Today, I share some materials not from my website — though not unrelated! Robert Wirtz As a young elementary school teacher and math specialist in the 1970’s I came across Robert Wirtz’s materials, and was inspired by them. Here is an example, the one I call “Wirtz’s flags": The idea is to draw vertical lines,… Continue reading Seen Elsewhere

# Tag: Arithmetic

## Fraction Rectangles

This is a sequel to my last post (Seeing is Believing?), addressing the same issue from a different point of view. Fractions, of course, are difficult. When teaching 4th and 5th grade in the 1970's I struggled with this, and came up with a powerful learning tool: fraction rectangles. The idea is that it is… Continue reading Fraction Rectangles

## Teaching the Distributive Property

A guest post by Rachel Chou I have been a classroom mathematics teacher for 20 years. I have heard students use the phrase “the distributive property” more times than I can count. Many of them misunderstand what “the distributive property” even is. But maybe I think that because I don’t really know what “the distributive property”… Continue reading Teaching the Distributive Property

## 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

## Vocabulary

In my last post, I offered guidelines for sequencing math curriculum. The response I got on Twitter (and in one comment to the post) was quite positive. However, one point I made triggered some disagreement:Start with definitions? No! Most students find it difficult to understand a definition for something they have no experience with. It is more effective to start… Continue reading Vocabulary

## 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

## More Notes from NCTM Phoenix

See Part 1 of my notes from Phoenix: A Brief History of Math Education (NCTM President Matt Larson's presentation.)Here is Part 2.Growth Mindset: telling is not teachingIn his short session, Dylan Kane pointed out that talking about growth mindset may be helpful to students "in the middle". But there are students in our classes who… Continue reading More Notes from NCTM Phoenix

## Partitions

In this post, I will outline my approach to this partition problem:How many ways can you write a positive integer n as a sum of three or fewer positive integers? Partitions are a standard topic in number theory, but I will limit myself to this specific question. I started trying to figure it out after… Continue reading Partitions

## Fractions

I have a new Fractions mini-home page, with links to three pages on my site. In this post, I'll use it as an excuse to discuss some general ideas about teaching.Visual RepresentationsIn my Fraction Arithmetic page, I present a visual strategy for figuring out how to add, subtract, and multiply fractions. (There is also a… Continue reading Fractions