• Title/Summary/Keyword: mathematics abstraction

### Understanding the Estimation of Circumference of the Earth by of Eratosthenes based on the History of Science, For Earth Science Education

• Oh, Jun-Young
• Journal of the Korean Society of Earth Science Education
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• v.10 no.2
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• pp.214-225
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• 2017
• The first accurate estimate of the Earth's circumference was made by the Hellenism scientist Eratosthenes (276-195 B.C.) in about 240 B.C. The simplicity and elegance of Eratosthenes' measurement of the circumference of the Earth by mathematics abstraction strategies were an excellent example of ancient Greek ingenuity. Eratosthenes's success was a triumph of logic and the scientific method, the method required that he assume that Sun was so far away that its light reached Earth along parallel lines. That assumption, however, should be supported by another set of measurements made by the ancient Hellenism, Aristarchus, namely, a rough measurement of the relative diameters and distances of the Sun and Moon. Eratosthenes formulated the simple proportional formula, by mathematic abstraction strategies based on perfect sphere and a simple mathematical rule as well as in the geometry in this world. The Earth must be a sphere by a logical and empirical argument of Aristotle, based on the Greek word symmetry including harmony and beauty of form. We discuss the justification of these three bold assumptions for mathematical abstraction of Eratosthenes's experiment for calculating the circumference of the Earth, and justifying all three assumptions from historical perspective for mathematics and science education. Also it is important that the simplicity about the measurement of the earth's circumstance at the history of science.

### An Analysis and Criticism on Subject Matter Related to Solid Figures in Korean Elementary School Mathematics Textbook (우리나라 초등학교 수학 교과서에서의 입체도형 관련 지도 내용에 대한 분석과 비판)

• Kwon, Seok-Il;Park, Kyo-Sik
• Journal of Educational Research in Mathematics
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• v.21 no.3
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• pp.221-237
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• 2011
• This paper focused on three drawbacks exposed in subject matter related to solid figures in elementary school math textbook. First, general solid figure are introduced before rectangular parallelepiped and cube in fifth grade math textbook, and prism and pyramid in sixth grade math textbook are introduced. Second, the process of abstraction from concrete objects to solid figures is insufficient in sixth grade math textbook. Third, some definitions in subject matter related to solid figures are inconsistent and ambiguous. The following four suggestions can be put forward as a conclusion based on these results. First, subject matter in textbooks must be correspond with that in curriculum. Second, it is necessary to inform teachers of range of subject matter through teachers guide book and manual for curriculum definitely. Third, each grade subject matter in math textbooks must be reexamined. Fourth, regular modification of math textbooks must be possible institutionally.