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Abstract

ABSTRACT. This paper examines the views of proof held by university level mathematics students and teachers. A framework is developed for characterizing people's views of proof, based on a distinction between public and private aspects of proof and the key ideas which link these two domains.

Didactic Potential of Using Mobile Technologies in the Development of Mathematical Thinking

“…Mathematical thinking is revealed through the ability of a person to argue his actions and ideas. Raman (2003) explores the nature of the proof, various approaches to argumentation in the course of mathematical activity. The author shows the difference between mathematical proof and other sciences.…”

Mathematical proof: from mathematics to school mathematics

“…Beyond the function of proof, several researchers speak about different types of proofs, putting the focus on this global understanding or empowerment that is deeply connected to proof, and Smith [19] makes a good synthesis of some of these distinctions. That is the case with Hanna [32], who distinguishes between 'proofs that explain' and 'proofs that prove'; the case with Tall [33], who speaks about 'logical' and 'meaningful' proofs; the case with Weber & Alcock [34], who distinguish between 'syntactic' and 'semantic' proofs; and the case with Raman's [35], who focuses on the kind of ideas used in the proof and considers 'heuristic ideas' and 'procedural ideas,' with the concept of a 'key idea' linking the two. The points of view of these authors are slightly different, but as Smith [19, p. 75] emphasizes, what all of them seem to be addressing is two distinct approaches to mathematical proof: 'a procedural, logical approach on which the prover's intuition is not necessarily engaged, and an approach relying on the prover's intuitive understanding of the mathematical structure involved'.…”

Daily Life and Mathematic: Student and Content Constructions of the Concepts of Proposition, Theorem, and Proof

“…Existence of numerous national and international studies on individuals' weaknesses or misconceptions about theorem and proof (Almeida, 2000;Arslan and Yıldız, 2010;Arslan,2007;Aydoğdu, Olkun and Toluk, 2003;Bahtiyari, 2010;Coşkun, 2009;Dane, 2008;Dreyfus, 1999;Güven, Çelik and Karataş, 2005;Harel and Sowder, 1998;İmamoğlu, 2010;Jones, 2000;Moore, 1990Moore, , 1994Moralı, Uğurel, Türnüklü, and Yeşildere, 2006;Özer and Arıkan, 2002;Raman, 2002Raman, , 2003Recio and Godino, 2001;Sarı, Altun, and Aşkar, 2007;Selden and Selden, 2003;Shipley, 1999;Stylianides, Stylianides and Philippou, 2007;VanSpronsen, 2008;Weber, 2001Weber, , 2005 shows that the gaps or misconceptions related to theorem and proof are not peculiar only to Turkish context. Studies, among these subjects, have focused on proof which is regarded very important for developing mathematical thinking (Hanna, 2000;Moralı, Köroğlu and Çelik, 2004;Moralı et al, 2006) and can be used as a means of persuading people (Harel, 2008;Harel andSowder, 1998, 2007) (persuading people would decrease the undesirable social events).…”

“…Beside these, in NCTM in 2000, it is reported that proof is an effective way which can be used in developing and explaining instincts. Studies with the purpose to find out the reasons underlying the difficulties with proof which is an important phenomenon show that students cannot remember what proof is (Moore, 1994;Raman, 2003), do not have right ideas about what a mathematical proof consists of (Weber, 2001), and cannot understand the concept of proof (Dane, 2008;Güler and Dikici, 2012;Moore, 1994). Defining a subject matter difficult or easy vary according to various criteria.…”

“…The field knowledge needed to be effective in mathematics teaching (Bayazıt and Aksoy, 2010;Escudero and Sanchez, 2002;Özmantar and Bingölbali, 2010;Tirosh, Even and Robinson 1998;Yeşildere and Akkoç, 2010) covers all of the views and perceptions of mathematics teachers about the definitions, axioms, undefined concepts, methods of proving, correlation, rules, and formulae used in the teaching of mathematical subjects (Ball, 1991;Shulman, 1986). Therefore, studies aiming at exploring pre-service teachers and teachers'' opinions about and their views of proof and their processes of proving (Almeida, 2000(Almeida, , 2003Dane, 2008;Dickersen, 2006;Harel and Sowder, 1998;İskenderoğlu, Baki and Palancı, 2011;Jones, 1997Jones, , 2000Knuth, 2002;Moralı et al, 2006;Raman, 2002Raman, , 2003Recio and Godino, 2001;Solomon, 2006;Stylianides, et al, 2007;Weber, 2001) have also been conducted. In addition, it is suggested that teaching programs should cover some activities for developing and evaluating mathematical discussions and proofs (NCTM, 2000).…”