Collaborative Partnership to Teach Mathematical Reasoning Through Computer Programming

SRI Education and faculty from the University of North Alabama (UNA) used design-based implementation research to iteratively revise and refine the design and implementation of the Collaborative Partnership to Teach Mathematical Reasoning through Computer Programming (CPR2). CPR2 is built on UNA’s years of experience providing middle and high school math and computer science teachers with professional development on how to use Python programming for teaching mathematical generalization. Through an intensive, 2-week summer institute and lesson plans using a four-step Instructional model, middle and high school teachers learned how to directly deliver CPR2-aligned lessons to help students learn mathematical generalization through novice Python programming.

With funding from the National Science Foundation, SRI Education researchers and faculty from the University of North Alabama (UNA) set out to iteratively revise and refine the Collaborative Partnership to Teach Mathematical Reasoning through Computer Programming (CPR2). CPR2 is built on UNA’s nearly decade-long experience providing middle and high school math and computer science teachers with professional development on how to use Python programming as a way to teach mathematical generalization.

The CPR2 study questions focused on examining the professional development and instructional resources, the implementation of CPR2 in middle school classrooms, and the potential of CPR2 to improve both students’ and teachers’ ability to engage in mathematical generalization.

Using design-based implementation research (DBIR), SRI researchers and UNA faculty conducted a 3-year study from 2019 to 2022. The study was divided into three phases:

• A co-design year with CPR2 designers and mentor teachers who had experience partnering with UNA to deliver CPR2 content in their classrooms, aimed at refining CPR2 instructional materials and training
• A pilot study year to test and further refine CPR2 instructional materials and training, which was particularly important given the unexpected COVID-19 pandemic
• An initial efficacy study year to measure the extent to which CPR2 activities improved teachers’ and students’ mathematical generalization skills and attitudes toward programming

Across all three years of this study, SRI Education engaged in the following major activities in partnership with UNA:

• Co-leading the co-design process of CPR2 professional development materials with 5 mentor teachers
• Conducting implementation analyses of 2 summers of professional development observations; 97 instructional lesson delivery observations; 81 artifacts; interviews and focus groups with 29 teachers; and 302 teacher survey responses across background surveys, feedback surveys and implementation surveys
• Completing teacher assessment piloting with 10 teachers, student survey reliability testing with 992 students and student assessment reliability testing with 200 students
• Recruiting 49 teachers for the initial efficacy study and an associated 911 students across those teachers
• Analyzing teacher impacts with 20 teachers and student impacts with 124 students

In the co-design year, we found that the CPR2 designers from UNA and the mentor teachers engaged in focused discussion about a shared problem of practice—teaching generalization in mathematics—and reflected on how CPR2 could help address it. The group shared ideas about integrating CPR2 into the classroom context, anticipated student reactions to the activities, examined related state standards, and suggested refinements to the program. CPR2 designers then revised the materials before the pilot study year.

In the pilot study year, we found that CPR2 was largely implemented as intended. CPR2 professional development activities provided teachers with the programming skills and preparation needed to deliver CPR2 lessons, teachers consistently implemented 3 of the 4 steps of the CPR2 instructional model (essential mathematical concepts, writing mini-programs and writing general expressions) and students largely completed the required activities. However, we seldom observed teachers leading students in Step 4 of the instructional model (making conjectures and writing convincing arguments). Also, we found CPR2 instruction to be mostly teacher-led, with little time for the exploration and discussion that the instructional model calls for.

In the initial efficacy study year, our observation data suggested that students without previous programming experience were able to successfully write simple Python programs for the CPR2 lessons. In interviews, teachers reported that their students improved their programming skills as a result of CPR2. Unfortunately, extensive attrition occurred across the school year: Over 80% of students in control (non-CPR2) classrooms and 90% of students in treatment (CPR2) classrooms did not complete outcome data collection. This attrition prevented the efficacy study from producing reliable findings regarding the impact of CPR2 on teachers’ and students’ mathematical generalization skills.

This efficacy study was conducted during the COVID-19 pandemic, which likely contributed to the attrition, general teacher stress and limitations on class time devoted to CPR2. Further study is needed to determine what conditions and lesson dosage would be required for teachers to adopt the CPR2 instructional model and realize its intended benefits. Additionally, more sensitive measures of generalization ability would strengthen a second efficacy study.

This project description is based on work supported by a grant from the National Science Foundation (#1933678). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.