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

# Tag: Arithmetic

## 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

## Animated Demonstrations

New on my Web site:→ Animated slides on the Lab Gear model for signed number arithmetic.Note that for each operation, the model is based on what students already know. For addition, you put down the first number, then the second number, and finally count. For subtraction, you put down the first number, take away the… Continue reading Animated Demonstrations

## Integer Sequences

Last winter, I attended an interesting meeting of mathematicians and math educators in Banff, Canada. Our charge was to compile a list of integer sequences that would offer suitable problems for students (and teachers) at each level from Kindergarten to 12th grade. It was a sequel to 2014's Unsolved K-12 meeting, and once again was… Continue reading Integer Sequences

## Geoboard Triangles

One way to discover or apply the formula for the area of a triangle is to explore area on the geoboard. The initial activities should be along the lines suggested in my Geometry Labs Lab 8.4. (Free download.)After that, one can zero in on triangles, by asking a question like: "Find triangles of area 15."… Continue reading Geoboard Triangles