Here’s a puzzle I just read in Clifford Stoll‘s book High Tech Heretic (paraphrased by me): Consider 12 identical resistors connected to form a cube. That is, each resistor lies on the edge of a cube, and there is an electrical connection joining three resistors at each of the cube’s eight vertices. What is the … Read more
We adults tend to fear making mistakes. We weren’t like that as children; watch any child learn to walk, or learn to ride a skateboard, shoot baseline jumpers over and over, or do just about anything that requires practice. Children keep at it, despite making mistakes repeatedly, because it’s fun. That is, the activity they’ve … Read more
Way back when I was a little high-school student, I recall the pride I felt when working through the nuclear reactor unit of our Grade 11 physics course. The pride derived from the featured CANDU reactor. Wow! Our little Canada somehow produced the best nuclear reactor in the world. How did I know CANDU was … Read more
From Indiscrete Thoughts, by Gian-Carlo Rota: The best introduction to mathematics is not achieved by rigorous presentation. No one can learn calculus, linear algebra, or group theory by reading an axiomatic presentation. What one wishes is a feeling for a piece of mathematics. Let the student work with unrigorous concepts that lead as quickly as … Read more
“A weed is a plant whose virtues have not yet been discovered,” said Ralph Waldo Emerson. This is a profound observation about judgements and the role of words in conveying judgements. Nowadays, with our quite extensive knowledge of plants and their benefits, we persist in calling quite useful plants weeds just because we don’t want … Read more
In teaching mathematics for many years, one of the things I emphasized over and over again was that students should memorize the absolute minimum necessary, and then I did my best to make explicit what this absolute minimum is. It is better, I explained, to spend time solving problems, discussing applications, “reading around the subject,” … Read more
A friend sent me this link to a New York Times article on improving lectures in university physics classrooms. A Toronto Star article based on the same research (led by University of British Columbia Nobel laureate Carl Wieman) is here. I would not be surprised if, after further testing, Wieman’s methods prove to be an … Read more
Jonah Lehrer, writing last month in the Wall Street Journal, makes the point that the kind of high-stakes testing popular in education is not very useful. He gives the example of supermarket cashiers who were given brief time trials to see how fast they worked. Careful analysis of electronic scanning records (for which cashiers did … Read more
This is a famous old problem. I shall just state the problem here for you, and will follow up in a day or two with a solution and some of its amusing history. Update: Scroll down for a straightforward solution and a “trick” solution. There are also, by now, various generalizations and different versions. Here’s … Read more
Our region experienced very strong winds recently, and there was significant damage, with lots of trees uprooted or snapped, fences flattened, and roof shingles blown off. My in-laws had a chimney topple, thanks in part to an old-style TV antenna attached to it. So my father-in-law, my son, and I spent much of this past … Read more