ThEMaTe: Thought Experiments in Mathematics Teaching

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This five-year research project focuses on secondary mathematics teachers of algebra and geometry. The basic premise is to examine what constitutes viable mathematics instruction from the perspective of the customary work of mathematics teachers. The PIs seek to understand the practical rationality that undergirds teachers' actions as they meet subject-specific goals of the teaching of algebra and geometry. A central aspect of the study is the development of a digital exploratorium for alternatives in teaching, using animations of real and possible episodes. The digital exploratorium will allow the researchers to examine the interplay between conceivable possibilities for instruction and what practitioners view as viable in mathematics teaching. This exploratorium will be used in study groups and summer academies for teachers. Teachers' conversations as they work with the Exploratorium examining alternative ways in which a practitioner could conceivably respond to a particular instructional situation in algebra or geometry, will provide data for the study. The methodology is based on the assumption that a relatively homogenous group (high school mathematics teachers) will examine a relatively diverse set of competing instances of a specific aspect of their job that can be used to elicit data that informs the construct of practical rationality, the practical decision-making of teachers. There will be four case studies focusing on equations, theorems, modeling and proving. These topics will be the focus of the animations.