ABSTRACT

This chapter discusses a research study that involved better understanding of students' learning processes when a state-of-the-art graphing calculator is used to conduct an activity concerning quadratic functions. The study explores the helping or hindering of the students' ability to bring mathematical concepts to their consciousness when they use dynamically linked multiple representations. This chapter focuses on students' conjectures, with connections to their exploring. Students' conjectures are characterized as viable, semi-viable, or naive. The participants in this study were seventh- or eighth-grade students enrolled in pre-algebra or algebra in a suburban public school near a large city in the Midwestern United States. Students' actions on pedagogically and mathematically faithful objects supported and enriched their explorations and their ability to make viable conjectures. The tendency of many students to make the sorts of non-viable conjectures that was observed clearly implies that students do need scaffolding when learning in a technological environment.