Trends concerning four misconceptions in students' intuitively-based probabilistic reasoning sourced in the heuristic of representativeness

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University of Alabama Libraries

Student difficulty in the study of probability arises in intuitively-based misconceptions derived from heuristics. One such heuristic, the one of note for this research study, is that of representativeness, in which an individual informally assesses the probability of an event based on the degree to which the event is similar to the sample from which it is selected or the degree the event is characterized by the notable features of the system from which it is derived. Four misconceptions were examined in this that study arise from this heuristic: the representativeness misconception, positive and negative recency effects, the distinction between compound and simple events, and the effect of sample size. Furthering the research of Fischbein and Schnarch (1997), this research sought Spearman correlations between frequencies of responses to items testing for the above misconceptions and grade level of students (7th, 9th, or 11th). A significant positive Spearman correlation was found for positive and negative recency effects and a significant negative correlation was found for the effect of sample size. Spearman correlations were also sought between correctness of student responses and perceived self-efficacy in those responses via a five-point Likert scale at each of the three grade levels. Significant positive correlations were found for positive and negative recency effects (all three grades), the distinction between compound events (7th), and the representativeness misconception (7th and 11th); significant negative correlations were found for the effect of sample size (11th) and the distinction between compound and simple events (9th and 11th).

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Mathematics education, Secondary education