Success and failure in school mathematics: effects of instruction and school environment.

Given the stubborn phenomenon of many children's serious difficulties and failure in mathematical learning, the hypothesis of developmental delay, or neurocognitively based deficiency should be complemented by further explanantions of children's weaknesses and substandard performance in mathematics. One obvious explanantion is that schooling and instruction for low ability children and for children with special needs is often inadequate. The present contribution examines selected research on mathematics learning under a cognitive instructional (didactical) perspective. Constructivist learning theory, the rooting of meaningful learning in concrete modeling activities, the balancing of understanding and practice in mathematics instruction, diagnostic and adaptive teaching, computer-assisted instruction, and the role of nonmathematical stumbling-blocks are discussed as principles and factors of effective mathematics learning and teaching.