Research on Statistical Probability Instruction Through Computer Simulation
BoMi Shin
bomi0210@hanmail.net
Gwangju Science High School
KyungHwa Lee khmath@knue.ac.kr
Mathematics Education Korea National University of Education South Korea
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 Scriptbased
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.
