aumann by blackboard 88.
(photo credit: )
This past week newspapers worldwide carried the smiling faces of Robert Aumann (Israel) and his family at the 2005 Nobel Prize ceremonies. It was a great moment for Jewish pride. This week, rather than filing that proud moment in the annals of Jewish history, we must seize Aumann's achievement as an opportunity to inspire and educate our children.
Educators and parents in Israel and worldwide complain about math education, and rightly so. Aumann's prize presents an opportunity to take action.
Studies emphasize the effectiveness of teaching math in real-world context. Elementary-school math textbooks in Israel have begun to focus on concepts. Some new Israeli math textbooks for grades seven to nine also emphasize understanding over memorizing, but they are not widely used. In high school, the testpreparation mentality, focused on the math matriculation exam (bagrut), limits any efforts in this direction.
Students need a certain level of technical proficiency, but teaching formulas devoid of meaning or application leaves students uninterested and tuned-out. What's more, they soon forget the techniques they learned. How many people remember the quadratic formula? How many ever knew that it is used to answer questions about the path of a baseball or a ballistic missile? WHAT DOES Robert Aumann's Nobel Prize have to do with this? A lot, actually. Aumann received the award for his work in game theory; this subject presents an excellent opportunity to inject a little meaning into math class. Let's see how.
The word "game" brings to mind chess, video games, sports, etc. A mathematical game is a decision-making problem involving more than one person, where the outcome depends on the course of action - or strategy - chosen by each player. This definition fits many scenarios. Elections, animal behavior and ethical conflicts are all examples, and the list is limitless.
Game theory is a mathematical tool for analyzing decision-making. It doesn't give a "right" answer, but it provides frameworks for people to choose strategies that lead to preferred outcomes. Even a math-phobic student can understand how game theory can be used to analyze Israeli elections or the value judgments underlying a soldier's decision to stay and fight or abandon his/her comrades.
For example, we can use game theory to examine the upcoming Likud leadership race. It's shaping up as a three-way contest between Binyamin Netanyahu, Silvan Shalom and Moshe Feiglin. If no candidate captures more than 50% of the votes, there will be a run-off. Polls show the race will likely result in a run-off between Netanyahu and Shalom, with Netanyahu ahead in this scenario.
Here's where game theory comes in: Given the right circumstances, Shalom supporters could adopt a clever strategy; some Shalom voters would strategically switch their votes to Feiglin, forcing a Shalom/Feiglin run-off that Shalom would likely win. Is this illegal or politics? Game theory doesn't create this possibility, but its tools bring it into focus.
We should take an hour in school to discuss the mathematics of Israeli elections and say, "this is where Aumann started; someday you could win the Nobel Prize."
While serious study of game theory is heavy-duty, Nobel-level stuff, on a basic level it is an easily understood way to see mathematics in real life. Just as junior league soccer is very different from the World Cup version, game theory can also be played by non-experts. Kids on the field don't enjoy soccer less because they are not professionals. In fact, playing gives them an appreciation of the professionallevel sport and gives them something to aim for. The same is true of game theory.
THERE IS already a high-school game-theory text in Hebrew, written with Aumann's informal guidance. One of the authors approached the Education Ministry offering teacher workshops on using the book - and was rebuffed.
Aumann's Nobel Prize is a great opportunity to renew the offer - and educators should eagerly reconsider.
Aumann's achievement presents even greater opportunity in the world of Jewish education. Some of his work has a direct connection to Jewish studies.
Aumann and co-author M. Maschler wrote an article applying game theory to a bankruptcy case that appeared in the Mishna. The distribution rules used to divide the assets puzzled talmudic scholars for centuries. By treating bankruptcy as a game, Aumann and Maschler figured out the rules used to distribute the assets.
Game theory solved a mishnaic mystery. The rabbis in the Mishna did not use modern game theory to distribute the assets. Rather, through its lens, Aumann and Maschler were able to determine the distribution strategy. What's more, the tools developed in the article apply to modern game-theory problems dealing with allocating limited resources.
The bankruptcy case is an excellent vehicle for offering Jewish students a short lesson integrating math, Talmud, social studies and Zionism in a real-life context. It would also celebrate a scholar we should hold up as a role model for our kids.
Israel and the entire Jewish world take tremendous pride in the achievement of Nobel Laureate Robert (Israel) Aumann. Using his work in game theory to further our educational goals is an excellent strategy. Let's do it.
The writer is a mathematician living in Ra'anana. She has a doctorate in mathematics from the University of Pennsylvania and was a member of the faculty of the Harvard University partment of Mathematics.