SARGE: A Program for Drilling Students in Freshman Calculus Integration Problems

Abstract

The SARGE program is a prototype of a program which is intended to be used as an adjacent to regular classroom work in freshman calculus. Using SARGE, students can type their step-by-step solution to an indefinite integration problem, and can have the correctness of their solution determined by the system. The syntax for these steps comes quite close to normal mathematical notation, given the limitations of typewriter input. The methods of solution is pretty much unrestricted as long as no mistakes are made along the way. If a mistake is made, SARGE will catch it and yield an error message. The student may modify the incorrect step, or he may ask the program for advice on how the mistake arose by typing "help". At present the program is weak in generating explanations for mistakes. Sometimes the "help" mechanisms will just yield a response which will indicate the way in which the erroneous step can be corrected. In order to improve the explanation mechanism one would need a sophisticated analysis of students solutions to homework or quiz problems. Experience with the behavior of students with SARGE, which is nil at present, should also help in accomplishing this goal. SARGE is available as SARGE SAVED in T302 2517.