Academic journal article
By Wilkins, Jesse L. M.; Reese, George C.
Focus on Learning Problems in Mathematics , Vol. 25, No. 3
People of all ages have been found to have misconceptions and lack sound intuition in situations of uncertainty (Kahneman, Slovic, & Tversky, 1982; Bar-Hillel & Falk, 1982; Shaughnessy, 1981; Shaughnessy, 1992). Further, many people hold to misconceptions even after being presented with evidence contradicting their intuitions (Kahneman & Tversky, 1982a; Tversky & Kahneman, 1982) or beliefs (Anderson, Lepper, & Ross, 1980; Slusher & Anderson, 1989). In order to overcome these misconceptions and build sound probabilistic understandings in school-age children, the National Council of Teachers of Mathematics (NCTM) has recommended that students be involved in hands-on activities and experiments, such as simulations, to model situations of uncertainty while determining probabilities and solving problems (NCTM, 1989; 2000; also see Konold, 1991,1994; Shaughnessy, 1981; 1992; Watson, 1995). Further, it has been suggested that using a computer to carry out simulations may help students overcome misconceptions, because students can generate large amounts of data and analyze sample distributions that are closer to actual population distributions (NCTM, 2000; also see Biehler, 1991). However, there is little research that systematically investigates the effects of different pedagogical techniques on students' misconceptions (Shaugnessy, 1992). Zhonghong and Potter (1994) found that computers can be a helpful tool for overcoming misconceptions and some studies have investigated the role of computers in students' understanding of distribution (Cohen & Chechile, 1997; Wilensky, 1997), however, beyond this, little research exists on the effectiveness of computer simulations in overcoming probabilistic misconceptions.
The purpose of this study is to investigate the persuasiveness of computer-based Monte Carlo simulations on students' decisions in situations of uncertainty. This study 1) compares the use of computer simulations as an investigative-pedagogical tool (teacher-facilitated) to more traditional instructional methods (teacher-directed) for teaching probability, 2) considers the impact of simulation on students' psychological attachment to their misconceptions, and 3) compares the impact of computer simulations on students of different achievement levels. While the main purpose of this study is to consider the instructional impact of computer simulations on students' misconceptions and decision making, the psychological barriers associated with these misconceptions are also discussed.
The work of Kahneman and Tversky (e.g., Kahneman, Slovic, & Tversky, 1982) was devoted to identifying misconceptions and notions of probability that people possess and the associated heuristics that they use to make probabilistic decisions. Misconceptions in conditional probability are some of the most interesting and have been found to be prevalent in school-aged children as well as adults (Bar-Hillel & Falk, 1982; Shaughnessy, 1992). In situations involving conditional probability, one must determine the probability of an event when certain information has been given or something has happened. Many people are confused by the information that they are given. They have difficulties determining what is the conditioning event and are further confused by the additional information that is presented in conditional situations (Shaughnessy, 1992).
Monty's Dilemma is a problem frequently associated with the teaching of conditional probability (Shaughnessy, 1992; Shaughnessy & Dick, 1991). Monty's Dilemma is an age-old problem whose interest was revitalized by the Parade Magazine's column "Ask Marilyn" (vos Savant, 1990a, 1990b, 1991a, 1991b, 1991c).
In a certain game show, a contestant is presented with three doors. Behind one of the doors is an expensive prize, behind the others are junk. The contestant is asked to choose a door. …