Development of Research to Inform the Design and Improvement of Mathematics Education for Teachers

Merrimack College, North Andover MA

Investigators

Abstract

This award will support the development of research to investigate key developmental mathematics understandings of undergraduates who are intending to become teachers. Many secondary teachers learned geometry through proving theorems. Current secondary standards and guidelines favor a vastly different approach that focuses on geometric transformations, such as reflection of a shape against an axis. This difference in learning approaches provides an important STEM education question: how do secondary teachers' understandings of proof-based geometry relate to their understanding of geometrical transformations? Work on this project will address this question by exploring how teachers use a transformational perspective to conceptualize two key concepts in geometry: congruence and similarity. This work will also produce a rich dataset for future modeling of teachers' thinking about congruence and similarity. This project builds on prior work led by the investigator, which hypothesized the existence of key developmental understandings for establishing congruence from a transformation perspective. The project will conduct additional research related to this hypothesis. It will also seek to develop hypotheses for similarity-proving activities through an adapted teaching experiment. In these efforts, the investigator will be mentored by Dr. Yvonne Lai. The specific aims of the research are to: (1) investigate prospective teachers' understandings of congruence and similarity-proving activities from a transformation perspective; and (2) increase the investigator’s capacity to design and conduct STEM education research using both qualitative and quantitative methods. Results of the research will inform the design and improvement of the mathematics curricula for teachers, and support teacher educators in designing and using formative assessments for understanding geometry from a transformation perspective. The new research has the potential to help more secondary mathematics teachers enter the classroom well-equipped to teach geometry in alignment with current standards. Additionally, the professional development activities will build capacity for the investigator to conduct STEM education research that will enhance the connection between research and practice at a primarily undergraduate institution. This work is supported by the EHR Core Research: Building Capacity in STEM Education Research Program, which supports projects that build individuals’ capacity to carry out high quality STEM education research. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.