• The Mathematical Education
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• v.50 no.3
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• pp.355-365
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• 2011

The purpose of this study is to provide mathematical knowledge for supporting the didactical knowledge on circular measure and radian in the high school curriculum. We show that circular measure related to arcs can be mathematically justified as an angular measure and radian is a well defined concept to be able to reconcile the values of trigonometric functions and ones of circular functions, which are real variable functions. Radian has two-fold intrinsic attributes of angular measure and arc measure on the unit circle, in particular, the latter property plays a very important role in simplifying the trigonometric derivatives. To improve students's low academic achievement in trigonometry section, the useful advantage and the background over the introduction of radian should be preferentially taught and recognized to students. We suggest some teaching plans to practice in the class of elementary and middle school for enhancing teachers' and students' understanding of radian.

• Korean Journal of Acupuncture
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• v.23 no.3
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• pp.123-131
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• 2006

목 적 : 과산화수소는 산화적 스트레스를 통해 아폽토시스를 유도하는 것으로 알려져 있다. 본 논문에서는 과산화수소로 유발된 신경아세포종 아폽토시스 과정에서 호도약침액의 효과를 관찰하였다. 방 법 : 과산화수소로 인한 신경아세포종의 아폽토시스에서 호도약침액의 효과를 알아보기 위해 배양 중인 신경아세포종에 과산화수소를 처리하고, 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide(MIT)분석법, 4,6-diamidino-2-phenylindole (DAPI) 염색법, reverse transcription-polymerase chain reaction (RT-PCR), western blotting의 방법으로 확인하였다. 결 과 : 과산화수소로 인한 신경아세포종의 아폽토시스에서 호도약침액을 처리한 결과, 약침액을 처리한 세포의 생존이 약 30% 정도 증가하고, 핵 응축과 단편화를 막아주며, CASP3와 BAX단백질의 발현이 감소되었다. 결 론 : 이러한 결과로 호도약침액이 과산화수소로 인한 신경아세포종의 아폽토시스과정에서 보호효과를 나타내는 것으로 사료된다.

• Journal of the Korean School Mathematics Society
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• v.6 no.1
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• pp.101-113
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• 2003

The purpose of this study is to analyze students misunderstood types relate to trigonometric function and to devise its teaching method using GSP. To do this, we performed several steps as followings: First, we performed questionnaire survey to 70 students belong to second year at high school to find students comprehension degree about radian angle representation and trigonometric function graph. Second, we devised the teaching-learning materials relate to trigonometric function graph using GSP. And then, we used them in the class of 35 students who are at the time to learn trigonometric function in the first year at high school. Third, we conducted Questionnaire survey to students studied through teaching and learning materials using GSP. As a result of doing the survey, we found that general students were interested in the class using GSP and they could also operate computer without difficulty.

• Journal of Educational Research in Mathematics
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• v.27 no.4
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• pp.833-855
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• 2017

This study aims to reinvestigate the reason for introducing radian as a new unit to express the size of angles, what is the meaning of radian measures to use arc lengths as angle measures, and why is the domain of trigonometric functions expanded to real numbers for expressing general angles. For this purpose, it was conducted historical, mathematical and applied mathematical analyzes in order to research at multidisciplinary analysis of the radian concept. As a result, the following were revealed. First, radian measure is intrinsic essence in angle measure. The radian is itself, and theoretical absolute unit. The radian makes trigonometric functions as real functions. Second, radians should be aware of invariance through covariance of ratios and proportions in concentric circles. The orthogonality between cosine and sine gives a crucial inevitability to the radian. It should be aware that radian is the simplest standards for measuring the length of arcs by the length of radius. It can find the connection with sexadecimal method using the division strategy. Third, I revealed the necessity by distinction between angle and angle measure. It needs justification for omission of radians and multiplication relationship strategy between arc and radius. The didactical suggestions derived by these can reveal the usefulness and value of the radian concept and can contribute to the substantive teaching of radian measure.

• School Mathematics
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• v.17 no.2
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• pp.309-329
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• 2015

This study is to provide didactical implications for teaching and learning of radian through a analysis of investigation result about pre-service teachers' understanding of radian. The results of this study are as follows. First, pre-service teachers understood the radian as ${\frac{180^{\circ}}{\pi}}$, rather than as the definition. Secondly, the definition style of radian affected the problem solving strategy for the measurement of the angle. Thirdly, pre-service teachers had insufficient content knowledge about properties of measurement as a pure number of radian. Lastly, They failed to describe the usefulness of circular measure. We suggested the definition of radian in textbooks should be changed from ${\frac{180^{\circ}}{\pi}}$ to mathematical definition of radian. And the general angle should be stated as the reason why the domain of trigonometric function is real numbers.

