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Instructional designs that include two or more artifacts (digital manipulatives, tables, graphs) have shown to support students’ development of reasoning about covarying quantities. However, research often neglects how this development occurs from the student point of view during the interactions with these artifacts. An analysis from this lens could significantly justify claims about what designs really support students’ covariational reasoning. Our study makes this contribution by examining the “messiness” of students’ transitions as they interact with various artifacts that represent the same covariational situation. We present data from a design experiment with a pair of sixth-grade students who engaged with the set of artifacts we designed (simulation, table, and graph) to explore quantities that covary. An instrumental genesis perspective is followed to analyze students’ transitions from one artifact to the next. We utilize the distinction between static and emergent shape thinking to make inferences about their reorganizations of reasoning as they (re-)form a system of instruments that integrates previously developed instruments. Our findings provide an insight into the nature of the synergy of artifacts that offers a constructive space for students to shape and reorganize their meanings about covarying quantities. Specifically, we propose different subcategories of complementarities and antagonisms between artifacts that have the potential to make this synergy productive.
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HOW TRANSITIONS BETWEEN RELATED ARTIFACTS SUPPORT STUDENTS’ COVARIATIONAL REASONING
Many studies use instructional designs that include two or more artifacts (digital manipulatives, tables, graphs) to support students’ development of reasoning about covarying quantities. While students’ forms of covariational reasoning and the designs are often the focus of these studies, the way students’ interactions and transitions between artifacts shape their actions and thinking is often neglected. By examining the transitions that students make between artifacts as they construct and reorganize their reasoning, our study aimed to justify claims made by various studies about the nature of the synergy of artifacts. In this paper, we present data from a design experiment with a pair of sixth-grade students to discuss how their transitions between artifacts provided a constructive space for them to reason about covarying quantities in graphs.
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- Award ID(s):
- 1742125
- PAR ID:
- 10383424
- Editor(s):
- Lischka, A. E.; Dyer, E. B.; Jones, R. S.; Lovett, J. N..; Strayer, J.; & Drown, S.
- Date Published:
- Journal Name:
- Proceedings of the forty-fourth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education.
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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