Henri Picciotto's

Math Education Newsletter

August 2023

Supertangrams Sale! Scroll down.

Hi all,

In the last issue of this newsletter, I mentioned that I had been working on a book about teaching math, and that a dozen math educators reacted enthusiastically to the manuscript. Alas, commercial publishers don't seem to agree, and I have received a stream of rejections. I am surprised and disappointed. I'll probably let you know the final fate of this project in the next issue of this newsletter.

For some time after I retired, I had a feeling of anticipation every August, even though nothing was about to happen for me. That was of course the result of 42 years in the classroom, and the internalizing of that yearly cycle: after the summer, school starts again! I am no longer subject to that feeling: for me, every month is pretty much like every other month, and in my old age I like it that way!

Still, for most of you, school will be starting again soon. I wish you a great year! I open this newsletter with some thoughts about the beginning of school.


Blog Posts and Updates to

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 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:

Geometry Labs

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

Other website news:

Most popular in the last three months, not including pages I already mentioned in this newsletter:


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.

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