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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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Extending the covariation framework: Connecting covariational reasoning to students’ interpretation of rate of change
Research on covariational reasoning has continued to evolve as researchers learn more about how students coordinate two (or more) quantities’ values as covarying. In this study, I examine the connection between students’ covariational reasoning and how they interpret the value of a rate of change. The findings suggest that attending to students’ quantification of a rate of change can provide insight into their covariational reasoning and how we might better support students in reasoning at higher levels. Additionally, this manuscript provides an update to the Carlson et al. (2002) Covariation Framework that includes two additional categories of student reasoning and an additional dimension that describes students’ interpretation of a rate value at each level of the framework.
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- Award ID(s):
- 2411661
- PAR ID:
- 10616864
- Publisher / Repository:
- JAI
- Date Published:
- Journal Name:
- The Journal of Mathematical Behavior
- Volume:
- 73
- Issue:
- C
- ISSN:
- 0732-3123
- Page Range / eLocation ID:
- 101122
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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null (Ed.)Integrating mathematics content into science usually plays a supporting role, where students use their existing mathematical knowledge for solving science tasks without exhibiting any new mathematical meanings during the process. To help students explore the reciprocal relationship between math and science, we designed an instructional module that prompted them to reason covariationally about the quantities involved in the phenomenon of the gravitational force. The results of a whole-class design experiment with sixth-grade students showed that covariational reasoning supported students’ understanding of the phenomenon of gravity. Also, the examination of the phenomenon of gravity provided a constructive space for students to construct meanings about co-varying quantities. Specifically, students reasoned about the change in the magnitudes and values of mass, distance, and gravity as those changed simultaneously as well as the multiplicative change of these quantities as they changed in relation to each other. They also reasoned multivariationally illustrating that they coordinated mass and distance working together to define the gravitational force. Their interactions with the design, which included the tool, tasks, representations, and questioning, showed to be a structuring factor in the formation and reorganization of meanings that students exhibited. Thus, this study illustrates the type of design activity that provided a constructive space for students’ forms of covariational reasoning in the context of gravity. This design can be used to develop other STEM modules that integrate scientific phenomena with covariational reasoning through technology.more » « less
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Abstract BackgroundThis study investigates undergraduate STEM students’ interpretation of quantities and quantitative relationships on graphical representations in biology (population growth) and chemistry (titration) contexts. Interviews (n = 15) were conducted to explore the interplay between students’ covariational reasoning skills and their use of disciplinary knowledge to form mental images during graphical interpretation. ResultsOur findings suggest that disciplinary knowledge plays an important role in students’ ability to interpret scientific graphs. Interviews revealed that using disciplinary knowledge to form mental images of represented quantities may enhance students’ covariational reasoning abilities, while lacking it may hinder more sophisticated covariational reasoning. Detailed descriptions of four students representing contrasting cases are analyzed, showing how mental imagery supports richer graphic sense-making. ConclusionsIn the cases examined here, students who have a deep understanding of the disciplinary concepts behind the graphs are better able to make accurate interpretations and predictions. These findings have implications for science education, as they suggest instructors should focus on helping students to develop a deep understanding of disciplinary knowledge in order to improve their ability to interpret scientific graphs.more » « less
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Lischka, A. E.; Dyer, E. B.; Jones, R. S.; Lovett, J. N..; Strayer, J.; & Drown, S. (Ed.)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.more » « less
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We designed an instructional module that seamlessly integrates mathematics, environmental science, and technology to help students think critically about climate change. The results from a design experiment in a sixth-grade classroom show that our tasks not only enhanced students' covariational reasoning in mathematics but also helped students identify the different traits of climate change they encounter every day in the news media.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.jmathb.2023.101122
