Probability by Surprise: The Pleasure of Paradoxes
The main idea of the project, "Probability by Surprise: Teaching with Paradoxes," is to unify the presentation of probability to a heterogenous audience through the interest we have in things that surprise us. Some examples we use in our probability classes include: 'the birthday problem,' 'say red,' 'russian roulette,' 'de Mere's problem,' and 'Monty Hall.' The tools developed are based on discoveries by cognitive pyschologists (in particular Tversky and Kanneman) over the last 20 years, that have not, as yet, been used in teaching probability in this country. The programs include simulation programs to give students a feel for probability, animated scenarios to help motivate and amuse them, as well as to make the material more memorable. The audience of high school teachers with no training in probability is especially adressed, with all the class notes complementary to the applets available online. The project weaves together an "Introduction to Probability" web-site including: - links to useful existing calculus material such as explanations of integration and summing rules. - interactive Venn diagrams, probability trees, densities as limits of histograms. - Relevant graphical animations written in java. - Historical material about probabilty. - Animations and simulations developed specifically. - Lists of team oriented project ideas that enable the students to try out their new computer simulation skills and compare these results to those of classical probabilistic analyses. All the material can be found here.