A Mathematical Microworld to Introduce Students to Probability

The objective of this paper is to describe a simulationoriented computer environment designed to introduce probability and a teaching experiment that evaluates its effectiveness. This learning environment is a mathematical microworld named Chance. It is a consensual opinion that an understanding of probability and the related area of statistics is essential to being an informed citizen (National Council of Teachers of Mathematics [NCTM], 1989; Shaughnessy, 1992). Some researchers even indicate that perhaps no other branch of the mathematical sciences is as important for all students, college-bound or not, as probability and statistics (Schultz, 1989; Shaughnessy, 1992). Among many attempts to encourage an increased emphasis on probability, the Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989) recommends including probability in the core curriculum at all levels. There is a wide gap between these ideals and reality, however, because probability is still a weak spot in school mathematics curriculum and instruction. Many researchers (e.g. Kaput, 1990; Konold, 1991) believe that computer technology is well suited to bridge this gap. We agree with them. According to the Standards, “the study of probability in grades 5-8 should not focus on developing formulas or computing the likelihood of events pictured in texts. Students should actively explore situations by experimenting and simulating probability models” (p. 109). “In grades 912, students should extend their K-8 experiences with simulations and experimental probability to continue to improve their intuition” (p.171). Therefore, devising and carrying out experiments or simulations to determine probabilities is important for all students. Some basic random devices such as coins, dice, and spinners are indispensable for students to perform experiments while they learn introductory probability concepts. Using physical manipulatives to do probability experiments, however, has its limitations. The limitations of physical manipulatives