Learning and development of probability concepts: Effects of computer-assisted instruction and diagnosis.

Abstract

This study considered spontaneous versus feedback induced changes in probability strategies using grouped trials of two-choice problems. Third and sixth grade Anglo and Apache children were the focus of computer assisted instruction and diagnostics designed to maximize performance and measure understanding of probability concepts. Feedback, using indeterminate problems directed at specific strategies, in combination with a large problem set permitted examination of response latency and hypothesis alternation. Explicit training, in the form of computer based tutorials administered feedback as: (a) correctness and frequency information, (b) mathematical solutions, or (c) in a graphical format, targeted by weaknesses in the prevailing strategy. The tutorials encouraged an optimal proportional strategy and sought to affect the memorial accessibility or availability of information through the vividness of presentation. As the subject's response selection was based on the query to select for the best chance of winning, each bucket of the two-choice bucket problems was coded as containing target or winner (W) balls and distractor or loser (L) balls. Third and sixth grade subjects came to the task with position oriented strategies focusing on the winner or target elements. The strategies' sophistication was related to age with older children displaying less confusion and using proportional reasoning to a greater extent than the third grade children. Following the tutorial, the subjects displayed a marked decrease in winners strategies deferring instead to strategies focusing on both the winners and losers; however, there was a general tendency to return to the simpler strategies over the course of the posttest. These simpler strategies provided the fastest response latencies within this study. Posttest results indicated that both third and sixth grade subjects had made comparable gains in the use of strategies addressing both winners and losers. Based on the results of a long-term written test, sixth grade subjects appeared better able to retain or apply the knowledge that both winners and losers must be considered when addressing the two-choice bucket problems. Yet, for younger children, knowledge of these sophisticated strategies did not necessarily support generalization to other mathematical skills such as fraction understanding.