楕円の極線の方程式に関する数学的探究とその様相  [in Japanese] Mathematical Inquiry about the Equation of the Polar Line of Ellipse and its Phase  [in Japanese]

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Abstract

<p>   The purpose of this paper is to investigate senior high school student's mathematical inquiry and its phase about the equation of the polar line of ellipse, which focus on comparing mathematical characters between circle and ellipse, reading the form of symbolic expression and reviewing the method of producing the equation of the polar line of circle, connecting with the method of producing the equation of the polar line of ellipse to the polar line of circle, considering mathematical characters of the polar line of ellipse repeatedly.  We investigated student's mathematical inquiry by teaching unit about the equation of the polar line of ellipse by qualitative methods.  As a result of our discussions, we obtained several insights:</p><p>(1)  Reading the equation of the polar line px/a<sup>2</sup> + qy/b<sup>2</sup> = 1 by paying attention to the pole (p, q), points of contact<b> </b>  between ellipse and its tangent, the points on the polar line is no easy matter for many students.</p><p>(2)  Considering the equation and symbolic expression from many angles and reading the figure about the polar line of ellipse from different angles become a foundation of producing the equation of the polar line.</p><p>  Reading symbolic expression can accelerate to understand the way of dicovering the equation of the polar line by connecting with reading the figure, especially the pole and the polar line in seeing continuous move by GeoGebra.</p><p>(3)  Discussion with others and reflection on own writing urge to explore about relation between the circle and the ellipse, the equation of the polar line of ellipse.  Reflecting on own writing and thinking process about the  polar line of ellipse accelerate student's further mathematical inquiry.</p>

Journal

  • Journal of JASME : research in mathematics education

    Journal of JASME : research in mathematics education 23(1), 63-73, 2017

    Japan Academic Society of Mathematics Education

Codes

  • NII Article ID (NAID)
    130007580624
  • NII NACSIS-CAT ID (NCID)
    AA11141495
  • Text Lang
    JPN
  • ISSN
    1341-2620
  • NDL Article ID
    029359187
  • NDL Call No.
    Z71-Y908
  • Data Source
    NDL  J-STAGE 
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