Fuzzy logic and Gagné learning hierarchy for assessing mathematics skills.

This study developed a fuzzy logic and Gagne learning hierarchy (FL-GLH) for assessing mathematics skills and identifying learning barrier points. Fuzzy logic was used to model the human reasoning process in linguistic terms. Specifically, fuzzy logic was used to build relationships between skill level concepts as inputs and learning achievement as an output. Gagne learning hierarchy was used to develop a learning hierarchy diagram, which included learning paths and test questions for assessing mathematics skills. First, the Gagne learning hierarchy was used to generate learning path diagrams and test questions. In the second step, skill level concepts were grouped, and their membership functions were established to fuzzify the input parameters and to build membership functions of learning achievement as an output. Third, the inference engine generated fuzzy values by applying fuzzy rules based on fuzzy reasoning. Finally, the defuzzifier converted fuzzy values to crisp output values for learning achievement. Practical applications of the FL-GLH confirmed its effectiveness for evaluating student learning achievement, for finding student learning barrier points, and for providing teachers with guidelines for improving learning efficiency in students.