Senior Middle School Students' Understanding About The Classic Probability: An Empirical Study Of Historical Parallelism

This paper is a report of an empirical study on senior middle school students' understanding about classical probability through a test on the problem of casting, which appears before the birth of theory of probability, and on the problem of points, which gave rise to the birth of the theory of probability. Mathematicians had discussed the two problems for three hundred years in the history and many of them got puzzled and made mistakes before they solved the problems in the end.It is found that historical parallism exists with respect to middle school student' difficulties with, wrong conceptions and correct strategies on the problem of casting and the problem of points. Senior middle school student' understanding about the classical probability supported the historical-genetic-principle, thus justifying M. Kline's statement that the history of mathematics was the guide to mathematics teaching.Finally some teaching implications are arrived at. First, the introduction of the instances in the history of mathmatics is helpful to teaching classical probability; Secondly, the adoption of tree diagrams in teaching will help students understand classical probability correctly.