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Order of Operations
A guest post by Rachel Chou I recently saw this in my Facebook feed: I had many questions: Why is this posted in a facebook group called “Grandma’s recipes?!” 462,000 people cared enough to leave a...
View ArticleGeometry Labs Notes
In this post, I share thoughts about my Geometry Labs (free download), and complement some of Mimi Yang’s notes about it. (In fact, this post was suggested by the existence of Mimi’s notes. You may...
View ArticleSimplify?
We ask students to simplify expressions in various arenas: fractions, order of operations, radicals, and no doubt other topics I’m not recalling right now. What is the purpose of this? When is it...
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Factoring Trinomials
A recent online conversation got me thinking about the factoring of trinomials. To start with, I would like to step back, and think about why this topic is prominent in the teaching of algebra. In the...
View ArticleTeacher-Created Materials
In this post I would like to discuss the place of teacher-created materials in the big picture of math curriculum. In some ways, the topic is of limited importance. Teachers in the US do not have a lot...
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A Construction Unit
I have written about geometric construction a number of times on this blog, and on my website. I outlined my philosophical outlook on this topic here. Today I summarize some construction activities, a...
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Functions from Tables
At some point, maybe thirty years ago, it became fashionable to emphasize functions and their multiple representations in secondary school math. This was in part driven by the newly available...
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Manipulatives
Liz Caffrey is a master middle school math teacher in the Boston area. She is the author of last year’s Lab Gear, the Great Connector, a guest post on this blog. Today, she shares her big-picture...
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Fractions
Last weekend, I shared my thoughts about teaching fractions with teachers of grades 3-5 at the Asilomar meeting of the California Math Council. After decades of work in high school, and hundreds of...
View ArticleWhat belongs in Algebra 2
In early December, I attended the California Math Council Northern Section conference in Asilomar, as I’ve done almost every year since the mid-1980’s. In my last post, I discussed my session on...
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Another Use for the Lab Gear
I am the creator of the Lab Gear, a manipulative environment for learning algebra. It is more expensive than the better-known algebra tiles, in their various versions, but it is much more effective in...
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The Three Triangles
I recently added a guided inquiry worksheet on my website’s Pythagorean theorem page. It leads students along a proof of the theorem based on similarity. It is called The Three Triangles. This is a...
View ArticleNCTM on Data Science
The National Council of Teachers of Math issued an official statement about data science. It is a Joint Position of NCTM, the National Science Teachers Association, the American Statistical...
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Tangram Puzzles
When I was a beginning K-5 teacher in the 1970’s, my father-in-law introduced me to pentominoes. It was clear to me that there had to be some way to incorporate those in my teaching. It wasn’t long...
View ArticleCan Bots Teach Math?
For many years, Dan Meyer has been challenging Sal Khan’s attempts to improve math education through technological innovation. In the latest episode of this ongoing saga, Dan concedes that bots may be...
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Working with Pentominoes
This is an update of a post from 2013, when Didax published my book Working with Pentominoes. You can still buy the book. It is geared to grades 4-8, though I used some of the content in high school....
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There Is No One Way!
This is the cover of my upcoming book about math pedagogy. Art teacher / artist Briana Loewinsohn created the image, based on this photo I came across ages ago: “There is no one way” has long been the...
View ArticlePreorder!
You can now preorder my new book, There Is No One Way to Teach Math (co-authored with Robin Pemantle). I wrote about it in my previous post, where I forgot to mention that I link to many resources...
View ArticleProof in High School
Proof in Geometry Many years ago, when I was still teaching high school, I added a Teaching Proof page to my website, which included a bit of philosophizing and links to the relevant parts of the site....
View ArticleMaking Struggle Productive
At the start of the opening chapter of our new book (There Is No One Way to Teach Math), Robin Pemantle and I argue that teachers should learn to embrace contraries. The idea is that instead of...
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