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1. 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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2. Semantic Fluency in Design Reasoning

   Quintana-Cifuentes, Jenny; Purzer, Senay (December 2022, International journal of engineering education)

   During design, different forms of reasoning shape the designers’ decision-making. As a result, the ability to fluently transition across various forms of reasoning is essential. The purpose of this study is two-fold: first is to introduce and explain the concept of Semantic Fluency in Design Reasoning, as the ability to transition across multiple forms of reasoning fluently. To identify these transitions, this study used the Design Reasoning Quadrants framework, which represents four quadrants: experiential observations (reasoning based on observations and experiences), trade-offs (reasoning recognizing multiple competing design requirements), first-principles (reasoning requiring disciplinary understandings), and complex abstractions (reasoning in envisioning new situations). The second purpose of this study is to illustrate semantic fluency in a design review conversation. We selected and presented three different forms of transitions identified through our analysis of conversations between students and design reviewers. Our analysis revealed evidence of semantic fluency in young designers. Mike, one of the students, demonstrated fluency across three quadrants (experiential observations, trade-offs, and first-principles). Lisa and David demonstrated two-quadrant transitions. Lisa had fluency from experiential observations to trade-offs, and David transitioned from experiential observations to first-principles. We recommend the intentional use of design reviews to elicit student reasoning in design and adopt questioning strategies to promote fluency across different forms of design reasoning. 

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3. Comparing introductory and beyond-introductory students’ reasoning about uncertainty

   https://doi.org/10.1103/PhysRevPhysEducRes.19.020147  

   Stump, Emily M; Hughes, Mark; Passante, Gina; Holmes, N G (October 2023, Physical Review Physics Education Research)

   Uncertainty is an important concept in physics laboratory instruction. However, little work has examined how students reason about uncertainty beyond the introductory (intro) level. In this work we aimed to compare intro and beyond-intro students’ ideas about uncertainty. We administered a survey to students at 10 different universities with questions probing procedural reasoning about measurement, student-identified sources of uncertainty, and predictive reasoning about data distributions. We found that intro and beyond-intro students answered similarly on questions where intro students already exhibited expert-level reasoning, such as in comparing two data sets with the same mean but different spreads, identifying limitations in an experimental setup, and predicting how a data distribution would change if more data were collected. For other questions, beyond-intro students generally exhibited more expertlike reasoning than intro students, such as when determining whether two sets of data agree, identifying principles of measurement that contribute to spread, and predicting how a data distribution would change if better data were collected. Neither differences in institutions, student majors, lab courses taken, nor research experience were able to fully explain the variability between intro and beyond-intro student responses. These results call for further research to better understand how students’ ideas about uncertainty develop beyond the intro level. 

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4. STUDENTS’ REORGANIZATIONS OF VARIATIONAL, COVARIATIONAL, AND MULTIVARIATIONAL REASONING

   York, T. Germia (January 2021, Proceedings of the forty-third annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education.)

   Olanoff, D.; Johnson, K.; Spitzer, S. (Ed.)

   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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5. What Are You Looking At? Shape Thinking and Eye-Tracking

   Waters, Kayla; Martsching, Wesley; Martin, Jason (February 2019, Proceedings of the Twenty-Second Annual Conference on Research in Undergraduate Mathematics Education)

   Previous research has illuminated and defined meanings and understandings that students demonstrate when reasoning about graphical images. This study used verbal and physical cues to classify students’ reasoning as either static or emergent thinking. Eye-tracking software provided further insight into precisely what students were attending to when reasoning about these graphical images. Eye-tracking results, such as eye movements, switches between depictions of relevant quantities, and total time spent on attending to attributes of the graph depicting quantities, were used to uncover patterns that emerged within groups of students that exhibited similar in-the-moment meanings and understandings. Results indicate that eye-tracking data supports previously defined verbal and physical indicators of students’ ways of reasoning, and can document a change in attention for participants whose ways of reasoning over the course of a task change. 

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