
handle: 11567/1105480
This chapter first analyses and compares mathematicians’ and mathematics educators’ different conceptualisations of proof and shows how these are formed by different professional backgrounds and research interests. This diversity of views makes it difficult to precisely explain what a proof is, especially to a novice at proving. In the second section, we examine teachers’, student teachers’ and pupils’ proof conceptions and beliefs as revealed by empirical research. We find that the teachers’ beliefs clearly revolve around the questions of what counts as proof in the classroom and whether the teaching of proof should focus on the product or on the process. The third section discusses which type of metaknowledge about proof educators should provide to teachers and thus to students, how they can do this and what the intrinsic difficulties of developing adequate metaknowledge are.
Aurora Universities Network, Research, Teaching, [SHS.EDU] Humanities and Social Sciences/Education, Conceptions of Proof, Elementary Teacher; Euclidean Geometry; Mathematical Proof; Proof Scheme; Secondary School Teacher
Aurora Universities Network, Research, Teaching, [SHS.EDU] Humanities and Social Sciences/Education, Conceptions of Proof, Elementary Teacher; Euclidean Geometry; Mathematical Proof; Proof Scheme; Secondary School Teacher
| citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 9 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Average | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Average | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Average |
