• Journal of Educational Research in Mathematics
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• v.20 no.3
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• pp.293-303
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• 2010

The purpose of this study is to classify a three-fold role of the history of mathematics through epistemological analysis. Based on the history of infinity and limit, the "potential infinity" and "actual infinity" discourses are described using four different historical epistemologies. The interdependence between the mathematical concepts is also addressed. By using these analyses, three different uses of the history of mathematical concepts, infinity and limit, are discussed: past, present, and future use.

• Research in Mathematical Education
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• v.17 no.4
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• pp.279-290
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• 2013

Presently, there has been growing interests in using mathematics' history in teaching mathematics [Katz, V. & Tzanakis, C. (Eds.) (2011). Recent Developments on Introducing a Historical Dimension in Mathematics Education. Washington, DC: Mathematical Association of America]. Thus, this article introduces some work of scholars from ancient East Indian culture like Bhaskara (AD 1114-1185) and Arabic culture such as Ibn Qurrah (AD 9th c) that are related to Pythagoras Theorem. In addition, some Babylonian creative works related to Pythagorean triples found in a tablet known as 'Plimpton 322', and an application of the Pythagorean Theorem found in another tablet named 'Yale Tablet' are presented. Applications of computer animation of dissection Motion Operations concept in 2D and 3D using dynamic software like Geometer's-Sketchpad and Cabri-II-and-3D. Nowadays, creative minds are attracted by the recent stampede in the advances of technological applications in visual literacy; consequently, innovative environments that would help young students, gifted or not, acquiring meaningful conceptual understanding would immerge.

• Research in Mathematical Education
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• v.17 no.1
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• pp.63-78
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• 2013

Trigonometric ratios are difficult concepts to teach and learn in middle school. One of the reasons is that the mathematical terms (sine, cosine, tangent) don't convey the idea literally. This paper deals with the understanding of a concept from the learner's standpoint, and searches the orientation of teaching that make students to have full understanding of trigonometric ratios. Such full understanding contains at least five constructs as follows: skill-algorithm, property-proof, use-application, representation-metaphor, history-culture understanding [Usiskin, Z. (2012). What does it mean to understand some mathematics? In: Proceedings of ICME12, COEX, Seoul Korea; July 8-15,2012 (pp. 502-521). Seoul, Korea: ICME-12]. Despite multi-aspects of understanding, especially, the history-culture aspect is not yet a part of the mathematics class on the trigonometric ratios. In this respect this study investigated the effect of history approach on students' understanding when the history approach focused on the mathematical terms is used to teach the concept of trigonometric ratios in Grade 9 mathematics class. As results, the experimental group obtained help in more full understanding on the trigonometric ratios through such teaching than the control group. This implies that the historical derivation of mathematical terms as well as the context of mathematical concepts should be dealt in the math class for the more full understanding of some mathematical concepts.

• Journal for History of Mathematics
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• v.29 no.4
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• pp.243-254
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• 2016

This research identifies the elements of the methodologies of Newton's discovery of his dynamics. These methodologies involve the transformation of preceding theoretical concepts and the discovery of common cause. This essay consists of two parts within historical case studies of Newton's works. The elements of the method of discovery consists of the transformation of preceding concepts and the identification of common cause in the formation of the research program's hard cores and protective belts. Newton transformed their predecessors' concepts to find out appropriate common causes in his dynamical theory. The transformed theoretical concepts are synthesized to be constructed as the elements of common cause which provide the foundations of Newtonian research programs.

• Journal of Educational Research in Mathematics
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• v.10 no.2
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• pp.263-277
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• 2000

