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 ››
Revisiting the Isosceles Triangle Challenge
In my last post, I presented a lovely geometry problem from Japan that was ideally suited to a dynamic geometry approach. Below is a new problem whose construction is nearly identical to the original one. The text says, "Five isosceles triangles have their bases on one line, and there are 10 rhombi. One length of the rhombus … Continue Reading ››
A Geometry Challenge from Japan
Here is a wonderful geometry problem from Japan: The five triangles below are all isosceles. The quadrilaterals are all rhombi. The shaded quadrilateral is a square. What is the area of the square?
I wondered at first whether the English translation of the problem was correct because with so many side … Continue Reading ››
I wondered at first whether the English translation of the problem was correct because with so many side … 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
Using dynamic geometry software, a student can draw what looks like a square by eyeballing the locations of the vertices. However, the quadrilateral will not stay a square when its vertices are dragged. Building a "real" square requires that it stay a square when any of its parts are dragged. This is only possible by baking … 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 ››
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 the mathematical … 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 and the … Continue Reading ››
Creating Mosaics Inspired by a Pattern from Sultan Ahmed Mosque
Mirek Majewski was born in Poland and studied mathematics at the Nicholas Copernicus University in Poland with an M.S. and Ph.D. in non-classical geometries. He is a professor of mathematics and computer science at several universities – PNG University of Technology, Inter-University of Macau (now Saint Joseph University), Zayed University in United Arab Emirates, and New York … Continue Reading ››