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Defining as vehicle for professional development of secondary school mathematics teachers. Mathematics Teacher Education and Development
, 2001
"... This paper describes a professional development program for secondary school mathematics teachers. The issue of mathematical definition is the focus of the program. The program aimed to develop teachers ’ subject matter knowledge including knowledge of substance of mathematics and knowledge about th ..."
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This paper describes a professional development program for secondary school mathematics teachers. The issue of mathematical definition is the focus of the program. The program aimed to develop teachers ’ subject matter knowledge including knowledge of substance of mathematics and knowledge about the nature and discourse of mathematics. The rationale of the course is described as well as some outcomes of its implementation. The activities included in the program deal with some mathematical concepts and different didactical approaches to secondary school mathematics. The two activities presented in this paper, exemplify some of the ideas. Mathematics teachers make critical decisions about the mathematics they teach and the way they teach mathematics. This requires teachers to be aware of reformoriented approaches for teaching mathematics as well as to be mathematically educated. Research in mathematics teacher education shows that teachers’ mathematical knowledge must be deep and robust in order to make intelligent decisions in the course of teaching mathematics (Ball, 1992, 1997; Ma, 1999). Thus,
Mathematical thinking & human nature: Consonance & conflict
, 2004
"... Human nature had traditionally been the realm of novelists, philosophers, and theologicians, but has recently been studied by cognitive science, neuroscience, research on babies and on animals, anthropology, and evolutionary psychology. In this paper I will show—by surveying relevant research and by ..."
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Human nature had traditionally been the realm of novelists, philosophers, and theologicians, but has recently been studied by cognitive science, neuroscience, research on babies and on animals, anthropology, and evolutionary psychology. In this paper I will show—by surveying relevant research and by analyzing some mathematical “case studies”—how different parts of mathematical thinking can be either enabled or hindered by aspects of human nature. This novel theoretical framework can add an evolutionary and ecological level of interpretation to empirical findings of math education research, as well as illuminate some fundamental classroom issues. A.
The Transition to Advanced Mathematical Thinking:
"... characterized by two important components: precise mathematical definitions (including the statement of axioms in axiomatic theories) and logical deductions of theorems based upon them. However, the printed word is but the tip of the iceberg the record of the ..."
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characterized by two important components: precise mathematical definitions (including the statement of axioms in axiomatic theories) and logical deductions of theorems based upon them. However, the printed word is but the tip of the iceberg the record of the
Running Head: Students, Functions, and Curriculum
"... recommendations stated here are those of the author and do not necessarily reflect official positions of NSF. Thompson Students, Functions, and Curriculum Someone, I cannot remember who, paraphrased Winston Churchill by saying that mathematics and mathematics education are two disciplines separated ..."
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recommendations stated here are those of the author and do not necessarily reflect official positions of NSF. Thompson Students, Functions, and Curriculum Someone, I cannot remember who, paraphrased Winston Churchill by saying that mathematics and mathematics education are two disciplines separated by a common subject. The mathematician is primarily concerned with doing mathematics at a high level of abstraction. The mathematics educator is primarily concerned with what it is that one does when doing mathematics and what kinds of experiences are propitious for a person’s later successes. Until recently mathematics education research has focused predominantly on the learning and teaching of early mathematics in the school curriculum, so it is natural that practicing mathematicians have found it difficult to relate to mathematics education research. I suspect that the current interest in calculus reform [21, 63] and the broader rethinking of the undergraduate curriculum, together with the advent of the AMS/MAA Joint Committee on Research in Undergraduate Mathematics Education, will lead to a wider recognition that mathematics and mathematics education
Demystifying Functions: The Historical and Pedagogical Difficulties of the Concept of the Function
, 2006
"... In this study, the author discusses the concept of function from a historical and pedagogical perspective. The historical roots, ranging from ancient civilizations all the way to the twentieth century, are summarized. The author then details several different function representations that have emerg ..."
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In this study, the author discusses the concept of function from a historical and pedagogical perspective. The historical roots, ranging from ancient civilizations all the way to the twentieth century, are summarized. The author then details several different function representations that have emerged over the course of the concept’s history. Special attention is paid to the idea of abstraction and how students understand functions at different levels of abstraction. Several middle school, high school, and college textbooks are then analyzed and evaluated based on their portrayal of the function concept. The author describes several common misconceptions that students have about functions and finally proposes a short educational module designed to help older high school students grow to a deeper level of understanding of this complex and often misunderstood concept.
MATHEMATICS EDUCATIONAL VALUES OF COLLEGE STUDENTS ' TOWARDS FUNCTION CONCEPT
"... ABSTRACT. Mathematics is usually seen as a field in which there is valuefree. Such a situation causes only a few studies about values teaching to be done in mathematics education. But, mathematics is a field that has various values in it, and that must be considered seriously from this perspective. ..."
