Feedback in an interactive equation solver

E-learning tools for mathematical problem solving such as solving linear equations should be interactive. As with pen and paper, a student constructs a solution stepwise. E-learning tools provide the capability to give feedback to a student at each step. Feedback is essential for effective learning and hence crucial for interactive e-learning tools. This paper describes a framework for providing feedback in interactive e-learning tools. The framework is particularly useful for domains with hierarchically structured terms, a set of rewrite rules to rewrite the terms from the domain into other terms, and a well-described goal. The framework is used to give feedback about syntactical errors, about several kinds of semantic errors, and about progression towards a solution. The framework explicitly uses the structure in the data to produce feedback. We discuss an e-learning tool for solving linear equations in which the framework for feedback is used. The techniques for providing feedback are taken from compiler technology and rewriting theory.