Supporting Teachers to Teach Mathematics Through Problem Posing

This project aims to support teachers to engage their students in mathematical problem posing (problem-posing-based learning, or P-PBL). P-PBL is a powerful approach to the teaching and learning of mathematics, and provides students with opportunities to engage in authentic mathematical practices. For example, conjecturing in mathematics, a form of problem posing, often plays an important role in solving complex problems, and problem posing is an important component of mathematical modeling. Yet despite its importance, widely used curriculum materials fail to incorporate P-PBL in substantial and consistent ways, leaving teachers with few resources to enact this process. This project will develop problem-posing lessons and illustrative cases of teachers implementing P-PBL that will not only support teachers to develop a vision of what P-PBL looks like and how to implement it in their own classrooms, but will also serve as rich resources for professional development (PD) providers. This project will generate valuable findings about teaching using problem posing for district administrators, mathematics teachers, educators, and researchers as well as curriculum developers and policy makers. The team will develop and pilot a set of 20−30 research-based P-PBL cases that provide critical details for the implementation of P-PBL and reveal “lessons learned” from the development process.

The project promises broader impact on the field of mathematics education as the first goal is to support teachers to teach mathematics through engaging their students in mathematical problem posing. By guiding students to construct and investigate their own problems, P-PBL both helps to create mathematical learning opportunities and develops students’ mathematical agency and positive mathematical identities. A networked improvement community of teachers and researchers will integrate problem posing into daily mathematics instruction and continuously improve the quality of P-PBL through iterative task and lesson design. The intellectual merit of this project is its contribution of new and important insights about teaching mathematics through problem posing. This will be realized through the second project goal which is to longitudinally investigate the promise of supporting teachers to teach with P-PBL for enhancing teachers’ instructional practice and students’ learning. A quasi-experimental design coupled with design-based research methodology and improvement science will be used to understand how, when, and why P-PBL works in practice. Specifically, we plan to follow a sample of 36 teachers and their approximately 3,600 students from six middle schools for multiple years to longitudinally explore the promise of P-PBL for developing teachers’ beliefs about problem posing, their beliefs about P-PBL, and their actual instructional practice. We will also investigate students’ learning as measured by problem-posing performance, problem-solving performance, and mathematics disposition. The findings of the project will add not only to the field’s understanding of the promise of supporting teachers to integrate P-PBL into their mathematics instruction, but also to its understanding of the challenges that teachers face when engaging in a networked improvement community that is focused on improving tasks and lessons by integrating P-PBL.