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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)

   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 providedmore »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.« less
2. 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.
3. 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 betweenmore »artifacts that have the potential to make this synergy productive.« less
4. Where’s My Whiteboard? The Challenge of Moving Active-learning Mathematics Classes Online

   Nelson, Jill K. ; Rosenberg, Jessica ; Fernandez, Kathryn ; Shank, Julie ( July 2021 , 2021 ASEE Virtual Annual Conference)

   This research paper studies the challenges that mathematics faculty and graduate teaching assistants (GTAs) faced when moving active and collaborative calculus courses from in-person to virtual instruction. As part of a larger pedagogical change project (described below), the math department at a public Research-1 university began transitioning pre-calculus and calculus courses to an active and collaborative learning (ACL) format in Fall 2019. The change began with the introduction of collaborative worksheets in recitations which were led by GTAs and supported by undergraduate learning assistants (LAs). Students recitation periods collaboratively solving the worksheet problems on whiteboards. When COVID-19 forced the rapid transition to online teaching, these ACL efforts faced an array of challenges. Faculty and GTA reflections on the changes to teaching and learning provide insight into how instructional staff can be supported in implementing ACL across various modes of instruction. The calculus teaching change efforts discussed in this paper are part of an NSF-supported project that aims to make ACL the default method of instruction in highly enrolled gateway STEM courses across the institution. The theoretical framework for the project builds on existing work on grassroots change in higher education (Kezar and Lester, 2011) to study the effect of communitiesmore »of practice on changing teaching culture. The project uses course-based communities of practice (Wenger, 1999) that include instructors, GTAs, and LAs working together to design and enact teaching change in the targeted courses alongside ongoing professional development for GTAs and LAs. Six faculty and five GTAs involved in the teaching change effort in mathematics were interviewed after the Spring 2020 semester ended. Interview questions focused on faculty and GTA experiences implementing active learning after the rapid transition to online teaching. A grounded coding scheme was used to identify common themes in the challenges faced by instructors and GTAs as they moved online and in the impacts of technology, LA support, and the department community of practice on the move to online teaching. Technology, including both access and capabilities, emerged as a common barrier to student engagement. A particular barrier was students’ reluctance to share video or participate orally in sessions that were being recorded, making group work more difficult than it had been in a physical classroom. In addition, most students lacked access to a tablet for freehand writing, presenting a significant hurdle for sharing mathematical notation when physical whiteboards were no longer an option. These challenges point to the importance of incorporating flexibility in active learning implementation and in the professional development that supports teaching changes toward active learning, since what is conceived for a collaborative physical classroom may be implemented in a much different environment. The full paper will present a detailed analysis of the data to better understand how faculty and GTA experiences in the transition to online delivery can inform planning and professional development as the larger institutional change effort moves forward both in mathematics and in other STEM fields.« less
5. Implementation of Security Modules with Model-Eliciting Activities in Computer Science Courses

   https://doi.org/10.18260/1-2--34776  

   Yang, Jeong ; Earwood, Brandon ; Kim, Young Rae ; Lodgher, Akhtar ( June 2020 , 2020 ASEE Virtual Annual Conference)

   Security is a critical aspect in the design, development, and testing of software systems. Due to the increasing need for security-related skills within software systems and engineering, there is a growing demand for these skills to be taught at the university level. A series of 41 security modules was developed to assess the impact of these modules on teaching critical cyber security topics to students. This paper presents the implementation and outcomes of the first set of six security modules in a Freshman level course. This set consists of five modules presented in lectures as well as a sixth module emphasizing encryption and decryption used as the semester project for the course. Each module is a collection of concepts related to cyber security. The individual cyber security concepts are presented with a general description of a security issue to avoid, sample code with the security issue written in the Java programming language, and a second version of the code with an effective solution. The set of these modules was implemented in Computer Science I during the Fall 2019 semester. Incorporating each of the concepts in these modules into lectures depends on both the topic covered and the approach to resolvingmore »the related security issue. Students were introduced to computing concepts related to both the security issue and the appropriate solution to fully grasp the overall concept. After presenting the materials to students, continual review with students is also essential. This reviewal process requires exploring use-cases for the programming mechanisms presented as solutions to the security issues discussed. In addition to the security modules presented in lectures, students were given a hands-on approach to understanding the concepts through Model-Eliciting Activities (MEAs). MEAs are open-ended, problem-solving activities in which groups of three to four students work to solve realistic complex problems in a classroom setting. The semester project related to encryption and decryption was implemented into the course as an MEA. To assess the effectiveness of incorporating security modules with the MEA project into the curriculum of Computer Science I, two sections of the course were used as a control group and a treatment group. The treatment group included the security modules in lectures and the MEA project while the control group did not. To measure the overall effectiveness of incorporating security modules with the MEA project, both the instructor’s effectiveness as well as the student’s attitudes and interest were measured. For instructors, the primary question to address was to what extent do instructors change their attitudes towards student learning and their teaching practices because of the implementation of cyber security modules through MEAs. For students, the primary question to address was how the inclusion of security modules with the MEA project improved their understanding of the course materials and their interests in computer science. After implementing security modules with the MEA project, students showed a better understanding of cyber security concepts and a greater interest in broader computer science concepts. The instructor’s beliefs about teaching, learning, and assessment shifted from teacher-centered to student-centered, during his experience with the security modules and MEA.« less