• The Mathematical Education
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• v.55 no.2
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• pp.233-249
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• 2016

In this study, we extracted the background meaning of the condition that four points lie on a circle, analyzed textbooks critically and proposed the orientation to improve the content in the textbook. As results, the condition has a realistic background meaning which is 'mathematical modeling of finding a fair location'. The condition has a mathematical background meanings which are 'a first complex situation distinguished from two points and three points', 'the condition described in the perspective of side and angle in order to overcome the disadvantages of the perpendicular bisectors context' and 'being possible to transfer more than five points'. However it is difficult to understand the reason why the condition is on four points in the current textbook. In addition, it is difficult to recognize the connectivity of a circumcenter of triangle. To overcome these problems, we proposed five orientations to improve the content in the textbook.

• Communications of Mathematical Education
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• v.35 no.4
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• pp.413-423
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• 2021

This study investigated the empty set which is one of the mathematical objects. We inquired some misconceptions about empty set and the background of imposing empty set. Also we studied historical background of the introduction of empty set and the axiomatic system of Set theory. We investigated the nature of mathematical object through studying empty set, pure conceptual entity. In this study we study about the existence of empty set by investigating Alian Badiou's ontology known as based on the axiomatic set theory. we attempted to explain the relation between simultaneous equations and sets. Thus we pondered the meaning of the existence of empty set. Finally we commented about the thoughts of sets from a different standpoint and presented the meaning of axiomatic and philosophical aspect of mathematics.

• East Asian mathematical journal
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• v.37 no.4
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• pp.461-480
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• 2021

There have been gradually a few studies on Noticing in the domestic and international area. For the purpose of increasing the concern on teacher noticing and pursuing the affluent studies on the noticing, this study tried to explore and understand the background, the meaning, and the properties of the teacher noticing while summing up the views of the various researchers. As a result, the teacher noticing could be defined as a cognitive process which is focused on mathematical objects, students' mathematical thinking, students' emotions, teaching strategies, classroom environment and interprets them to determine how to react. From this, noticing might be cognitive process which is a combined form of the objects and cognitive behavior, while the objects whom teachers notice covers up the mathematical objects and the teaching objects. Eventually, this study expects to serve as a basis to foster the in-depth understanding of teacher noticing and to derive the follow-up studies.

• The Mathematical Education
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• v.57 no.4
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• pp.371-391
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• 2018

The purpose of this study is to analyze manifestation examples and effects of group creativity in mathematical modeling and to discuss teaching and learning methods for group creativity. The following two points were examined from the theoretical background. First, we examined the possibility of group activity in mathematical modeling. Second, we examined the meaning and characteristics of group creativity. Six students in the second grade of high school participated in this study in two groups of three each. Mathematical modeling task was "What are your own strategies to prevent or cope with blackouts?". Unit of analysis was the observed types of interaction at each stage of mathematical modeling. Especially, it was confirmed that group creativity can be developed through repetitive occurrences of mutually complementary, conflict-based, metacognitive interactions. The conclusion is as follows. First, examples of mutually complementary interaction, conflict-based interaction, and metacognitive interaction were observed in the real-world inquiry and the factor-finding stage, the simplification stage, and the mathematical model derivation stage, respectively. And the positive effect of group creativity on mathematical modeling were confirmed. Second, example of non interaction was observed, and it was confirmed that there were limitations on students' interaction object and interaction participation, and teacher's failure on appropriate intervention. Third, as teaching learning methods for group creativity, we proposed students' role play and teachers' questioning in the direction of promoting interaction.

• Journal of Educational Research in Mathematics
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• v.8 no.2
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• pp.621-634
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• 1998

Emthusiasm about the introduction of computers into mathematics education is widespred. But, the perspectives about the relationship between mathematics education and computer are diverse. The purpose of this study is to examine theoretical background for using computers in mathematics education. In spite of the pedagogical possibilities of computers. only a small minority of mathematics teachers are using computers in mathematics classroom. It is natural to seek this obstacles within theoretical background of the teachers who manage computers, In this study, We discuss the problems in the two sides. First, due to increased computer activity, relationship of mathematics in school with mathematics in society is changing. It is tension between academic mathematics and practical mathematics. School mathematics have to be changed toward stressing practical mathematics. Second problem is the dialectical relationship between the individual and the collective. While maintaining a respect for the individuality of student contributions. We take into account the social dimension of mathematical meaning-making. We discussed theoretical clarification of work collaborative learning. We propose the case study for the roles of computer in collaborative mathematics learning.

