Category: General

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 division before, and I was inspired to explore it again because of some multiplication he’d…

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 1952 movie Hans Christian Andersen. On the other hand, by the early 1960s, the Beatles were using…

Consumer math represents the most immediate and practical response to the student mantra, “When am I ever going to use this?” I was thinking about this yesterday during a late night run to Meijer to get some paper. They had two options: A ream of 500 sheets for $4, or a ream of 750 sheets…

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 and iterated addition will return the same numbers. Historically, it may be the case…

There are a lot of trite websites and apps available for teaching elementary education concepts. And then there are the occasional gems. Zip and Abby, from The Learning Chest, is one of the true gems. The goal of Zip and Abby is not to teach simple “math facts” or to drill on numbers as abstract…

I’ve noticed that the teachers of fractions tend to make a strong distinction between division and ratios, but I haven’t entirely understood why. In my mind, ratios and division are intimately related, even inextricably so. However, my reflections on the abstract unit has brought me to a realization that there is one significant difference between…

Several of my math teacher colleagues are of the opinion that calculators have destroyed math sense. I am not convinced that this is directly true: Calculators are a tool, nothing more. A few months ago, I saw a video by the mythically amazing Vi Hart which led me to an epiphany: Perhaps the problem isn’t…

This is my translation of Lucas’s 1877 proof that a square pyramid of balls will only have a square number of balls if the base side is twenty-four. “Solutions to questions posed in The New Annals: Question 1180.” M. Édouard Lucas, Nouvelles annales de mathématiques. Journal des candidats aux écoles polytechnique et normale, second series,…

I have been spending my free time the last few days on the task of working backwards through three proofs in a 19th century French language mathematics journal. This started with a simple question in the G+ Mathematics community, posted by Jeremy Williams: “Who can find the largest tetrahedral number that is also a square?”…

In an earlier post, I reflected on the relationship between mathematics, language, and computer programming. One detail of that has been on my mind quite a bit lately, as I’ve been teaching geometry. While early computer programming was heavily reliant on a strong knowledge of mathematics, particularly algebra, I think that programming has evolved to…