Tag: CW Math
-
[mathjax]I’m going to build a simple set of functions. This set will wind up being very familiar when I’m done, but let’s pretend for a few minutes first. Function and Operators In case you’ve forgotten what a mathematical function is, there are a few quick ways to refresh your memory. A common way is to…
-
[mathjax]I’m currently reading selected parts of “Analytical Institutions”, the 1801 edition of John Colson’s translation of Maria Gaetana Agnesi’s 1748 text. Near the beginning of her second book, she presents the following theorem. Consider the diagrams: In each diagram, H, I, and M are points along the x-axis and are equally spaced. A, B, and E…
-
Another Rant on “Mathematical” Puzzles A few months ago, I complained about those internet memes which claim to be mathematics. My complaint about them is about the presentation, not the underlying problems: “Only 1% of people get this right!” The questions are framed to encourage people to feel stupid about math. Please don’t feel stupid about math.…
-
We obscure the beauty of mathematics when we jump straight to the end. The last few weeks, for our virtual, quarantine edition of Algebra II, we’ve been exploring the unit circle. I’ve been trying to wrap my mind around how to describe the way I see too many mathematical concepts introduced, with a standard presentation…
-
One word is being scapegoated for student misunderstanding. [mathjax]A recent trend in mathematics education is the idea that we should never, ever say the word “cancel”. The argument for the prosecution is reasonable, and I will lay it out first. But I think the problem isn’t the word itself, but rather how we approach language…
-
A tale of carts and horses. [mathjax]My child is in fifth grade. Last Friday, we received the second volume of his mathematics workbook. It starts with multiplication of fractions; the next chapter is division of fractions. Addition (and subtraction) of fractions with different denominators is in the first volume. I believe this order persists partly…
-
Mathematics isn’t about finding answers. It’s about asking questions. As a mathematician, here’s a question I usually find boring: What’s the answer? Consider this manifestation of a sort of meme that wanders the internet: [mathjax]The most likely intended answer is 73, just to get that out of the way. I’ll call this “Witch”. This is…
-
[mathjax]This is one of the most common mistakes students make when adding fractions: \[\frac34 + \frac67=\frac9{11}\] For a long time, I thought that students did this solely based on confusion with multiplication. While we teach addition of integers before multiplication, addition of fractions is a more complicated process. To multiply fractions, multiply the numerators and…
-
[mathjax]I teach two sections of Honors Algebra II and two sections of Algebra II. Today, I introduced the concept of finding roots of rational functions. I did this with a discovery-based task. The student response to the task contained a lot of learning for me, and not just in the form of what they wrote…
-
Mathematics is beautiful. Mathematical notation, meanwhile, is a horrid mess second only to English itself for its arbitrariness. For instance, basic arithmetic operators have three levels: Addition, Multiplication, and Exponentiation. Addition notation is tidy: We add forward (a + b) or backward (a – b). We call these “addition” and “subtraction” for historical reasons, but…