• School Mathematics
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• v.13 no.3
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• pp.405-422
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• 2011

In this study, we consider the meaning of one-to-one correspondence through theoretical background under operation of matrix. On algebraic point of view, its significance is 'through one-to-one correspondence from a set with given structure, become a methods in order to induce an algebraic system in to a new set.' That is a key idea making isomorphic structure. Such process experiences necessity of mathematical fact, as well as the deep understanding of one-to-one correspon -dence. Also that becomes a base for develop a various mathematical concepts, such as matrix, exponential laws, symmetric difference, permutation and so on. This study help teachers and students to understand of mathematical concepts meaningfully and to facilitate teacher's professional development.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.611-626
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• 2010

The purpose of this study is to explore the composite properties of linear functions using CAS calculators. The meaning and processes in which technological tools such as CAS calculators generated to instrument are reviewed. Other theoretical topic is the design of an exploring model of observing-conjecturing-reasoning and proving using CAS on experimental mathematics. Based on these background, the researchers analyzed the properties of the family of composite functions of linear functions. From analysis, instrumental capacity of CAS such as graphing, table generation and symbolic manipulation is a meaningful tool for this exploration. The result of this study identified that CAS as a mediator of mathematical activity takes part of major role of changing new ways of teaching and learning school mathematics.

• Journal of the Korean School Mathematics Society
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• v.1 no.1
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• pp.59-67
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• 1998

Probability and statistics is an important section in mathematics which is deeply related to everyday living, natural science and social science. In spite of its importance, many students will throw away it because it becomes very harder as its step(stage) deepens and probability and statistics' relative importance is very small in Korea-SAT(the test of college entrance in Korea). Therefore, by analyzing the involvement carefully between the curriculum in the elementary, middle, high school and the text book, by studying the problem and improvement direction, it is necessary to investigate an effective teaching method. This study intends to give the students the confidence, interests, and accomplishment motive about probability and statistics field and to make a rational and creative decision-making through mathematical speculation by proposing an effective teaching method through analyzing an existing facts in school's probability and statistics field. The contents of this study are composed of four chapters. Chapter three looks into the mathematical curriculum in the elementary, middle, high school and its teaching meaning, the outline of contents, some tips on teaching and problems and presents an effective and concrete teaching method on the basis of the theoretical background in the chapter two. Chapter four is a conclusive part and gives the general improvement and intentional direction in educating the probability and statistics.

• Journal of the Korean School Mathematics Society
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• v.9 no.2
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• pp.229-248
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• 2006

In creative society, fluency in technology means the ability to reformulate knowledge, to express oneself creatively and appropriately, to produce and generate information in computer environment. Fluency in technology is essential for mathematics education with a point of constructivist view. In this paper, we study the meaning of fluency in technology, related to mathematics education. For this purpose, we suggest Papert's constructionism as a theoretical background and consider the principle of 'Learning through design' for fluency in technology. And we consider some principles for designing a mathematical microworld and implement a mathematical microworld for fluency in technology. With this microworld, we consider the after-school-program where students have participated a design activity.

• School Mathematics
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• v.5 no.2
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• pp.167-189
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• 2003

Mental arithmetic has recently gained a higher profile in primary school mathematics. The study aims to reflect didactical background of mental arithmetic in number and operations curriculum for primary school mathematics. In order to attain these purposes, the present paper describes the meaning of mathematical literacy and didactical background of mental arithmetic on which have been laid emphasis in relation to mathematical literacy in many countries. Also it shows current suggestions for mental arithmetic instruction in Everyday Mathematics Project in USA, Numeracy Number Project in Great Britain, TAL project based on Realistic Mathematics Education in the Netherlands, and mathe 2000 project in German in order to gain practical ideas for teaching mental arithmetic. Furthermore, it discusses mental strategies of students and didactical models for improving mental arithmetic instruction based on the results of many researches. Under these theoretical foundations, it is analyzed how mental arithmetic is developed in our number and operations curriculum, focused on mental strategies and didactical models. Finally, implications for improving our mental arithmetic instruction are discussed.