PROCEEDINGS OF THE 21ST ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2018
San Diego, California
Student’s Semantic Understanding of Surjective Functions
Page: 1521
Reasoning and proof are essential to mathematics, and surjective functions play important roles in every mathematical domain. In this study, students in a transition to proof course completed tasks involving composition and surjective functions. This paper explores students’ semantic understandings of surjective functions, both individually and in the context of composition of functions. Most students demonstrated productive semantic understandings of surjective functions that allowed them to produce counterexamples and arguments for the truth of statements. Furthermore, in the struggle of using the syntactic definition of surjective in a proof, some students used their semantic understanding to try to make sense of the definition. This demonstrates the potential of students’ ability to reason semantically to build understanding of the syntactic definition and structure of proofs of surjective functions.