Chapter 15: Designing Tasks for the Codevelopment of Conceptual and Technical Knowledge in CAS Activity: An Example From Factoring

In this chapter we describe a classroom instructional activity that integrates the use of Computer Algebra Systems (CAS) in a manner aimed at engaging high school students in substantive mathematical reasoning. The activity draws on students’ prior knowledge of factoring and pushes them to use and develop this knowledge beyond what is usual for highschool-level algebra. In particular, we discuss the attendant design and mathematical principles of the activity at some length, explicating the intended role of the CAS. We then highlight aspects of engagement and student reasoning that emerged with the unfolding of the activity in a high school mathematics classroom. Three features of the design of the activity are considered to have played important roles in the further development of students’ conceptual and technical knowledge of factoring: reconciling the forms generated by the CAS in relation to the forms they had generated with paper and pencil, reflecting on the objects they had reconciled, and proving the relations they had generalized.