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 ››
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 ››