Category: Pedagogy

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…

A friend of mine, a father, recently posted this item on his Facebook feed. It’s from Pearson, and he was struggling figuring it out. I also had to read it several times to figure it out. (Edit 6/17/23: I lost the original graphic; I located a version that has the answers on it, so ignore…

The first shoe: Multiplying Adding complex numbers is a straightforward task. Given two numbers, \(a + bi\) and \(c + di\), the sum is the sum of the real portion and the sum of the imaginary portion: \((a + c) + (b + d)i\). When working with the standard form, multiplication (and division) is a…

Students often struggle with the concept of multiplying negative numbers, particularly with the notion that multiplying two negative numbers results in a positive. I’ve seen numerous attempts by teachers and teacher educators to explain why, conceptually, it is that the product of two negative numbers is a positive number. However, what if the underlying presupposition…

This is an example of a common sort of story problem encountered in standardized tests: “1. A team of five professionals can do a certain job in nineteen days; a team of nine apprentices can do the same job in the same amount of time. Assuming all professionals work at the same rate and all…

At a recent workshop on collaboration, the other participants and I were presented with a version of this problem: Adam hits 60% of his free throws. He gets fouled just before the buzzer, and his team is down by one point. Based on the rules in play, he can shoot up to twice. If he…

The version of Geometry most widely taught in high schools in the United States is an amalgam of the two most basic fields of geometry: Synthetic and analytic. The mixing of these two is done in such a way as to suggest that the fields are complementary, and so the points of differentiation between the…

The Internet is in a tizzy yet again about the evils of mathematics education. At least Common Core isn’t being demonized quite as front-and-center as in the recent past, but still. This time it’s about pizza. Which means every mathematics educator reading this will know it’s about fractions, because that’s why we ever mention pizza…

In this post, I’ll discuss two issues. First, I’ll look at a problem taken from a major textbook, and explain why the solution is wrong. Then, I’ll discuss why this particular problem bothers me in the greater context of mathematics education. First, the problem. This is a question from Pearson’s Common Core Geometry supplemental materials…

Here’s another meme criticizing the Common Core: The criticism is that the student has provided a fully correct answer and gotten dinged for not providing an estimate. This is, of course, taken as yet another illustration of why Common Core is ruining America’s future. In other cases of Common Core outrage, the problem has been…