Blog Posts and Updates to MathEducation.page
Here are links to posts on my Math Education Blog that you might find interesting.
If you are so moved, you may comment on the posts, and/or subscribe to the blog.
I also update you on what is new on my MathEducation.page website, where I share my views as well as tons of curricular materials.
The Start of School
I never liked starting a class with a boring overview of rules and regulations, the sharing of a syllabus whose content means nothing to most students, or "getting to know each other" games. Instead, I favored doing math from Day 1. I discussed this in this 2015 blog post: First Day of School.
Another problematic way to start the year is to review material from previous years. Review is an essential part of any math class, but it should be handled with care! It's not whether to engage in review, but when and how. I discussed this in a blog post last year: We Need to Review!
Order of Operations
Every once in a while, a meme takes off on the Internet and in the press, pointing out that a given calculation can yield two different results, depending on how you interpret it. In a guest post on Order of Operations, Rachel Chou takes on one of those, arguing that instead of wasting time discussing ambiguous expressions, we should encourage students to slow down, think about the meaning of operations, and (unlike the author of that meme) communicate clearly.
Supertangrams are the shapes you get by connecting four congruent isosceles right triangles edge-to-edge. Many years ago, I created dozens of supertangram puzzles which were made available by my then publisher in four books. A few weeks ago, I added a fifth book to that collection. All five books are now available for free download on my website.
More supertangram news:
- I told some of my history with supertangrams, and explained a little of the math underlying the puzzles in a blog post.
- I created a Supertangrams home page with links to all the supertangram materials on my site.
- I sell plastic supertangrams — read about a special sale at the end of this newsletter.
Back in 1999, I created my Geometry Labs book (free download) as a sequel of sorts to my Lab Gear algebra materials. The idea for both projects is that while manipulatives are not magic, they do offer an alternate representation, and can trigger engagement, reflection, and discussion.
24 years later, the book is still going strong and generates interesting feedback from its users, which I incorporate on the site. High school teacher Mimi Yang created a correlation of the labs with the topics they support. This led me to write some additional teacher notes, and to tweak the book's home page.
Let me know if you have ideas for Geometry Labs connections, corrections, extensions, or revisions!
My first attempts at teaching about matrices was as a way to solve systems of equations. It did not go well: a highly technical approach to a highly technical topic is not a recipe for student engagement. Some time later, in Space, my elective geometry course, I developed an approach based on geometric transformations and complex numbers. This went so well that students consistently rated matrices as one of their favorite parts of the course. I summarized this approach here.
Tweaks, Updates, and Stats
- A new directory: For Math Circles, in which I link to "enrichment" materials, for use by math clubs, Math Circles, Math Teachers' Circles, and perhaps some classrooms.
- New home pages for Pentominoes and Supertangrams.
- Tweaks and updates to the Geometric Puzzles directory.
- Tweaks and updates to the links on my Publications page.
Most popular in the last three months, not including pages I already mentioned in this newsletter:
- Virtual Grid Paper (always the front-runner)
- Virtual Pentominoes (addictive!)
- Fractions (← I will present this at Asilomar this December)
- Proving Pick's Formula (I have no explanation for why this page is so consistently popular)
- Some Rights Reserved (where I make clear my materials are free for non-commercial use)
- Search (and you shall find?)
Discounter Introduces Reductions
Everything on my website is free, except for one thing: plastic supertangrams. Until August 22, I am dropping their price dramatically: $2.00 per set, plus $10 for shipping and handling. They come in four colors, so I recommend buying a multiple of four. If you buy four or more sets, you'll get a hard copy of Supertangrams for Beginners Book 2. In any case, you'll have access to dozens of supertangram puzzles, free of charge on my website. Your students will love them! (And so will you.)
For more information, email me.