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: 242
This study investigates one student’s meanings for negations of complex mathematical statements. One student from a Transition-to-Proof course participated in two clinical interviews. The student was first presented with several statements with either one quantifier or one logical connective and asked to negate these statements. Then, the student was presented with statements containing a combination of quantifiers and logical connectives and was asked to negate these statements. Lastly, the student was also presented with several complex Calculus statements and 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.