This blog has been quiet for a while, but the conversations it hosted are something I’ve never stopped thinking about. The forums here brought together teachers, mathematicians, curriculum developers, and parents who were willing to think hard together about mathematics education. I learned a lot from those exchanges, and I’ve missed them.

I’m relaunching Mathematical Musings as a Substack newsletter. The welcome post is live today. After that I’ll post every Friday, with occasional midweek extras. Everything will be free, comments will be open, and I’ll be in the conversation.

The focus is the same as it always was: specific examples, particular problems, classroom moments, questions about curriculum and teaching—and the occasional piece of mathematics I find beautiful. The founding principle is dialog. I’m not interested in winning arguments; I’m interested in the moments when two people who see things differently discover something neither of them could have found alone.

You can subscribe here.

I’d love to have you in the conversation. And if you know someone who’d want to be part of it, please pass this along.

Cathy Kessel wrote an article  with Liping Ma that discuss “unit fraction” vs “fractional unit” and has added a remark to the appendix about this.

Here is the new version.

Hi everybody, Cathy Kessel has compiled all the suggestions that people have made here and other places over the years to produce a final version of the progressions. Here is the compiled document of all the progressions.

And here are two documents outlining the major changes from previous versions.

Note that the University of Arizona has deleted the website that used to host the progressions. I am working to have that url redirect here.

Hi everybody, in order to deal with the spam problem I have deleted all users regarded by WordPress as spam users. These are defined as users who have never posted. Unfortunately this seems to have caught some legitimate users as well. Their content is still on the blog, with the author marked as anonymous.

By popular demand Cathy Kessel has produced a document outlining the major changes in the recent version of the progressions.

Cathy Kessel is working on editing the progressions documents into final versions, incorporating comments from this blog and elsewhere and filling in gaps.  Here is the fractions progression. We will be rolling out the others over the next few months. Comments welcome!

With the high school writing work in full swing, I’ve been remiss in posting here lately. I do have some ideas saved up! Meanwhile, Kate Nowak and I have a piece about instructional routines over at the IM blog.

I’ve been meaning to let you know about the Illustrative Mathematics blog, which launched a few weeks ago. It has blog posts by members of the IM community about our grades 6–8 curriculum and about teaching practice, including a whole series on the 5 practices framework of Smith and Stein. Also, we will be cross posting any IM related posts I write here over there as well. I hope you find our new blog useful!