• School Mathematics
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• v.19 no.3
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• pp.461-480
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• 2017

The aim of this study was to analyze characteristics of teachers' knowledge about correlation with data presented in $2{\times}2$ tables. In order to achieve the aim, this study conducted didactical analysis about two-way tables through examining previous researches and developed a questionnaire with reference to the results of the analysis. The questionnaire was given to 53 middle and high school teachers and qualitative methods were used to analyze the data obtained from the written responses by the participants. This study also elaborated the framework descriptors for interpreting the teachers' responses in the light of the didactical analysis and the data was elucidated in terms of this framework. The specific features of teachers' knowledge about correlation with data presented in $2{\times}2$ tables were categorized into three types as a result. This study raised several implications for teachers' professional development for effective mathematics instruction about correlation and related concepts dealt with in probability and statistics.

• Journal of the Korean School Mathematics Society
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• v.25 no.1
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• pp.61-77
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• 2022

This study looked at the deviation of each textbook, focusing on the detailed learning content related to the quadratic curve properties contained in high school geometry textbooks. Rather than criticizing the diversity of content elements covered in high school geometry textbooks and suggesting alternatives, it focused on analyzing the actual conditions of content element diversity. The curriculum specifies that the practical application of the quadratic curve should be emphasized so that student could recognize the usefulness and value. However, as a result of the analysis, it was confirmed that the purpose of the curriculum and the structure of the textbook did not match somewhat, the deviation of content elements for each textbook was quite large. In terms of acknowledging the diversity of teaching and learning, the diversity of each textbook on the methods of the introduction and the natures related to the quadratic curve can be fully recognized. But in our educational reality, which is aiming for the university entrance examination system through national evaluation such as CSAT, the results are too sensitive in society as a whole, so the diversity of expressions in mathematics textbooks is sometimes interpreted as a disadvantage of evaluation. It is time to reconsider the composition of textbooks that recognizes the diversity of content elements in textbook teaching and learning and at the same time reflects the aspect of equality in evaluation.

• Journal of the Korea Society of Computer and Information
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• v.16 no.11
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• pp.145-152
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• 2011

The study analyzed effects of the problem-based learning utilizing cognitive algorithms in elementary mathematics education in terms of academic achievement and math attitude changes. In order to solve the research questions, a cognitive algorithm-based PBL model was derived based on N. Landa's algorithm-based instructional design theory. And the model was applied to a part of second semester math curriculum for 4th grade of an elementary school located in Seoul. The results showed that the PBL utilizing algorithms can be said to have effects on academic achievement. The PBL model is also considered to have positive effects in enhancing mathematical attitudes of the learners.

• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.599-614
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• 2017

The purpose of this study is to compare and analyze middle school students' understanding of constant rate of change, in terms of observing, representing and interpreting dynamic functions in various ways using the SimCalc MathWorlds. For this purpose, parts of a class conducted for six students in the first grade of middle school were analyzed. The results suggested two implications for a class that used this program (SimCalc MathWorlds): First, we confirmed that the relationships between the two quantities that students notice in the same situation can be different. Second, the program helped students to develop a more comprehensive understanding of the meaning of the constant rate of change. The study also revealed the need to use technology in teaching and learning about functions, particularly to represent and interpret a given situation that involves the constant rate of change in various ways. Further, the results can contribute to developing contents and methods to teach functions using technology in consideration of students' different levels of understanding.

• Education of Primary School Mathematics
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• v.25 no.3
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• pp.251-278
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• 2022

The purpose of this study is to obtain implications for mathematical education by analyzing how the multiplication and division of decimal numbers are presented in the elementary mathematics textbooks in Korea, Japan, Singapore, and Finland. Compared to the fact that students often have misconceptions about multiplication and division of decimal numbers, there have been not many comparative studies in recent elementary mathematics textbooks. For this study, we selected elementary mathematics textbooks those are widely used in Japan, Singapore, and Finland along with Korean elementary mathematics textbooks. We chose the textbooks because the students in the selected countries have scored high in international achievement studies such as TIMSS and PISA. The analysis was examined in terms of elementary mathematics curriculum related to multiplication and division of decimal numbers, introduction and content, real-life situations, use of visual models, and formalization methods of algorithms. As a result of the study, the mathematics curricula related to multiplication and division of decimal numbers includes estimation in Korea and Finland, while Japan and Singapore emphasize real-life connections more, and Finland completes the operations in secondary schools. The introduction and content are intensively provided in a short period of time or distributed in various grades and semesters. The real-life situations are presented in a simple sentence format in all countries, and the use of visual models or formalization of algorithms is linked to the operations of natural numbers in unit conversions. Suggestions were made for textbook development and teacher training programs.

