PROCEEDINGS OF THE 19TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2016
Pittsburgh, Pennsylvania
Students’ explicit, unwarranted assumptions in “proofs” of false conjectures
Page: 588
Although evaluating, refining, proving, and refuting conjectures are important aspects of doing mathematics, many students have limited experiences with these activities. In this study, undergraduate students completed prove-or-disprove tasks during task-based interviews. This paper explores the explicit, unwarranted assumptions made by six students on tasks involving false statements. In each case, the student explicitly assumed an exact condition necessary for the statement in the task to be true although it was not a given hypothesis. The need for an ungiven assumption did not prompt any of these students to think the statement may be false. Through prompting from the interviewer, two students overcame their assumption and correctly solved the task and two students partially overcame it by constructing a solution of cases. However, two other students were unable to overcome their assumptions. Students making explicit, unwarranted assumptions seems to be related to their limited experience with conjectures.