Graphing in Groups: Learning About Lines in a Collaborative Classroom Network Environment

Abstract

This article presents a design experiment in which we explore new structures for classroom collaboration supported by a classroom network of handheld graphing calculators. We describe a design for small group investigations of linear functions and present findings from its implementation in three high school algebra classrooms. Our coding of the problem-solving efforts of six student focus pairs in this environment over the course of several class sessions indicates that these students tended to move from exploratory and visual to more analytic means of establishing lines of a specified slope. As they adopted these analytic approaches, they were also more likely to enact their strategies jointly. In closer examination of emerging analytic strategies in episodes selected from the work of one of the pairs, we argue that the processes by which these students discovered the need for coordinated action on their respective points, and came to establish mathematical meaning for the relations between their coordinate locations as slope, were overlapping and intertwined.

ACKNOWLEDGEMENTS

Funding for this work was provided through an NSF Early Career Development Award, DRL-0747536, through a collaborative research grant from the UC Davis CRESS Center, and through an equipment grant from Texas Instruments. Dor Abrahamson and three anonymous reviewers provided insightful critical feedback on earlier drafts.

Notes

¹The total number of strategies in Table 2 (n = 174) is higher than in Table 1 (n = 147) because some were implemented independently by each student in the same pair at different instances during work on the same task; these were counted as a single instance of the approach being applied to the task in Table 1, but as multiple instances of individuals attempting to implement the approach in Table 2.

²Although she was taking a full-year Algebra course for the first time, Amber had attended a summer school math pre-Algebra course that introduced several Algebra I topics.

³In this and all subsequent transcription excerpts, we adopt the convention that italicized text indicates segments of speech that occurred simultaneously with actions described in the brackets immediately following.

⁴In this excerpt, instances of overlapping speech are indicated by vertical alignment of text in lines 27–28 and 29–30.