Collaborative Research: Collaborative Partnership to Teach Mathematical Reasoning Through Computer Programming (CPR2)

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As a result of the powerful innovation and application of computing in STEM disciplines, the STEM+C program addresses an urgent need for real-world, interdisciplinary, and computational preparation of students from the early grades through high school (preK-12). The Collaborative Partnership to Teach Mathematical Reasoning through Computer Programming (CPR2) project will investigate whether computer programming is an effective tool for teaching and learning generalization in 7th and 8th grade math classrooms. Understanding and interpreting general expressions can be difficult for students, but it is a key to advancing in STEM disciplines. The failure to "catch" this skill in middle school is a major roadblock to pursuit of STEM in college and career. The CPR2 Instructional Model (IM) will help students come to understand, interpret, and even generate general or algebraic expressions. The team has developed an explicit method for teaching generalization that is intended for learners with no background in programming or formal mathematical argumentation. Students will write mini computer programs and then recognize and recover general behaviors from their code. Next, students will learn to describe these behaviors using abstract mathematical language. An additional benefit of the CPR2 IM is that learners will gain experience, skill, and confidence in using programming as a tool for scientific exploration. This experience advances STEM fields by opening a door for all students to recognize, understand and apply abstractions, and to experience writing their own computer programs. The CPR2 IM has the potential to pave the way for all student participants, including those currently underrepresented in computer science, to succeed in future STEM studies. The researchers will refine the instructional model in a design-based implementation research approach. In a two-week summer institute, teachers will be immersed in the four-step model and learn how it builds the mental frameworks necessary for generalization. The teachers will then implement the model in their classes with support from the team. Finally, researchers will determine the effects on students in an experimental pilot study. The researchers hypothesize that teachers who participate in the professional development offered by the project will improve their own ability to generalize over a mathematical concept and will become more comfortable using computer programming as a tool in the classroom. Students and teachers will use computer programming to explore ideas, which will improve their ability and confidence to think computationally and to generalize over a mathematical concept.The teachers will be immersed in a collaborative environment with professionals from high schools and institutes of higher education. The network created will facilitate and sustain change in mathematics education at all levels. Ultimately, this will lead to broader participation of teachers and students in programming and computational thinking.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.