With a few adjustments, we can make the Hundred Chart more intuitive and more useful for students. This post explains why the improvements are needed and describes how students can build a physical model that more accurately corresponds to the number system.

# All posts by Scott Steketee

# Multiplication Is Not Repeated Addition

On the NCTM discussion site myNCTM, there's currently an extended discussion about "Division and multiplication of fractions." As the discussion has continued, I've grown concerned with what I see as a fundamental problem with the way we often introduce multiplication as repeated addition: "Multiplying 4 by 5 means we're combining five groups of four items. … Continue Reading ››

# Adding and Subtracting Integers

A recent post on the my NCTM discussion group asked about tools to help students visualize and understand addition and subtraction of integers.

I always found this confusing for some of my Algebra 1 students, mainly because they had been told to memorize some rules about whether to add or subtract the two integers and … Continue Reading ››

# Binomial Multiplication and Concreteness Fading

I was delighted that Daniel recently posted our Binomial Multiplication sketches in Web Sketchpad format. I thought about those sketches when I noticed a fairly new myNCTM thread on "When and How do we phase out the body in math education?"

This thread raises a very important question for us as … Continue Reading ››

# Enhancing Web Sketchpad

As a longtime Sketchpad fan, one of the most interesting features of Web Sketchpad (WSP) for me is the way its behavior can be customized. WSP makes it possible to add JavaScript to a web page in order to interact directly with objects in the sketch. For instance, a JavaScript function could use the … 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 ››

# 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 ››

# 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 ››

# Dilation Games: Assessment That’s Fun

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 I call *geometric functions*). I got lots of good ideas for improving the activities not only by watching the students, but also but also from their suggestions … Continue Reading ››