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The Perils of Conditional Statements and the Notion of Logical Equivalence

Authors: Jeff Gregg;

The Perils of Conditional Statements and the Notion of Logical Equivalence

Abstract

Increased attention should be given to the expression of deductive arguments in high school geometry, according to the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989). In general, the standards for grades 9-12 emphasize helping students develop their logical-reasoning skills. One means by which high school geometry textbooks typically introduce the notion of deductive reasoning and the principles oflogic is by examining conditional statements and their converses, inverses, and contrapositives. This article describes an episode involving conditional statements and the notion oflogical equivalence that occurred in a tenth-grade college-preparatorygeometry class. The episode illustrates some of the confusion that can arise in connection with this topic for both students and teachers. The ensuing discussion

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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Average
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