Evaluation of Formal-Rhetorical and Problem-Centered Mathematical Proof of Students

Year 2016, Volume: 7 Issue: 2, 39 - 47, 21.08.2016

Hasan - Hamid

Abstract

Evaluation of Formal-Rhetorical and Problem-Centered Mathematical Proof of Students

Abstract

This is the result of a study aimed at evaluating the process of verification of student mathematics education in performing of proof using of the formal-rhetorical part and problem-centered part as proof structure. Description of a combination of the understanding of the formal-rhetorical part and problem-centered part in proving the lemma, theorem and the corollary in Real Analysis will bring the creative side of the students in understanding and validating as well as constructing proof. The formal-rhetorical part sometimes said to be a proof of proof framework, while the problem-centered part relying purely on mathematical problem solving, intuition, and understanding that are more related to the concept. Selden and Selden (2013) stated that two aspects of the structure of this evidence is proof genre.

Keywords: Proof, the formal-rhetorical part, the problem-centered part.

Keywords

Proof, the formal-rhetorical part, the problem-centered part

References

• Bartle and Sherbert (2010). Introduction To Real Analysis. John Wiley & Son, Inc. Singapore.
• Chen, Y. (2008). From formal proofs to informal proofs-teaching mathematical proofs with the help of formal proofs. International Journal of Case Method Research & Application. XX, 4,pp. 398-402.
• Cheng, Ying-Hao & Lin, Fou-Lai (2009). Developing Learning Strategies for Enhancing below Average Students’ Ability In Constructing Multiple-Steps Geometry Proof. Proceedings of the ICMI Study 19 Conference: Proof and Proving in Mathematics Education, Vol. 1, pp. 124-129
• Lee, Kosze & Smith III, John P. (2009). Cognitive and Linguistic Challenges in Understanding Proving. Proceedings of the ICMI Study 19 Conference: Proof and Proving in Mathematics Education, Vol. 2, pp. 21-26.
• Mariotti, M. A. (2006). Proof and proving in mathematics education. In A. Gutierrez, & P. Boero (Eds.), Handbook of research on the psychology of mathematics education (pp. 173-204). Rotterdam, The Netherlands: Sense Publishers.
• Pedemonte, B. (2007). How can the relationship between argumentation and proof be analysed?. Journal Educational Studies in Mathematics, 66:23-41.
• Selden, A., & Selden, J. (2013). Proof and Problem Solving at University Level. Journal The Mathematics Enthusiast. 10(1&2), 303-334.
• Stylianides, A. J. (2007). Proof and proving in school mathematics. Journal for
• Research in Mathematics Education, 38(3), 289-321.
• Toulmin, S. E. (2003). The Uses of Arguments (Updated Edition). Cambridge: University Press.
• Weber, K., & Mejia-Ramos, J. P. (2011). Why and how mathematicians read proofs: An exploratory study. Journal Educational Studies of Mathematics, 76, 329-344.
• Yumoto, T & Miyazaki, M. (2009). Teaching and Learning a Proof as an Object in Lower Secondary School Mathematics of Japan. Proceedings of the ICMI Study 19 Conference: Proof and Proving in Mathematics Education, Vol. 2, pp. 76-81.