• Bulletin of the Korean Mathematical Society
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• v.26 no.1
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• pp.53-67
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• 1989

• Journal of Educational Research in Mathematics
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• v.14 no.1
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• pp.39-69
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• 2004

This paper investigates the teaching and learning of Linear function relating functional contexts and suggests the improved methods of representation-shift through this analysis. The methods emphasize the link between students' preacquired knowledge of mathematical representations and the way of using those. This methods are explanatory teaching, teaching and teaming based on modelling perspectives or tasks (interpretation, prediction, translation and scaling). We categorize the 8th grade middle school students' errors on the linear function relating real contexts and make a comparative study of the error-remedial effects and the teaching and teaming methods. We present the results of a study in which representation-shift methods based on modelling perspectives and tasks are more effective in terms of flexible connection of representations and error remediation. Also, We describe how students used modelling perspective-taking to explain and justify their conceptual models, to assess the quality of their models and to make connection to other mathematical representation during the problem solving focusing on the students' self-diagnosis.

• 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.

• Education of Primary School Mathematics
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• v.26 no.4
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• pp.257-275
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• 2023

In this study, we designed and implemented a instruction emphasizing mathematical argument for fifth-grade students and analyzed the teaching practices. Through a literature review related to instruction emphasizing mathematical argument, we organized a teaching model of five phases that explain why the general claim that the sum of consecutive odd numbers equals a square number is true: 1) noticing patterns, 2) articulating conjectures, 3) representing through visual model, 4) arguing based on representation, 5) comparing and contrasting. Then, we analyzed the argumentation stream by phases to observe how the instruction emphasizing mathematical argument is implemented in the elementary classroom. Based on the results of this study, we discuss the implications of teaching a mathematical argument in elementary school.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.575-585
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• 2008

Suppose that D is a $C^*$-discrete quantum group and $D_0$ a discrete quantum group associated with D. If there exists a continuous action of D on an operator algebra L(H) so that L(H) becomes a D-module algebra, and if the inner product on the Hilbert space H is D-invariant, there is a unique $C^*$-representation $\theta$ of D associated with the action. The fixed-point subspace under the action of D is a Von Neumann algebra, and furthermore, it is the commutant of $\theta$(D) in L(H).

• Journal of the Korea Computer Industry Society
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• v.9 no.5
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• pp.191-196
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• 2008

The purpose of this study is to investigate the effect of number representation activities using computer software on young children's ability in mathematics. The effect of the number representation activities using computer software will be shown differently according to the age. The effect of the number representation activities using computer software will be shown differently according to the genders. The result of this study has shown that it gives a positive influence to the young children's mathematical ability.

• The Mathematical Education
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• v.46 no.2 s.117
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• pp.141-153
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• 2007

The purpose of the study is to analyze children's proportional reasoning and problem solving in proportional problems with/without iconic representations. Proportional problems include 3 tasks such as (a) without any picture, (b) with simple picture, and (c) with/without iconic representation. As a result, children didn't show any significant differences in two tasks such as (a) and (b). However, children showed better proportional reasoning with iconic representation. In addition, 'build-up expression' strategy was used mostly in solving problems and 'additive strategy' was shown as an error which students didn't make an appropriate proportional relation expression and they made a wrong additive strategy.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.3
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• pp.495-510
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• 2010

An Einstein's connection which takes the form (2.23) is called a $^*g$-ME-connection and the corresponding vector is called a $^*g$-ME-vector. The $^*g$-ME-manifold is a generalized n-dimensional Riemannian manifold $X_n$ on which the differential geometric structure is imposed by the unified field tensor $^*g^{{\lambda}{\nu}}$, satisfying certain conditions, through the $^*g$-ME-connection and we denote it by $^*g-MEX_n$. The purpose of this paper is to derive a general representation and a special representation of the $^*g$-ME-vector in $^*g-MEX_n$.

• The Mathematical Education
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• v.56 no.2
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• pp.131-145
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• 2017

The representation of irrational numbers has a key role in the learning of irrational numbers. However, transparent and finite representation of irrational numbers does not exist in school mathematics context. Therefore, many students have difficulties in understanding irrational numbers as an 'Object'. For this reason, this research explored how mathematics textbooks affected to students' understanding of irrational numbers in the view of process and object. Specifically we analyzed eight textbooks based on current curriculum and used framework based on previous research. In order to supplement the result derived from textbook analysis, we conducted questionnaires on 42 middle school students. The questions in the questionnaires were related to the representation and calculation of irrational numbers. As a result of this study, we found that mathematics textbooks develop contents in order of process-object, and using 'non repeating decimal', 'numbers cannot be represented as a quotient', 'numbers with the radical sign', 'number line' representation for irrational numbers. Students usually used a representation of non-repeating decimal, although, they used a representation of numbers with the radical sign when they operate irrational numbers. Consequently, we found that mathematics textbooks affect students to understand irrational numbers as a non-repeating irrational numbers, but mathematics textbooks have a limitation to conduce understanding of irrational numbers as an object.

• School Mathematics
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• v.18 no.2
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• pp.323-348
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• 2016

The 2009 revised national mathematics curriculum have inserted mathematical 'linking cube' activities in the 6th grade math classes to improve students' spatial problem solving abilities and communication skills. However, we found that it was hard for teachers to teach problem solving and communication skills due to the absence of mathematical way of representing linking cubes in the classroom. In this paper, we propose 3D 'turtle representation system' as teaching and learning tools for linking cube activities. After using turtle representation system for linking cube activities, teachers responded that turtle representation system is a valuable problem solving and communication tools for the linking cube mathematics classes. We conclude that turtle representation system is a well designed teaching and learning tools for linking cube activities, and there are lots of educational meanings in the 3D turtle representation system.