For the second time this summer, I taught a version of my Visual Algebra workshop, this time as part of a summer institute at the Atrium School near Boston. (Earlier in the summer, I did this at Synapse School, in Silicon Valley, and wrote about it here.) Once again, I walked away from the workshop… Continue reading Learning from Teaching (cont.)

# Tag: Algebra

## Learning from Teaching

Now that I’m retired from the classroom, summer tends to be my busy time. I just taught the grades 6-9 version of my Visual Algebra workshop. There were quite a few familiar faces among the participants. Some had seen me present at the Asilomar (California Math Council) conference, others at NCTM, yet others at a… Continue reading Learning from Teaching

## Story Tables in Middle School

In a recent post, I discussed story tables, mostly in the context of teaching about functions in high school, and as a springboard to discuss priorities in tool selection. I first heard about story tables from Shira Helft, who I believe was the first to appreciate the power of that representation. Today, a conversation with Shira.… Continue reading Story Tables in Middle School

## Asilomar Notes: Story Tables

In my last post, I shared notes from the California Math Council meeting last weekend. I focused on a couple of talks about the use of technology (Asilomar Notes: Tech). Today I write about a different sort of tool, the story table. Shira Helft and Taryn Pritchard’s Asilomar workshop introduced us to this powerful representation of algebraic expressions,… Continue reading Asilomar Notes: Story Tables

## Asilomar Notes: Tech

It is widely agreed among its attendees that the Asilomar meeting of the California Math Council is the best math teacher conference anywhere. Certainly, the setting is beautiful. Over the decades, I have attended some great talks there, and this year was no exception. I will post some notes and reactions here, starting with two tech-oriented talks I… Continue reading Asilomar Notes: Tech

## April Travels, May Webinar, Summer Workshops

I'll be traveling a lot this month. Here's the plan, should you want to say hello.New York City April 5, 4:30pm: I will present Geometric Puzzles at the Museum of Math Teachers’ Circle. Geometric puzzles are accessible to solvers of all ages, but they can also challenge even the most tenacious of solvers. Join math education author… Continue reading April Travels, May Webinar, Summer Workshops

## Puzzles for the Classroom

In my last post, I shared some generalities about puzzle creation. Today, I will zero in on the specifics of creating puzzles for the mathematics classroom. I will do this by way of analyzing some examples. Multiple PathsA characteristic of all classrooms is that they are constituted of students whose backgrounds and talents vary widely. … Continue reading Puzzles for the Classroom

## Calculation

Many students have weak arithmetic skills. Many teachers blame this on calculator use, but it is just as likely that the real reason lies elsewhere. For one thing, the teaching of arithmetic traditionally does not involve developing any understanding, so the learning is shallow and fragile. For another, students correctly feel that mindless arithmetic is… Continue reading Calculation

## Comparing two approaches

Much can be said in defense of practice exercises, but when all is said and done, very few students develop deep understanding from routine practice. For example, compare these two approaches to the area of a trapezoid. Approach 1The teacher says: ”The area of a trapezoid is given by the formula h(b1+b2)/2, where h is… Continue reading Comparing two approaches

## Algebra Manipulatives

A middle school teacher writes: Just a little note and question about Lab Gear. I have been having so much fun with my students using Lab Gear again this year. The 3D-ness of it totally blows the other (cheaper) algebra tiles that I used last year out of the water! I have heard this often… Continue reading Algebra Manipulatives