id: 06428421
dt: j
an: 2015c.00619
au: Leung, K. C. Issic
ti: Prospective teachers’ understanding of the constant $π$ and their
knowledge of how to prove its constant nature through the concept of
linearity.
so: J. Korean Soc. Math. Educ., Ser. D, Res. Math. Educ. 18, No. 1, 1-29
(2014).
py: 2014
pu: Korean Society of Mathematical Education (KSME), Seoul
la: EN
cc: F59 G49 E59
ut: professional knowledge; proofs; proving tasks; mathematical constants;
linearity
ci:
li:
ab: Summary: When taught the precise definition of $π$, students may be simply
asked to memorize its approximate value without developing a rigorous
understanding of the underlying reason of why it is a constant.
Measuring the circumferences and diameters of various circles and
calculating their ratios might just represent an attempt to verify that
$π$ has an approximate value of 3.14, and will not necessarily result
in an adequate understanding about the constant nor formally proves
that it is a constant. In this study, we aim to investigate prospective
teachers’ conceptual understanding of $π$, and as a constant and
whether they can provide a proof of its constant property. The findings
show that prospective teachers lack a holistic understanding of the
constant nature of $π$, and reveal how they teach students about this
property in an inappropriate approach through a proving activity. We
conclude our findings with a suggestion on how to improve the
situation.
rv: