More Like this

1. Mathematical Reasoning and Proving for Prospective Secondary Teachers.

   Buchbinder, O; McCrone, S (September 2018, Proceedings of the 21st Annual Conference of the Research in Undergraduate Mathematics Education, Special Interest Group of the Mathematical Association of America)

   The design-based research approach was used to develop and study a novel capstone course: Mathematical Reasoning and Proving for Secondary Teachers. The course aimed to enhance prospective secondary teachers’ (PSTs) content and pedagogical knowledge by emphasizing reasoning and proving as an overarching approach for teaching mathematics at all levels. The course focused on four proof-themes: quantified statements, conditional statements, direct proof and indirect reasoning. The PSTs strengthened their own knowledge of these themes, and then developed and taught in local schools a lesson incorporating the proof-theme within an ongoing mathematical topic. Analysis of the first-year data shows enhancements of PSTs’ content and pedagogical knowledge specific to proving. 

   more » « less
2. Preparing prospective secondary teachers to teach mathematical reasoning and proof: the case of the role of examples in proving

   https://doi.org/10.1007/s11858-023-01493-4  

   Buchbinder, O; McCrone, S (August 2023, ZDM – Mathematics Education)

   Buchbinder, O; Wasserman, N; Buchholtz, N (Ed.)

   Abstract Mathematics teacher education programs in the United States are charged with preparing prospective secondary teachers (PSTs) to teach reasoning and proving across grade levels and mathematical topics. Although most programs require a course on proof, PSTs often perceive it as disconnected from their future classroom practice. Our design research project developed a capstone courseMathematical Reasoning and Proving for Secondary Teachersand systematically studied its effect on PSTs’ content and pedagogical knowledge specific to proof. This paper focuses on one course module—Quantification and the Role of Examples in Proving,a topic which poses persistent difficulties to students and teachers alike. The analysis suggests that after the course, PSTs’ content and pedagogical knowledge of the role of examples in proving increased. We provide evidence from multiple data sources: pre-and post-questionnaires, PSTs’ responses to the in-class activities, their lesson plans, reflections on lesson enactment, and self-report. We discuss design principles that supported PSTs’ learning and their applicability beyond the study context. 

   more » « less
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. 

   more » « less
4. Opportunities to Engage Secondary Students in Proof Generated by Pre-service Teachers

   Buchbinder, O; McCrone, S. (May 2019, Research in Undergraduate Mathematics Education)

   For reasoning and proving to become a reality in mathematics classrooms, pre-service teachers (PSTs) must develop knowledge and skills for creating lessons that engage students in proof-related activities. Supporting PSTs in this process was among the goals of a capstone course: Mathematical Reasoning and Proving for Secondary Teachers. During the course, the PSTs designed and implemented in local schools four lessons that integrated within the regular secondary curriculum one of the four proof themes discussed in the course: quantification and the role of examples in proving, conditional statements, direct proof and argument evaluation, and indirect reasoning. In this paper we report on the analysis of 60 PSTs’ lesson plans in terms of opportunities for students to learn about the proof themes, pedagogical features of the lessons and cognitive demand of the proof-related tasks. 

   more » « less
5. Cultivating Online Instructional Competencies: Prospective Secondary Teachers' Learning to Teach Reasoning and Proof with Digital Technology

   https://doi.org/10.29275/jerm.2025.35.3.633  

   Buchbinder, Orly Buchbinder; Liu, Jinqing; Towle, Sophia Towle (August 2025, The Korean Society of Educational Studies in Mathematics - Journal of Educational Research in Mathematics)

   The rapid development of digital technologies and online learning platforms has profoundly impacted the landscape of mathematics teaching and learning. These changes raise critical questions regarding mathematics teacher preparation, as future teachers must cultivate competencies in integrating innovative technological tools with ambitious pedagogical practices to enhance students' mathematical reasoning and communication skills. An additional layer of complexity arises when considering these competencies for teaching in an online environment. In this paper, we report on two in-depth case studies conducted in the United States with prospective secondary mathematics teachers (PSTs) who taught four online lessons during the global pandemic. The teaching occurred as part of the PSTs' participation in a course, Mathematical Reasoning and Proving for Secondary Teachers. Data sources included lesson plans, Zoom video recordings of the lessons, and PSTs' written reflections. Utilizing the Mathematical Knowledge for Teaching Proof and the Instructional Technology Tetrahedron frameworks, we explored how the PSTs' competence in reasoning and proving evolved. The analysis employed two complementary perspectives: the researcher-observer and the PSTs' reflective notice of their teaching. The results reveal complex trajectories of pedagogical growth and technology integration into mathematics teaching. Throughout the semester, both PSTs' practices transitioned from teacher-centered to more student-driven engagement and sophisticated technology integration. Structured reflection, peer discussion, and iterative lesson design were vital supports in their professional learning. This study demonstrates how PSTs can develop essential competencies for teaching reasoning and proof in online environments and emphasizes the necessity for intentional preparation in both digital pedagogy and mathematical reasoning within teacher education programs. 

   more » « less