• Journal of Elementary Mathematics Education in Korea
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• v.17 no.1
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• pp.105-128
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• 2013

One of the biggest changes in 2007 Curriculum Revision is introduction of letter, equation, direct proportion and inverse proportion in fifth and sixth grade of mathematics. The purpose of this study is to provide some implications about teaching-learning method for introduction of letters, teaching and learning activities of equation between the 6th Curriculum and 2007 Curriculum Revision. The below conclusions were drawn from findings obtained in this study. First, the letter and expression were learned in fifth and sixth grade until 6th Curriculum and were learned in seventh grade in middle school of 7th Curriculum. But letter, equation are introduced in 2007 Curriculum Revision again. The overall contents of letter and expression were learned on the 'Relationship' domain in the 6th Curriculum, it were learned on the 'Letter and expression' domain in the 7th Curriculum and is learned on the 'Regularity and problem-solving' domain in the 2007 Curriculum Revision. Second, teaching method of these contents was to promise some definitions at first and then to solve exercises in the 6th Curriculum. But leaning was forced to improve student's problem-solving in the 7th Curriculum. To reduce student's pressure offers at a minimum mathematics terms and to provide problem situations to students who contact daily, it is emphasized on learner's communication in the 2007 Curriculum Revision. We want to be easily connected elementary mathematics and higher mathematics through this study about letter, equation. We recognized how we teach the letter and expression to reduce misconceptions and draw a transition from arithmetic thinking to algebraic thinking and want to be continue of another studies.

• School Mathematics
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• v.9 no.4
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• pp.507-521
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• 2007

The purpose of this study was to investigate the effects of memory retention of mathematical concepts in multiplication in the inquiry-based pantomime instructions. Three months later after the pre-test, a comparison was made between traditional class (TC) and class with the inquiry-based pantomime (IP) approach in terms of students retention of mathematical understandings. Results of the study indicated that the If instructions promoted effective long-term retention of knowledge. We concluded that instructional strategies that promoted active engagement in learning using life examples and drawings produced effective long-term retention of knowledge.

• School Mathematics
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• v.4 no.4
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• pp.643-655
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• 2002

In this paper we emphasize the introduction of ‘incommensurability’ on the teaching and learning the irrational number because we think of the origin of number as ‘ratio’. According to Greek classification of continuity as a ‘never ending’ divisibility, discrete number and continuous magnitude belong to another classes. That is, those components were dealt with respectively in category of arithmetic and that of geometry. But the comparison between magnitudes in terms of their ratios took the opportunity to relate ratios of magnitudes with numerical ratios. And at last Stevin coped with discrete and continuous quantity at the same time, using his instrumental decimal notation. We pay attention to the fact that Stevin constructed his number conception in reflecting the practice of measurement : He substituted ‘subdivision of units’ for ‘divisibility of quantities’. Number was the result of such a reflective abstraction. In other words, number was invented by regulation of measurement. Therefore, we suggest decimal representation from the point of measurement, considering the foregoing historical development of number. From the perspective that the conception of real number originated from measurement of ‘continuum’ and infinite decimals played a significant role in the ‘representation’ of measurement, decimal expression of real number should be introduced through contexts of measurement instead of being introduced as a result of algorithm.

• School Mathematics
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• v.15 no.4
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• pp.785-799
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• 2013

The researchers developed the teaching-learning materials for 9th grade mathematically gifted students in terms of the hypothesis that the students would have opportunity for problem solving and develop various mathematical thinking through the mathematical modeling lessons. The researchers analyzed what mathematical thinking abilities were shown on each stage of modeling process through the application of the materials. Organization of information ability appears in the real-world exploratory stage. Intuition insight ability, spatialization/visualization ability, mathematical reasoning ability and reflective thinking ability appears in the pre-mathematical model development stage. Mathematical abstraction ability, spatialization/visualization ability, mathematical reasoning ability and reflective thinking ability appears in the mathematical model development stage. Generalization and application ability and reflective thinking ability appears in the model application stage. The developed modeling assignments have provided the opportunities for mathematically-gifted students' mathematical thinking ability to develop and expand.

• Education of Primary School Mathematics
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• v.19 no.1
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• pp.1-18
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• 2016

Patterns are of great significance to develop algebraic thinking of elementary students. This study analyzed teaching methods of patterns in current elementary mathematics textbook series in terms of three main activities related to pattern generalization (i.e., analyzing the structure of patterns, investigating the relationship between two variables, and reasoning and representing the generalized rules). The results of this study showed that such activities to analyze the structure of patterns are not explicitly considered in the textbooks, whereas those to explore the relationship between two variables in a pattern are emphasized throughout all grade levels using function table. The activities to reason and represent the generalized rules of patterns are dealt in a way both for lower grade students to use informal representations and for upper grade students to employ formal representations with expressions or symbols. The results of this study also illustrated that patterns in the textbooks are treated rather as a separate strand than as something connected to other content strands. This paper closes with several implications to teach patterns in a way to foster early algebraic thinking of elementary school students.

