I saw a tweet this morning from Patrick Honner pointing to a blog post asking how you might teach derivatives of sines and cosines differently. One thing I think deserves more emphasis is that “co” in cosine etc. stands for…
Blog Archives
Dual polyhedra for kids
Here are a dodecahedron (left) and icosahedron (right) made from Zometool pieces. These figures are duals of each other: If you put a vertex in the middle of each face of one of the shapes, and connect all the new…
How long will there be computer science departments?
The first computer scientists resided in math departments. When universities began to form computer science departments, there was some discussion over how long computer science departments would exist. Some thought that after a few years, computer science departments would have…
How long can you think about a problem?
The main difficulty I’ve seen in tutoring math is that many students panic if they don’t see what to do within five seconds of reading a problem, maybe two seconds for some. A good high school math student may be…
Crayons to Computers
I saw a daycare named “Crayons to Computers” recently. I assume the implication is that crayons are basic and computers are advanced. Programming a computer is more advanced than writing with crayons, but surely their clients don’t learn to program…
Easiest and hardest classes to teach
I’ve taught a variety of math classes, and statistics has been the hardest to teach. The thing I find most challenging is coming up with homework problems. Most exercises are either blatantly artificial or extremely tedious. It’s hard to find…
Tagged with: Differential equations, Education, Probability and Statistics
Posted in Math, Statistics
Posted in Math, Statistics
It's not what you cover
Walter Lewin on teaching physics: What counts, I found, is not what you cover but what you uncover. Covering subjects in a class can be a boring exercise, and students feel it. Uncovering the laws of physics and making them…
What do colleges sell?
Universities are starting to give away their content online, while they still charge tens of thousands of dollars a year to attend. Just what are they selling? Credentials, accountability, and feedback. Some people are asking why go to college when…
Educational monoculture
I ran across the term “educational monoculture” this weekend. What a great phrase! Rather than write a long post, I’ll restrain myself and simply say that I’d like to hear more people talk about “educational monoculture.” Related post: Don’t standardize…
Cartoon guide to the uninteresting
If you’re not interested in a subject, do cartoons make it more palatable? My guess is that cartoons may help keep your attention if you’re moderately interested in a subject. If you’re fascinated by something, cartoons get in the way.…
When are we ever going to use this?
“When are we ever going to use this?” What a great question! This is a teachable moment. Too bad most teachers blow it. Instead of seizing the opportunity, they reprimand the student for asking. At least that was my experience.…
Useful education
“Of course, education has always aimed to be useful. The question has been, and continues to be, useful to what end?” — Richard Gamble
Demonstrating persistence
“A college degree shows you can finish something.” I’ve heard this forever, but I don’t believe it. Of course a college degree shows that someone finished one thing, namely a college degree. But I don’t think that’s the best predictor…
Advanced or just obscure?
Sometimes it’s clear what’s meant by one topic being more advanced than another. For example, algebra is more advanced than arithmetic because you need to know arithmetic before you can do algebra. If you can’t learn A until you’ve learned…
Teaching Bayesian stats backward
Most presentations of Bayesian statistics I’ve seen start with elementary examples of Bayes’ Theorem. And most of these use the canonical example of testing for rare diseases. But the connection between these examples and Bayesian statistics is not obvious at…
