“Playing the game” of story problems: Coordinating situation-based reasoning with algebraic representation

• Published in: The Journal of mathematical behavior Vol. 31; no. 2; pp. 174 - 195
• Main Authors: Walkington, Candace, Sherman, Milan, Petrosino, Anthony
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.06.2012; Elsevier
• Subjects: Algebra; Grade 9; Individualized Instruction; Logical Thinking; Mathematics education; Mathematics Instruction; Problem Solving; Story problems; Urban Schools; Word problems; Word Problems (Mathematics); Problem solving; Story problems; Algebra; Mathematics education; Word problems
• ISSN: 0732-3123; 1873-8028
• DOI: 10.1016/j.jmathb.2011.12.009

► We examine algebra students from a low-performing school solving story problems. ► Students used informal, situation-based reasoning on personalized problems. ► Connections between situational reasoning and formal problem-solving were weak. ► Results suggest that contextualization through story scenarios can be problematic. This study critically examines a key justification used by educational stakeholders for placing mathematics in context –the idea that contextualization provides students with access to mathematical ideas. We present interviews of 24 ninth grade students from a low-performing urban school solving algebra story problems, some of which were personalized to their experiences. Using a situated cognition framework, we discuss how students use informal strategies and situational knowledge when solving story problems, as well how they engage in non-coordinative reasoning where situation-based reasoning is disconnected from symbol-based reasoning and other problem-solving actions. Results suggest that if contextualization is going to provide students with access to algebraic ideas, supports need to be put in place for students to make connections between formal algebraic representation, informal arithmetic-based reasoning, and situational knowledge.