Virtual Manipulatives, Part 1: Some philosophizing about learning tools, and an introduction to the Virtual Lab Gear.
And Virtual Manipulatives, Part 2: A discussion of several GeoGebra-based virtual manipulatives, including the Virtual Geoboard , Virtual Grid Paper, Virtual Circle Geoboard, Virtual Tangrams, and Virtual Pentominoes.
Sum and Difference of Cubes: How to use the Lab Gear to prove those formulas.
Updates to my Math Education Page
New Applets: I used GeoGebra to make new applets — Virtual Geoboard, Virtual Circle Geoboard, Virtual Grid Paper, Virtual Pentominoes, Virtual Tangrams, and Symmetry with Pattern Blocks. In each case, my goal was to offer useful features to compensate for the loss of immediacy of physical materials.
Virtual Lab Gear: I created Google Drawings that teachers and students can use to make Lab Gear graphics. Useful for remote learning and collaboration, for presentations, to include in other documents — and who knows what else.
Symmetry: I created a home page for this topic, including links to existing materials, to photos of student-created designs, and to a brand new 10-lesson unit for elementary school.
What else is new
17 June 2020: I sent out my e-newsletter. Topics included: “There is no one way”, a GeoGebra animations tutorial, sum and difference of cubes, Lab Gear graphics, symmetry, and my wallpapers catalog. Also: an announcement of my online summer / fall workshop — Hands-On Geometry.
10 February 2020: I sent out my e-newsletter. Topics included guided inquiry, conic sections, a polyomino puzzle, a grid approach to fractions, graphing ax+by=c, and number pyramids. Also: an announcement of my summer workshop — Hands-On Geometry on both coasts. Alas, there was a wrong date for the latter, and a couple of broken links. It’s all fixed online!
4 February 2020: Infinity is a mind-bending topic that everyone finds interesting. I shared infinity paradoxes, puzzles, problems, and proofs from a high school course I developed at the Berkeley Math Teachers’ Circle.
27 November 2018: I moved my blog into WordPress (here.) I thought the move had happened smoothly, but some graphics, and some entire posts, failed to materialize. Also, many links are broken. If you come across these problems, please notify me, indicating which post had the issue. Thanks!
I have retired from the classroom after 42 years as a math teacher in K-12 — from counting to calculus. I now work with teachers and schools:
Math Education Consulting
On this page: announcements about new material, updates, etc. on the site; new publications; my appearances at conferences; and my other activities in math education.
Note: All material on this site is copyrighted. You may reproduce it for any non-commercial purpose, as long as you credit me and link to the blog. More info.
(I am also involved in word puzzles, especially cryptic crosswords.
More on this.)