THE EVOLVING STRUCTURE OF STATISTICAL KNOWLEDGE IN HIGH AND LOW MATH ANXIOUS STUDENTS (PROBABILITY, PIAGET, COGNITION)

The problems students encounter in learning statistics at a college level was the focus of the present investigation. To ascertain these difficulties, three major concerns that dealt with mathematics, probability, and statistics were explored: (1) The mathematics background of incoming students, particularly any type of "math anxiety"; (2) The intuitive/everyday conceptions of probability, particularly as emphasized by Piaget; and (3) The formal/cognitive structuring of statistical material learned in the actual course itself.;Results indicated that "math anxiety" tended to have developed from and be centered on formal mathematics classrooms, as opposed to everyday uses of mathematics. Intuitive concepts of probability tended to be split between those concepts involving a correct notion of chance and irreversibility and those showing incorrect assumptions of determinism (such as the reversibility of probabilistic phenomena and the so-called gambler's fallacy). The tasks which measured formal learning in the classroom revealed that students very often make intuitive, concrete mistakes in learning concepts; for example, a bimodal distribution was "seen" as two separate distributions instead of one. The integration of material clustered on two major categories, those of PROBABILITY AND HYPOTHESIS TESTING. In general, anxiety level showed no effect on performance.;Implications for classroom teaching include being aware of background anxieties students display about mathematics combined with explaining the nature of probability which sets it apart from other types of mathematics courses.;Twenty introductory psychological statistics students were selected for the study. Ten of these were HIGH MATH ANXIOUS and ten were LOW MATH ANXIOUS based on scores on the Mathematics Anxiety Rating Scale. Each of these twenty were given several instruments: an initial open-ended interview concerning the experience of mathematics; an everyday probability explanation task; weekly self-report sheets during the course; and a final interview that tapped experiences in the course, together with problem solving and problem sorting tasks.