Research on Statistical Probability Instruction Through Computer Simulation

Abstract

In the current school mathematics, the concept of probability is mainly based on classical perspectives (mathematical probability), with frequency (statistical probability) and axiomatic perspectives partly introduced. However, as school mathematics chooses classical perspectives as the concept of probability, it has been criticized for deviating from realistic thinking, focusing on learning based on complicated calculations (Fischbein, E. 1975; Freudenthal, H., 1973; Hawkins, A. and Kapadia, R., 1984; Konold. C., 1991). Today's research on probability instruction has commonly pointed out that further research is required to modify classical perspectives and highlight various features of probability concepts, due to the failure of classical perspectives to fully express the fundamental concepts of probability(Lee, 1996). Shaughnessy(1992) proposed simulation as a teaching method which helps students recognize statistical concepts by gathering and analyzing frequency information regarding probability. There are two different simulations such as a physical simulation using dice or a coin and a computer simulation obtaining all the data from a computer. Unlike the physical simulation which has realistic limitations in the implementation of repetitions, the computer simulation can fully increase the number of repetitions and enable random experiments by using random numbers. Namely, using the computer simulation can help to teach students statistical probability more effectively in the current curriculum where mathematical probability is emphasized more. Various past research applied the computer simulation to probability instruction. For example, Cho(2004) shows that the law of great numbers can be taught in an easier and meaningful way by using fathom. Shin & Lew(2002) describes the formation of the central limit theorem by using the random number generation function of Excel. Other research describes Bertrand's chord (Bogomolny, A, 2000) or Buffon's needle (Reese, G., 1996) through the Java Script-based simulation designed to be activated on the Web. The three purposes of this research can be summarized as follows: 1) Review how the characteristics of mathematical knowledge are changed when statistical probability is introduced through the computer simulation, considering Brousseau (1997)'s situation theories in teaching. 2) Present how the probability curriculum should be improved when statistical probability is introduced through the computer simulation. 3) Develop specific teaching materials to introduce statistical probability through the computer simulation.