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1. Using public records to support the productive use of student mathematical thinking

   Freeburn, B.; Leatham, K. R.; Graff, S.; Kamlue, N.; Stockero, S. L.; Peterson, B. E.; Van Zoest, L. R. (January 2022, Proceedings of the 44th 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.)

   The more researchers understand the subtleties of teaching practices that productively use student thinking, the better we can support teachers to develop these teaching practices. In this paper, we report the results of an exploration into how secondary mathematics teachers' use of public records appeared to support or inhibit their efforts to conduct a sense-making discussion around a particular student contribution. We use cognitive load theory to frame two broadways teachers used public records—manipulating and referencing—to support establishing and maintaining students' thinking as objects in sense-making discussions. 

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2. USING PUBLIC RECORDS TO SUPPORT THE PRODUCTIVE USE OF STUDENT MATHEMATICAL THINKING

   Freeburn, B.; Leatham, K. R.; Graff, S.; Kamlue, N.; Stockero, S. L.; Peterson, B. E.; Van Zoest, L. R. (November 2022, USING PUBLIC RECORDS TO SUPPORT THE PRODUCTIVE USE OF STUDENT MATHEMATICAL THINKING)

   Lischka, A. E.; Dyer, E. B.; Jones, R. S.; Lovell, J. N.; Strayer, J.; Drown, S. (Ed.)

   The more researchers understand the subtleties of teaching practices that productively use student thinking, the better we can support teachers to develop these teaching practices. In this paper, we report the results of an exploration into how secondary mathematics teachers’ use of public records appeared to support or inhibit their efforts to conduct a sense-making discussion around a particular student contribution. We use cognitive load theory to frame two broad ways teachers used public records—manipulating and referencing—to support establishing and maintaining students’ thinking as objects in sense-making discussions. 

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3. Design principles for the development of professional noticing of students’ technological mathematical practices.

   McCulloch, A. W.; Lovett, J. N.; Cayton, C.; Dick, L. K.; Lee, H. (October 2018, Proceedings of the 40th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   In support of standards for the learning and teaching of mathematics and statistics that advocate for the use of technology to promote reasoning and sense making, and to elicit student thinking, we draw on the use of authentic student work in the form of video case instruction to develop prospective secondary mathematics teachers’ [PSMTs] knowledge of students’ understanding, thinking, and learning with technology in mathematics. Specifically, we draw on the extant literature related to TPACK, video cases as learning objects, and noticing to propose a set of design principles intended to guide the development of materials to support PSMTs’ acquisition of TPACK. Here we explicate six design principles situated in the literature, provide an example of a module designed based on these principles, and share findings from pilot studies utilizing the module. 

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4. Using evidence of student thinking as resources in a digital collaborative platform

   Park, Sunyoung; Edson, Alden J (August 2024, Mathematics education research and practice)

   Learning mathematics in a student-centered, problem-based classroom requires students to develop mathematical understanding and reasoning collaboratively with others. Despite its critical role in students’ collaborative learning in groups and classrooms, evidence of student thinking has rarely been perceived and utilized as a resource for planning and teaching. This is in part because teachers have limited access to student work in paper-and-pencil classrooms. As an alternative approach to making student thinking visible and accessible, a digital collaborative platform embedded with a problem-based middle school mathematics curriculum is developed through an ongoing design-based research project (Edson & Phillips, 2021). Drawing from a subset of data collected for the larger research project, we investigated how students generated mathematical inscriptions during small group work, and how teachers used evidence of students’ solution strategies inscribed on student digital workspaces. Findings show that digital flexibility and mobility allowed students to easily explore different strategies and focus on developing mathematical big ideas, and teachers to foreground student thinking when facilitating whole-class discussions and planning for the next lesson. This study provides insights into understanding mathematics teachers’ interactions with digital curriculum resources in the pursuit of students’ meaningful engagement in making sense of mathematical ideas. 

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5. The Effectiveness of Synchronous vs Asynchronous Modes of Instruction in an Online Flipped Design Thinking Course

   Mohandas, L. (July 2021, 2021 ASEE Annual Conference & Exposition)

   Motivation: This is a complete paper. There was a sudden shift from traditional learning to online learning in Spring 2020 with the outbreak of COVID-19. Although online learning is not a new topic of discussion, universities, faculty, and students were not prepared for this sudden change in learning. According to a recent article in ‘The Chronicle of Higher Education, “even under the best of circumstances, virtual learning requires a different, carefully crafted approach to engagement”. The Design Thinking course under study is a required freshmen level course offered in a Mid-western University. The Design Thinking course is offered in a flipped format where all the content to be learned is given to students beforehand and the in-class session is used for active discussions and hands-on learning related to the content provided at the small group level. The final learning objective of the course is a group project where student groups are expected to come up with functional prototypes to solve a real-world problem following the Design Thinking process. There were eighteen sections of the Design Thinking course offered in Spring 2020, and with the outbreak of COVID-19, a few instructors decided to offer synchronous online classes (where instructors were present online during class time and provided orientation and guidance just like a normal class) and a few others decided to offer asynchronous online classes (where orientation from the instructor was delivered asynchronous and the instructor was online during officially scheduled class time but interactions were more like office hours). Students were required to be present synchronously at the team level during the class time in a synchronous online class. In an asynchronous online class, students could be synchronous at the team level to complete their assignment any time prior to the deadline such that they could work during class time but they were not required to work at that time. Through this complete paper, we are trying to understand student learning, social presence and learner satisfaction with respect to different modes of instruction in a freshmen level Design Thinking course. Background: According to literature, synchronous online learning has advantages such as interaction, a classroom environment, and better course quality whereas asynchronous online learning has advantages such as self-controlled and self-directed learning. The disadvantages of synchronous online learning include the learning process, technology issues, and distraction. Social isolation, lack of interaction, and technology issue are a few disadvantages related to asynchronous online learning. Problem Being Addressed: There is a limited literature base investigating different modes of online instruction in a Design Thinking course. Through this paper, we are trying to understand and share the effectiveness of synchronous and asynchronous modes of instruction in an online Flipped Design Thinking Course. The results of the paper could also help in this time of pandemic by shedding light on the more effective way to teach highly active group-based classrooms for better student learning, social presence, and learner satisfaction. Method/Assessment: An end of semester survey was monitored in Spring 2020 to understand student experiences in synchronous and asynchronous Design Thinking course sections. The survey was sent to 720 students enrolled in the course in Spring 2020 and 324 students responded to the survey. Learning was measured using the survey instrument developed by Walker (2003) and the social presence and learner satisfaction was measured by the survey modified by Richardson and Swan (2003). Likert scale was used to measure survey responses. Anticipated Results: Data would be analyzed and the paper would be completed by draft paper submission. As the course under study is a flipped and active course with a significant component of group work, the anticipated results after analysis could be that one mode of instruction has higher student learning, social presence, and learner satisfaction compared to the other. 

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