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1. Articulating the student mathematics in student contributions

   https://doi.org/https:/doi.org/10.51272/pmena.42.2020-354  

   Van Zoest, L. R.; Stockero, S. L.; Leatham, K. R.; Peterson, B. E.; Ruk, J. M. (October 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.)

   We draw on our experiences researching teachers' use of student thinking to theoretically unpack the work of attending to student contributions in order to articulate the student mathematics (SM) of those contributions. We propose four articulation-related categories of student contributions that occur in mathematics classrooms and require different teacher actions:(a) Stand Alone, which requires no inference to determine the SM; (b) Inference-Needed, which requires inferring from the context to determine the SM; (c) Clarification-Needed, which requires student clarification to determine the SM; and (d) Non-Mathematical, which has no SM. Experience articulating the SM of student contributions has the potential to increase teachers' abilities to notice and productively use student mathematical thinking during instruction. 

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2. Articulating the student mathematics in student contributions

   Van Zoest, Laura R; Stockero, Shari L; Leatham, Keith R; Peterson, Blake E; Ruk, Joshua M (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; Cortés-Zavala, J; null (Ed.)

   We draw on our experiences researching teachers’ use of student thinking to theoretically unpack the work of attending to student contributions in order to articulate the student mathematics (SM) of those contribution. We propose four articulation-related categories of student contributions that occur in mathematics classrooms and require different teacher actions:(a) Stand Alone, which requires no inference to determine the SM; (b) Inference-Needed, which requires inferring from the context to determine the SM; (c) Clarification-Needed, which requires student clarification to determine the SM; and (d) Non-Mathematical, which has no SM. Experience articulating the SM of student contributions has the potential to increase teachers’ abilities to notice and productively use student mathematical thinking during instruction. 

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3. Undergraduates' perceptions of the bene ts of working tasks focused on analyzing student thinking as an application for teaching in abstract algebra

   Álvarez, James A.; Kercher, Andrew; Turner, Kyle (January 2020, Proceedings of the 23rd Annual Conference on Research in Undergraduate Mathematics Education)

   Karunakaran, S.S.; Reed, Z.; Higgins, A. (Ed.)

   The Mathematical Education of Teachers as an Application of Undergraduate Mathematics project provides lessons integrated into various mathematics major courses that incorporate mathematics teaching connections as a legitimate application area of undergraduate mathematics. One feature of the lessons involves posing tasks that require undergraduates to interpret or analyze the work of another student. This paper reports on thematic analysis of hour-long interviews for eight participants enrolled in an undergraduate abstract algebra course from two different implementation sites. We focus on student work and reactions to these interpreting or analyzing student thinking (AST) applications as they relate to their perceptions regarding the use of AST applications as a mechanism to both deepen their content knowledge and improve their skills for communicating mathematics. Several participants identify positive benefits, but more research is needed to determine the how to incorporate AST applications to accommodate some participants’ reluctance to engage in new mathematical contexts. 

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4. Improving Automated Scoring of Student Open Responses in Mathematics

   Baral, Sami; Botelho, Anthony; Erickson, John; Benachamardi, Priyanka; Heffernan, Neil (June 2021, Educational Data Mining EDM 2021)

   Open-ended questions in mathematics are commonly used by teachers to monitor and assess students’ deeper conceptual understanding of content. Student answers to these types of questions often exhibit a combination of language, drawn diagrams and tables, and mathematical formulas and expressions that supply teachers with insight into the processes and strategies adopted by students in formulating their responses. While these student responses help to inform teachers on their students’ progress and understanding, the amount of variation in these responses can make it difficult and time-consuming for teachers to manually read, assess, and provide feedback to student work. For this reason, there has been a growing body of research in developing AI-powered tools to support teachers in this task. This work seeks to build upon this prior research by introducing a model that is designed to help automate the assessment of student responses to open-ended questions in mathematics through sentence-level semantic representations. We find that this model outperforms previously published benchmarks across three different metrics. With this model, we conduct an error analysis to examine characteristics of student responses that may be considered to further improve the method. 

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5. Improving Automated Scoring of Student Open Responses in Mathematics

   Baral, Sami; Botelho, Anthony; Heffernan, Neil T. (January 2021, International Conference on Educational Data Mining)

   null (Ed.)

   Open-ended questions in mathematics are commonly used by teachers to monitor and assess students’ deeper conceptual understanding of content. Student answers to these types of questions often exhibit a combination of language, drawn diagrams and tables, and mathematical formulas and expressions that supply teachers with insight into the processes and strategies adopted by students in formulating their responses. While these student responses help to inform teachers on their students’ progress and understanding, the amount of variation in these responses can make it difficult and time-consuming for teachers to manually read, assess, and provide feedback to student work. For this reason, there has been a growing body of research in developing AI-powered tools to support teachers in this task. This work seeks to build upon this prior research by introducing a model that is designed to help automate the assessment of student responses to open-ended questions in mathematics through sentence-level semantic representations. We find that this model outperforms previouslypublished benchmarks across three different metrics. With this model, we conduct an error analysis to examine characteristics of student responses that may be considered to further improve the method. 

   more » « less