Al-khorezmi--an intelligent algebra tutoring system
Garland James Bayley · 1988
This thesis presents our investigation of the problem of creating an intelligent tutor for solving algebra word problems that employs effective pedagogy. Among our major concerns are the problems of sufficient knowledge and proper knowledge organization. From student protocols and test papers, we derived sets of general purpose strategic rules and computation rules to formulate a cognitive model of problem solving. The model incorporates levels of strategic ability that form a progression from novice to expert. Additional analysis of the data was done to uncover, categorize, generalize, and explain the errors made by students when solving algebra word problems. We implemented a computer program, al-Khorezmi, that exploits the model to trace a student's performance, catch errors and provide corrective feedback explaining the cause of the error, and give help that relates the help to knowledge that it has discussed with the student. The cognitive model emphasizes simulating correct, but not necessarily optimal, strategies that students employ. With our model, we can ensure that a student performs correctly when he employs his own approach before he is taught advanced strategies. Therefore, al-Khorezmi exploits an understanding of the student's approach to problem solving. The model incorporates three levels of expertise in the form of strategic rule sets. Al-Khorezmi correlates the strategies with student actions to determine the student's problem-solving skill. We studied the rules of our model to identify relationships important to learning and to interconnect the rules in an extended genetic graph. This knowledge structuring process led to observing that skill improvement can be accomplished (or explained to the student) by applying analogous rules that exploit more powerful methods. Furthermore, problem solving efficiency can be increased (or explained to the student) by combining rules into more powerful rules. Rule simplification can be exploited to establish a simulation model of the generation of errors. Errors are classified as incorrect applications of correct rules, correct applications of incorrect or deviant rules, and incorrect applications of deviant rules. The latter category allows al-Khorezmi to recognize compound errors and account for some of the otherwise unexplained student errors found in our data.