• Korean Journal of Child Studies
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• v.35 no.6
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• pp.93-110
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• 2014

The purpose of this study was to examine the effects of cookbook making activities on young children's mathematical concept and writing development. The participants were comprised of 50 five-year-old children from two intact classes from a kindergarten in Gyeonggi province, and they were divided into an experimental and a comparison group. The experimental group participated in cooking activities and produced cookbooks as extension activities whereas the comparison group carried out only cooking activities. The results indicated that the children in the experimental group received statistically higher scores in mathematical concept- and writing-tests, suggesting that cookbook making activities are a useful educational tool for enhancing young children's mathematical concepts and facilitating their writing development.

• Communications of Mathematical Education
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• v.33 no.3
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• pp.255-273
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• 2019

In order to help students to understand the essence of prime concepts, this study looked at the history of prime concept development and analyzed how to introduce the concept of textbooks. In ancient Greece, primes were multiplicative atoms. At that time, the unit was not a number, but the development of decimal representations led to the integration of the unit into the number, which raised the issue of primality of 1. Based on the uniqueness of factorization into prime factor, 1 was excluded from the prime, and after that, the concept of prime of the atomic context and the irreducible concept of the divisor context are established. The history of the development of prime concepts clearly reveals that the fact that prime is the multiplicative atom is the essence of the concept. As a result of analyzing the textbooks, the textbook has problems of not introducing the concept essence by introducing the concept of prime into a shaped perspectives or using game, and the problem that the transition to analytic concept definition is radical after the introduction of the concept. Based on the results of the analysis, we have provided several pedagogical implications for helping to focus on a conceptual aspect of prime number.

• Journal of Educational Research in Mathematics
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• v.10 no.1
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• pp.73-84
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• 2000

This study, after careful consideration on Piaget's structuralism, showed the relationship between Bourbaki's matrix structure of mathematics and Piaget's structure of mathematical thinking. This, studying the basic characters that structure of knowledge should have, pointed out that 'transformation' and to it, too. Also it revealed that group structure is a 'development' are essential typical one which has very important characters not only of mathematical structure but also general structure, and discussed the problem that learners construct the group structure as a mathematical concept.

• Journal for History of Mathematics
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• v.18 no.2
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• pp.9-22
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• 2005

Natural numbers have not yet been studied adequately on the aspect of its historical development in spite of its mathematical and educational importance. This article studied the historical development of natural number concept, that is, its historical meaning in the mathematical development process and influence of cultural and social element in relation with way of understanding number. From these examinations, we identified some characteristics in the history of natural number concept.

• Journal for History of Mathematics
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• v.12 no.2
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• pp.15-23
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• 1999

This paper deals with the origin of the concept of lattices in mathematics and its development until 1930's. Although it is purely mathematical, its formation is due to the development of symbolic logic Further, logicians were mostly concerned about how to imitate the methods and duplicate the problems of algebra but not the application to mathematics. The first purely mathematical approach was given by Dedekind and his results were neglected and then reappeared in 1930's.

• Journal of the Korean School Mathematics Society
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• v.6 no.1
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• pp.163-175
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• 2003

The research was aimed to find a special quality to the mathematical concept development using a graphing calculator in the collaborative learning. I could observe the process in which the students had formed the generalized and abstract mathematical concepts after they were given different concepts. I \ulcorner-Iso observed the characteristics of how they started with a vague syncretic conglomeration and approached to the complicated thoughts and genuine concepts. The advance of the collection type was achieved in the process of teacher's confirming of what the students had observed with a calculator. The language and the instrument were used in order for students to control the partial process. Also, they were given similar types of problems to make them clear when the students confronted 'the crisis of thoughts' at the level of pseudo-concept.

• The Mathematical Education
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• v.42 no.3
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• pp.303-325
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• 2003

This study sought to provide an explanation of university students' concept understanding on the infinity and infinite process and utilized a psychological constructivist perspective to examine the differences in transitions that students make from static concept of limit to actualized infinity stage in context of problems. Open-ended questions were used to gather data that were used to develop an explanation concerning student understanding. 47 university students answered individually and were asked to solve 16 tasks developed by Petty(1996). Microgenetic method with two cases from the expert-novice perspective were used to develop and substantiate an explanation regarding students' transitions from static concept of limit to actualized infinity stage. The protocols were analyzed to document student conceptions. Cifarelli(1988)'s levels of reflective abstraction and Robert(1982) and Sierpinska(1985)'s three-stage concept development model of infinity and infinite process provided a framework for this explanation. Students who completed a transition to actualized infinity operated higher levels of reflective abstraction than students who was unable to complete such a transition. Developing this ability was found to be critical in achieving about understanding the concept of infinity and infinite process.

