\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2015c.00619}
\itemau{Leung, K. C. Issic}
\itemti{Prospective teachers' understanding of the constant $\pi$ and their knowledge of how to prove its constant nature through the concept of linearity.}
\itemso{J. Korean Soc. Math. Educ., Ser. D, Res. Math. Educ. 18, No. 1, 1-29 (2014).}
\itemab
Summary: When taught the precise definition of $\pi$, 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 $\pi$ 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 $\pi$, 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 $\pi$, 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.
\itemrv{~}
\itemcc{F59 G49 E59}
\itemut{professional knowledge; proofs; proving tasks; mathematical constants; linearity}
\itemli{}
\end