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1. Comparing STEM Majors, Practicing and Prospective Secondary Teachers’ Feedback on Mathematical Arguments: Towards Validating MKT-Proof

   Butler, R. ; Buchbinder, O. ; McCrone, S. ( January 2022 , Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education)

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

   Mathematical Knowledge for Teaching Proof (MKT-P) has been recognized as an important component of fostering student engagement with mathematical reasoning and proof. This study is one component of a larger study aimed at exploring the nature of MKT-P. The present study examines qualitative differences in feedback given by STEM majors, in-service and pre-service secondary mathematics teachers on hypothetical students’ arguments. The results explicate key distinctions in the feedback provided by these groups, indicating that this is a learnable skill. Feedback is cast as a component of MKT-P, making the results of this study significant empirical support for the construct of MKT-P as a type of knowledge that is unique to teachers. 

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2. MATHEMATICAL KNOWLEDGE FOR TEACHING PROOF: COMPARING SECONDARY TEACHERS, PRE-SERVICE TEACHERS AND UNDERGRADUATE STEM MAJORS

   Buchbinder, O. ; McCrone, S. ; Capozzoli, M. ; Butler, R. ( January 2021 , Proceedings of the 43rd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

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

   It has been suggested that integrating reasoning and proof in mathematics teaching requires a special type of teacher knowledge - Mathematical Knowledge for Teaching Proof (MKT-P). Yet, several important questions about the nature of MKT-P remain open, specifically, whether MKT-P is a type of knowledge specific to teachers, and whether MKT-P can be improved through intervention. We explored these questions by comparing performance on an MKT-P questionnaire of in-service secondary mathematics teachers, undergraduate STEM majors, and pre-service secondary mathematics teachers. The latter group completed the questionnaire twice- before and after participating in a capstone course, Mathematical Reasoning and Proving for Secondary Teachers. Our data suggest that MKT-P is indeed a special kind of knowledge specific to teachers and it can be improved through interventions. 

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3. Learning to Teach Reasoning and Proof in an Online Setting: The Case of Nancy.

   Liu, J. ; Buchbinder, O. ( January 2022 , Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education)

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

   Preparing prospective secondary teachers (PSTs) to teach mathematics with a focus on reasoning and proving is an important goal for teacher education programs. A capstone course, Mathematical Reasoning and Proving for Secondary Teachers, was designed to address this goal. One component of the course was a school-based experience in which the PSTs designed and taught four proof-oriented lessons in local schools, video recorded these lessons, and reflected on them. In this paper, we focus on one PST – Nancy, who took the course in Fall 2020 during the pandemic, when the school-based experience moved online. We analyzed how Nancy’s Mathematical Knowledge for Teaching Proof (MKT-P) evolved through her attempts to teach proof online and through repeated cycles of reflection. 

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4. Mathematical Errors When Teaching: A Case of Secondary Mathematics Prospective Teachers’ Early Field Experiences

   Bieda, K. ; Voogt, K. ( January 2019 , Proceedings of the 22nd Annual Conference on Research in Undergraduate Education)

   The construct of mathematical knowledge for teaching (MKT) has transformed research and practice regarding the mathematical preparation of future teachers. However, the measures used to assess MKT are largely written tasks, which may fail to adequately represent the nature of content knowledge as it is used in instructional decision making. This preliminary report shares initial findings into one measure of MKT in practice – mathematical errors made during planning and enactment of mathematics instruction. We analyzed lesson plans and classroom video from prospective secondary mathematics teachers (PSTs)’ supervised field experiences in college algebra course. We found that there tended be more errors related to understanding of functions (especially logarithmic), but relatively few errors happened overall during instruction. Of the errors made during planning, the majority of these errors were issues of mathematical precision. Implications for the mathematical preparation of secondary PSTs, as well as research on MKT in practice, are discussed. 

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5. Engaging preschoolers in data collection and analysis with manipulatives, body movement, and digital technology

   Lewis Presser, A. E. ( February 2021 , Early Childhood STEM Conference)

   null (Ed.)

   This workshop will focus on how to teach data collection and analysis to preschoolers. Our project aims to promote preschoolers’ engagement with, and learning of, mathematics and computational thinking (CT) with a set of classroom activities that engage preschoolers in a data collection and analysis (DCA) process. To do this, the project team is engaging in an iterative cycle of development and testing of hands-on, play-based, curricular investigations with feedback from teachers. A key component of the intervention is a teacher-facing digital app (for teachers to use with students on touch-screen tablets) to support the collaboration of preschool teachers and children in collecting data, creating simple graphs, and using the graphs to answer real-world questions. The curricular investigations offer an applied context for using mathematical knowledge (i.e., counting, sorting, classifying, comparing, contrasting) to engage with real-world investigations and lay the foundation for developing flexible problem-solving skills. Each investigation follows a series of instructional tasks that scaffold the problem-solving process and includes (a) nine hands-on and play-based problem-solving investigations where children answer real-world questions by collecting data, creating simple graphs, and interpreting the graphs and. (b) a teacher- facing digital app to support specific data collection and organization steps (i.e., collecting, recording, visualizing). This workshop will describe: (1) the rationale and prior research conducted in this domain, (2) describe an intervention in development focused on data collection and analysis content for preschoolers that develop mathematical (common core standards) and computational thinking skills (K-12 Computational Thinking Framework Standards), (3) demonstrates an app in development that guides teacher and preschoolers through the investigation process and generates graphs to answer questions (NGSS practice standards), (4) report on feedback from a pilot study conducted virtually in preschool classrooms; and (5) describe developmentally appropriate practices for engaging young children in investigations, data collection, and data analysis. 

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