ThEMaTe: Thought Experiments in Mathematics Teaching

这个为期五年的研究项目主要针对中学数学代数和几何教师。本文的基本前提是从数学教师的习惯工作的角度来考察什么是可行的数学教学。pi试图理解教师在满足代数和几何教学的特定学科目标时所采取的行动背后的实践合理性。该研究的一个核心方面是开发一个数字化的教学探索馆，使用真实和可能的情节动画。数字探索馆将允许研究人员检查可想象的教学可能性和实践者认为可行的数学教学之间的相互作用。这个探索馆将用于教师的学习小组和暑期学院。教师在探索馆工作时的对话将为研究提供数据，这些对话将考察实践者可能对代数或几何的特定教学情况做出反应的替代方法。该方法基于这样的假设：一个相对同质的群体（高中数学教师）将检查他们工作的一个特定方面的相对多样化的竞争实例，这些实例可以用来引出数据，为实践理性的构建提供信息，即教师的实际决策。将有四个案例研究，重点是方程，定理，建模和证明。这些主题将是动画的重点。

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.