| This research study was conducted to investigate prospective secondary mathematics teachers' conceptions of proof and refutations as they were near completion of their preparation program. To research the primary question of the study, the researcher addressed two components of participants' conceptions of proof—(1) understanding of the logical underpinnings of proof, and (2) ability to complete mathematical proofs. The researcher developed a questionnaire composed of two parts in order to assess the two components of proof. Both components focused on direct proof, indirect proof, and refutations. The sample for the study were 23 prospective secondary mathematics teachers that had completed an introduction to proof course, geometry course, and at least two calculus courses.; Results show that only 30% of the prospective teachers correctly answered 9 or more items, of 12 items, for the logical underpinnings of proof. The results show that participants have a weak understanding of the truth of a conditional statement and its related statements (e.g., converse, negation of conditional statement).; Examining prospective teachers' ability to complete mathematical proofs show that only 57% of the participants were able to write a valid direct proof of the Perpendicular Bisector Theorem, a proof common to the high school geometry curriculum. Only 39% of the participants were able to write a valid indirect proof about even integers. Results show that only 39% of the sample recognized and were able to refute a false conjecture about perimeter and area of rectangles.; Results of participants' overall performance on both parts of the questionnaire show that 52% of the sample scored 60% or less on both parts of the questionnaire. The vision of the MAA (1998) and the NCTM (2000) recommendations for teaching reasoning and proof to all students grades K–12, and in all mathematics content areas, may not be attainable by all of the prospective secondary mathematics teachers in this study. The finding suggest that prospective teachers need more experiences in determining the true values of conjectures and that there is a correlation between an individual's understanding of the logical underpinnings of proof and ability to complete proofs. |
