Knowledge of the equal sign as an indicator of mathematical equality is foundational to children's mathematical development and serves as a key link between arithmetic and algebra. The current findings reaffirmed a past finding that diverse items can be integrated onto a single scale, revealed the wide variability in children's knowledge of the…

Illustrates use of rule space as a tool for cognitive analysis of students' mathematical behavior. The rule-space approach is explained and used to classify students according to two methods for solving linear algebraic equations in one unknown and diagnose their knowledge states on this topic. (Author/MDH)