RSUSSH 2020

IN20-203 High School Students’ Understanding and Retention of the Connection between Two Ways of Constructing an Ellipse

Presenter: Phitchayaphat Luengwattanachod
Mahidol University, Thailand

Abstract

      Conic section is the study of various types of shapes resulted from cutting cones with planes. Another way to construct these shapes is to consider loci of points under certain conditions. An ellipse is one type of conic sections. Here, the cutting plane is flatter than the surface of the cone. The foci of the resulting ellipse are the points where the plane touches Dandelin’s spheres—the spheres that fit inside the cone. An ellipse is also the locus of points whose sums of distances to the two foci are constant. One of the problems of learning conic section is the lack of connection between the two constructions. Therefore, we constructed a set of concrete manipulatives based on Dandelin’s spheres to enhance high school students’ understanding and retention of the connection between the two ways of constructing an ellipse. Four high school students participated in this study wherein learning process proceeded through group discussion. They explored the manipulatives by following a guided worksheet. After one month, we assessed their retention by using a semi-structured interview whose result was analyzed to extract common themes. The result showed that two students were able to see the connection between the two ellipse constructions while the others could not.

Keywords: Dandelin's spheres; Conic section; Ellipse; Concrete manipulative; Retention; Cutting cone

Citation format:

Luengwattanachod, P., Wongkia, W., & Laosinchai, P.. (2020). High School Students’ Understanding and Retention of the Connection between Two Ways of Constructing an Ellipse. Proceeding in RSU International Research Conference, May 1, 2020. Pathum Thani, Thailand.

QUESTIONS & ANSWERS

ดร.ดารุณี เสริฐผล (Chairperson)

Can we use this technique for different age student such as younger than this?

Phitchayaphat Luengwattanachod (Presenter)

Yes, I can. We can use this technique with different ages of students such as students' grade 8. If we want to use with the lower students more than grade 8, we should develop the tools.