Students' understanding of the core concept of function

This thesis is concerned with students' understanding of the core concept of function which cannot be represented by what is commonly called the multiple representations of functions. The function topic is taught to be the central idea of the whole of mathematics. In that sense, it is a model of mathematical simplicity. At the same time it has a richness and has mathematical complexity. Because of this nature, for students it is so difficult to grasp. The complexity of the function concept reveals itself as cognitive complications for weak students. This thesis investigates why the function concept is so difficult for students. In the Turkish context, students in high school are introduced to a colloquial definition and are presented with four different aspects of functions, set-correspondence diagrams, sets of ordered pairs, graphs and expressions. The coherency in recognizing these different aspects of functions by focusing on the definitional properties is considered as an indication of an understanding of the core concept of function. Focusing on a sample of a hundred and fourteen students, their responses in the questionnaires are considered to select nine students for individual interviews. The responses from these nine students in the interviews are categorized as they deal with different aspects of functions. The data indicates that there is a spectrum of performance of students. In this spectrum, responses range from the responses which handle the flexibility of the mathematical simplicity and complexity to the responses which are cognitively complicated. Successful students could focus on the definitional properties by using the colloquial definition for all different aspects of functions. Less successful students could use the colloquial definition for only set-correspondence diagrams and sets of ordered pairs and gave complicated responses for the graphs and expressions. Weaker students could not focus on the definitional properties for any aspect of functions

Students' understanding of the core concept of function

This thesis is concerned with students' understanding of the core concept of function which cannot be represented by what is commonly called the multiple representations of functions. The function topic is taught to be the central idea of the whole of mathematics. In that sense, it is a model of mathematical simplicity. At the same time it has a richness and has mathematical complexity. Because of this nature, for students it is so difficult to grasp. The complexity of the function concept reveals itself as cognitive complications for weak students. This thesis investigates why the function concept is so difficult for students. In the Turkish context, students in high school are introduced to a colloquial definition and are presented with four different aspects of functions, set-correspondence diagrams, sets of ordered pairs, graphs and expressions. The coherency in recognizing these different aspects of functions by focusing on the definitional properties is considered as an indication of an understanding of the core concept of function. Focusing on a sample of a hundred and fourteen students, their responses in the questionnaires are considered to select nine students for individual interviews. The responses from these nine students in the interviews are categorized as they deal with different aspects of functions. The data indicates that there is a spectrum of performance of students. In this spectrum, responses range from the responses which handle the flexibility of the mathematical simplicity and complexity to the responses which are cognitively complicated. Successful students could focus on the definitional properties by using the colloquial definition for all different aspects of functions. Less successful students could use the colloquial definition for only set-correspondence diagrams and sets of ordered pairs and gave complicated responses for the graphs and expressions. Weaker students could not focus on the definitional properties for any aspect of functions.EThOS - Electronic Theses Online ServiceTurkey. Millí Eğitim BakanlığıGBUnited Kingdo

Examining professional identity through story telling

[No abstract available

Curriculum reform in primary mathematics education: teacher difficulties and dilemmas

This paper examines primary classroom teachers\" preparedness of implementing a new curriculum model. The new curriculum displays a paradigmatic shift from a behaviourist approach to more of a constructivist one. The development of problem solving skills is particularly emphasised in the new curriculum. Two questionnaires including items on students\" different solution strategies to problems are applied to roughly 500 teachers to seek how teachers value and make sense of different strategies. The data reveals that the teachers are not open to different strategies, have difficulties in evaluating students responses to the open-ended questions and experience serious mathematical difficulties in assessing students\" solutions. We discuss issues raised by the findings with regard to the curriculum implementation

Investigating the development of prospective mathematics teachers' technological pedagogical content knowledge

[No abstract available

Mathematical thinking research by turkish community

In this article we give a brief overview of the present state of research conducted by Turkish community on mathematical thinking. Particularly, the goal of this paper is to share some prototypical examples of research conducted in mathematics education by the Turkish mathematics education community, around the theme of mathematical thinking and supporting its development. The research on mathematics education is quite a recent achievement. To review the research on mathematical thinking mathematics educators\" studies were researched extensively. Later a series of content analyses of the research publications were conducted to determine the contribution of Turkish researchers on mathematical thinking. Our examination of the selected research studies reveals that the Turkish researcher has contributed rarely to the process aspect of mathematical thinking and extensively to the product of this process and the issues that support or hinder the development of mathematical thinking

Examining socio-mathematical norms related to problem posing: a case of a gifted and talented mathematics classroom

In this study, we propose the notion of a socio-mathematical norm to explore the affective aspects of a classroom in the context of problem posing. Our case is a gifted and talented mathematics classroom with twelve students. The primary source of data consists of forty-three mathematics lessons. Our theoretical stance defines two dimensions of a socio-mathematical norm: student and teacher. The findings revealed three socio-mathematical norms (reformulations of problems, generating new problems, evaluation and correction based on the sufficiency of the information) that reflect the classroom's micro-culture, which involves problem posing. In addition to these basic norms, normative understanding related to posing more challenging problems allowed for challenging mathematical situations in the classroom, which is of particular importance for gifted and talented students. We discuss the teacher's and students' roles in problem posing activities. We also explore possible reasons for not observing socio-mathematical norms regarding the assessment of posed problems on a criterion that could support students for posing more original, more complex, and more realistic problems. The study suggests practical implications for the dynamics of a classroom where students engage in problem posing activities and theoretical implications regarding the two dimensions of a norm