kitchen table math, the sequel: 2/6/11 - 2/13/11

Wednesday, February 9, 2011

AMC 10 Sample Question

Three children have a foot race in which the leader after 1 minute is declared the winner. Each child runs at a constant speed. At the end of the minute, Alicia has run 720 feet. Ben, who started 40 feet in front of Alicia, has run 600 feet from his starting point. Cheryl, who started 40 feet in front of Ben, has run 400 feet from her starting point. For how many seconds during the race was Ben in the lead?

A) 8
B) 10
C) 12
D) 15
E) 20

How would you tackle this using rote knowledge or memorization? What conceptual understanding is enough to solve this problem? Draw a picture? Work backwards? If you could solve this problem in the allocated 3 minutes rather than 20, what would that mean? What do you do to get to the point where you can solve virtually any D=RT problem quickly? Is that done with some sort of better conceptual understanding? Is speed meaningless? At what point, if ever, does it become meaningless? What happens when you practice? Is that just about speed? Is experience just about speed? When you see a new problem for the first time, will you be as slow as the first time you solved a DRT problem?

I think it would be hard to argue that experience and practice just mean speed; that they are not transferable to new problem types. We are told, however, that some sort of vague conceptual understanding is all that you need, even if it takes a long time to solve a problem. So what happens with practice and experience? What is that called? Drill and kill? Either practice matters or it doesn't.

Monday, February 7, 2011

A view from computer science college professors

I hear from a friend who teaches college computer science that many CS educators agree on the following:
  1. There is too much emphasis on calculus, and more focus should be placed on discrete mathematics (graph theory, logic, automata theory, etc) and statistics.
  2. K-12 education places too much emphasis on memorization at the expense of conceptual understanding.  This leaves college students ill-prepared for their computer science course work.

Cross posted at Education Quick Takes