This study took a broad view of generalization, exploring how classroom instruction within opportunities of implicit generalization may be related to students' abilities to generalize. From an integrated perspective of generalization and problem solving, we investigated twelve lessons of two middle level teachers based on three pattern-based…

Teachers and researchers have long recognized that students tend to misunderstand the equal sign as an operator; that is, a signal for "doing something" rather than a relational symbol of equivalence or quantity sameness. Students' equal sign misconception has been researched for more than thirty years (Weaver, 1971, 1973) with little…

This study reports findings from comparative samples of sixth-grade Chinese and U.S. students' interpretations of the equal sign. Ninety-eight percent of the Chinese sample correctly answered 4 items indicating conceptions of equality and provided conceptually accurate explanations. In contrast, only 28% of the U.S. sample performed at this level.…