Partnering with Principals Through Formal and Informal Professional Development

Mathematics Specialists and administrators need to define what they should see students and teachers doing in classrooms that promote proficiency and understanding in mathematics. Formal, divisionwide professional development on this topic can quickly guide and inform a large group of administrators in one setting. However, potentially more powerful professional development can occur on a small scale one building at a time through mathematics department learning walks

Discriminating strategic reciprocity and acquired trust in the repeated trust-game

In repeated trust-game offers made by investors can be attributed to strategic reciprocation-based behavior. However, when a trustee is loyal, personal trust can build up between players, in the same way that lack of positive reciprocation on the part of trustees can motivate investors' distrust. Acquired personal trust or distrust and strategic reciprocation of the opponent's offers have then a cumulative and convergent influence on behavior in the trust game and are not prima facie distinguishable. We propose an experimental protocol which discriminates between these two determinants of trust. We furthermore show that acquired trust is the mere outcome of anonymous repeated interactions taking place during the experiment in the sense that it does not co-vary with an initial and independent baseline disposition to trust among investors: acquired trust crowds out background trust. Moreover, offers are sensitive to the amount and variance of trustees' returns. High returns-rate contribute to increase acquired trust between the players while the volatility of trustees' counter-offers makes them perceive as opportunistic, triggers investors' strategic behavior and detriments the acquisition of personal trust.repeated trust-game, reputation, strategic reciprocation.

"Illusion of control" in Minority and Parrondo Games

Human beings like to believe they are in control of their destiny. This ubiquitous trait seems to increase motivation and persistence, and is probably evolutionarily adaptive. But how good really is our ability to control? How successful is our track record in these areas? There is little understanding of when and under what circumstances we may over-estimate or even lose our ability to control and optimize outcomes, especially when they are the result of aggregations of individual optimization processes. Here, we demonstrate analytically using the theory of Markov Chains and by numerical simulations in two classes of games, the Minority game and the Parrondo Games, that agents who optimize their strategy based on past information actually perform worse than non-optimizing agents. In other words, low-entropy (more informative) strategies under-perform high-entropy (or random) strategies. This provides a precise definition of the "illusion of control" in set-ups a priori defined to emphasize the importance of optimization.Comment: 17 pages, four figures, 1 tabl

Abstracts of theses and related literature indicating current trends in arithmetic for the academically talented elementary school child written between 1957 and 1961

Thesis (Ed.M.)--Boston Universit