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Prospective teachers’ understanding of the constant $π$ and their knowledge of how to prove its constant nature through the concept of linearity. (English)
J. Korean Soc. Math. Educ., Ser. D, Res. Math. Educ. 18, No. 1, 1-29 (2014).
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.
Classification: F59 G49 E59
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