Connecting Programming to Mathematical Generalization: A Pilot Study of Professional Development and Instructional Materials

It is important to introduce computer programming concepts to K-12 students in preparation and motivation for college-level programming courses. Furthermore, generalization and abstraction are skills needed in computer science and other STEM majors. The Collaborative Partnership to teach mathematical Reasoning through Computer PRogramming (CPR2) Instructional Model (IM) was developed to use Python programming as a vehicle for explicit instruction in mathematical generalization and abstraction. Students are introduced to programming for the purpose of exploring mathematical concepts. They write code embedded with mathematical general expressions, observe the behavior of those expressions at scale in the execution of their programs, make conjectures about emerging patterns, and write convincing arguments to support these conjectures. During a two-week summer institute in 2020, middle school math teachers participated in professional development using the CPR2 instructional model. Teachers were provided with an introduction to programming and then shown how to apply the instructional model to math concepts while addressing computer science and math standards in the process. During the following fall and spring, the CPR2-trained teachers piloted lessons using Python programming to explore math concepts in their own classrooms. In this paper, details about the instructional model, the collaborative design research process used to refine professional development sessions, the key role of experienced teacher mentors in supporting new participants, and the incorporation of programming into the teachers' math classrooms are detailed. The results of design sessions and the pilot implementation are also discussed.