| Reasoning and proof is one of the five major process standards proposed by the National Council of Teachers of Mathematics (NCTM, 2000). NCTM claims that the notion of proof is a fundamental element of mathematics and therefore should be a fundamental element of mathematics education for all students. Given the centrality of proof to mathematics and its potential to play a significant role in students' development of reasoning abilities, the following study has been conducted.;The purpose of the study was to investigate in-service high school mathematics teachers' conceptions of and practices with mathematical proof. Three-hundred and seventy-four high school mathematics teachers participated in an original online survey, which was based on a substantial theoretical framework drawn from both mathematics and mathematics education.;The findings of this study suggest that teachers' conceptions of proof are composed of four principle components: (i) teachers' ability to understand, produce, and appreciate the value of mathematical proofs, (ii) teachers' conceptions of the importance of proof in mathematics, (iii) teachers' perceptions of students' capacity to understand proof, (iv) teachers' intellectual awareness of the philosophy, history, and teaching and learning standards of mathematics. Teachers' reported classroom practices with proof appear to vary according to the academic ability level of the students as well as the particular mathematical sub-discipline being taught. These findings bear implications to teachers, teacher educators, textbook authors, and those that create teaching and learning standards as well as government sponsored testing. |
