Tag: CW Math
-
This is making its internet rounds again: These days, I see it in math teacher forums clucking about our colleagues. There is often a microaggressive wink-wink against elementary school teachers or misogynistic pronoun use where the brilliant student is “he” and the teacher is “she”. First, as a real thing that a real teacher wrote…
-
[mathjax]Teaching students how to add fractions can be a real struggle. A big part of this is that we tend to get conceptually complicated about what fractions are. And a big part of this is because fractions can be conceptually complicated. I teach Algebra II. (For an elementary teachers reading this, though, hold on: I’m not…
-
I’m going to talk about logs here. I have more to say later, but this is a basic intro sketch. First I’m going to talk about the stuff of elementary school. When it comes to mathematics, most people find comfort in elementary school mathematics. So, consider the humble number line: We want to move along…
-
[mathjax]Mathematical terminology and notation through a linguistic lens Introduction The first time I attended graduate school was for Linguistics. My first year, I taught English as a Second Language. My most resistant students were Mathematics majors, because many of them held the opinion that mathematics is a universal language. Why bother getting fluent in English?…
-
[mathjax]Consider the following task: \[1.\quad \text{Simplify the expression }\frac{3}{4}\div\frac{2}{5}.\] It is very common for students to struggle with this sort of task. A common teaching approach is “Keep Change Flip,” but too often that’s presented as a mechanical trick without any deeper understanding of why it works. In proper mathematical language, “Keep Change Flip” translates…
-
[mathjax]This is a common criticism of Common Core (CCSS): It offers these strange new methods that students must use. Except… only the first part of that is true. CCSS does offers some new strategies, but it doesn’t say that students have to use them. This article isn’t a defense of CCSS, by the way. It’s…
-
[mathjax]When I was in school, I was taught the Quadratic Formula. I was taught that it was the most efficient, more reliable way to find the roots of a quadratic function. This is what I was taught: Given a function in Standard Form, \(ax^2+bx+c\), its roots can be found by evaluating \(\frac{-b\pm\sqrt{b^2-4ac}}{2a}\). I was instructed…
-
[mathjax]I have taught high school mathematics for nearly a decade. I have a BS in Mathematics. The Algebra II curriculum, which I largely built for my school, is based on “the story of functions”. And yet, it was only the other day that I noticed something that was woefully wrong about the way that I’ve…
-
[mathjax]I’ll keep this one short. Also, it’s on calculus, for whatever that’s worth. The Power Rule for Differentiation says that the derivative of a monomial \(ax^b\) is \(abx^{b-1}\). Last night I noticed a way to derive this for positive integers that I believe I’ve seen before (so I’m not claiming originality), but which is different…
-
Don’t get caught up on the concept of “fractions”. [mathjax]There is one topic students of mathematics consistently struggle with, to the point that it has become legendary: Fractions. I teach Algebra II. Fractions don’t exist. I’m not saying, of course, that \(\frac12\) and \(\frac5{31}\) aren’t things that might occur. I mean that I encourage students…