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

 The CPR2 project will investigate whether computer programming is an effective tool for teaching and learning generalization in 7^th and 8^th 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 CPR2 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. All students who participate in the CPR2 IM, even those currently underrepresented in computer science, will pave their way to success in future STEM studies.

Researchers will refine the CPR2 IM 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 generalizing. The teachers will then implement the CPR2 IM in their classes. Researchers will study how teachers implement the CPR2 IM in their classrooms and provide support. Finally, researchers will determine the effects on students in an experimental pilot study. The researchers hypothesize that teachers who do CPR2 IM professional development 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.