PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
A comparison of calculus, transition-to-proof, and advanced calculus student quantifications in complex mathematical statements
Page: 903
This study investigates Calculus, Transition-to-Proof, and Advanced Calculus students’ meanings for quantifiers in conditional statements involving multiple quantifiers. Three students from each course participated in clinical interviews. Students were presented with the Intermediate Value Theorem (IVT) and three other statements whose sentence structure was similar to the IVT except for reordered quantifiers and their attached variables. The results reveal that Advanced Calculus and Transition-to-Proof students made distinctions between the different statements more often than Calculus students. Several student meanings for quantification were found to be necessary for making distinctions between each of the four statements. We also address student quantifications that emerged for the phrase “Suppose f is a function.”