Once a week I dedicate a period of our math study to looking at famous stories, paradoxes, inquiries and problems that real mathematicians have gone through in the past. I approach it through the following general outline;
- Recreate the historical story, understand who the players were and define the problem
- Have the students attempt to work through the problem and come to their own conclusion on the outcome
- Show the students how the actual mathematician solved the puzzle, and compare it to their own solution
- Connect the concept studied to the larger picture of the history of math, society and how it shaped life and knowledge
So far, we have looked at the following problems this year;
- The Case of the Lady Drinking Tea - Dr Ronald Fisher is at a party and serves a lady a cup of tea, however she declines and says she prefers her tea with the milk added first, not second. He does a scientific test to see if she can actually tell the difference. The results of that test are the foundations of statistical methods (1925).
- Pascal and Fermat and the Coin Flipping Game (The Problem of Points) - the two mathematicians are playing a coin flipping game (flip a coin, winner gets a point, first to ten points wins) in a Paris cafe when Pascal gets called away for an emergency. The score was 8-7 at the time. Fermat works out a fair solution as to how they should divide the pot and who wins. The solution he comes up with are the foundations of modern probability (17th century).
- Eratosthenes - measures the circumference of the Earth in ancient Greece, using sections of a circle, distance and angle.
- Seven Bridges of Konigsberg - There are seven bridges in the city of Konigsberg, Prussia, and Eulid tried to work out to walk through the city and cross each bridge once and only once. The solution to this problem led to the foundations of graph theory and prefigured the idea of topology (1735)
This is what I have so far, and I have a few more in the pipeline, but am hoping that I can continue these lessons all year long (the kids love them and they are great mathematical problem solving inquiries), but I am afraid I will run out of ideas. There are tons of these problems out there, but I need help finding them.
Any advice for more?
- PS – I am in the process of creating PDF files for teachers to use, and once I get to it (its on my list of things to do) I will post them here for you to use.
- PSS – Bear in mind that I teach Elementary grade 5-6!