Common Sense and Calculus

Posted on by Denise Gaskins

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.

2007 Mathematics Game

Posted on by Denise Gaskins

Are your students ready for a challenge?
The Math Forum: 2007 Mathematics Game will be a tricky one:

Use the digits in the year 2007 and the operations +, -, x, ÷, sqrt (square root), ^ (raise to a power), and ! (factorial), along with grouping symbols, to write expressions for the counting numbers 1 through 100.

  • All four digits must be used in the expression.
  • Only the digits 2, 0, 0, 7 may be used.
  • Multi-digit numbers such as 20, 207, or .02 MAY be used this year.
  • The square function may NOT be used.
  • The integer function may NOT be used.

Continue reading 2007 Mathematics Game

Harmonic Series Quotation

Posted on by Denise Gaskins

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

Finding the Limit

Posted on by Denise Gaskins

[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.

So You Think You Know Calculus?

Posted on by Denise Gaskins

[Rescued from my old blog.]

Rudbeckia Hirta over at Learning Curves submits a great idea for a new TV blockbuster:

So You Think You Know Calculus?

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.”

Continue reading So You Think You Know Calculus?