Children's strategy use and interpretations of mathematical representations

Abstract

This is a summary of research, from an information processing perspective, of children's interpretation and use of strategies and representations for place value, subtraction and addition in the first three years of school. Representations are defined broadly to include concrete embodiments of numbers, symbols for numbers and operations, and combinations of the latter in number sentences and algorithms. The objective was to assess the value and limitations of the use of representations in early mathematics learning and teaching and hence to identify, describe and examine critically some of the strategies and representations that children and teachers use in early mathematics. Children generally chose to use verbal and mental strategies in preference to formal algorithms, and did not want to use analogs unless they could not perform the task in any other way. The latter preference is explained on the basis of the extra demand that use of analogs adds to the cognitive process unless they are used automatically.