Learning algebra is difficult for many students in part because of an emphasis on the memorization of abstract rules. Algebraic reasoners across expertise levels often rely on perceptual-motor strategies to make these rules meaningful and memorable. However, in many cases, rules are provided as patterns to be memorized verbally, with little overt…

This study examined the effects of change in teacher goal emphases on students' efficacy beliefs in mathematics across the transition to middle school. The sample (N = 929) included primarily White (65%) and Black (27%) students, and approximately one third received free or reduced-fee lunch. Analyses grouped children by cross-classification of…