This video and its comments got me thinking about how difficult it really is to read an analog clock: There are multiple comments on TikTok sneering at how inane and unintelligent modern children must be to need more than ten minutes, let alone more than two days, to learn how to read a clock. So…
Category: Mathematics
The Language of Mathematics
Mathematical notation is a language. The study of mathematics is about finding patterns in our universe, but we need a method of communicating those patterns to other people. That’s where notation comes in. Like the languages that we speak, this system of notation did not spring up all at once. It was not the result…
Synthetic Division
Synthetic Division is one of three common techniques for dividing one polynomial by another. The other two are long division and the box method. Of the three methods, students generally prefer synthetic division. It has the advantage of having minimal writing and being strictly algorithmic: Add, multiply, add, multiply…. First, let’s see how it works….
When Am I Ever Going To Use This?
The question is the bane of the math teacher’s existence. It probably comes up in other classes as well, but it seems to be particularly associated with mathematics. Here are two truths (and no lies): From the time I graduated from high school in 1985 to the time I started training to be a math…
Exponents: Language
Our language surrounding exponents is confusing and, I think, misleading. Power An exponential relationship involves three values. Historically, these were called the base, the exponent, and the power. On a logarithmic scale, the base represents the step size, the power represents the target value, and the exponent represents the number of steps. For instance, if…
There Is No Spoon (QF Edition)
As I was nearing the end of my article yesterday, something creeped into my head and lingered in the shadows for a while. This morning, it came into the light. The function that allows us to find the input that corresponds to the output of another function has a name: It’s the inverse function. One…
The Quadratic Formula (Vertex Form)
I really don’t like the quadratic formula. As a teacher, it feels like one of the absolute worst examples of what’s wrong with mathematics education: An arbitrary formula with weird aspects, including what is often the first appearance for students of the plus-minus sign. Sure, we can do algebraic manipulation to show why it is…
Why 0! = 1 (Set Theory Explanation)
I’ve been seeing a few videos lately explaining why 0!=1. Over my time as a teacher, I’ve seen a lot of various explanations for this equality, and they generally fall into these categories: What I don’t recall seeing is a complete explanation from the perspective of set theory, so I’ll provide that in this article….
Rough draft: Thoughts on Sets
I woke up this morning thinking about sets. I recently bought the (Canadian) French, (Mexican) Spanish, and German editions of “Dog Man”. This gave me a set of books in languages I can at least make a real effort to read, and the child already has a set of “Dog Man” books in English. Yesterday…
Scaffolding and Multiplication
There are two basic conceptual ways that multiplication is explained: Repeated addition and the area model. Many people who are adept at multiplication (including teachers) take for granted what many students have trouble connecting; in the case of multiplication, it’s not immediately obvious why repeated addition and the area of a region ought to result…