Student justifications regarding converse independence

Abstract

This paper presents five categories of undergraduate student justifications regarding the question of whether a converse proof proves a conditional statement. Two categories of justification supported students’ judgments that converse proofs cannot so prove, which is the normative interpretation. These normative judgments depended upon students spontaneously seeking uniform rules of proving across various conditional statements or assigning a direction to the statements and proof. The other three categories of justification supported students to affirm that converse proofs prove. Students offering these justifications do so because they do not perceive any distinction in meaning between a statement and its converse when both are true. The rationality of these nonnormative justifications suggests the need for further work to understand how we can help students understand the normative rules of logic.