The purpose of this study is to find the undergraduates¡¯ mathematical reasoning of a geometric con
cept in science activity contexts. Through the given activity it was found that a variety of mathemati
cal misconceptions were possessed by students. We clustered students into two groups: one group had
a 10-minute long short lesson to remind them of definitions of circle and ellipse during the introduc
tory science course. The other group without this lesson. The science activity allowed students to use
such knowledge in determining the shape. In this scientific context, the key to the determination is
whether students bring up the definition of the orbit appropriately. It was connected with how the prior
scientific knowledge affected their decision of the shape through mathematical reasoning. In most
answers of student subjects, we found that students used naive and non-mathematical concepts such as
¡°not a perfect circular shape¡± and ¡°twisted circle¡±. Only a very few students succeeded in using the
mathematical definitions of the ellipse.
