Examination of the Mathematical Problem-Solving Beliefs and Success Levels of Primary School Teacher Candidates Through the Variables of Mathematical Success and Gender

Abstract

Since the 1970s, developments in the field of social psychology have brought the concepts of cognition and belief into question; research that had been performed on the concept of belief in the 1980s especially gained importance and were applied to different disciplines such as psychology, political science, anthropology, and educational sciences (Thompson, 1992). Belief can be defined as feeling that something is good, right, or valuable, (Merriam-Webs ter, 2014), or as being bonded with an idea in the heart, (Turk Dil Kurumu, 2011, p. 1186). As in the scope of educational sciences, many researchers have defined the concept of belief in different ways. According to Pajares (1992) for example, belief means the choices and behaviors of people based on their life experiences. For Richardson (1996), beliefs are the assumptions and thought patterns that individuals develop due to conditions in their life. Thompson (1992) defined belief as a diagram of the emotions, value judgments, and past experiences of an individual. Schoenfeld (1998) defined belief as the experiences and understandings of individuals coded into mental diagrams. Deryakulu (2004, p. 260) defined belief as the internal acceptance or statements assumed to be right by an individual that determine how one perceives, intends, and acts towards every event, fact, person, or object. As can be gathered from these opinions, there is not a common, agreed-upon definition regarding the concept of belief in terms of the educational literature. In terms of mathematical education, it has been evaluated that many researchers point out mathematical belief and its importance with the concept of problem-solving (Bishaw, 2010; De Corte & Opt Eynde, 2002; Philipp, 2007; Raymond, 1997; Schoenfeld, 1992; Silver 1985; Thompson, 1985, 1992). In this scope, Raymond (1997) defines mathematical belief as value judgements towards mathematics that an individual has obtained from past experiences. Pehkonen and Torner (2003) define mathematical belief as an individual understanding of the mathematical world while identifying mathematical tasks alongside this. Again, Ernest (1989) defines mathematical belief as the concepts, ideologies, values, and philosophies of an individual on life and mathematics. Dede and Karakuc (2014) define it as the psychological understandings and mental structures of an individual that are shaped from past experiences. Mathematical belief is also handled as the sum of value judgments and subjective approaches that an individual has developed due to their past experiences in this study.When evaluating the concept of in terms ofwords, many sources define problem as acondition that needs to be solved but whose solution is not known directly from daily life (Blum & Niss, 1991; Polya 1990, Van De Walle, Karp, & Bay-Williams, 2013). Mathematically, problems should need a solution; having made no preparations for finding the solution, there should be attempts at solving it (Jonassen, 2000; Reys, Suydam, Lindquist, & Smith, 1998; Schoenfeld, 1992; Van De Walle, 2007). Based on this, problem solving is the period of completing facts or complicated situations by checking over different ways of obtaining solutions (NCTM, 2000; Schoenfeld, 1992). Since problem solving is a basic part of mathematical learning, it is also an important area in the development of mathematical knowledge and thought processes of students (Ho, 2009; Lester, Garofalo, & Kroll, 1989; Malloy, 2002; NCTM, 2000; Reys et al, 1998; Schoenfeld, 1992; Thompson, 1985). The development of problem-solving skills is an important skill that needs to be developed slowly and continuously from kindergarten to higher education (Van De Walle, 2007). Many researchers that have examined the stages of problem solving emphasize the importance of internal and external factors in problem solving (Jonassen, 2000; Smith, 1991). In this scope, external problems are reasons that originate from the problem itself, such as the structure of the problem, its complexity, abstractness, and presentation. …