• Journal of Elementary Mathematics Education in Korea
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• v.3 no.1
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• pp.1-20
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• 1999

What do our mathematics teachers now do in the classroom？ What does it actually mean to teach mathematics？ Every preparatory mathematics teacher is confronted with these questions since they have studied to become a teacher. Almost all in-service teachers are faced by of questions, too, as they evaluate their teaching in the light of that of their colleagues. In this sense, Jon L. Higgins has proposed mathematics teaching patterns of five categories, i. e., exploring, modeling, underlining, challenging, and practicing, for the sake of our all teachers. Next, J. P. Guilford has suggested three faces of intellect presented by a single solid model, which we call the 'structure of intellect' Each dimension represents one of the modes of variation of the factors. It is found that the various kinds of operations are in one of the dimensions, the various kinds of products are in another, and the various kinds of contents are in the other one. In order to provide a better basis for understanding this model and regarding it as a picture of human intellect, I've explored it systematically and shown some concrete examples for its tests. Each cell in the model stands for a certain kind of ability that can be described in terms of operation, content, and product, for each cell is at the intersection uniquely combined with kinds of ope- ration, content, and product. In conclusion, how could we use the teaching patterns of five categories, that is, exploring, modeling, underlining, challenging, and practicing, according to the given mathematics learning substances？ And also, how could children constitute the learning sub- stances well in their mind with a viewpoint of constructivism if teachers would connect the mathematics teaching patterns of five categories with any factors among the three faces of intellect？ I've made progress this study focusing on such problems.

• Journal of Educational Research in Mathematics
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• v.13 no.2
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• pp.123-141
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• 2003

This study investigated the understanding level and the using level of mathematical language for middle school students in terms of Freudenthal' language levels. It was proved that the understanding level task developed by current study for geometric concept had reliability and validity, and that there was the hierarchy of levels on which students understanded mathematical language. The level that students used in explaining mathematical concepts was not interrelated to the understanding level, and was different from answering the right answer according to the sorts of tasks. And, the level of mathematical language that was understood easily as students' thought, was the third level of the understanding levels. Mathematics teachers should consider the students' understanding level and using level, and give students the tasks which students could use their mathematical language confidently.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.3
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• pp.393-406
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• 2016

In the sixth grade mathematics, drawing of development figures of the triangular prism and the quadrangular prism is recommended in terms of the creativity. In this sense, the teacher has the need to check in advance all the possible development figures of the triangular prism and the quadrangular prism before teaching on them. However, previous studies that currently give all the possible development figures of the triangular prism and the quadrangular prism are hard to find. For this reason, in this paper, as a study of teaching materials for the professional development of elementary school teachers, the method of finding all the possible development figures of the triangular prism and all the possible development figures of the quadrangular prism without omissions and overlaps and the number of each of development figures which can be obtained by that method are discussed. Here lengths of the three sides of base planes of the triangular prism are different each other and lengths of the four sides of base planes of the quadrangular prism are different each other. This discussion is needed in terms of a study of teaching materials in order to prepare for predictable questions to ask the number of the possible development figures of the triangular prism and the number of the possible development figures of the quadrangular prism in classes. In addition, through this discussion, this paper presents the development figures of the triangular prism and the development figures of the quadrangular prism without omissions and overlaps. And teachers can take advantage of them for determining the correctness of the development figures drew by students and guiding students to draw the development figures creatively in actual classes.

• The Mathematical Education
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• v.58 no.2
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• pp.161-185
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• 2019

This study aims to examine pre- and in-service mathematics teachers' reasoning and how they justify their reasoning. For this purpose, we developed a set of mathematical tasks that are based on mathematical contents for middle grade students and conducted the survey to pre- and in-service teachers in Korea. Twenty-five pre-service teachers and 8 in-service teachers participated in the survey. The findings from the data analysis suggested as follows: a) the pre- and in-service mathematics teachers seemed to be very dependent of the manipulation of algebraic expressions so that they attempt to justify only by means of procedures such as known algorithms, rules, facts, etc., rather than trying to find out a mathematical structure in the first instance, b) the proof that teachers produced did not satisfy the generality when they attempted to justify using by other ways than the algebraic manipulation, c) the teachers appeared to rely on using formulas for finding patters and justifying their reasoning, d) a considerable number of the teachers seemed to stay at level 2 in terms of the proof production level, and e) more than 3/4 of the participating teachers appeared to have difficulty in mathematical reasoning and proof production particularly when faced completely new mathematical tasks.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.4
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• pp.485-499
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• 2015

In this paper, focusing on definitions of terms related to ratio (a:b, external ratio, internal ratio, percentage, proportion, bi-ui-gap(value of a:b)), elementary school mathematics textbooks of Korea and Japan are compared. We can find significant differences between Korean and Japanese textbooks. In Korean textbook, 'bi-yul' includes both of the internal ratio and the external ratio. In Japanese textbooks, the external ratio(amount of unit size) and the internal ratio(wariai) are defined independently. And a:b is set to a subconcept of the internal ratio. In addition, a:b and percentage are presented as methods to express the internal ratio. From these results, the following four implications for developing our mathematics textbooks can be presented as conclusions. First, it is necessary to limit the ratio to mean the internal ratio. Second, it is necessary to define connotatively the ratio as the internal ratio and to set it as a prior concept of a:b. Third, it is necessary to define 1% as the internal ratio 0.01. Fourth, it is necessary to define bi-ui-gap as a number for expressing a:b, when viewing a:b as the expression method of the internal ratio.