• School Mathematics
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• v.11 no.1
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• pp.111-129
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• 2009

This paper is about didactical transposition, which is to transpose academic knowledge into practical knowledge intended to teach. The research questions are addressed as follows. 1. Are the 13 mathematics textbooks of the 10-Na level indisputable regarding with the didactical transposition, in terms that the order of arrangement and the way of explaining the knowledge of trigonometric functions being analyzed and that its logical construction and students' understandings are considered? 2. Can some transpositions for easier use of didactical manipulative, for more practical and for more principle based be proposed? To answer these questions, this research examined previous studies of mathematics education, specifically the organization of the textbook and the trigonometric functions, and also compared orders of arranging and ways of explaining trigonometric functions from the perspective of didactical transposition of 13 versions of the 10-Na level reorganized under the 7th curriculum. The paper investigated what lacks in the present textbook and sought a teaching guideline of trigonometric functions(especially about sector and graph, period, characters of trigonometric function, and sine rule).

• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.135-152
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• 2013

The purpose of this study is to navigate to the desired direction for the figure of number line through the extensive analysis of number line in middle school textbooks and literatures. For the efficient achievement of this purpose, three research questions were posed as follows: First, we compare the figures of number line in textbooks of Korea and other countries. Korean math textbooks mark the arrow on both sides of number line. But, however, coordinate plane was marked with arrow on only positive direction of number line. In contrast, the majority of secondary school textbooks in several foreign countries has the arrow only on positive direction. Second, the change in the figure of number line has been analyzed historically from two perspectives. From the first to 2007-revised curriculum, math textbooks of Korea were analyzed. Since the 6th curriculum, the number of textbooks with arrows on both sides has increased sharply. That is, textbooks with one arrow almost have disappeared. It is strange that any explanation for this abrupt change can't be found. The following analysis was also performed on published foreign literatures since Descartes. There was no arrow in the early figures of number line. But after 19th century, number lines with one arrow have begun to appear. Third, based on the previous study, we propose a reasonable way for the figure of number line. In fact, we claim that, in terms of linguistic symbols, the number line should be with only one arrow on positive side.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.405-432
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• 2022

Cracks in beams and shallow arches are modeled by massless rotational springs. First, we introduce a specially designed linear operator that "absorbs" the boundary conditions at the cracks. Then the equations of motion are derived from the first principles using the Extended Hamilton's Principle, accounting for non-conservative forces. The variational formulation of the equations is stated in terms of the subdifferentials of the bending and axial potential energies. The equations are given in their abstract (weak), as well as in classical forms.

• School Mathematics
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• v.10 no.3
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• pp.423-441
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• 2008

The purpose of this study was to examine the Pedagogical Content Knowledge(PCK) of teachers and their educational practice in the category of plane figure, to make a comparative analysis of their PCK and educational practice, and to discuss the relationship between their PCK and the characteristics of their instruction. Instruction of four selected elementary school teachers was analyzed to find out their educational practice. In conclusion, the characteristics of the PCK and actual instruction of the teachers could be listed as below: First, as a result of comparing their PCK and educational practice on plane figure by applying selected analysis criteria, there was a close correlation between their PCK and actual instruction. Second, the teachers had various levels of PCK on different areas. Especially, there was a large disparity in mathematical content knowledge and knowledge of teaching methods. Third, the teachers who had plenty of PCK were more excellent in textbook reconstructing, and those who fell behind in terms of PCK were more reliant on textbooks as if the textbooks had been the Bible.

• Journal of Educational Research in Mathematics
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• v.22 no.2
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• pp.117-136
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• 2012

The goal of this study is to investigate a didactic transposition method of text books and high school students' understanding for the Normal Distribution. To accomplish this goal, framework descriptors were developed to analyse the didactic transposition method and interpret the students' understanding based on the Historico-Genetic process of the Normal Distribution, the meaning of the Normal Distribution as a scholarly knowledge and the results of previous studies on students' understanding for the Normal Distribution. This study presented several recommendations for instruction of the Normal Distribution according to the results of analysing the didactic transposition method and interpreting the students' understanding in terms of the developed framework.