Euler’s Identity has been called “the most beautiful equation” in mathematics. It neatly encapsulates five key values and three operators into a true equation: \[e^{\pi i} – 1 = 0\] But why is it true? In this entry, I’m going to take it apart. Fully understanding the equation involves looking at various parts of algebra…
Author: Clio
Man Caves and Toxic Masculinity
I’ve said it before, I’ll say it again: Not all masculinity is toxic. I’ve been seeing a lot of men suggesting that manhood is under attack. That everything to do with men is considered toxic. That the only “non-toxic” form of manhood is some sort of feminized masculinity, stripped of everything that traditionally made men,…
The Natural Base \(e\): Thoughts on Teaching
In “Burn Math Class”, Jason Wilkes spends quite a few pages deriving the value of \(e\). I did not notice him at any point mentioning compound interest. Since we’re currently wrapping up the chapter on exponential functions and logarithms in the Algebra II classes I’m teaching, I was already thinking about the best way to…
Two Shootings, Two Standards
On March 7, 2018, a student at Huffman High School in Birmingham, AL, fired a gun, killing a girl and injuring himself. On March 20, 2018, a student at Great Mills High School in Lexington Park, MD, fired a gun, killing a girl and injuring another student. He was killed in the incident. We can,…
The Problem with Problems
I’m currently reading “Burn Math Class,” and it’s got me thinking about language. Yesterday, I saw an item about teaching students why cancelling works in this case: \[5 + 3 – 3\] but not in this case: \[5 + 3 = 5 – 3\] The conclusion that the students were led to is that the…
Why “Not All Men” is a Poor Response
“Not all men.” There was a time, years ago, when I used to start many responses with those three words. “Men commit rape.”: “Not all men.” “Men are violent.”: “Not all men.” “Men hide their feelings.”: “Not all men.” This is a defensive response that refocuses the discussion. It’s also highly patronizing: Few people who…
Some Thoughts on Teaching Mathematics
This morning, I was reading the NCTM blog, and the subject was on students struggling with systems of linear inequalities. First, as background: I don’t have any difficulty with systems of linear inequalities, and I don’t remember ever being taught such things (although I may have, I just don’t remember). But then I get two…
Not All Masculinity is Toxic
As the term “toxic masculinity” gets more widespread, I see more people complain about it. The interpretation is that the term implies that all men are toxic. In reality, it does exactly the opposite. To see why, I need to give a brief grammar lesson. First, I’ll talk about restrictive vs non-restrictive clauses. Then I’ll…
Attacking the Roots of White Male Entitlement
In 1992, two white Detroit police officers assaulted Malice Green, a black man. He died after the assault, and while he did have drugs in his system, the courts decided that the brutal assault by the officers was what led to his death. They were sentenced to multiple years in prison. Twenty years later, in…
It’s Time to Retire the “Good Guy” Narrative
“The only thing that stops a bad guy with a gun,” we are told repeatedly, “is a good guy with a gun.” On Thursday, March 1, 2018, a high school teacher in Georgia named Randal Davidson showed up for work. He was by all accounts a good guy: The principal characterized him as a “very…