Toward an Understanding of Mathematical Procedures

Research suggests that algebraic skill is intricately connected to understanding. Without understanding, algebraic performance is fraught with error and skills are quickly forgotten. In this article, we review one model of algebraic understanding and offer five easy-to-use classroom questions that are based upon this model. These questions represent a concrete approach to achieving the level of student understanding that is advocated in the Common Core Mathematics Standards. Through the use of these questions and related "understanding" investigations and assessments, students can attain both computational fluency and conceptual understanding. In-depth examples of the application of these questions to a linear equation task are provided, as are sample student investigations that can be used to promote an understanding of mathematical procedures