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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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STUDENTS’ REORGANIZATIONS OF VARIATIONAL, COVARIATIONAL, AND MULTIVARIATIONAL REASONING
In this paper we examine sixth grade students’ constructions and reorganizations of variational, covariational, and multivariational reasoning as they engaged in dynamic digital tasks exploring the science phenomenon of weather. We present case studies of two students from a larger whole-class design experiment to illustrate students’ forms of reasoning and the type of design that supported those constructions and reorganizations. We argue that students constructed multivariational relationships by bridging, transforming, and reforming their reasoning and that the nature of the multivariational relationship being constructed affected this process.
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- Award ID(s):
- 1742125
- PAR ID:
- 10383421
- Editor(s):
- Olanoff, D.; Johnson, K.; Spitzer, S.
- Date Published:
- Journal Name:
- Proceedings of the forty-third 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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