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1. Examining the Social Aspect of Climate Change through Mathematics

   https://doi.org/10.1109/ISECon.2019.8882109  

   Basu, Debasmita; Panorkou, Nicole; Zhu, Michelle (March 2019, 2019 IEEE Integrated STEM Education Conference (ISEC))

   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. 

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2. Integrating math and science content through covariational reasoning: the case of gravity

   https://doi.org/10.1080/10986065.2020.1814977  

   Panorkou, Nicole; Germia, Erell Feb (January 2020, Mathematical Thinking and Learning)

   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. 

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3. HOW TRANSITIONS BETWEEN RELATED ARTIFACTS SUPPORT STUDENTS’ COVARIATIONAL REASONING

   Germia, E.; York, T.; Panorkou, N. (January 2022, Proceedings of the forty-fourth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education.)

   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. 

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4. Strategies Used by Students with Learning Disabilities for Reasoning about Slope.

   DeJarnette, A. F; Hord, C. (November 2019, North American Chapter of the International Group for the Psychology of Mathematics Education)

   Students with learning disabilities (LD), like other learners, show a range of resources and strategies for reasoning about complex concepts in mathematics. This study comes from a project in which a group of five ninth-grade students with LD participated in a once-weekly tutoring program with university pre-service teachers. We asked, what strategies did students use to reason about slope? Students drew upon knowledge of concepts related to constant covariation when given the opportunity. This study suggests that students with LD have rich conceptual knowledge that can be leveraged to improve their success in Algebra. 

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5. Examining the “Messiness” of Transitions Between Related Artifacts

   https://doi.org/10.1007/s40751-022-00112-3  

   Panorkou, Nicole; York, Toni; Germia, Erell (January 2022, Digital Experiences in Mathematics Education)

   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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