The purpose of this study was to investigate first year elementary mathematics teacher education students' knowledge of prism. For this goal, the participants were asked to define the geometric concept of prism. The participants were 158 first year elementary mathematics teacher education students from a public university in Southern Turkey. The researchers analyzed the participants' definitions of prism. Additionally, 12 of the participants were selected for semi-structured interviews. The data were analyzed via content and frequency analysis techniques. Based on the content analysis, the themes that each participant used were determined. After this evaluation, the frequency of each of the themes was calculated. The findings indicated that the participants experienced difficulties in defining the concept of prism. It was also found out that the participants could not adequately use the mathematical language and define the concept.
Geometry Teaching, Geometric Concepts, Prism, Concept Definition, Teacher Education.
Individuals understand their surrounding environment through sense making and concept mapping (Schoenfeld, 1992). A concept is an umbrella term that is used to portray main characteristics of an object or thought (Türk Dil Kurumu [TDK], 2005). It can be argued that concept is an element of understanding and knowledge (Öksüz, 2010). Teaching without conceptual understanding may just lead to memorizing, drill and practice, and computational learning (Sigler & Saam, 2006; Snowman & Biehler, 2003).
There can be a wide range of individual differences in definitions of a single concept (Vinner, 1991). Hence, we can classify concept definitions in two large categories; formal and personal definitions. In mathematics, formal definitions are the ones which are formally accepted and respected by the large community of mathematicians (Tall & Vinner, 1981). On the other hand, personal definitions reflect individuals' thoughts and experiences or, more technically, their concept images (Tall, 1991). Definitions based on personal experiences make more sense than other definitions. If the concept image or the individuals' thoughts about the concept is inaccurate, their concept definitions may contain errors (Vinner); and the concept image draws boundaries of the concept (Keiser, Klee, & Fitch, 2003).
As a branch of mathematics, in geometry, it is essential to visualize geometric concepts in the mind for conceptual understanding (Hershkowitz, Parzysz, & Dormolen, 1996). Higher level geometric thinking requires at least a basic understanding of concept definition (Linchevsky, Vinner, & Karsenty, 1992). Thus, understanding and accurate explanations of definitions is essential for geometric understanding (Hiebert & Lefevre, 1986).
In the literature, we see a number of studies that investigated K-12 and teacher education students' definitions of geometric concepts and their misconceptions (Clements, Sarama & Battista, 1998; Cunningham & Roberts, 2010; de Villers, 1998; Gutierrez & Jaime, 1999; Isiksal, Koç, & Osmanoglu, 2010; Koç & Bozkurt, 2011; Linchevsky et al., 1992; Matos, 1994; Tunç & Durmus, 2012; Zembat, 2007). Such studies indicate that students experience difficulties in defining geometric concepts.
Teacher knowledge is important to form desired learning environments (Putnam, Heaton, Prawat, & Remillard, 1992). This is also valid in teaching geometry (Swafford, Jones, & Thornton, 1997). For this reason, teachers should understand the geometry they teach and also prepare the students for advanced levels. Teachers' content knowledge is generally shaped during their pre-service education and before. Yet, pre-service teachers do not always have adequate knowledge of the mathematics they would teach in the future. Pre-service teachers' limited knowledge of mathematics is one of the major obstacles in teacher education programs (Brown & Borko, 1992). …