In a CAI system for teachig elementary mathematical logic, in order to provide tutorial advice similar to the suggestions a human tutor might give, a theorem-prover is employed as a proof-analyzer to generate appropriate dialogue with students who need help with a proof. It is shows that the heuristically programmed theorem-prover, by embodying techniques thought to be used by the students, constructs derivations for expressions in the elementary theory of Abelian groups within the constraints on rule usage imposed on these students. To demonstrate its capabilities, the theoremprover was tested on a list of theorems and problems chosen arbitrarily from a standard curriculum in elementary algebra. The proof-analyzer mocks the adaptive behavior of a human tutor; it can determine relevant hints when a student requires help in completing a soultion paths. The proof-analyzer is incorporated in a new instructional system or mathematical logic, an examle of a "student-oriented" CAI system which emphasizes active participation of the students with the computer by providing methods by which a student can initially specify or extend the axiomatic theory he is studying, while still retaining the error analysis and teaching facilities of an interactive proof-checker.