Wednesday, May 16, 2007

BayWatch Part 2

From the previous episode on "Baywatch" (see previous post), you realise after you reach the swimmer at A, you realise there is another swimmer who is drowning at B. As a life guard, you can only bring the swimmer at A to shore at some point C so that he can be attended by paramedics, before you can swim towards B. This is illustrated by the diagram below.

Where should point C be in order for you to reach the other swimmer at B in the shortest length of time? Assume you swim at a constant speed throughout course of action.


Have you ever watched Baywatch? It features David Hasselhoff and Pamela Anderson, 2 life guards at a Miami beach. Imagine you are one of the life guards at point A on the beach (shown below), and a swimmer needs your help at point B. How would you reach the swimmer?

There are obviously 2 choices:
1) Take the shortest distance between A and B. Just run straight and swim straight towards B
2) Run at an angle before swimming perpendicular to the shoreline. This ensures that you swim the least.

Note that you can run faster on land than you can swim in the water.
Which way would you take? Is there a faster way?

Thursday, May 03, 2007

Skill mastery v.s. Conceptual approach

We all learn arithmetic in Primary school using the standard multiplication and division algorithms. NTCM has reformed their curriculum using 8 Focal points (see previous post) to develop mastery of these skills by the 5th grade. However, there are many books which focus on problem solving rather than skill mastery. The video below shows out two reference books for elementary school show alternate approaches to arithmetic, namely multiplication and division.

Math Education: An Inconvenient Truth

A very informative video of different approaches and techniques to solve the same problem. Ultimately, this is a question of efficiency vs understanding. Stay tuned till the end of the video for a surprise.