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1. 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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2. Documenting two emerging sociomathematical norms for examining functions in mathematics teachers’ online asynchronous discussions

   https://doi.org/10.1007/s10857-022-09563-2  

   Matranga, Anthony ; Silverman, Jason ( December 2022 , Journal of mathematics teacher education)

   This study investigated novice mathematics teachers participating in an online teacher education course focused on covariational reasoning and understanding the behavior of functions. The analysis centered on documenting the emergence of participants’ sociomathematical norms for engaging in online asynchronous discussions. In this paper, we characterized participants’ initial mathematical discourse and documented two emergent sociomathematical norms, namely explaining why and emergent shape discourse. When participants explained why, they used specific quantities or symbolic representations of functions to justify why function graphs have particular visual features. When participants engaged in emergent shape discourse, they coordinated change between covarying quantities to justify why function graphs behave in certain ways. This study provides evidence that online settings can provide context for mathematics teachers engaging in legitimate collaborative mathematical activity and that activity can be enhanced by participation in discourse featuring specific sociomathematical norms. We discuss conjectures regarding the potential of reflective discussion activities paired with the Notice and Wonder Framework to support the emergence of generative sociomathematical norms. We also discuss potential relationships between characteristics of participants’ mathematical discourse and their membership with the core and periphery of a social network. 

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3. The Physics Inventory of Quantitative Reasoning: Assessing Student Reasoning About Sign

   Olsho, Alexis ; White Brahmia, Suzanne ; Boudreaux, Andrew ; Smith, Trevor I. ( January 2019 , Proceedings of the 22nd Annual Conference on Research in Undergraduate Mathematics Education)

   An increase in general quantitative literacy and discipline-specific Physics Quantitative Literacy (PQL) is a major course goal of most introductory-level physics sequences—yet there exist no instruments to assess how PQL changes with instruction in these types of courses. To address this need, we are developing the Physics Inventory of Quantitative Literacy (PIQL), a multiple-choice inventory to assess students’ sense-making about arithmetic and algebra concepts that underpin reasoning in introductory physics courses—proportional reasoning, covariational reasoning and reasoning about sign and signed quantities. The PIQL will be used to not only to assess students’ PQL at specific points in time, but also to track changes in and development of PQL that can be attributed to instruction. Data from early versions of the PIQL suggest that students experience difficulty reasoning about sign and signed quantities. 

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4. Partnering with undergraduate engineering students to unearth cultural practices within a Science, Technology, and Society (STS) program

   Turpen, C. ; Radoff, J. ; Rahman, K. ; Adkins, P. ; Sangha, H. ; Bikki, S. ( August 2022 , Paper presented at 2022 ASEE Annual Conference & Exposition, Minneapolis, MN)

   Our research team is currently conducting an ethnographic investigation of a Science, Technology, and Society Living Learning Community (STS-LLC). Our investigation focuses on understanding how engineering students’ macro-ethical reasoning develops within the cultural practices of this community. Our approach to this investigation deliberately partners faculty research leads and a group of undergraduate research fellows (RFs) chosen based on their “insider” status within the STS-LLC cohort being investigated. This collaboration required building substantial infrastructure and routines for disrupting the usual hierarchies that exist between researchers and “participants.” This paper will share multiple perspectives, from both RFs and research leads, on the mutually beneficial relationships that emerged within this research collaboration. We will draw on research team meeting notes, research team meeting recordings, and formative feedback survey responses to support our claims. Research leads will share their perspectives on recruiting, onboarding and working with the RFs and describe some of the macro-ethical considerations that motivated their partnership with RFs. RFs will also describe the multiplicity of ways they have participated in and benefited from this research collaboration. This paper will share sociotechnical innovations that supported the development of effective co-learning and co-working processes. These innovations will be described both in terms of the activities, routines, and artifacts that structured our work and the purposes these activities served. Some innovations were constructed by the research leads in order to: (a) support collaboration and mutual engagement, (b) support engineering students in developing competence with ethnographic methods, (c) expand awareness of the engineering education research literature, (d) empower students to refine their own thinking about macroethics and the purpose of education, (e) recognize particular “knowledge-building” games within research activities, and (f) create space for students’ values and political agendas to shape the direction of the research. We will share some example innovations that were iteratively refined in dialogue with RFs and other example innovations that were developed through the process of coworking with RFs, such as GroupMe communication channels, multi-vocal field noting, and prompts for scaffolding reflections on classroom events. We will describe how the deliberate social and technical organization of this collaboration enabled particular forms of mutually beneficial relationships. 

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5. 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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