# Multiplication Arrays

I've lost track of how many  parents have quizzed me as to why the mathematics their children are learning is so different from what they remember in school. "Why must my kids study more than one way to multiply? Isn't memorizing their multiplication facts enough?" is a frequent lament. James Tanton, Mathematician in Residence at the … Continue Reading ››

# Cross Number Puzzles

We live in a golden age of number puzzles. Sudoku is probably the most famous of all modern-day number puzzles, but there are many Japanese puzzles that are also gaining popularity, such as KenKen and Menseki Meiro. In this post, I'd like to introduce a number puzzle for young learners that predates … Continue Reading ››

# 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 ››

# 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

The November 2016 issue of Mathematics Teaching in the Middle School features the article Leveraging Interactive Geometry Software to Prompt Discussion by Priya V. Prasad. The article focuses on how the use of dynamic geometry technology can encourage students to think abstractly about geometric objects by having them construct those objects from their definitions. For example, … 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. 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 ››

# 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 article* where … Continue Reading ››