As I write this, it’s Father’s Day. I wish a Happy Father’s Day to every decent person who identifies as a father figure in somebody’s life, be it as a parent, a teacher, a mentor, or a caregiver. This article is dedicated to you. This is the ninth Father’s Day I have been a fatherless…
Author: Clio
Geometry for multiplication, division, and roots
Contemporary plane geometry of the sort taught in the standard American high school is most heavily informed by two books and a third mathematician. The first of these is Euclid’s Elements, which is so conceptually tied to planar geometry that it is typically referred to as Euclidean geometry. However, it is only part of the…
Factoring and long division
This morning, I’ve been watching YouTube videos. I started with Tarleen Kaur’s video on Middle Term Splitting. What I find interesting about Kaur’s Chapter to Chapter videos is that, because she’s a student in India, her methods are often different from those I’m familiar with. That’s the case in this video as well. I haven’t…
Positive numbers and absolute value
They say that when you’re a hammer, everything looks like a nail. Since I’m currently thinking about conceptual vs procedural teaching, I’m noticing examples. Here’s a good definition of absolute value: “the magnitude of a real number without regard to its sign; the actual magnitude of a numerical value or measurement, irrespective of its relation…
The smallest angle
I have been thinking about procedural vs conceptual thinking, which Skemp’s seminal article refers to as relational vs instructional. One of the questions on this year’s geometry final asks: Given a triangle ABC with sides AB = 5, BC = 6, and AC = 7, what is the smallest angle? (Edit for clarity: The question is simply…
Bill Maher: Typical White Male Liberal
On Friday’s episode of Real Time, Bill Maher provided a clinic on some of the worst white male verbal behaviors, and in how not to take full responsibility. In two segments, he illustrated deflection, microaggression, defensiveness, gaslighting, and tone-deafness. This was in the form of an apology. On the previous episode, Maher referred to himself…
A Writer
A writer writes: That’s what writers do If you’re writing something, then you’re a writer too Whether it’s a fiction, biography, or poem Or just a love note meant for a partner back at home Sometimes we overthink things, and sink inside our gloom That to be a proper writer, we’re locked inside a room…
Concepts vs procedures
A persistent topic in mathematics education is whether to focus on conceptual or procedural knowledge. After reading Kris Boulton’s recent post that argues, “It depends,” I found myself thinking about the disconnect between arithmetic and algebra. What is needed to understand algebra? The first leap that students need to be able to make is from the…
Triangular Gaps
There is an unfortunate gap in the triangle congruency theorems. It would be nice to be able to say that we can declare that two triangles are congruent based on a pair of sides and exactly two other bits of information, but we cannot. If we can match up all three pairs of sides as…
Moving From Shock to Resolve
Author’s Note: There are a lot of links in this article, many of which are from black voices. Particularly if you are white, I encourage you to read those articles and strive to understand their perspectives. The links are set up to open in a new window. In my previous article, I wrote about a handful…