# Abstract Unit

## What is Multiplication, Anyway?

Yet again, the internet has seized upon an elementary student’s math homework and has decided to argue about Common Core. This time, it’s about a test question. The student was asked to “Use the repeated addition strategy to solve :…

## Types of Numbers

Elementary school students spend most of their time working with counting numbers, that is, the non-negative integers. As students progress through secondary school, they work increasingly with non-integers, eventually entering the complex number plane. However, many of them maintain the…

## Improper vs Mixed Fractions: A Six-Year-Old’s Perspective

I often discuss mathematics with my six-year-old son. As a teacher, my goal is to try to pinpoint where it is that student understandings go astray. As a parent, my goal is to teach my son some mathematics. We’ve discussed…

## Milne: “Are” vs “Is”

I noted in an earlier post that in 1893, Milne used “are” as a casual speech reading of the equality sign, rather than the “is” that I’m used to. Adam Liss notes that “are” is also used in Danny Kaye’s…

It is the habit among mathematics teachers, particularly at the elementary level, to present multiplication as repeated addition. The inimitable Keith Devlin, among others, has ranted about this, but it’s easy enough to see the temptation. When dealing with integers, multiplication…

## Ratios vs Fractions

Several middle school math teachers have told me that there’s an important distinction between fractions and ratios that students don’t get. When I ask them what it is, the teachers can’t tell me; “it’s complicated”, they say. I’ve been troubled…

## White and Blue Elephants

First, a riddle… Q. How do you shoot a white elephant? A. With a white elephant gun. Q. How do you shoot a blue elephant? A. Paint him white, then shoot him with a white elephant gun. Back to Units…

## Pizza Math

This gem is timely to my thinking about ratios and units:   It seems to have situated itself broadly enough across the Internet that I don’t know if it’s real or a fabrication, but it seems plausible enough. There are,…