Constructing a Computer Algebra System Capable of Generating Pedagogical Step-by-Step Solutions

Abstract: For the problem of producing pedagogical step-by-step solutions to mathematical problems in education, standard methods and algorithms used in construction of computer algebra systems are often not suitable. A method of using rules to manipulate mathematical expressions in small steps is suggested and implemented. The problem of creating a step-by-step solution by choosing which rule to apply and when to do it is redefined as a graph search problem and variations of the A' algorithm are used to solve it. It is all put together into one prototype solver that was evaluated in a study. The study was a questionnaire distributed among high school students. The results showed that while the solutions were not as good as human-made ones, they were competent. Further improvements of the method are suggested that would probably lead to better solutions.