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1. 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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2. Cognitive agency and computer-based tasks

   Riling, M. (January 2018, Proceedings of the 40th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   As computer-focused policies and trends become more popular in schools, more students access math curriculum online. While computer-based programs may be responsive to some student input, their algorithmic basis can make it more difficult for them to be prepared for divergent student thinking, especially in comparison to a teacher. Consider programs that assess student work by judging how well it matches pre-set answers. Unless designed and enacted in classrooms with care, computer-based curriculum materials might encourage students to think about mathematics in pre-determined ways. How do students approach the process of mathematics while using online materials, especially in terms of engaging in original thought? Drawing on Pickering’s (1995) dance of agency and Sinclair’s (2001) conception of students as path-finders or track-takers, I define two modes of mathematical behavior: trail-taking and bushwhacking. While trail-taking, students follow an established approach, often relying on Pickering’s (1995) disciplinary agency, wherein the mathematics “leads [them] through a series of manipulations” (p. 115). The series of manipulations can be seen as a trail that a student may choose to follow. Bushwhacking, on the other hand, refers to actions a student takes of their own invention. It is possible that, unknown to the student, these actions have been taken before by others. In bushwhacking, the student possesses agency, which Pickering (1995) describes as active (rather than passive) and as hallmarked by “choice and discretion” (p. 117). In this study, students worked in several dynamic geometric environments (DGEs) during a geometry lesson about the midline theorem. The lesson was originally recorded as part of a larger study designing mathematically captivating lessons. Students accessed both problems and online addresses for corresponding DGEs via a printed packet. Students interacted with the DGEs on individual laptops, but were seated in groups of three or four. Passages of group conversations in which students transitioned between trail-taking and bushwhacking were selected for closer analysis, which involved identifying evidence of each mode and highlighting the curricular or social forces that may have contributed to shifts between modes. Of particular interest were episodes in which students asked one another to share results, which led to students reconsidering previously set approaches, and episodes in which students interacted with DGEs containing a relatively high proportion of drag-able components, which corresponded to some students working in bushwhacking mode, spontaneously suggesting and revising approaches for manipulating the DGE (e.g., “unless you make this parallel to the bottom, but I don’t think you... yes you can.”). Both types of episodes were found in multiple groups’ conversations. Further analysis of student interactions with tasks, especially with varying levels of student control and sharing, could serve to inform future computer-based task design aimed to encourage students to productively engage in bushwhacking while problem-solving. 

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3. Building a reinforcement learning environment from limited data to optimize teachable robot interventions.

   Maidment, T.; Yu, M.; Lobczowski, N. G; Kovashka, A.; Walker, E.; Litman, D.; & Nokes-Malach, T. (January 2022, Proceedings of the 15th International Conference on Educational Data Mining)

   Mitrovic, A.; & Bosch, N. (Ed.)

   Working collaboratively in groups can positively impact performance and student engagement. Intelligent social agents can provide a source of personalized support for students, and their benefits likely extend to collaborative settings, but it is difficult to determine how these agents should interact with students. Reinforcement learning (RL) offers an opportunity for adapting the interactions between the social agent and the students to better support collaboration and learning. However, using RL in education with social agents typically involves training using real students. In this work, we train an RL agent in a high-quality simulated environment to learn how to improve students’ collaboration. Data was collected during a pilot study with dyads of students who worked together to tutor an intelligent teachable robot. We explore the process of building an environment from the data, training a policy, and the impact of the policy on different students, compared to various baselines. 

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4. Student inquiry in interesting lessons

   Nieves, Hector I.; Singh, Rashmi; Dietiker, Leslie (January 2020, Mathematics Education Across Cultures: Proceedings of the 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Sacristán, A. I.; Cortés-Zavala, J. C.; Ruiz-Arias, P. M. (Ed.)

   What impact, if any, do interesting lessons have on the types of questions students ask? To explore this question, we used lesson observations of six teachers from three high schools in the Northeast who were part of a larger study. Lessons come from a range of courses, spanning Algebra through Calculus. After each lesson, students reported interest via lesson experience surveys (Author, 2019). These interest measures were then used to identify each teachers’ highest and lowest interest lessons. The two lessons per teacher allows us to compare across the same set of students per teacher. We compiled 145 student questions and identified whether questions were asked within a group work setting or part of a whole class discussion. Two coders coded 10% of data to improve the rubric for type of students’ questions (what, why, how, and if) and perceived intent (factual, procedural, reasoning, and exploratory). Factual questions asked for definitions or explicit answers. Procedural questions were raised when students looked for algorithms or a solving process. Reasoning questions asked about why procedures worked, or facts were true. Exploratory questions expanded beyond the topic of focus, such as asking about changing the parameters to make sense of a problem. The remaining 90% of data were coded independently to determine interrater reliability (see Landis & Koch, 1977). A Cohen’s Kappa statistic (K=0.87, p<0.001) indicates excellent reliability. Furthermore, both coders reconciled codes before continuing with data analysis. Initial results showed differences between high- and low-interest lessons. Although students raised fewer mathematical questions in high-interest lessons (59) when compared with low-interest lessons (86), high-interest lessons contained more “exploratory” questions (10 versus 6). A chi-square test of independence shows a significant difference, χ2 (3, N = 145) = 12.99, p = .005 for types of students’ questions asked in high- and low-interest lessons. The high-interest lessons had more student questions arise during whole class discussions, whereas low-interest lessons had more student questions during group work. By partitioning each lesson into acts at points where the mathematical content shifted, we were able to examine through how many acts questions remained open. The average number of acts the students’ questions remained unanswered for high-interest lessons (2.66) was higher than that of low-interest lessons (1.68). Paired samples t-tests suggest that this difference is significant t(5)=2.58, p = 0.049. Therefore, student interest in the lesson did appear to impact the type of questions students ask. One possible reason for the differences in student questions is the nature of the lessons students found interesting, which may allow for student freedom to wonder and chase their mathematical ideas. There may be more overall student questions in low-interest lessons because of confusion, but more research is needed to unpack the reasoning behind student questions. 

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5. Impact of changing physical learning space on GTA and student behaviors

   https://doi.org/10.1119/perc.2020.pr.Doty  

   Doty, Constance M.; Wan, Tong; Geraets, Ashley A.; Nix, Christopher A.; Saitta, Erin K.; Chini, Jacquelyn J. (January 2020, Physics Education Research Conference 2020)

   null (Ed.)

   We investigated how changing the physical classroom impacted graduate teaching assistant (GTA) and student behaviors in tutorial sections of an introductory algebra-based physics sequence. Using a modified version of the Laboratory Observation Protocol for Undergraduate STEM (LOPUS), we conducted 35 observations over two semesters for seven GTAs who taught in different styles of classrooms (i.e., active learning classrooms and traditional classrooms). We found that both GTAs and students changed behaviors in response to a change from an active learning classroom to a traditional classroom. GTAs were found to be less interactive with student groups and to lecture at the whiteboard more frequently. Correspondingly, student behaviors changed as students asked fewer questions during one-on-one interactions. These findings suggest that the instructional capacity framework, which typically focuses on interactions between instructors, students and instructional materials, should also include interactions with the learning space. We suggest administrators and departments consider the impact of changing to a traditional classroom when implementing student-centered instruction and emphasize how to use classroom space in GTA professional development. 

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