Effect on Superficial Variability of Examples on Learning Applied Probability

Learning through examples is a central and widely used instructional device for teaching mathematically-based subjects such as statistical probability. However, the applications of the superficial variability of examples remain controversial. This dissertation investigates how the superficial variability of multiple examples influences students' learning and transfer of probability problem-solving. Moreover, the author discovers whether content difficulty affects the influence of examples' superficial variability. Three conditions were developed and compared: consistent-surface condition (CS), varied-surface-within-rule condition (VSWR), and varied-surface-between-rule condition (VSBR). For the purpose of exploration and methodology improvement for the dissertation study, two pilot studies were conducted. However, conflicting results were shown in those two studies. In the first pilot study, students in CS condition performed the worst. In the second pilot study, students in VSBR condition performed the worst. These conflicting results encouraged the author, even more, to conduct the dissertation study with a larger sample size and improved methodology. In this dissertation study, the author found that students' performance on the posttests in VSBR was significantly worse than in the other two conditions, which was consistent with the second pilot study, and that their performance in CS and VSWR condition was not different. Contrary to expectation, the strength of the pattern of the effect of the superficial variability of examples did not vary between the easy and difficult types of problems. Moreover, the pattern was the same when the difficulty variable was not included. These results suggested that examples' superficial consistency between different problem types promotes more effective learning than superficial variation between different problem types. The consistency can be one single cover story used multiple times for each type of problem or the same battery of varied cover stories used repeatedly for different types of problem. Moreover, the pattern of the influence of superficial variability of examples is robust among types of the problem at varying difficulty levels.