Algebraic Thinking Tools

This Note describes several versions of an intelligent tutor for basic algebra that has been in development at RAND since 1986. The versions of the tutor are built around several core components, including an algebra expert system and a student modeling component that can make inferences about misconceptions underlying students' errors. The different versions help students learn distinct kinds of mathematical reasoning skills. The Note discusses the equation-solving tutor, which focuses on the acquisition of relatively low-level symbol manipulation skills. It reviews the model-building tutor, a recent version that helps students acquire important mathematical reasoning skills that are not part of most algebra curricula, including the ability to formulate a mathematical model of real-world situations and to test mathematical hypotheses. Finally, it discusses the implications of the tutors for curriculum change. The authors note how the pedagogical approach implicit in the tutor diverges from most classroom teaching principles. While traditional classrooms often engage in isolated and bottom-up practice, the authors advocate embedded and global-before-local practice.