PROCEEDINGS OF THE 21ST ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2018
San Diego, California
When “Negation” Impedes Argumentation: The Case of Dawn
Page: 988
This study investigates one student’s meanings for negations of various mathematical statements. The student, from a Transition-to-Proof course, participated in two clinical interviews in which she was asked to negate statements with one quantifier or logical connective. Then, the student was asked to negate statements with a combination of quantifiers and logical connectives. Lastly, the student was presented with several complex mathematical statements from Calculus and was asked to determine if these statements were true or false on a case-by-case basis using a series of graphs. The results reveal that the student used the same rule for negation in both simple and complex mathematical statements when she was asked to negate each statement. However, when the student was asked to determine if statements were true or false, she relied on her meaning for the mathematical statement and formed a mathematically convincing argument.