I recently read John Derbyshire’s book, Unknown Quantity: A Real and Imaginary History of Algebra (Plume 2007 edition). I recommend it overall, although the second half becomes increasingly inaccessible to the layperson. One bit that particular stuck in my head, because of the way it caused me to rethink a mathematical concept, was this passage…
Category: Mathematics
The Prefix Dia-
A good teacher is always aware that there are things they can learn. One of the ways in which I encourage students to connect mathematics to other topics is by showing how words and morphemes used in mathematics are used elsewhere. For instance, “median” in mathematics refers to a number in the middle of a…
PEMDAS and negative numbers
By standard mathematical convention, \(-1^2=-1\). At the same time, students are taught to refer to \(-1\) as a negative number. A friend recently led me to realize that these two conventions are at logical odds with each other, as discussed below. Furthermore, while the first convention is generally taught in high school, the mathematical argument…
Well… is algebra necessary?
Except for the final grades, I’ve just wrapped up teaching six weeks of credit recovery for Freshman Algebra. It’s tough enough packing nine months’ of material into six weeks, but consider these are the students who didn’t do well enough the first time to get a passing grade (in this case, a C or higher),…
Trick question memes
From time to time, a mathematical question of some sort will make its rounds on Facebook and other social media platforms. For instance, the one making the rounds most recently in my portion of the blogosphere was: \[5 + 5 + 5 – 5 + 5 + 5 – 5 + 5 \cdot 0 =…
Introduction and purpose
As of this summer, the summer of 2012, I am qualified to teach mathematics at the high school level in the state of Michigan. I am expecting to be doing so full-time this fall. I am also qualified to teach English, but so far my major focus has been on mathematics, and that’s also the focus…
“Yeah, I know that.”
This morning, I was directed to an online vocabulary test that claimed to be able to estimate one’s vocabulary. I did take the test, but I also spotted several problems with it: It’s self-selecting. That means that people who value high vocabularies are more likely to take it, and are more likely to pass it…