WHAT IS THE NATURE OF HIGH SCHOOL STUDENTS' CONCEPTIONS AND MISCONCEPTIONS ABOUT PROBABILITY?

But it is important to stress that the relationship between intuition and logical structures plays an essential part in the domain of probability, perhaps more conspicuously and strikingly than it does in other domains of mathematics. (Fischbein, 1975, p.5) In high school, students are expected to determine the likelihood of an event by constructing probability distributions for simple s ample spaces, compute and interpret the expected value of random variables in simple ca ses, and describe sample spaces in compound experiments. They are also expected to learn to identify mutually exclusive and joint events, understand conditional probabilit y and independence, and draw on their knowledge of combinations, permutations, and counting principles to compute these different probabilities. By the end of high s chool, students should understand how to draw inferences about a population from random s amples; a process that involves understanding how these samples might be distributed. Such an understanding can be developed with the aid of simulations, that enable students to explore the variability of sample statistics from a known population and to ge nerate sampling distributions (NCTM, 2000; Pfannkuch, Chapter 11 in this book). Borovcnik and Peard (1996) remark that probabilisti c reasoning is different from logical or causal reasoning and that counterintuiti ve results are found in probability even at very elementary levels. By way of contrast, in o ther branches of mathematics counterintuitive results are encountered only when working at a high degree of

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