Jeopardy and Probability

posted in: Blog, CV STEM 2015 | 0

Michael Leventhal, Chief Nerdy Development Officer

July 21, 2015

We start each week of the Colonie de Vacances with something we call “Teach Back”; a review of the previous week’s lessons. The students actively demonstrate their understanding of the material, reinforcing what they have learned. This week took the form of a game of Jeopardy where teams of students selected questions at augmenting values in iNERDE’s core categories of Science, Technology, Engineering, and Mathematics and a fifth having to do life goals, social responsibility, and the overall role of STEM in society. The game format was great, fun and motivational … once the students understood it. None of them had ever seen the game of Jeopardy before and it took them some time to get it. There is a surprising amount of cultural information embedded in the structure of the game. The player strategy is also complex, requiring some sense of how to assess the probability of having the right answer against the value of question against one’s position in relation to the other teams. The great thing about the game format is that the students absorb its complex principles bit by bit, simply by seeking to improve the outcome. Each question is like a mini-experiment; one sees the result, whether positive or negative, and adjusts their strategy for the next round, eventually absorbing the principles that lead to an optimum result.

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Our game of Jeopardy led to an impromptu lesson the next day on basic probability. We began simply with flipping a coin to convey the idea of equal probability and the random nature in a single instance of the coin falling on heads or tails. The kids gathering in a circle around me, excitedly yelling their guesses for each coin flip; we must have looked like an impromptu back-alley craps game. We then recorded the result for ten coin flips and verified that while one could have the same side of the coin appear on multiple experiments, after enough experiments the result arrives, as it happened, at exactly 50-50. I added a second coin and we discussed the probability of each combination of coins. Pas evident! (Not obvious) I showed that in enumerating the possible outcomes one could easily see the probability of each: heads-heads, heads-tails, tails-heads, and tails-tails each being one possibility of a total of four, if one didn’t consider heads-tails or tails-heads there are 2 possibilities out of 4 and so on. The main objective was to enable the students to grasp the idea of approximating the probability and being able to select the most probable outcome. To reinforce that we did one final exercise. We took several die and colored different number of sides one color or another. The objective was for the students to make a rough calculation if the probability was more or less for each combination of colors.

Finally, I wanted to make a combination between randomness, probability and our studies in computer science. I gave the example of a video game where the programmer must make decide how to make a character move and act. I explained that the software does the equivalent of a coin flip, or in the case where one wants one thing sometimes but something else more often, it is like using the die with an uneven distribution of colors.

I think these lessons gave the students the beginning of thinking in a mathematically precise way, and how mathematical thinking can be applied in every day life. The lessons were very exciting because they were delivered in the forms of games, with the opportunity for each student to form and express a theory about the possible outcomes and to see if their theory worked. And if we do not succeed in forming excellent future computer scientists (the probability is extremely high), our iNERDE students may become successful gamblers (the probability of that is very, very low).