Mathematical Reasoning and Proving for Secondary Teachers
Purpose:
The Mathematical Reasoning and Proving for Secondary Teachers course aims to enhance preservice secondary teachers' (PSTs') knowledge and disposition for integrating reasoning and proof into classroom practices. Through content, methods, and clinical practice, PSTs are able to learn about the importance of the logical aspect of proof and apply it to pedagogical implications. The four aspects of proof utilized for the course are (1) quantification and the role of examples in proving, (2) conditional statements, (3) direct proof and argument evaluation and (4) indirect reasoning. The modules of the course are sectioned by these aspects. Information and materials for each module can be found either at the top of this page or within the diagram of the course structure.
Pedagogical Approach:
To support future teachers in integrating reasoning and proving in their classroom instruction, for any content of grade level. This is done with the methods of crystalizing, connecting and applying outlined in the pull downs below. Increase PST's awareness of the importance of logical aspects of proof, and students difficulties with proving
Teach PSTs to identify within regular school curricula opportunities to integrate proof-related tasks.
Equip PSTs with the pedagogical tools to create or modify mathematical tasks that integrate reasoning and proof.
Course Overview:
Preservice secondary teachers (PST's) will learn about the integration of proof and reasoning in their mathematics classrooms. This capstone course first uses a pre-test to identify PST's Mathematical Knowledge for Teaching of Proof (MKT-P), which includes Subject Matter Knowledge (SMK) and Pedagogical Content Knowledge (PCK). Additionally, a dispositions survey is used prior to the modules to determine PST's attitudes and confidence levels in regards to teaching proof and reasoning. Each of the four modules focuses on a different proof aspect. The course spends about three weeks on each module. Within this time PSTs are engaged in opportunities to integrate proof and reasoning into the traditional US curriculum, provided class time to lesson plan, and are shown modeled types of proof tasks for support. Lessons are planned and implemented in Middle or Secondary classrooms. For each lesson PST's record, reflect, receive feedback, and review. By the end of the course, post MKT-P test and post disposition surveys will be given to track progress throughout. The diagram below provides a visual for the course structure.
Capstone Course Design
Click each Module to go to that Module's Page
Publications
Buchbinder, O. & McCrone, S. (2020). Preservice Teachers Learning to Teach Proof Through Classroom Implementation: Successes and Challenges. Journal of Mathematical Behavior, 58, https://doi.org/10.1016/j.jmathb.2020.100779
Buchbinder, O. & McCrone, S. (2021). Advancing reasoning and proof in secondary mathematics classrooms: instructional modules for supporting teachers. In Sacristán, A.I., Cortés-Zavala, J.C. & Ruiz-Arias, P.M. (Eds.). Proceedings of the 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, (pp. 890) Mexico. Cinvestav / AMIUTEM / PME-NA. https:/doi.org/10.51272/pmena.42.2020
Buchbinder, O. & McCrone, S. (2020). Secondary Prospective Teachers’ Strategies to Determine Equivalence of Conditional Statements. Proceedings of the 23rd Annual Conference on Research in Undergraduate Mathematics Education, Special Interest Group of the Mathematical Association of America. (pp. 62 – 69) Boston, MA http://sigmaa.maa.org/rume/RUME23.pdf
Buchbinder, O. & McCrone, S. (2019). Indirect reasoning task for prospective secondary teachers: opportunities and challenges. In Otten, S., Candela, A. G., de Araujo, Z., Haines, C., & Munter, C. (2019). Proceedings of the 41st Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. (pp. 1259 – 1263). St Louis, MO: University of Missouri. https://www.pmena.org/pmenaproceedings/PMENA%2041%202019%20Proceedings.pdf
Buchbinder, O. & McCrone, S. (2019). Prospective teachers enacting proof tasks in secondary mathematics classrooms. Jankvist, U. T., Van den Heuvel-Panhuizen, M., & Veldhuis, M. (Eds.). (2019). Proceedings of the 11th Congress of the European Society for Research in Mathematics Education (pp. 147 – 154). Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME. http://www.mathematik.uni-dortmund.de/~prediger/ERME/CERME11_Proceedings_2019.pdf
Buchbinder, O. & McCrone, S. (2019). Prospective teachers enacting proof tasks in secondary mathematics classrooms. Jankvist, U. T., Van den Heuvel-Panhuizen, M., & Veldhuis, M. (Eds.). (2019). Proceedings of the 11th Congress of the European Society for Research in Mathematics Education (pp. 147 – 154). Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME. http://www.mathematik.uni-dortmund.de/~prediger/ERME/CERME11_Proceedings_2019.pdf
Buchbinder, O. & McCrone, S. (2019). Opportunities to Engage Secondary Students in Proof Generated by Pre-service Teachers. Proceedings of the Annual Conference of the Research in Undergraduate Mathematics Education, Special Interest Group of the Mathematical Association of America. (pp. 76-83) Oklahoma City, OK. February 2019. http://sigmaa.maa.org/rume/RUME22_Proceedings.pdf
Buchbinder, O. & McCrone, S. (2018) Taking proof into secondary classrooms – supporting future mathematics teachers. In T. E. Hodges, G, J. Roy, & A. M. Tyminski, (Eds.), Proceedings of the 40th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA), Greenville, SC. (pp. 711- 714). https://s3.us-east-2.amazonaws.com/pmena2018/documents/public/PMENA+2018+Proceedings.pdf
Buchbinder, O. & McCrone, S. (2018) Mathematical Reasoning and Proving for Prospective Secondary Teachers. Proceedings of the 21st Annual Conference of the Research in Undergraduate Mathematics Education, Special Interest Group of the Mathematical Association of America: San Diego, CA. (pp. 115-128). http://sigmaa.maa.org/rume/RUME21.pdf