id: 06606477
dt: j
an: 2016d.00676
au: Kang, Jeonggi
ti: An educational consideration on the condition that four points lie on a
circle.
so: J. Korean Soc. Math. Educ., Ser. A, Math. Educ. 55, No. 2, 233-249 (2016).
py: 2016
pu: Korean Society of Mathematical Education (KSME), Seoul
la: KO
cc: G43
ut: circle; background meaning; realistic background meaning; geometry
ci:
li:
ab: Summary: We extracted the background meaning of the condition that four
points lie on a circle, analyzed textbooks critically and proposed the
orientation to improve the content in the textbook. As results, the
condition has a realistic background meaning which is ‘mathematical
modeling of finding a fair location’. The condition has a
mathematical background meanings which are ‘a first complex situation
distinguished from two points and three points’, ‘the condition
described in the perspective of side and angle in order to overcome the
disadvantages of the perpendicular bisectors context’ and ‘being
possible to transfer more than five points’. However it is difficult
to understand the reason why the condition is on four points in the
current textbook. In addition, it is difficult to recognize the
connectivity of a circumcenter of triangle. To overcome these problems,
we proposed five orientations to improve the content in the textbook.
rv: