The Examination of Representations used by Classroom Teacher Candidates in Solving Mathematical Problems

Abstract

AbstractThis study was designed according to the mixed research method in which quantitative and qualitative research methods were used in order to identify the challenges confronted by classroom teacher candidates in solving mathematical problems and the factors affecting how they choose these representations. The population of this study consisted of 100 3rd year students attending the primary teaching department of Cukurova University during the 2012-2013 academic year. In identifying the samples, the criterion sampling method, a purposeful sampling method, was used. The data collection tools consisted of The Use of Multi pie-Representations in Problem Solving Test and a semi-structured interview form prepared by the researcher. At the end of the research it was discovered that classroom teacher candidates could use different types of multiple representations in solving mathematical problems. However, they used spoken language and algebraic representations the most. During the interviews, teacher candidates emphasized that experience arid the content of the problem are the most important factors in identifying which multiple representations to use. Another important result obtained from the research is that teacher candidates can have problems forming a suitable theme for problems and shifting between representations. For this situation, it can be suggested that giving importance to the concept of multiple representations in the teaching of mathematics as well as doing in-class application studies intended to solve and associate problems using the concept of multiple representations would be beneficial. In that way, teacher candidates can guide their students towards different points of view while solving problems.KeywordsMultiple Representations, Classroom Teacher Candidates, Problem Solving, Mathematics, Polya.The concept of using multiple representations has an important place in the teaching of mathematics (Cai, 2005; Cobb, Yackel, & Wood, 1992; Goldin, 1998; Janvier, 1987), especially in the understanding of mathematical concepts and interpreting them from different points of view through the use of multiple representations (Cathcart, Pothier, Vance, & Bezuk, 2006; Hjalmarson, 2007; Pape & Tchoshanov, 2001). According to Tripathi (2008), the use of multiple representations in teaching mathematics is a strong instrument that eases the understanding of mathematical subjects for students. Also, the use of multiple representations strengthens the understanding of students for learning how to form and solve problems in a mathematics course.The new standards of the American National Council of Teachers of Mathematics (NCTM) published in 2000 especially emphasize the importance of the concept of representation. Within this context, according to the NCTM, the use of diagrams, graphics, tables and symbols, as well as transitioning between them, is of capital importance in expressing mathematical thoughts and relations. Stemming from the NCTM (2000) standards, representations are also a part of the required abilities in the mathematics curriculum of Turkey for use in problem solving, communication (verbal lectures, written statements, images, graphics, concrete concepts), and associations (Milli Egitim Bakanligi [MEB], 2005, 2009). Stylianou (2010) also states that students should be effective in using representations and their transitions for solving mathematics and understanding mathematical concepts.As a general term, a representation is a way to show an actual situation from a different point of view (Even, 1998; Goldin & Kaput, 1996). In mathematics, however, teaching representation is a part of forming or shaping a mathematical concept. The different representations that teachers use during in-class activities affect the knowledge, and accordingly, the success of students (Cai, 2005; Neria & Amit, 2004; Stylianou & Silver, 2004). That is why the understanding of representations and how to use different types of representations should be an active part of the teaching process (Hjalmarson, 2007; Pape & Tchoshanov, 2001). …