The role of problem representation and feature knowledge in algebraic equation-solving

• Both feature encoding and feature knowledge are correlated with equation-solving success.
• Only feature knowledge independently predicted success, and feature encoding did not mediate the relationship.
• Findings were similar for general conceptual knowledge and that of specific problem features (e.g., equals sign, negative signs, variables).
• Helping students to develop feature knowledge within a meaningful conceptual context may improve both encoding and problem-solving performance.

Domain experts have two major advantages over novices with regard to problem solving: experts more accurately encode deep problem features (feature encoding) and demonstrate better conceptual understanding of critical problem features (feature knowledge). In the current study, we explore the relative contributions of encoding and knowledge of problem features (e.g., negative signs, the equals sign, variables) when beginning algebra students solve simple algebraic equations. Thirty-two students completed problems designed to measure feature encoding, feature knowledge and equation solving. Results indicate that though both feature encoding and feature knowledge were correlated with equation-solving success, only feature knowledge independently predicted success. These results have implications for the design of instruction in algebra, and suggest that helping students to develop feature knowledge within a meaningful conceptual context may improve both encoding and problem-solving performance.