• School Mathematics
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• v.13 no.4
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• pp.651-674
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• 2011

Functional thinking is a central topic in school mathematics and the purpose of teaching functional thinking is to develop student's functional thinking ability. Functional thinking which has to be taught in elementary school must be the thinking in terms of phenomenon which has attributes of 'connection'- assignment and dependence. The qualitative methods for evaluation of development of functional thinking can be based on students' activities which are related to functional thinking. With this purpose, teachers have to provide students with paradigm of the functional situation connected to the other subjects which have attributes of 'connection' and guide them by proper questions. Therefore, the aim of this study is to find teaching method for functional thinking by situation posing connected with other subject. We suggest the following ways for functional situation posing though the process of three steps : preparation, adaption and reflection of functional situation posing. At the first stage of preparation for functional situation, teacher should investigate student's environment, mathematical knowledge and level of functional thinking. With this purpose, teachers analyze various curriculum which can be used for teaching functional thinking, extract functional situation among them and investigate the utilization of functional situation as follows : ${\cdot}$ Using meta-plan, ${\cdot}$ Using mathematical journal, ${\cdot}$ Using problem posing ${\cdot}$ Designing teacher's questions which can activate students' functional thinking. For this, teachers should be experts on functional thinking. At the second stage of adaption, teacher may suggest the following steps : free exploration ${\longrightarrow}$ guided exploration ${\longrightarrow}$ expression of formalization ${\longrightarrow}$ application and feedback. Because we demand new teaching model which can apply the contents of other subjects to the mathematic class. At the third stage of reflection, teacher should prepare analysis framework of functional situation during and after students' products as follows : meta-plan, mathematical journal, problem solving. Also teacher should prepare the analysis framework analyzing student's respondence.

• School Mathematics
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• v.14 no.1
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• pp.85-107
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• 2012

Problem solving is important in school mathematics as the means and end of mathematics education. In elementary school, inductive reasoning is closely linked to problem solving. The purpose of this study was to examine ways of improving problem solving ability through analysis of inductive reasoning process. After the process of inductive reasoning in problem solving was analyzed, five different stages of inductive reasoning were selected. It's assumed that the flow of inductive reasoning would begin with stage 0 and then go on to the higher stages step by step, and diverse sorts of additional inductive reasoning flow were selected depending on what students would do in case of finding counter examples to a regulation found by them or to their inference. And then a case study was implemented after four elementary school students who were in their sixth grade were selected in order to check the appropriateness of the stages and flows of inductive reasoning selected in this study, and how to teach inductive reasoning and what to teach to improve problem solving ability in terms of questioning and advising, the creation of student-centered class culture and representation were discussed to map out lesson plans. The conclusion of the study and the implications of the conclusion were as follows: First, a change of teacher roles is required in problem-solving education. Teachers should provide students with a wide variety of problem-solving strategies, serve as facilitators of their thinking and give many chances for them ide splore the given problems on their own. And they should be careful entegieto take considerations on the level of each student's understanding, the changes of their thinking during problem-solving process and their response. Second, elementary schools also should provide more intensive education on justification, and one of the best teaching methods will be by taking generic examples. Third, a student-centered classroom should be created to further the class participation of students and encourage them to explore without any restrictions. Fourth, inductive reasoning should be viewed as a crucial means to boost mathematical creativity.

• 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.