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 the classroom. At least that is the opinion of those teachers I know who have used both. As one of them put it, ” I have been having so much fun with my students using Lab Gear this year. The 3D-ness of it totally blows the other (cheaper) algebra tiles that I used last year out of the water!” (You can read a detailed comparison of the various algebra manipulatives here. For a basic introduction ..read more

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 fractions. For various reasons, I only attended two other sessions. The first was by Eric Muller, who works at the Exploratorium, San Francisco’s amazing science museum. He presented an extraordinarily entertaining middle school activity about air pressure. You can read all about it here and here. The second was Gail Burrill’s excellent talk on “What belongs in Algebra 2”. This is a crucially important ..read more

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 presentations to teachers of grades 7-12, this was a bit of a departure from my normal routine, and somewhat anxiety-provoking. The reason I decided to step out of my comfort zone was that I wanted to share some of the ideas I came up with back in the 1970’s when I was an elementary school teacher. Pretty much everything I presented can be found on my website’s Fractions home page. The biggest part ..read more

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 thoughts about manipulatives. I inserted some links to pages on my website — you can find many more links on my Manipulatives home page. — Henri Manipulatives  by Liz Caffrey Recently I had the chance to lead a workshop on hands-on math for middle school teachers at the Atrium Summer Math Institute. I featured a wide array of manipulatives in the workshop, and it was clear that some were better r ..read more

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 electronic graphing technology, and in part by the realization that important curricular ideas should be approached in more than one way. As is often the case in math education pendulum swings, some people took this too far, asserting that functions were the key to everything, and could for example be the unifying thread in Algebra 2 or even all of high school math. While I steered clear of this extreme i ..read more

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 subset of the unit you can find on my website. —————————————————————————————————— Geometric construction with straightedge and compass is a standard topic in high school geometry classes. Typically, students are shown specific procedures to construct bisectors, right angles, and so on. Often, they are encouraged to create aesthetically pleasing designs as a follow-up application. There is n ..read more

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 of time and energy for this once they are done with lesson planning, paper grading, and assorted additional responsibilities. This reflects teachers’ low status and limited power. Still, if they can create curriculum materials, those will have the advantage of being based in their lived classroom experience. During my 43 years in the classroom, I did develop assorted curriculum materials to use ..read more

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 age of computer algebra systems (CAS), factoring trinomials is not an important skill, except of course for the purposes of school math. Most of the trinomials we ask students to factor are created specifically so that students can actually factor them. It is a curious, circular situation, and we’re back to asking why we do this. As I see it, it’s a little bit like multi-digit arithmetic: we can ..read more

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 find those useful, as she lists which topics are supported by various labs.) First, big-picture thoughts.  The book includes obviously curricular content, but also material which is not standard classroom fare. I hope you can find a use for the labs about puzzles, symmetry, tiling, and so on. Some are not so far from things you have to teach, and some are just, well, interesting.  Most of ..read more

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 comment? 6,900 people cared enough to re-share it? Most importantly: I hope no one is posing this question to schoolchildren! I decided to google the phrase “facebook order of operations meme”, and I was shocked to find the following: a Slate article, a Reddit thread, a Newsweek article, and even a New York Times article. It appears that annoying order of operation problems have riled up so many ..read more