Abstract

The tutor for doing proofs in high school geometry consists of a cot of ideal and buggy rules (IRR), a tutor, and an interface. The IBR is responsible for ehiuertly computing matcher, to all the correct and incorrect rules The interface is responsible for interacting with the student and graphically representing the proof. The tutor is responsible for directing the IBR and interface to achieve a current tutorial strategy. The strategy wo employ involves tracing the student's behavior in terms of what rules in the IBR it instantiates, correcting the student when behavior deviates below a minimum threshold, and helping the student over hurdles. While incomplete, current evidence indicates the geometry tutor is guite effective. The Advanced Computer Tutoring Project has been working on the development of intelligent computerhased tutors for mathematics and science subjects in the range of senior high-school to junior college. This paper describes the general framework that we have developed and its instantiation in the case of a tutor tor generating proofs in geometry. First, we will describe the general philosophy of out tutoring efforts. Second, we will describe the basic structure of the geometry tutor that we have built. Third, we will describe the ongoing efforts to evaluate the tutor. General Philosophy Our approach to tutoring stems from two observations about the nature of learning in domains like high-school geometry. First, the major learning hurdle is acquiring domain-specific problem-solving skills (e.g, generating proofs in geometry), and the way they are learned is by practicing the problem-solving skill. We have intensively observed numerous students going through the first half of high school geometry (Anderson, 1001). We have not yet seen a case where a student was tible to absorb abstract instruction (from the text or the teacher) and go off and use that knowledge effectively in problem-solving. Students only acquired effective use of problem-solving knowledge by struggling with its application through a series of problems. The second observation is that students learn these problem-solving skills much more effectively if they learn with a full-time, private, human tutor who knows the domain well than if

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