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Title: 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.
Karunakaran, S. S.; Reed, Z.; Higgins, A.
Award ID(s):
Publication Date:
Journal Name:
Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education
Page Range or eLocation-ID:
62 – 69
Sponsoring Org:
National Science Foundation
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