Students' Strategies on Reallocation and Covariation Items

A successful design for building a Learning Trajectory (LT) requires an understanding of how students think and successive refinements on LT based on the empirical data. As a result this study aims to understand students' strategies and students' performance differences as they worked on reallocation and covariation items by using Piagetian clinical interview methodology (Opper, 1977). Covariation and Reallocation are two levels of Equipartitioning Learning Trajectory (Confrey, 2009). Several factors (item-stem formats, classes and types, manipulative usage) may affect students‘ performance, and mathematical strategies.The findings from this study indicate that there is a significant difference in younger and older students' mathematical strategies on given problems. Younger students demonstrated a significant change in their problem-solving strategies and performance when presented with manipulatives. In addition students of all ages demonstrated changes in their problem-solving strategies when item-stems were presented in different formats and from varied item classes. This study supports teachers to diagnose students' need as they learn these key mathematics concepts.