CHILDRENS CONCEPTUAL STRUCTURES FOR MULTIDIGIT NUMBERS AND METHODS OFMULTIDIGIT ADDITION AND SUBTRACTION

Researchers from 4 projects with a problem-solving approach to teachin g and learning multidigit number concepts and operations describe (a) a common framework of conceptual structures children construct for mul tidigit numbers and (b) categories of methods children devise for mult idigit addition and subtraction. For each of the quantitative conceptu al structures for 2-digit numbers, a somewhat different triad of relat ions is established between the number words, written 2-digit marks, a nd quantities. The conceptions are unitary, decade and ones, sequence- tens and ones, separate-tens and ones, and integrated sequence-separat e conceptions. Conceptual supports used within each of the 4 projects are described and linked to multidigit addition and subtraction method s used by project children. Typical errors that may arise with each me thod are identified. We identify as crucial across all projects sustai ned opportunities for children to (a) construct triad conceptual struc tures that relate ten-structured quantities to number words and writte n 2-digit numerals and (b) use these triads in solving multidigit addi tion and subtraction situations.