Comparisons of Rule Usage in Probability Reasoning Based on OT and ISM

Abstract

The purpose of this study is to implement an Internet assessment of probability reasoning that provides graphs of rule usage and similarity coefficients compared to expert reasoning. The probability reasoning assessment is based on the rule-assessment approach provided by R. S. Siegler. The method of constructing the structural graphs of rule usage in probability reasoning combines ordering theory (OT) with interpretive structural modeling (ISM). Additionally, set operations are adopted to calculate the similarity coefficient for graphs of rule usage compared with expert reasoning. Several programming languages, including PHP, MySQL and FLASH, are used to implement the assessment system. An empirical study of pupils shows that rule usage varied with the total score and response patterns. In addition, there is a significant difference in the similarity coefficients based on the variables of age and gender and their interaction. Finally, some recommendations and suggestions for future research are discussed based on the findings and results.