• School Mathematics
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• v.8 no.4
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• pp.417-439
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• 2006

Many studies indicate the emerging crisis of education of calculus even though the emphasis of calculus have been widely recognized. In our classrooms, the education of calculus also has been faced with its bounds. Most instructions of calculus is too much emphasis on the algebraic approach, thus students solve mathematical problems without truly understanding the underlying concept. The purpose of this study is to develop mathematization teaching and learning materials and methods in caculus based on the mathematization teaching and learning theories by Freudenthal and the variability principles of conceptual learning by Dienes, In order to this purpose, first, we analyzed the high school mathematics II textbook of 7th curriculum in Korea. Second, we developed mathematization teaching and learning materials and methods in highschool calculus. Consequently, the following conclusions have been drawn: we have reorganized and reconstructed the context problem in calculus based on concepts of tangent line and instantaneous rate of change.

• Journal of Educational Research in Mathematics
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• v.11 no.2
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• pp.307-320
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• 2001

Traditionally, there are many inherent restrictions in highschool mathematics textbooks. They are restricted in its contents and inevitably resorted to reader's ability of intuition. So they are usually lacked logical precisions and have various differences in expressions. We are mainly concerned with the definite integral and its applications in current highschool mathematics II textbooks according to 6th curriculum. We choose 6 of them arbitrarily and survey by comparison to deduce some controversial topics among them as follows. 1) absurd metaphors in formula process 2) confusions in important notations and too much choices in terms and statements. 3) lack of precisions in - teaching hierarchy (between some contents of Physics and the applications of definite integral) - introducing a proof of theorem (fundamental theorem of Calculus I) - introducing the methods (integral substitutions 1, ll) 4) adopting small topics such as - mean value theorem of integral - integrals with variable limits. In coming 7th curriculum, highschool students in Korea are supposed to choose calculus as a whole, independent course. So we hope that the suggested controversial topics are to be referred by authors to improve the preceding Mathematics ll textbooks and for teachers to use them for better mathematics education.

• Communications of Mathematical Education
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• v.21 no.4
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• pp.613-620
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• 2007

We made an investigation into basic mathematical abilities and made university freshmen an object of this study in order to find out the reason why their capabilities are remarkably behind in studies year by year. According to the survey, we confirmed that recent university freshmen's basic abilities to attend calculus class, right away after entering university, are insufficient for that class. In particular, a matter of grave concern is that score variations are so big despite the equal major of the same university. The aim of the study is to evaluate university freshmen's basic mathematical abilities in nationwide university and to figure out the real situation, then to give assistance to the proper calculus curriculum of university by reflecting the result in it. And also we wish to be helpful to propose proper policy plan in natural science system of highschool.

• Journal of Gifted/Talented Education
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• v.26 no.2
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• pp.405-421
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• 2016

The purpose of this study was to investigate students' perception of Advanced Placement Program. Participations of this study were 1144 students from 14 science high schools. The results showed as follows. First, students perceived positively regarding AP program and were willing to take AP courses because of interesting and challenging in academic area which is provided by AP courses. Secondly, many students would like to take AP courses in Differential and Integral Calculus 1, General Physics I, General Chemistry I and General Biology. Also, they would like to take AP courses in first term as a mandatory subjects. Third, responses perceived that AP courses were challenging, difficult, and of high quality. Finally, students perceived the benefit of AP courses in earing college credit. However, 35% of responses wished to receive an exemption for all AP courses. Also, they wished to have dual-major or participate in students exchange program as a benefit of AP program. Implications of the study were discussed in depth based on the results.

• School Mathematics
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• v.18 no.2
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• pp.349-373
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• 2016

Comparison of curriculum between various countries is a major research method for studying a course and content quoted on Korea's national curriculum. Therefore this research focuses on comparing and analyzing a new curriculum which Australia has announced on 2012 and conducting since 2015. From this research result, we found that Australia's curriculum achievement shows some unique characteristics. Such examples can be dealing a concept with real life context and proposing a mathematical content specifically. Also they introduce the definite integral by defining to the sum of series. There are other characteristics such as modelling motion, and numerical integration which Korea's highschool curriculum achievement doesn't deal with, and the content of vector calculus is handled more deeply. As a result of analyzing Australia's textbook, it fully deals with the supplementary notion to help understand mathematical definition. Hence further research will be needed later on to relieve the aspect of cognitive burden on Korean learners.