I want to tell you a story. Everyone likes a story, right? But at the heart of my story lies a confession that I am afraid will shock many readers. People assume that because I teach math, blog about math, give advice about math on internet forums, and present workshops about teaching math — because I do all this, I must be good at math.
Apply logic to that statement. The conclusion simply isn’t valid. …
Update: This post has moved.
One more quote from W. W. Sawyer’s Mathematician’s Delight before I have to return the book to the library:
If you cannot see what the exact speed is, begin to ask questions. Silly ones are the best to begin with. Is the speed a million miles an hour? Or one inch a century? Somewhere between these limits. Good. We now know something about the speed. Begin to bring the limits in, and see how close together they can be brought. Study your own methods of thought. How do you know that the speed is less than a million miles an hour? What method, in fact, are you unconsciously using to estimate speed? Can this method be applied to get closer estimates?
You know what speed is. You would not believe a man who claimed to walk at 5 miles an hour, but took 3 hours to walk 6 miles. You have only to apply the same common sense to stones rolling down hillsides, and the calculus is at your command.
If you’d like to start your week with a laugh, here’s a great quote:
Today I said to the calculus students, “I know, you’re looking at this series and you don’t see what I’m warning you about. You look and it and you think, ‘I trust this series. I would take candy from this series. I would get in a car with this series.’ But I’m going to warn you, this series is out to get you. Always remember: The harmonic series diverges. Never forget it.”
—Rudbeckia Hirta
Learning Curves Blog: The Harmonic Series
quoting Alexandre Borovik
[Rescued from my old blog.]
Eldest dd had her first calculus lesson last night: derivatives. The teacher found the speed of a car at a given point by using the distance function, calculating the average speed over shorter and shorter time intervals. Dd summarized the lesson for me:
“If you want to divide by zero, you have to sneak up on it from behind.”
Of course, she understands you can’t really divide by zero, but I thought her tongue-in-cheek comment was a pretty good description of the process of finding the limit as delta-t approached zero.
[Rescued from my old blog.]
Rudbeckia Hirta over at Learning Curves submits a great idea for a new TV blockbuster:
I’ve read that Charlotte Mason used oral exams like this with her students, though of course without the pressure and sarcastic comments. I’d love to hear how this works in “real life.”
Denise Gaskins' Let's Play Math 