• Journal of Educational Research in Mathematics
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• v.12 no.1
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• pp.125-143
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• 2002

The concept of "set" in school mathematics has undergone many changes according to the revision of curriculum and the transition of the paradigm in mathematics education. In the discipline-centered curriculum, a set was a representative concept which reflected the spirit of New Math. After the Back to Basics period, the significance of a set concept in school mathematics has been diminished. First, this paper elaborated several controversial aspects of the terms related to set, such as a collection and a set, a subset, and an empty set. In addition, the changes of the significance imposed to a set concept in school mathematics were investigated. Finally, this paper provided two alternative approaches to introduce and explain a set concept which emphasized both mathematical rigor and learner's psychology.

• School Mathematics
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• v.11 no.3
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• pp.335-349
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• 2009

The purpose of this study is to explore how a mathematics teacher's beliefs about mathematics and teaching and learning and mathematics and how such beliefs are related to her knowledge manifested in her mathematics instruction. The study illustrates images of teaching practice of an American mathematics teacher in middle grades mathematics classrooms. Results suggest that the teacher seems consistent in teaching in terms of her beliefs about mathematics and learning and teaching mathematics in some degrees. In particular, the teacher's beliefs affected the ways in which mathematics teacher organized and structured her lessons.

• Journal of Educational Research in Mathematics
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• v.21 no.2
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• pp.165-180
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• 2011

Mathematical symbols concisely represent mathematical contents related to terms by describing their mathematical meanings implicitly. All symbols in elementary school mathematics textbooks are stated as to be read so that elementary school students could understand their mathematical meanings. The same is somewhat true as in middle school mathematics textbooks, however it is often the case that some symbols are difficult to be read and understood because their statements are unclear or different. In this study, we analyze problems and suggest implications on teaching and learning mathematics based on the statements and understanding of reading symbols in middle school mathematics textbooks.

• Journal of the Korean School Mathematics Society
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• v.15 no.1
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• pp.27-51
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• 2012

This paper analyzed the pedagogical content knowledge (PCK) presented in three novice teachers' mathematics instruction. PCK was analyzed in terms of the knowledge of mathematics content, the knowledge of students' understanding, and the knowledge of teaching methods. Teacher A executed a concept-oriented instruction with manipulative materials because she had difficulties in learning mathematics during her childhood. Teacher B attempted to implement an inquiry-centered instruction in the lesson of looking for the area of a trapezoid. Teacher C focused on the real-life connection to mathematics instruction. There were substantial differences among the teachers' PCK revealed in mathematics teaching, depending on their instructional goals. The detailed analyses of three teachers' teaching in terms of their PCK will give rise to the issues and suggestions of professional development for beginning elementary school teachers in mathematics teaching.

• Communications of Mathematical Education
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• v.33 no.2
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• pp.123-139
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• 2019

This study analyzed how problem-posing tasks included in Korean middle school mathematics textbooks were distributed in terms of content area, task type, and context of task to investigate that the mathematics textbooks are giving students ample opportunities for problem-posing activities. The analysis of 10 mathematics textbooks for first grade in middle school according to the revised mathematics curriculum in 2015 found that the problem-posing tasks contained in the textbooks are insufficient in quantity and not evenly distributed in terms of content areas. There were also more problem-posing tasks with relatively moderate constraints than those with strong or weak constraints in terms of mathematical constraints. In addition, there were more problem-posing tasks that were not requiring students to make a new context, and more often camouflage contexts were used. Based on this, implications for improving mathematics problem-posing tasks in mathematics textbook were suggested.

• Journal of the Korean School Mathematics Society
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• v.17 no.4
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• pp.437-464
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• 2014

Curriculum for mathematic sis the system that selects and organizes the contents which have to be taught in school. Ultimately it can be the whole plan of school mathematical education. The study about curriculum for mathematics is the basic study field of the mathematical education, so curriculum-related studies have been continuously promoted in terms of character, organization and implement of the curriculum, learning contents contained by the curriculum, the connection between school levels, and comparison and analysis of domestic and foreign curricula. Thus, this paper investigated the 2009 Revised Curriculum for Mathematics, which is the curriculum of Korea and the CCSSM which is the curriculum of the U.S. Both have been adopted in schools recently. The purpose of this study is to understand the curricula for mathematics in elementary school of Korea and the U.S. in depth and obtain the implication for the further curriculum revision, by comparing and analyzing the curricula of two countries.

• School Mathematics
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• v.1 no.2
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• pp.605-615
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• 1999

In this paper, we explain the pedagogical phenomena appeared in the learning of 0.$\dot{9}$ = 1 in terms of its intrinsic mathematical structure, and investigate the reason why such phenomena happen. Also we analyze such phenomena through the dialogue between student and teacher, and present some instruction idea from the mathematical and educational view points.

• The Mathematical Education
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• v.37 no.1
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• pp.35-54
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• 1998

Half century has passed since Korean peninsula was divided into South and North Korea. Now a days, there are many differences of politics, economy, culture and education between South and North Korea. Especially mathematics education in which I am interested has a lot of changes and differences. This is proved true by defects' proof. For those reasons, I compared South Korea's education ideology, goal and system, and goals of mathematics education with North Korea's. I compared geometric(1-4 years, published by Pyong-yang Educational Book Publication Co. 1991) of mathematics texts(1-6 years) which are used in the secondary school with mathematics text of South Korea in contents and organization of them. As a result of this comparison, education ideology and goal are distinctly different from those of South Korea because of the difference of pursuing humanity. In North Korea, the curriculum is very strict without autonomy. There are 1283 mathematics classes which are occupied 19% for six years during the secondary school. The contents are very similar, but there is a little difference in the definition of a term. The problems which praise Kim Il-sung and his son and reveal loyalty to them were found, and there were a lot of problems in order to promote hostile feeling against U.S.A and South Korea, too. In conclusion, mathematics education of Korean peninsula should be reunified in the fields of the terms and contents at first.

• The Mathematical Education
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• v.47 no.2
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• pp.181-195
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• 2008

The purpose of this study was to investigate the understanding of basic knowledge of mathematics for $6^{th}$ grade students in elementary school by an essay test and provide instructional suggestions for teachers. A total of 132 students from 6 classes in 3 elementary schools were tested and analyzed in terms of the characteristics of correct answers and types of incorrect answers. The results showed that students had poor understanding of basic conceptual concepts and principles throughout six content areas of school mathematics curriculum, despite their good performance on mathematical skills. This study included implications to teaching and learning for each of the content areas.

• The Mathematical Education
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• v.41 no.3
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• pp.233-256
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• 2002

This study investigated school mathematics curriculum of England, newly revised in 1998, focused on the 'number and algebra' domain among three major domains of the English curriculum. On the basis of its understanding, this domain was compared and analyzed with school mathematics curriculum of Korea. In doing so, this study explored its plans and procedures and established a frame of comparison for the curriculums between the two countries. The structure of the National Curriculum in England is composed of programmes of study and attainment targets. The former sets out what should be taught in mathematics at key stages 1, 2, 3, and 4 and provides the basis for planning schemes of work, and the latter sets out the knowledge, skills, and understanding that pupils of different abilities and matures are expected to have by the end of each key stage. Attainment targets are composed of eight levels and an additional level of increasing difficulty. According to the results of the present study, Korea focuses on the formal and systematic mathematical knowledge on the basis of sound understanding of certain mathematical terms or concepts. On the other hand, England tends to deal with numbers more flexibly and naturally through the aquisition of mental methods, calculator use methods, etc, and emphasizes that mathematics be realistic and useful in solving a diverse number of problems confronted in everyday life.