2009

ThEMaT II

ThEMaT II

 

 

ThEMaT II

Thought Experiments in Mathematics Teaching II
“Supports for learning to manage classroom discussions: Exploring the role of practical rationality and mathematical knowledge for teaching”, also known as ThEMaT II or ThEMaT Online, was funded by NSF in 2009 and closed in 2018 (NSF Grant DRL–0918425). Like ThEMaT I, the basic premise of this research project was that practicing teachers have a shared sense of what practices are viable in instruction, and that confronting them with representations of conceivable practice might elicit from them the rationality that makes some of those practices viable. It sought to test some of the theoretical ideas developed in that project by designing measures of constructs that were hypothesized to influence the instructional decisions of mathematics teachers in particular instructional situations in high school algebra and geometry, administering those measures to a national sample of practicing high school mathematics teachers, then using statistical models to test theorized associations between those constructs. The constructs measured included teachers’ recognition of the norms of various instructional situations, recognition of the professional obligations of mathematics teaching, and mathematical knowledge for teaching. In order to develop and administer those measures, as well as to manage prior graphics, the project also developed a Flash-based web application, the LessonSketch platform: LessonSketch included a variety of tools for multimedia content and questionnaire creation, as well as questionnaire delivery and reporting. It was also used to develop and deliver content for teacher education, including modules for inservice teachers around the Common Core Standards for Mathematical Practice. These modules reused content developed during ThEMaT I (e.g., the animations). 

In order to test a theory of mathematics teacher decision making developed in the context of a previous project (ThEMaT I), in ThEMaT II (a.k.a., ThEMaT Online), we developed survey measures of constructs that we hypothesized influence the instructional decisions made by mathematics teachers in particular recurrent instructional situations in high school geometry and algebra. Those constructs include high school mathematics teachers’ recognition of, and attitude towards, both norms of those instructional situations and professional obligations of mathematics teaching, as well as the mathematical knowledge needed to teach high school geometry and algebra. Those instructional situations included doing proofs and geometric calculations in geometry, solving equations and doing word problems in algebra.

Those measures included both traditional text-based questionnaires as well as scenario-based questionnaires, which confronted participants with storyboard representations of classroom scenarios or images of mathematical problems. The development of both those representations of practice and the questionnaires that contained them involved several stages, including reviews by our team of mathematics educators as well as by experienced teachers, during focus groups. The questionnaires were also piloted with several small samples of teachers and revised again before eventually being administered to a national sample of high school mathematics teachers.

Using latent variable models, we explored the dimensionality of several constructs and evaluated the validity and reliability of the determined scales. We were also able to estimate the relationships between various constructs (using both structural equation models and more-traditional regression techniques). For example, we provided evidence that the mathematical knowledge needed to teach geometry, as well as the mathematical knowledge needed to teach algebra, depend on the task of teaching being completed (e.g., whether the teacher is choosing the givens for a problem or interpreting student work) and the instructional situation (e.g., whether the class is composing a geometric proof or solving an equation). We also demonstrated that one’s mathematical knowledge for teaching a given course is positively associated with their experience teaching that course. Similarly, we demonstrated that a teacher’s attitudes towards breaching a given norm are positively correlated with both their experience teaching and their mathematical knowledge for teaching (in particular, when that norm is breached in a way that allows the teacher to attend to one of their professional obligations as mathematics teachers). We also demonstrated that a teacher’s preference for following a norm of an instructional situation is associated with their recognition of that norm.

The project also supported the development of a Flash-based web application, the LessonSketch platform, that was used to develop and administer those questionnaires. LessonSketch included a variety of tools for multimedia content and questionnaire creation, as well as questionnaire delivery and reporting. LessonSketch was also used and made available for others to use to develop and deliver content for teacher education. These teacher education uses included a series of modules for inservice teachers to learn the Common Core Standards for Mathematical Practice, which reused content developed during ThEMaT I (e.g., the animations). The project tested the role the tools could support in teacher education using various online experiences and forums for teachers.

Thus the project contributed to three of the five components of NSF’s cycle of innovation: synthesizing and theorizing notions of teacher knowledge and practical rationality; hypothesizing and clarifying how those participate in decision-making in specific situations in algebra and geometry instruction; and designing, developing, and testing a “virtual setting” for practice-based teacher education.

This material is based upon work supported by the National Science Foundation under Grant DRL-0918425. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.