Secondary Mathematics Teachers' Pedagogy through the Tool of Computer Algebra Systems

Computer algebra systems (CAS) have been available for over 20 years and yet minimal CAS-rich opportunities present themselves formally to high school students. CAS tools have become readily accessible through free or inexpensive versions. Educators are emboldened to integrate essential mathematical tools in the reasoning and sense making of mathematical knowledge for students. It is the teacher that is at the heart of technology instruction, creating authentic environments for all learners. This study investigated two secondary teachers pedagogy in classes that exploited CAS in the development of mathematical knowledge. A qualitative within-site case study design was used to explore each teacher’s instructional practices. Teachers that exemplified qualities of CAS-infused instruction were purposively selected. Rich descriptive lesson vignettes as captured from classroom observations, written reflections, and interviews revealed participants’ pedagogy. The pedagogical map framework guided the identification of participant pedagogical affordances of the utilization of CAS. Eight opportunities were observed as exploited by the participants that included subject level adjustments; classroom interpersonal dynamics with students; and mathematical tasks. Data revealed several emergent themes in operation as the teacher participants oriented their mathematics instruction: viewing CAS as a mathematical consultant, verifying answers, applying multiple representations, regulating access, providing guidance, and outsourcing procedures. The components interlock with one another to form a cohesive depiction of pedagogical decisions in the presence of CAS-rich classroom instruction. The schema of CAS-oriented instruction serves as a methodology for educators to create opportunities that enrich the development of mathematical content knowledge