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…
Author: Clio
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…
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….
Language and Miscommunication
Consider this dialogue, not uncommon on today’s social media: A: “Cis is a slur!” B: “It is NOT, you’re such a transphobe.” A: “What? I don’t fear trans people.” While there is a high likelihood that person A in this conversation has unfairly negative beliefs about transgender people, there are also several points in this…
09/28 – Seeing What Was
I was thinking this morning about two different issues in my life right now, and both of them coalesced around: When you only see what is, not what was, you’re only seeing part of the picture. Let’s start with Henry Ford, who is credited with creating the 40-hour work weeks. I’ve been seeing memes booing…
09/27 (Ceci n’est pas une pipe)
This post is not about a computer. Last year, I bought a new laptop. It had occasional problems charging, but nothing major. Then, over a month ago and outside its warranty window, the battery completely drained while charging and would not register the charger. I researched online, and was told that sometimes the Microsoft-proprietary charging…
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…