• Journal of The Korean Association For Science Education
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• v.27 no.5
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• pp.456-464
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• 2007

The aims of this research are to analyze the representations and conceptual sequence of eye vision in Korean science textbooks and to suggest a contents construct about eye vision where the conceptual sequence is considered. Research method was literature review, and the literatures that were used for analysis were the 7th Korean science curriculum which was revised in 1997, and the science and physics textbooks developed based on the 7th Korean science curriculum. The research results are as follows: 1) Although the science curriculum seems to have no problem on sequence in the eye vision concepts, the science and physics textbooks based on the curriculum reveal problems on the sequence in the eye vision concepts; 2) Some Korean science textbooks explain retinal image formation according to the Alhazen's idea, except in inverse image; 3) Some Korean science textbooks explain about the reasons of near- and far-sightedness without consistency between the textbooks for 7th and 8th grade students; 4) A few Korean science textbooks give an inappropriate explanation about the principle of eye sight correction by eye glasses; 5) According to the analysis result, the concepts related to eye vision should be presented in the order of explanation about light refraction phenomena, image formation process by convex lens, structure of human eye and retinal image formation process, correction of eye sight using lens.

• East Asian mathematical journal
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• v.34 no.4
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• pp.403-427
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• 2018

The purpose of this paper is to reinterpret and visualize the medieval Arab's studies on the geometric methods of solving the cubic equation by utilizing Apollonius' symptom of the parabola. In particular, we investigate the results of $Kam{\bar{a}}l$ $al-D{\bar{i}}n$ ibn $Y{\bar{u}}nus$, Alhazen, Umar al-$Khayy{\bar{a}}m$ and $Al-T{\bar{u}}s{\bar{i}}$ by 4 steps(analysis, construction, proof and examination) which are called the complete solution in the constructions. This paper is available in the current middle school curriculum through dynamic geometry program(Geogebra).

• Journal of The Korean Association For Science Education
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• v.27 no.6
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• pp.488-496
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• 2007

The aims of this study are to investigate how Kepler found a scientific problem for the retinal image theory and to investigate how Korean middle-school students respond when the same situation is applied to them. Kepler found the scientific problem in the eye vision through the critical analysis of contemporary theories of vision, based on his relevant knowledge of optics. When the same situation was applied to the Korean middle-school students, only a few students found the same scientific problem as Kepler. From the results, it is suggested that in developing creativity teaching materials, situations like Kepler's problem finding need to be included in programs.

• Journal for History of Mathematics
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• v.27 no.2
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• pp.127-138
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• 2014

In this paper we investigate how Newton discovered the generalized binomial theorem. Newton's binomial theorem, or binomial series can be found in Calculus text books as a special case of Taylor series. It can also be understood as a formal power series which was first conceived by Euler if convergence does not matter much. Discovered before Taylor or Euler, Newton's binomial theorem must have a good explanation of its birth and validity. Newton learned the interpolation method from Wallis' famous book ${\ll}$Arithmetica Infinitorum${\gg}$ and employed it to get the theorem. The interpolation method, which Wallis devised to find the areas under a family of curves, was by nature arithmetrical but not geometrical. Newton himself used the method as a way of finding areas under curves. He noticed certain patterns hidden in the integer binomial sequence appeared in relation with curves and then applied them to rationals, finally obtained the generalized binomial sequence and the generalized binomial theorem.