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ABSTRACT. Mathematics is usually seen as a field in which there is valuefree. Such a situation causes only a few studies about values teaching to be done in mathematics education. But, mathematics is a field that has various values in it, and that must be considered seriously from this perspective. Values are taught implicitly rather than explicitly in mathematics classes when comparing to others. Function concept also take place among the most essential concepts of mathematics. It concept has affected the whole maths cirruculum. Therefore, being unable to comprehend this concept will make mathematical concepts understanding harder. Knowledge defiencies of teachers and undergrade students this concept understanding much harder. So, in this article, it has been tried that the mathematics students' mathematics educational values towards function concept have been determined. The subject of this work consist of undergrade students who have studied at Cumhuriyet University in Sivas and also Cumhuriyet University's Mathematics Educational Department in Sivas. Data were collected from 10 openended and 11 items reasons of question choose. As a result of this research, it was realized that the students from all grades preferred, in terms of learning the function concept, those questions that hold the formalistic view values, relavance values, instrumental understanding/learning values, accessibility values, and reasoning values. KEYWORDS. Values, Mathematical Values, Mathematics Educational Values, Function Concept.
1 Foundational Reasoning Abilities that Promote Coherence in Students ' Function Understanding
"... The concept of function is central to undergraduate mathematics, foundational to modern mathematics, and essential in related areas of the sciences. A strong understanding of the function concept is also essential for any student hoping to understand calculus – a critical course for the development ..."
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The concept of function is central to undergraduate mathematics, foundational to modern mathematics, and essential in related areas of the sciences. A strong understanding of the function concept is also essential for any student hoping to understand calculus – a critical course for the development of future scientists, engineers, and mathematicians. Since 1888, there have been repeated calls for school curricula to place greater emphasis on functions (College Entrance Examination Board, 1959; Hamley, 1934;
Mathematical Association of America. Foundational Reasoning Abilities that Promote Coherence in Students ' Function Understanding
"... The concept of function is central to undergraduate mathematics, foundational to modern mathematics, and essential in related areas of the sciences. A strong understanding of the function concept is also essential for any student hoping to understand calculus – a critical course for the development ..."
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The concept of function is central to undergraduate mathematics, foundational to modern mathematics, and essential in related areas of the sciences. A strong understanding of the function concept is also essential for any student hoping to understand calculus – a critical course for the development of future scientists, engineers, and mathematicians. Since 1888, there have been repeated calls for school curricula to place greater emphasis on functions (College Entrance Examination Board, 1959; Hamley, 1934;
CORRESPONDENCES, FUNCTIONS AND ASSIGNATION RULES
"... In this paper we put forward a theoretical position that, in cognitive terms, a differentiation should be made between a correspondence and a function. Important in understanding this difference is the role of an assignation rule; the correspondence acts as a way to identify a rule in context, whils ..."
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In this paper we put forward a theoretical position that, in cognitive terms, a differentiation should be made between a correspondence and a function. Important in understanding this difference is the role of an assignation rule; the correspondence acts as a way to identify a rule in context, whilst the function accommodates the rule in a more formal framework providing a secure base for argumentation. This perspective is used to interpret some students ’ behavior in a task where the identification of a particular relationship is crucial for its solution.
an introduction to a formal characterization
, 1298
"... Abstract: We investigate in this paper the complexity of modeling students knowing of mathematics under the constraints of acknowledging both their possible lack of coherency and their local efficiency. For this purpose we propose a formalization of the notion of “conception ” as a possible tool to ..."
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Abstract: We investigate in this paper the complexity of modeling students knowing of mathematics under the constraints of acknowledging both their possible lack of coherency and their local efficiency. For this purpose we propose a formalization of the notion of “conception ” as a possible tool to answer the epistemological problem we identify. We apply then this approach to the study of the possible conceptions of “function”, from an historical and then an epistemic point of view. We report the result of a case study in order to illustrate the benefit we expect from this approach. The notions of “conception”, “knowing ” and “concept ” are then related the one to the other within the model presented. 1.!!FROM BEHAVIOR TO MEANING The only indicators we have of the good or of the bad functioning of teaching are students ’ behaviors and productions, which are consequences of the knowing1 they have constructed and of their relationships to the content taught. But such evaluations are possible and their results are significant only in the case where one is able to establish a valid relationship between these observed behaviors and the considered knowledge itself. This relation between behaviors and knowing is crucial. It has been hidden as a result of the fight against behaviorism, but it has always been implicitly present in educational research at least at the methodological level. The key issue is that the meaning of a piece of knowledge cannot be reduced to