This research paper is focused on identifying and exploring problems that high school students have with the mathematical proof process. The study described in this report was designed to answer the question, do students who tend to struggle with mathematical proofs also struggle with understanding what is known and unknown in a proof, making assumptions about figures, and understanding mathematical converses? To answer these questions, students at three Dayton area high schools completed tasks relating to proofs and converse statements as well as a questionnaire. Contrary to the initial hypothesis, students who were perceived to have greater proof abilities did not always excel with various aspects of proofs. Similarly, students who were perceived to have lesser proof abilities did not always struggle with aspects of proofs. It was found that students tend to struggle with two major aspects of proof: Making assumptions when part of an if-then statement is not satisfied, and understanding that a statement and its converse are not equivalent. In general, this study found that the topic of if-then statements, their converses, and the differences between the two needs more attention by students of all levels of ability.
Collier, S. (2018). Investigating Problems with Mathematical Proof Skills. Wright State University, Dayton, Ohio.