Key Misconceptions in Algebraic Problem Solving

The current study examines how holding misconceptions about key problem features affects students’ ability to solve algebraic equations correctly and to learn correct procedures for problem solution. Algebra I students learning to solve simple equations using the Cognitive Tutor curriculum (Koedinger, Anderson, Hadley, & Mark, 1997) completed a pretest and posttest designed to evaluate their conceptual understanding of problem features (including the equals sign and negative signs) as well as their equation solving skill. Results indicate that students who begin the lesson with misconceptions about the meaning of the equals sign or negative signs solve fewer equations correctly at pretest, and also have difficulty learning how to solve them. However, improving their knowledge of those features over the course of the lesson increases their learning of correct procedures.