Examines teachers' judgments of the difficulties of algebra problems. Offers classroom-tested instructional approaches that build directly on students' mathematical intuitions and inventions. (KHR)

Examined beliefs of elementary, middle, and high school mathematics teachers regarding algebra development. Found that teachers held a symbol-precedence view of student mathematical development. High school teachers were most likely to hold the symbol-precedence view and made the poorest predictions of students' performance, whereas middle school…

How the self-explanation process relates to learning and subsequent problem-solving performance was studied in two experiments with college students to examine whether students taught to self-explain during a study phase show greater test gains than control group counterparts; this is an attempt to replicate the results of M. T. H. Chi and others.…

Presents research in which mathematics teachers and educational researchers ordered arithmetic and algebra problems according to their predicted problem-solving difficulty for students. Analysis of students' problem-solving strategies indicates specific ways that students' algebraic reasoning differs from that predicted by most teachers and…

This paper presents a developmental model of students' acquisition of competence in quantitative and algebraic problem solving. A key notion underlying the developmental model is a distinction between grounded and abstract representations. Grounded representations, like story problems, are more concrete and familiar, closer to physical objects and…