• Journal of Educational Research in Mathematics
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• v.24 no.4
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• pp.607-622
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• 2014

The purpose of this paper is that it analyzes the historical development of the concept of trigonometric functions and discuss some didactical implications. The results of the study are as follows. First, the concept of trigonometric functions is developed from line segments measuring ratios to numbers representing the ratios. Geometry, arithmetic, algebra and analysis has been integrated in this process. Secondly, as a result of developing from practical calculation to theoretical function, periodicity is formalized, but 'trigonometry' is overlooked. Third, it must be taught trigonometry relationally and structurally by the principle of similarity. Fourth, the conceptual generalization of trigonometric functions must be recognized as epistemological obstacle, and it should be improved to emphasize the integration revealed in history. The results of these studies provide some useful suggestions to teaching and learning of trigonometry.

• Journal of the Korea Computer Graphics Society
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• v.6 no.1
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• pp.37-50
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• 2000

Using the complex formulation of plane curves which R. T. Farouki introduced, we can identify any plane polynomial curve with only a polynomial with complex coefficients. In this paper, using the well-known fundamental theorem of algebra, we completely factorize the polynomial over the complex number field C and from the completely factorized form of the polynomial, we find a new necessary and sufficient condition for a plane polynomial curve to be a Pythagorean-hodograph curve, obseving the set of all roots of the complex polynomial corresponding to the plane polynomial curve. Applying this method to space polynomial curves in the three dimensional Minkowski space $R^{2,1}$, we also find the necessary and sufficient condition for a polynomial curve in $R^{2,1}$ to be a PH curve in a new finer form and characterize all possible curves completely.

• Journal of Educational Research in Mathematics
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• v.19 no.3
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• pp.443-459
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• 2009

Despite the many discussions of mathematics education, there are a lot of controversy of the Radian. Generally, Radian is taken to have two properties. One property is an angular property and other is a property of fore numbers. For this reason, both Students and teachers are hard to understand the radian. This study is to provide a base of the radian understand. In essence, radian has only angular property, and other property is a derived property. So radian is to be understood in an angle.

• Sleep Medicine and Psychophysiology
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• v.18 no.1
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• pp.35-39
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• 2011

Objective: Diurnal preference is an attribute reflecting whether people are alert and preferring to be active either early or late in the day. It also referred to as chronotype or morningness-eveningness trait. The PER3 genes have been known to influence diurnal preference. In this study, we have investigated the associations between the PER3 gene polymorphisms and diurnal preference in a healthy young population, controlling for the social and environmental confounding factors. Methods: The participants in this experiment included 299 unrelated medical college students (M=191, F=108), with a mean age of 22.9 years. Diurnal preference was measured by a single administration of the 13-item Composite Scale for Morningness (CSM). Genotyping of the PER3 VNTR (rs57875989) was performed using polymerase chain reaction. A two-tailed alpha of 0.05 was chosen. Results: The mean${\pm}$SD score on the CSM scale for all subjects was 31.90${\pm}$6.39. There was no significant difference in total CSM score between gender groups, although females showed a trend towards higher morningness score. Although PER3 5R/5R showed the tendency towards high CSM scores, there were no significant differences on CSM scores among genotypes and allele status of PER3 VNTR (rs57875989). Conclusions: We could not confirm that the PER3 VNTR is associated with diurnal preference in a Korean healthy young population. The future studies need to investigate the association between diurnal preference and other polymorphisms of PER3 gene in larger sample of Korean young healthy population.

• Journal of Educational Research in Mathematics
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• v.18 no.2
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• pp.263-281
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• 2008

This study is to provide a base for discussions on teaching and teaming of radian through a theoretical analysis of it. Radian possesses two-fold comprehensive properties of measurement as a magnitude and a pure number. As a magnitude of an angle, it has some theoretical advantages in mathematics and in physics, in spite of its non-superiority to other angular measures in practical sense. As a pure number, it has some advantages in that it simplifies theoretical developments of trigonometric functions and justifies omitting the unit in the calculations and final expressions in physics. Radian should be taught and learnt with an appreciation of the advantages of the two-fold properties. Activities to measure angles from various viewpoints may be helpful for this. Students' awareness of the advantages of radian needs to be stimulated and deepened repeatedly as related content appears.