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.
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Secondary Prospective Teachers’ Strategies to Determine Equivalence of Conditional Statements
Future mathematics teachers must be able to interpret a wide range of mathematical statements, in particular conditional statements. Literature shows that even when students are familiar with conditional statements and equivalence to the contrapositive, identifying other equivalent and non-equivalent forms can be challenging. As a part of a larger grant to enhance and study prospective secondary teachers’ (PSTs’) mathematical knowledge for teaching proof, we analyzed data from 26 PSTs working on a task that required rewriting a conditional statement in several different forms and then determining those that were equivalent to the original statement. We identified three key strategies used to make sense of the various forms of conditional statements and to identify equivalent and non-equivalent forms: meaning making, comparing truth-values and comparing to known syntactic forms. The PSTs relied both on semantic meaning of the statements and on their formal logical knowledge to make their judgments.
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- Award ID(s):
- 1711163
- NSF-PAR ID:
- 10223827
- Editor(s):
- Karunakaran, S. S.; Reed, Z.; Higgins, A.
- Date Published:
- Journal Name:
- Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education
- ISSN:
- 2474-9346
- Page Range / eLocation ID:
- 62 – 69
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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We use a curriculum design framework to analyze how prospective secondary teachers (PSTs) designed and implemented in local schools, lessons that integrate ongoing mathematical topics with one of the four proof themes addressed in the capstone course Mathematical Reasoning and Proving for Secondary Teachers. In this paper we focus on lessons developed around the conditional statements proof theme. We examine the ways in which PSTs integrated conditional statements in their lesson plans, how these lessons were implemented in classrooms, and the challenges PSTs encountered in these processes. Our results suggest that even when PSTs designed rich lesson plans, they often struggled to adjust their language to the students’ level and to maintain the cognitive demand of the tasks. We conclude by discussing possible supports for PSTs’ learning in these areas.more » « less
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