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…
Author: Clio
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…
Graphing and the coordinate plane
Dan Meyer’s latest post is on an exercise involving using a gridless coordinate plane to place fruit along two dimensions. The goal is a worthy one: To give students the opportunity to explore what the coordinate plane is without getting tied down by its rigid formalism. However, the nature of the exercise highlights that there are…
Police Racism: A White Man’s Experiences
I still see white people claiming that there’s no systemic racism among police, and that racist police officers are the exception, not the rule. Even though I’m white, I have had multiple experiences with police officers that have had a racial component. From 1989 to 1997, I lived in a poor neighborhood in Lansing, Michigan;…
Can’t
I was in seventh grade, or maybe eighth, when the girl in the fuzzy sweater told me I was cute. I still don’t know why she decided that I was going to be her boyfriend. I was awkward and out of place. I don’t remember ever fitting in, and certainly not with the girl in…
Talking Politics with Students
I was raised to believe that it was best to avoid talking about religion or politics in mixed company. The political environment of the United States has become particularly rocky in recent years, making such discussions a potential powderkeg. The election of Donald Trump, billed as an attempt to bring an end to that divisiveness,…