Sınıf Öğretmeni Adaylarının Geometrideki Zihinsel Alışkanlıkları

Abstract

AbstractGeometric of are productive ways of that support learning and using geometric concepts. Identifying primary school teacher candidates' geometric of is important as they affect the development of their future students' geometric thinking. Therefore, this study attempts to determine primary school teachers' geometric of mind. Participants were 57 primary school teacher candidates in their third year studying Primary School Education in a Faculty of Education at a state university in Turkey. The data were collected through four open-ended geometry problems on concepts of perimeter and area. The collected data were then analyzed based on the theoretical framework of the components of geometric of and in accordance with the stages of descriptive analysis. The results showed that the primary school teacher candidates did not possess different ways of about the components indicating geometric of mind. The study also found that the candidates could not analyze the given problems appropriately and acted on the first idea they came up with, but they were unable to apply these actions on the problem and, therefore, their geometric of were not at the desired level.Key WordsGeometric Habits of Mind, Mathematics Education, Perimeter and Area, Teacher Training.Habits of are intellectual problem-solving skills necessary to promote reasoning, perseverance, creativity, and craftsmanship. Leikin (2007) suggested that of means inclination and ability to choose effective patterns of intellectual behavior (p. 2333). Cuoco, Goldenberg, and Mark (1996) identified two classes of of mind: general of that surpass every discipline and content-specific of specific to the discipline of mathematics. General of include basic qualities such as recognizing figures, exploring, describing, discovering, visualizing, conjecturing, and guessing. In contrast, mathematical of involve continuous reasoning, performing experiments in extraordinary situations, and employing abstraction used by mathematicians in their work (Mark, Cuoco, Goldenberg, & Sword, 2009).The main characteristics of mathematical of develop according to levels of learning (Cuoco, Goldenberg, & Mark, 2010; Goldenberg, Shteingold, & Feurzeig, 2003; Levasseur & Cuoco, 2003). In fact, the term habits of mind involves two major characteristics: thinking and habituation. Harel (2007, 2008) explained the dimension with ways of and regarded of as internalized ways of thinking. Goldenberg (2009) described the habituation dimension as that acquires well, makes natural, and incorporates fully into one's repertoire, that they become mental habits-one not only can draw upon them easily, but one is likely to do so (p. 13). Mason and Spence (1999) explained the habituation character with their notion of knowing-to act in the moment, while Lim (2008) explained it with the notion of spontaneous anticipation developing when a student instantly anticipates and performs an action in a problem case based on the first idea that comes to mind. Lim also regarded a habit of as a cognitive tendency to mentally act in a certain way in certain situations. By the habituation character, Lim (2009) referred to the tendency of doing whatever first comes to mind or diving into the first approach that comes to mind (Watson & Mason, 2007, p. 207). Mathematical of come to the fore in areas of mathematics such as geometry and algebra, and they are defined as geometric or algebraic of (Driscoll, 1999; Mark et al., 2009). A geometric habit of is a productive way of that promotes learning and practicing geometry. This way of involves exploring geometric relationships and reasoning with these relationships, generalizing geometric ideas, investigating variants and invariants in these relationships, and assessing a geometric figure with all these components (Driscoll, DiMatteo, Nikula, & Egan, 2007). …