Automated Checking of Flexible Mathematical Reasoning in the Case of Systems of (In)Equations and the Absolute Value Operator

Abstract

We present an approach and a tool for automatically providing feedback on solutions that involve complicated reasoning patterns. Currently the tool supports linear systems of equations and inequations that may also contain the absolute value operator and a restricted form of rational functions. This suffices for designing problems that are laborious to solve with standard mechanical procedures, but much easier using short-cuts that students may find by creative thinking. Earlier research has found that struggling with important mathematics promotes conceptual development. Our goal is to encourage students to such struggling. A crucial feature is to give them great freedom to choose the paths via which they solve problems, and at any time ask the tool to check the work done so far, no matter what path was chosen. This was implemented by adopting standard notation from mathematical logic, and developing some new logical notation. The tool has been used in a course on elementary universi ty-level mathematics. It has worked reliably, but there is not yet any statistics on the pedagogical merits. The tool is expected to also support quadratic (in)equations in the near future.