The Role of the Proof in Math Essay - 2675 Words

The Role of the Proof in Math The notion of proof has long played a key role in the study of mathematics. It is in my opinion the role of proof that separates mathematics from the sciences and other fields of study. It is the existence of proofs that give mathematicians the confidence that their work is credible and thus allows them to continue to build upon prior work without the need to second guess what has previously been accomplished. Based upon this observation, it becomes natural to ask the questions pertaining to the use of proof in learning and understanding mathematics. If the concept of proof is so important to the field of mathematics, then is it possible that by writing proofs and studying proofs that an†¦show more content†¦construction of an empirical theory (taken from Hanna) 7.exploration, to understand the meaning and/or consequences of a definition or statement 8.incorporation of a well known fact into a new framework (taken from Hanna) This list is essentially taken from Hanna’s paper, but upon review of Knuth’s paper one would see that the first five functions are the same as the the conceptions of the role of proofs given by the teachers within his study. There are far less of these given in Tucker’s paper, but in order to show some continuity across the literature, I have included it because amongst his list of common reason’s why proofs should be used to teach mathematics is that â€Å"proofs help students understand concepts and believe results† (although he doesn’t share this view). Clearly this statement falls within items one and two, where â€Å"believe results† can be interpreted as verification and understanding goes along with the idea of explanation. If we are to believe that this list of the functions of proof in mathematics has any credibility, then we should at least be tempted to believe that the use of proofs can play a vital role in learning and understanding mathematics. If proofs can provide a means of explanation, discovery, communication, and exploration; then wouldn’t the use of proofs be a powerful tool for learning mathematics? It is my opinion that the answer to this question is a resounding yes and consequently that means should be foundShow MoreRelatedWhy Math Is Important For Teaching Mathematics And How Students Learn Mathematics870 Words   |  4 PagesMath Philosophy Paper Math is developing concepts or standards that’s important for teaching mathematics to students from Pre-K to high school. 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