Henri Picciotto's

Math Education Newsletter

October 2018

Free math teacher conference in Walnut Creek, CA!

Seven months have passed since my last newsletter! This is the longest gap between issues in the seven-year run of the newsletter. The main reason is that summer travels (both work and vacation) severely limited my ability to blog and to add materials to my Web site.

Anyway, I'm back in the Bay Area. If you live around here, I may see you this weekend!


Blog Posts

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.

Understanding "understanding"

As you probably know, I'm an advocate of "teaching for understanding". But what does that mean? "I know it when I see it", you might reply, and I believe you, but nevertheless, it is useful to be more specific. I list some easily observed components of understanding in this post. The post quickly became one of the top three most-visited on my blog in the past year. (Which is not saying much, admittedly, but still.) I'm hoping the list can help you improve your teaching and assessment strategies. It certainly has helped me develop worthwhile activities as a curriculum developer.

More on extending exposure

A recurring theme of this newsletter (and my blog) is how to address the fact that students learn at different rates. The question, of course, is fundamental to teaching math effectively at any level. Unfortunately, many of the standard responses have problematic side effects. If schools heed the "detracking" advice in NCTM's Catalyzing Change document, the question will gain even more urgency. A full answer is of necessity multidimensional, but one component I've been promoting is extending exposure, a set of practices that rearrange how things are sequenced without taking more time. This includes lagging homework, separating related topics, and as I suggest in this new post, pursuing two units at the same time.


I have come up with various slogans over the years, mostly aimed at teachers. I decided to list them in a blog post. They include the ever-cheerful "Nothing Works!", the cryptic "Fast is slow, and slow is fast!", and one so long that it barely qualifies as a catchphrase: "Formulas and tricks should encapsulate understanding, not substitute for it." See the whole annotated list here. (A day or two later, I remembered some slogans of mine that I hadn't included. Maybe in a future post!)

Some articles and curriculum materials, free downloads on my Web site.

Letters and Postcards

An introduction to linear inequalities in two variables, and linear programming. Two versions: middle school, and high school. Start here. If you create a Desmos version of this, let me know!

letter-stamppostcard stamp

New GeoGebra Applets

Creating a sine curve is an original animation suggested by Rachel Chou, along with some questions to trigger reflection, discussion, or writing.

Representations of a trinomial (symbols, graph, Lab Gear — manipulable) This is a conversation starter or writing prompt to consolidate what was learned by other means in middle school or in Algebra 1.

Iterating Linear Functions. What happens when you use the output of a linear function as its next input? This supports some curriculum materials available here. (Algebra 1, Algebra 2, Precalculus)

More advanced: iterating f(x) = rx(1 – x), in two representations. Chaos lurks! (Part of my Infinity course.)

Referenced On Twitter

Here are links to various items on my Web site that were referenced on Twitter in the past few months (in reverse chronological order). I'm guessing that if they were useful to the tweeter, they may be useful to some of you!

As if you had time for all this! I'll stop now.

A Taste of TMC

TMC is Twitter Math Camp, an annual summer grassroots gathering of math teachers. Each year, a teacher hosts the event in their town, and the next iteration is in Berkeley, CA. (Woohoo, as I would say if I were young. I live in Berkeley!)

A Taste of TMC is a free one-day math teacher conference this Saturday, October 13. in Walnut Creek, CA. It was inspired by TMC, and will use some of its structures. It is a great opportunity to meet some terrific Greater Bay Area math teachers. Take a look at the program and directions here, then register here.

I will be there, and will present "Reaching the Full Range" at 9:30am. I am in the process of writing a substantial article on teaching heterogeneous classes, so preparing for the talk is also preparing for the article. I hope some of you will attend! Whether you can make it or not, you can go to my Talks page for relevant links.

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