Open questions in utility theory

Throughout this paper, our main idea is to explore different classical questions arising in Utility Theory, with a particular attention to those that lean on numerical representations of preference orderings. We intend to present a survey of open questions in that discipline, also showing the state-of-art of the corresponding literature.This work is partially supported by the research projects ECO2015-65031-R, MTM2015-63608-P (MINECO/ AEI-FEDER, UE), and TIN2016-77356-P (MINECO/ AEI-FEDER, UE)

Methodological Considerations in the Analysis of Classroom Interaction in Community College Trigonometry

We report analyses of classroom interaction in trigonometry classes taught at an American community college focusing on two dimensions: the mathematical novelty of questions that instructors and students ask and the interactional moves that the instructors use to encourage student involvement in the lesson. The analyzed lessons were particularly challenging because existing frameworks that analyze classrooms did not account for the cases in which the delivery mode was lecture. We discuss the analytical strategies we used and show data to illustrate how they help us in capturing the complexity of classroom interaction and differences between instructors when lecture is the primary mode of instructional delivery. We conclude with suggestions for further work.National Science Foundation CAREER award DRL-0745474 to the first authorPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/96961/1/Mesa_Lande_MetConsClassInt_DEEPBLUE.pd