• Research in Mathematical Education
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• v.18 no.4
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• pp.257-272
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• 2014

This paper examines and presents descriptions of 12 prospective primary teachers' views on the nature of mathematics in USA. All the participants were elementary teacher candidates enrolled in the same mathematics method courses. Interview data show that the prospective primary teachers possess two kinds of views on the nature of mathematics: primarily traditional and even mix of traditional and nontraditional beliefs in terms of Raymond's (1997) belief criteria. Implications for teacher education were discussed at the end of the paper.

• The Mathematical Education
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• v.51 no.2
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• pp.161-171
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• 2012

Generally mathematics is regarded as a subtle subject to grasp their true meaning. And teacher's personal conceptions of mathematics influence greatly on the teaching and learning of mathematics. More over often teachers confess their difficulties in explaining the true nature of mathematics. In this paper, applying the theory of epistemology, we tried to search factors that must be counted important when trying to understand the true nature of mathematics. As results, we identified five characteristics of mathematical knowledge such as logical reasoning, abstractive concept, mathematical representation, systematical structure, and axiomatic validation. Next, we tried to investigate math education major students' conception of mathematics using these items. To proceed this research we asked 51 students from three Universities to answer their opinion on 'What do you think is mathematics?'. Analysing their answers in the light of the above five items, we got the following facts. 1. Only 38% of the students regarded mathematics as one of the five items, which can be considered to reveal students' low concern about the basic nature of mathematics. 2. The status of students' responses to the question were greatly different among the three Universities. This shows that mathematics professors need to lead students to have concern about the true nature of mathematics.

• Journal for History of Mathematics
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• v.14 no.2
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• pp.69-76
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• 2001

This paper aims to show an inner, basic harmony between metaphysics and current directions in mathematics and in the philosophy of mathematics. In this attempt, the general truths of metaphysics and the truths particularly relevant to the nature of mathematical abstraction serve as speculative guides in ordering the content and discussing the nature of the multiple questions lie between and disputed frontiers of metaphysics and mathematics.

• Journal for History of Mathematics
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• v.16 no.4
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• pp.53-58
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• 2003

The aim of this paper is to outline a nature of pure mathematics up to the point at which its main theses can be clearly grasped and compared with other philosophical positions. Also, We analyze the contents and discuss the nature of questions which lie in pure mathematics.

• School Mathematics
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• v.4 no.2
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• pp.205-222
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• 2002

In school mathematics, the negative numbers have been instructed using the intuitive models such as the number line model, the counting model, and inductive-extrapolation on the additionand multiplication and using inverse operation on the subtraction and division. Theseinstructions on the negative numbers did not present their formal nature and caused the difficulty for students to understand their operations because of the incomplete function of the intuitive models. In this study, we tried to improve such problems of the instructions of the negative numbers on the basis of the didactical phenomenological analysis. First of all, we analysed the nature of the negative numbers and the cognitive obstructions through the examination about the historic process of them. Second, we examined hew the nature of the negative numbers were analysed and described in mathematics. Third, we explored the improving directions for them on the ground of the didactical phenomenological analysis. In school mathematics, the rules of operations using the intuitive models of the negative numbers have been Instructed rather than approaching toward the nature of them. The negative numbers have been developed from the necessity to find the general solution of equations. The study tries to approach the operations instructions of the negative numbers formative]y to overcome the problems of those that are using the intuitive models and to reflect the formative Furthermore of the negative numbers. Furthermore, we examine the way of the instruction of the negative numbers in real context so that the algebraic feature and the real context should be Interactive.

• Journal of Educational Research in Mathematics
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• v.8 no.1
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• pp.351-364
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• 1998

This thesis analyzes the nature of proof in the perspective on the philosophy of mathematics. such as absolutism, quasi-empiricism and social constructivism. And this thesis searches for the improvement of teaching proof in the light of the result of those analyses of the nature of proof. Though the analyses of the nature of proof in the perspective on the philosophy of mathematics, it is revealed that proof is a dynamic reasoning process unifying the way of analytical thought and the way of synthetical thought, and plays remarkably important roles such as justification, discovery and conviction. Hence we should teach proof as a dynamic reasoning process unifying the way of analytic thought and the way of synthetic thought, avoiding the mistake of dealing with proof as a unilaterally synthetic method. At the same time, we should make students have the needs of proof in a natural way by providing them with the contexts of both justification and discovery simultaneously. Finally, we should introduce the aspect of proof that can be represented as conviction, understanding, explanation and communication to school mathematics.

• Journal for History of Mathematics
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• v.15 no.3
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• pp.49-58
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• 2002

The present paper aims to show basic substitution between metaphysics and mathematical abstraction in the philosophy of mathematics. The general troths of metaphysics and the truths particularly relevant to tile nature of mathematical abstraction serve as speculative guides in ordering the content and discussing the nature of the multiple questions which lie between the disputed frontiers of metaphysics and mathematical abstraction.

• Journal of Applied and Pure Mathematics
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• v.5 no.1_2
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• pp.55-68
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• 2023

Character education is an important educational purpose in the current situation of secondary mathematics education. In the current mathematics curriculum, character education is mentioned in terms of core competencies. However, it is very difficult to concretely practice character education in secondary mathematics education. This paper examines the theoretical background of character education in the tradition of mathematics education, and suggests that mathematics is regarded as a practical tradition by the nature of mathematics from a value-intrinsic perspective. In this respect, mathematics education is defined as an intrinsic and nurturing character through long history of practice. This paper searched for an integrated approach to practicing character education in of secondary mathematics education, and argued that the teacher's personal approach including the class model approach of the human factors by an example of the exponential law a^maⁿ = a^m+n and the value-oriented activities according to the nature of the mathematics was the core.

• Education of Primary School Mathematics
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• v.21 no.3
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• pp.329-349
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• 2018

The purpose of this study is to investigate the mathematical belief of elementary school preservice teachers and elementary school teachers and to analyze their differences in mathematical belief. The results of the analysis are as follows. First, Elementary school preservice teachers generally regard the belief in the nature of mathematics as 'rules and procedures' and emphasize the 'process of inquiry' about the beliefs of learning mathematics. When comparing the beliefs according to gender, there is a significant difference only in the category of 'teacher instruction' among the beliefs of learning mathematics. Second, elementary school teachers generally regard the nature of mathematics as a 'inquiry process' and have a 'student-led' belief about the learning mathematics. There is no significant difference of the belief about the nature of mathematics and learning mathematics between the elementary school teachers by gender and majors. However, when comparing the mathematical beliefs according to educational level, there is a difference in beliefs about the nature of mathematics. Third, comparing the mathematical beliefs of elementary school preservice teachers and elementary school teachers, there is no statistically significant difference between the two groups in the 'rules and procedures' subcategories of the nature of mathematics, but there is a significant difference in 'inquiry process'.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.295-308
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• 2016

Depending upon the nature of the problem, different divergence measures are suitable. So it is always desirable to develop a new divergence measure. In the present work, new information divergence measure, which is exponential in nature, is introduced and characterized. Bounds of this new measure are obtained in terms of various symmetric and non- symmetric measures together with numerical verification by using two discrete distributions: Binomial and Poisson. Fuzzy information measure and Useful information measure corresponding to new exponential divergence measure are also introduced.