A locus (plural loci) is a set of all the points that satisfy a particularly mathematical statement or rule. Such statements or rules can contain any number of distinct variables, but we can only easily graphically represent statements with two or three distinct variables. If a statement contains only one distinct variable, the graph of…
Author: Clio
How to Read a Clock
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…
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….
How Are You?
This TikTok got me thinking: I see a lot said and written about how Neurotypical people usually ask “How are you?” as part of a script, and don’t particularly care for an honest and complete answer. I figured that out myself a long time ago, and have had many conversations with strangers that consist of:…
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…
Interest Convergence and TERFs
This TikTok makes a point that deserves more oxygen: While TERFs engage in transphobic rhetoric and indeed act out of bigotry by equating trans women with men, they can at least reasonably argue that their primary goal is defending cis women from the threat of SA and other violence by men. The point of disagreement…