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Toward Students' Full Understanding of Trigonometric Ratios

  • Yi, Jung-A;Yoo, Jae-Geun;Lee, Kyeong Hwa
    • Research in Mathematical Education
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    • v.17 no.1
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    • pp.63-78
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    • 2013

  • Trigonometric ratios are difficult concepts to teach and learn in middle school. One of the reasons is that the mathematical terms (sine, cosine, tangent) don't convey the idea literally. This paper deals with the understanding of a concept from the learner's standpoint, and searches the orientation of teaching that make students to have full understanding of trigonometric ratios. Such full understanding contains at least five constructs as follows: skill-algorithm, property-proof, use-application, representation-metaphor, history-culture understanding [Usiskin, Z. (2012). What does it mean to understand some mathematics? In: Proceedings of ICME12, COEX, Seoul Korea; July 8-15,2012 (pp. 502-521). Seoul, Korea: ICME-12]. Despite multi-aspects of understanding, especially, the history-culture aspect is not yet a part of the mathematics class on the trigonometric ratios. In this respect this study investigated the effect of history approach on students' understanding when the history approach focused on the mathematical terms is used to teach the concept of trigonometric ratios in Grade 9 mathematics class. As results, the experimental group obtained help in more full understanding on the trigonometric ratios through such teaching than the control group. This implies that the historical derivation of mathematical terms as well as the context of mathematical concepts should be dealt in the math class for the more full understanding of some mathematical concepts.

  • https://doi.org/10.7468/jksmed.2013.17.1.063 인용 PDF KSCI

A Preconditioned Time Method for Efficient Calculation of Reactive Flow (예조건화 시간차분을 통한 화학반응유동의 효율적 계산)

  • Kim, Seong-Lyong;Jeung, In-Seuck;Choi, Jeong-Yeol
    • 한국연소학회:학술대회논문집
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    • 1999.10a
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    • pp.219-230
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    • 1999

  • The Equations of Chemical kinetics are very stiff, which forces the use of an implicit scheme. The problem of implicit scheme, however, is that the jacobian must be solved at each time step. In this paper, we examined the methodology that can be stable without full chemical jacobian, This method is derived by applying the different time steps to the chemical source term. And the lower triangular chemical jacobian is derived. This is called the preconditioned time differencing method and represents partial implicit method. We show that this method is more stable in chemical kinetics than the full implicit method and that this is more efficient in supersonic combustion problem than the full jacobian method with same accuracy.

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Full mouth rehabilitation with vertical dimension increase in patient with severely worn out dentition (과도한 마모를 가진 환자의 수직 고경 증가를 동반한 전악수복 증례)

  • Jung, Ji-Hye
    • The Journal of the Korean dental association
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    • v.54 no.6
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    • pp.438-446
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    • 2016

  • Severe tooth wear may cause the pathologic change of the TMJ and masticatory muscles, unesthetic facial appearance, pathogenic pulp and occlusal disharmony. Treating patients with severely worn dentition often requires full mouth rehabilitation with increasing vertical dimension. Proper diagnosis and treatment planning are important for esthetic and functional definitive restorations and the long term stability of the neuromuscular system and the TMJ. In this case, 66 year-old female presented with generalized worn dentition. Based on assessment, pathologic destruction of teeth structure on entire dentition was caused by masticatory force and diet habit without loss of vertical dimension. Subsequently, 3 mm increase of vertical dimension that based on incisor for tooth restoration and esthetic improvement was determined. After 8 weeks stabilization period with temporary fixed prostheses, definitive prostheses were fabricated. After 6 months follow up period, satisfactory outcomes were attained both functional and esthetic aspects through this procedure.

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