# Algebra decoded: individual differences in strategy selection when solving for 'x'

- Jeffrey Bye, Educational Psychology, University of Minnesota, Minneapolis, Minnesota, United States
- Rina Harsch, Educational Psychology, University of Minnesota, Minneapolis, Minnesota, United States
- Sashank Varma, Educational Psychology, University of Minnesota, Minneapolis, Minnesota, United States

**Abstract**Understanding variables and solving algebraic equations are essential to advanced mathematical thinking. ‘Missing-operand’ problems (e.g., x + 3 = 5) are solvable via two strategies: 1) pattern-matching, or direct arithmetic fact retrieval (e.g., 2 + 3 = 5), and 2) algebraic symbol-manipulation, or performing the inverse operation (e.g., 5 – 3 = 2). U.S. undergraduates made speeded verifications of arithmetic sentences like 2 + 3 = 5 and 5 – 3 = 2. They then solved missing-operand problems like x + 3 = 5. We ‘decoded’ individual differences in strategy choice by whether speed on missing-operand problems was better predicted by speed on verifying direct- or inverse-matched arithmetic facts. We found individual differences in strategy choice, although these were not significantly associated with mathematical achievement.