# Tag Archives: NCTM

# 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 ››

# 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 ››

# 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 ››

# 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 ››

# Connecting Functions in Geometry and Algebra

News alert! Scott and I wrote the cover story, Connecting Functions in Geometry and Algebra, in this month's *Mathematics Teacher.* You can read the article in print, but better yet, go to the free online version. This is the first time *Mathematics Teacher* has incorporated live dynamic-mathematics figures into its online offerings, allowing readers to manipulate … Continue Reading ››

# Dilation Challenges

For a while now, I’ve been intrigued by the ways in which the study of geometric transformations can provide students with a very effective introduction to function concepts. Daniel and I have written a couple of articles about this topic, and we created a number of activities to take advantage of what can arguably be … Continue Reading ››

# Understand the Sine Function by Dancing It

In *Where Mathematics Comes From*, cognitive scientists George Lakoff and Rafael Nuñez assert that our understanding of abstract mathematical concepts relies upon our sensory-motor experiences:

“For the most part, human beings conceptualize abstract concepts in concrete terms, using ideas and modes of reasoning grounded in the sensory-motor system. The mechanism by which the … Continue Reading ››

# Iteration in the Complex Plane

The cover story of the April 2014 issue of Mathematics Teacher is on "Iteration in the Complex Plane", by Robin S. O'Dell. It sounds like pretty advanced mathematics, but is surprisingly accessible with *The Geometer's Sketchpad.*

It's all based on the surprising principle that you can multiply two complex numbers very easily if … Continue Reading ››

# The Wavy Wavy Bridge

At the 2013 Baltimore Regional NCTM Meeting, I gave a presentation on *Picturing Functions and Functions of Pictures.* In the description of my presentation I’d promised to show how to use Sketchpad to create special effects, so when it came time to prepare, I figured I needed to deliver on my promise.

So I wrote a … Continue Reading ››