NCTM’s Virtual 2021 Annual Meeting ran from April 21 through May 1, and in Session 299 Daniel Scher, Karen Hollebrands, and I presented an on-demand video workshop to introduce Web Sketchpad (WSP). Even if you weren't able to attend the conference, you can still take … Continue Reading ››

# Category Archives: Geometric Functions

# 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 ››

# 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 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 ››

# Reflecting on the Annual NCTM Meeting

This Thursday, Scott Steketee and I will be presenting two sessions at the NCTM 2015 Annual Meting in Boston:

**Functions as Dances: Experience Variation and Relative Rate of Change**

Session 52 on Thursday, April 16, 2015: 8:00 AM-9:15 AM in 157 B/C (BCEC)

How better to explore rate of change than as independent and … Continue Reading ››

# Tribute to Zalman Usiskin

On November 6 I had the honor of being one of the panelists in a Symposium Honoring Zalman Usiskin, held to honor Zal’s many years of contributions to mathematics education, from his groundbreaking 1971 textbook *Geometry: A Transformation Approach (GATA)* to his continuing activities today.

My panel was supposed to discuss his work on … 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 ››

# Parents, Children, and Functions in Sketchpad

Functions are hard for students.

Students seem to master various families of functions – linear, polynomial, exponential, trigonometric, and so forth. They can graph them, evaluate them, transform them, and answer a variety of questions about them. But ask even our better students a question that’s out of the ordinary and we’re likely to be taken … Continue Reading ››