• Journal of Educational Research in Mathematics
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• v.22 no.2
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• pp.229-259
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• 2012

The purpose of the present study is to develop instrument of mathematical belief of middle school and high school students and to analysis results of test using the instrument. Based on the results of literature review, mathematical belief is the cumulative effects of self-assessment and self-concept in mathematical learning and achievement experience. Four sub-components of mathematical belief is identified belief of school mathematics, belief of mathematical problem solving, mathematical self-concept, belief of mathematical teaching and learning. The instrument was developed to investigate mathematical belief by reflecting Korean middle school and high school students' psychological characters. To develop the appropriate items for the mathematical belief, after reviewing literature thoroughly, first version of the instrument was developed and exploratory factor analysis and confirmatory factor analysis were conducted. Then, to reduce the effect of the gender difference and achievement level difference, Correlation Analysis and 1-way ANOVA was performed. Also, using multiple group confirmatory factor analysis, this instrument was investigated to see whether this can be used for both middle school and high school. The final items for middle school students is consisted 7 items of belief of school mathematics, 9 items of belief of mathematical problem solving, 11 items of mathematical self-concept, 10 items of belief of mathematical teaching and learning. Instrument of mathematical belief for high school students is consisted 9 items of belief of school mathematics, 9 items of belief of mathematical problem solving, 11 items of mathematical self-concept, 11 items of belief of mathematical teaching and learning. This study examined the differences about mathematical belief's sub-factors shown by three groups of mathematics achievement level. Students of higher achievement level showed that the degree of most factors ware the highest excepting stereotype of belief of school mathematics. Also, Male students preferred more positive in mathematics belief than female students.

• Journal of Educational Research in Mathematics
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• v.17 no.1
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• pp.1-31
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• 2007

Negative numbers have been one of the most difficult mathematical concepts, and it was only 200 years ago that they were recognized as a real object of mathematics by mathematicians. It was because it took more than 1500 years for human beings to overcome the quantitative notion of numbers and recognize the formality in negative numbers. Understanding negative numbers as formal ones resulted from the Copernican conversion in mathematical way of thinking. we first investigated the historic and the genetic process of the concept of negative numbers. Second, we analyzed the conceptual fields of negative numbers in the aspect of the additive and multiplicative structure. Third, we inquired into the levels of thinking on the concept of negative numbers on the basis of the historical and the psychological analysis in order to understand the formal concept of negative numbers. Fourth, we analyzed Korean mathematics textbooks on the basis of the thinking levels of the concept of negative numbers. Fifth, we investigated and analysed the levels of students' understanding of the concept of negative numbers. Sixth, we analyzed the symbolizing process in the development of mathematical concept. Futhermore, we tried to show a concrete way to teach the formality of the negative numbers concepts on the basis of such theoretical analyses.

• Journal of Educational Research in Mathematics
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• v.12 no.2
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• pp.213-228
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• 2002

We know that curriculum is, first of all, related to teaching materials, namely, contents. Therefore, when we think of mathematics curriculum, we must take account of characteristic of mathematics. Vygotsky has studied the development of scientific concepts and everyday concepts. According to Vygotsky, scientific concepts grow down through spontaneous concepts; spontaneous concepts grow upward through scientific concepts. And mathematics is a representative of subjects dealing with scientific or theoretical concept. Therefore, his study provides scientific basis for mathematics curriculum design. In this context, Davydov notes that everyday concepts are developed through empirical abstraction, while scientific concepts require a theoretical abstraction. And Davydov constructed the curriculum materials for the teaching of number concept. Davydov's curriculum is an example of reflecting Vygotsky' theoretical view and his view about the types of abstraction. In particular, it represents mathematical characteristic of a 'science' by introducing number concept through quantitative relationship and use of signs. In conclusion, stance mathematical concepts have scientific characteristic, mathematics curriculum reflects this characteristic.