic both challenging and tense.  Given a numerical target, you have just 15 seconds to pick numbers from a list of possible addends that will sum to that value. A target of 10 is no big deal, but when the target escalates … Continue Reading ››