The designbased 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 proofthemes: 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 prooftheme within an ongoing mathematical topic. Analysis of the firstyear data shows enhancements of PSTs’more »
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 nonequivalent 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 nonequivalent forms: meaning making, comparing truthvalues 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.
 Editors:
 Karunakaran, S. S.; Reed, Z.; Higgins, A.
 Award ID(s):
 1711163
 Publication Date:
 NSFPAR ID:
 10223827
 Journal Name:
 Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education
 Page Range or eLocationID:
 62 – 69
 ISSN:
 24749346
 Sponsoring Org:
 National Science Foundation
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