• Journal of Educational Research in Mathematics
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• v.9 no.1
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• pp.229-237
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• 1999

In this paper I examined the tangents to curves through the history of mathematics, expecially that of the Greek geometry and seventeenth century. The purpose of this examination is to show that the mathematical concept of curves is changed by the problems. And I analyzed the text books from the junior to high school. I found that the tangents which aretaught in junior school correspond to those of Greece, and the tangents in high school those of seventeenth century.

• The Mathematical Education
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• v.39 no.1
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• pp.1-9
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• 2000

Now, mathematics textbook is being developed in accordance with the 7th educational curriculum. It is expected that qualified textbook reflecting 'differentiated education' concept be developed and published. But there are still many limitations of textbook authorization system to develop 'such' textbook. Many authors of textbook have difficulty in developing creative and qualified textbooks in their own way. In this paper, we deal with what the authors should keep in mind and could reflect related on textbook authorization system in developing textbook. For this purpose, focusing on new 'content principle' of mathematics textbook authorization, the paper presented its educational background.

• Journal of Educational Research in Mathematics
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• v.8 no.1
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• pp.313-326
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• 1998

The purpose of this study is to verify the meaning of preformal proof and its didactical significance in mathematics education. A preformal proof plays a more important role in mathematics education, because nowadays in mathematics a proof is considered as an important fact from a sociological point of view. A preformal proof was classified into four categories: a) action proof, b) geometric-intuitive proof, c) reality oriented proof, d) proof by generalization from paradiam. An educational significance of a preformal proof are followings: a) A proof is not identified with a formal proof. b) A proof is not only considered from a symbolic level, but also from enactive and iconic level. c) A preformal proof generates a formal proof and convinces pupils of a formal proof d) A preformal proof is psychologically natural. e) A preformal proof changes a conception of what is a proof. Therefore a preformal proof is expected to teach in school mathematics from the elementary school to the secondary school.

• East Asian mathematical journal
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• v.27 no.2
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• pp.243-259
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• 2011

The Yang-Hui arithmetic(楊輝算法) is a crucial textbook on mathematics for make out the Orient mathematics. In this thesis, compare the Yang-Hui arithmetic and the part of the equation and the function both in the middle school mathematics of the 7th Educational Curriculum Revision. As well, drawing a parallel between two things is the solution that had given in the Yang-Hui arithmetic and have given in the middle school textbook of the 7th Educational Curriculum Revision.

• Journal of Educational Research in Mathematics
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• v.10 no.2
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• pp.161-182
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• 2000

This study is to develop assessment framework, test items and questionnaire for the National Assessment of Educational Achievement(NAEA), which administered in the elementary and secondary schools across the country in this year(2000). According to the first year study result of the NAEA, the test was administered in two core subjects, Mathematics and Social Studies. In this study, test items and sets of questionnaire and administered pretest were developed in the last year. In this year, the NAEA was administered with the adjusted test items and questionnaires and the results was analyzed and would be reported to the public. NAEA was developed on the basis of national curriculum, especially of the nature and objectives of subject curriculum in Mathematics (and also Social Studies). In the framework of assessment, we set up four differentiated levels of student achievement: 'under basic', 'basic', 'intermediary', and 'advanced'. Here 'the intermediary level' means the level of educational achievement in which students can understand average content of subject curriculum. 'Advanced level' indicates the level of educational achievement in which students master all the content of subject curriculum and apply basic concepts and principles to a variety of situations. 'The basic level' means the level of educational achievement in which students do not achieve the intermediary level. Students who do not understand average content of subject curriculum are classified as belonging to the basic level. Finally, this study would explain how to administer and analyze the test in the future. The test result was analyzed to report students' educational achievement according to regions, content areas, behavioral characteristics, and etc. This study would show how to report test result\ulcorner and how to set up students' academic achievement.

• Journal of Educational Research in Mathematics
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• v.11 no.2
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• pp.291-305
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• 2001

The major purpose of this study is to show the insufficiency of traditional epistemology and consructivism as epistemology of mathematics education. Traditional epistemology such as empiricism, rationalism, Kant's epistemology, and Piaget's genetic epistemology is not sufficient to explain episteme in educational situation because it regards that epsteme is the phenomenon occurs between the abstract individual subject and the object world. Modern epistemology like constructivism recognize the public or social character of epsteme. So it is more appreciate than traditional epistemology to explain episteme in math educational situation. But constructivist pedagogy derived from constructivist learning theory has the following important shortcoming: The lack of clear criteria by which instructional effectiveness might be evaluated from a constructivist perspective.

• Journal of Educational Research in Mathematics
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• v.8 no.2
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• pp.679-690
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• 1998

I wish to search for educational alternatives which improve students' mathematical creativity. As the first attempt for this, theories of general creativity and characters of mathematical creativity are discussed. And four factors( teacher variables. student variables, teaching and learning variables. environment variables) affecting mathematical creativity are analyzed. It is a educational well-known fact that students should think creatively and solve the problems for themselves. We postulate the fact that students' mathematical creativity can be developed. I think it is a mission and a duty for mathematics educators to develop the students' mathematical creativity fully. Mathematics educators should search for the methods which encourage the students to have mathematical creativity and should develop them.

• Journal of Educational Research in Mathematics
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• v.8 no.2
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• pp.621-634
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• 1998

Emthusiasm about the introduction of computers into mathematics education is widespred. But, the perspectives about the relationship between mathematics education and computer are diverse. The purpose of this study is to examine theoretical background for using computers in mathematics education. In spite of the pedagogical possibilities of computers. only a small minority of mathematics teachers are using computers in mathematics classroom. It is natural to seek this obstacles within theoretical background of the teachers who manage computers, In this study, We discuss the problems in the two sides. First, due to increased computer activity, relationship of mathematics in school with mathematics in society is changing. It is tension between academic mathematics and practical mathematics. School mathematics have to be changed toward stressing practical mathematics. Second problem is the dialectical relationship between the individual and the collective. While maintaining a respect for the individuality of student contributions. We take into account the social dimension of mathematical meaning-making. We discussed theoretical clarification of work collaborative learning. We propose the case study for the roles of computer in collaborative mathematics learning.

• School Mathematics
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• v.8 no.2
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• pp.239-263
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• 2006

The purpose of the National Assessment of Educational Achievement(NAEA) is not only to assess educational progress and achievement but also to collect background information affecting educational achievement. It is important to know which factors affect the National Assessment of Educational Achievement(NAEA) and to explore how much those factors show the educational effect. In this study, first, we examined general characteristics of the survey with relation to the background information. Second, we analyzed the relationships between test scores and information on the students' profile such as background, extracurricular activities, and information on the school profile in NAEA 2004. Third, we suggested some educational policies on the basis of those analysis and indicated the limitation of this study.

• Journal of Educational Research in Mathematics
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• v.14 no.2
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• pp.157-170
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• 2004

This study, in the view of the particulars on mathematics, tried to criticize the way how they have reformed mathematics curriculums, which moreover have been executed without any official investigation of the ways up to the recent curriculum. On the basis of these critics, this study suggested a few desirable ideas about how to reform the mathematics curriculum which were investigated from a mathematics educational standpoint. For this purpose this study was executed as followings : first, there has been reflective investigations about the existing ways of reforming mathematics curriculums ; second, there suggested a new way of reforming the mathematics curriculum which we may consider as the way for the future mathematics curriculum reform.