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 ››
A recent post on an NCTM discussion group asked about tools to help students visualize and understand addition and subtraction of integers. We wanted to make a visualization tool for students that they could use in multiple ways. The result is the Web Sketchpad model below (and here). Page one focuses on addition while … Continue Reading ››
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 ››
We live in a golden age of number puzzles. Sudoku is probably the most famous of all modern-day number puzzles, but there are many Japanese puzzles that are also gaining popularity, such as KenKen and Menseki Meiro. In this post, I'd like to introduce a number puzzle for young learners that predates … Continue Reading ››
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 ››
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, and … Continue Reading ››
Using dynamic geometry software, students can use a Segment tool to draw what looks like a square by eyeballing the locations of the vertices. However, the resulting quadrilateral will not stay a square when its vertices are dragged. Building an “UnMessUpAble” square requires that the quadrilateral stay a square when any of its parts are … Continue Reading ››