A system for grading symbolic mathematical expressions using Maple with fuzzy sets.

摘要

Grader is a Maple Programming Language module designed to be used with a math tutorial system. The module uses certain artificial intelligence techniques and fuzzy sets to form a heuristic to return the degree of similarity or correctness of one symbolic mathematical expression to another. Grader Demonstration is additionally included as a relatively unsophisticated GUI to indicate possible applications of the grader module. Grader Demonstration is program that passes symbolic math problems stored in Microsoft Access to a Java student interface and is based on the previous work on similar systems designed at the Speed Scientific School in projects headed by Troy Howe and including the author. In these systems a student may answer a math problem. The interface then obtains the correct answer from the database and compares the answer to the student answer by passing it to grader, the Maple Programming Language module evaluated by the Maple math kernel. The result is returned to the interface as a fractional or percentage degree of correctness. In addition, the Maple module allows a user to express the fuzzy grading method used by the Maple code as any differentiable function. This belief function allows the code to make decisions concerning the degree of inclusion of individual portions of the problem in the correct set.; Finally, recommendations for implementing an online tutorial system using Grader are included.