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Belief in Equally-Likely vs. Unequally-Likely Events. Draft

Konold, C.
Massachusetts Univ , Amherst Scientific Reasoning Research Inst

One of the most common misconceptions about probability is the belief that successive outcomes of a random process are not independent. This belief has been dubbed the "gambler's fallacy". The belief that non-normative expectations such as the gambler's fallacy are widely held has inspired probability and statistics instruction that attempts to counter such beliefs. This study presents an investigation of student performance pre and post instruction on problems dealing with these kinds of statistical misconceptions. Instruction consisted of 10 laboratory sessions, 1.5 hours each, delivered to 16 high school students attending a summer mathematics program at Mount Holyoke College (Massachusetts). The instruction included computer simulations that were intended to provide students with sufficient data to refute expectations based on the representativeness heuristic, as well as other misconceptions about chance. Student performance suggests that a belief in representativeness may not be as widespread as thought, and that curriculum development aimed at countering this belief should proceed cautiously. In addition, student who apparently do not have a well-developed understanding of independence in random sampling may nevertheless answer such problems correctly based on reasoning that is fundamentally non-probabilistic. Thus, many items currently being used to assess conceptual development may be insensitive to certain misconceptions about probability. Student misconceptions about probability need to be better understood if more appropirate mathematics instruction is to be achieved. (KR)