mathematics holds a key position among the subject-matters of school education. Nevertheless, beyond Its Instrumental one, humanity-educational value of mathematics for the general public has been under estimated. For the past fifty years, in the our country there has not been enough systematic and profound examination and discussion concerning the goals of mathematics education in order to establish the philosophy of mathematics education. Thus, in this thesis we argue how mathematics education could contribute to the humanity education. For this, we examine how western educational theorists have emphasized the value of mathematics as humanity education and how their theories have been reflected in the goals of the modern mathematics education. First of all, we discuss Platonism as a philosophical basis of the traditional mathematics teaching mainly with Euclid's "Elements" since the ancient Greece and the relationship between mathematics education and humanity education in the light of this traditional thought. Next, we examine the thoughts of Pestalozzi, Harbert, Froebel who provided the theoretical basis for the public education since 19th century, and discuss the value of mathematics teaching in their humanistic educational thoughts. Also we examine the humanistic value of mathematics education in Dewey's educational philosophy, which criticized the traditional western ethics and epistemology, and established instrumen talism. Further, we analyze how such a philosophy of mathematics teaching is reflected mathematics education of 20th century, and confirm that the formation of Dewey's rational intelligence is one of the central aims of mathematics education of late 20th century. Finally, we discuss the ideals of humanistic mathematics education ; develop ment of the rational intelligence via 'doing knowledge'and change of mind via 'looking knowledge'. In this paper identify the humanistic values of mathematics education through the historical examination of the philosophies of mathematics education, and we could find significance as a fundamental study for one of the most important problems which Korean mathematics educational society confronts, that is establishing the philosophy of mathematics education.

• 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 the Korean School Mathematics Society
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• v.1 no.1
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• pp.185-196
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• 1998

This study is undertaken to clarify the evolution of the mathematics regarding the $\pi$ ratio, square root, trigonometric ration which are dealing by approximate value according to the curriculum of Korean Middle School and its subsequent growth of methods for attaining the approximate value. Furthermore a brief survey has been thought for assessing the significance of the core of approximate value and its utility which will be given a guide line to many young learners. I'd better teach these historical background to the students and it makes clear the approximate value and the content about the approximate value. This research should help to improve the student's ability of solving a problem by making them think it mathematically through the life and the effort of the mathematician.

• Journal for History of Mathematics
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• v.31 no.1
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• pp.37-51
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• 2018

In this paper, our main concern is the historical development of the Finsler geometry in Debrecen, Hungary initiated by L. Berwald. First we look into the research trend in Berwald's days affected by the $G{\ddot{o}}ttingen$ mathematicians from C. Gauss and downward. Then we study how he was motivated to concentrate on the then completely new research area, Finsler geometry. Finally we examine the course of establishing Hungarian Debrecen school of Finsler geometry via the scholars including O. Varga, A. $Rapcs{\acute{a}}k$, L. $Tam{\acute{a}}ssy$ all deeply affected by Berwald after his settlement in Debrecen, Hungary.

• Communications of Mathematical Education
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• v.30 no.2
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• pp.139-159
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• 2016

This study is the field of mathematics education on the assumption that they can extend outside the classroom. Recent mathematics education is increasing the importance of field experience and various activities based on real-life math education. Thus, it is necessary to consider this situation in pre-service teacher's education. The purpose of this study is to apply the 'Mathematics Field Trips Activities' in the pre-mathematics teacher education. So the specific case of 'Mathematics Field Trips Activities' was analyzed. Mathematics teachers conducted preliminary exploration activities on the historical cultural property which were effective in the following four aspects. First, cognitive effects and second, definitive effect. Third, cultural-mathematical effect. Fourth, the effect on improving math class. Finally they were summarized and divided into classes target content knowledge and teaching knowledge both sides. As a result, the 'Mathematics Field Trips Activities' were found to have significant effects on pre-service math teacher. Finally, ongoing research is needed to settle into a new teaching and learning methods.

• Journal of the Korean School Mathematics Society
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• v.26 no.1
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• pp.21-47
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• 2023

This study examines the activity system of teaching and learning about informal statistical inference using sampling simulation, based on cultural-historical activity theory. The research explores what contradictions arise in the activity system and how the system changes as a result of these contradictions. The participants were 20 elementary school students in the 5th to 6th grades who received classes on informal statistical inference using sampling simulations. Thematic analysis was used to analyze the data. The findings show that a contradiction emerged between the rule and the object, as well as between the mediating artifact and the object. It was confirmed that visualization of empirical sampling distribution was introduced as a new artifact while resolving these contradictions. In addition, contradictions arose between the subject and the rule and between the rule and the mediating artifact. It was confirmed that an algorithm to calculate the mean of the sample means was introduced as a new rule while resolving these contradictions.