The architecture of mental addition and subtraction

Year: 1997

Author: Heirdsfield, Ann, Cooper, Tom

Type of paper: Abstract refereed

Research has shown that mental computation is a valid computational method which contributes to mathematical thinking as a whole (e.g., Sowder, 1990). It is also a process for which young children have exhibited a variety of proficient spontaneous strategies contrary to instruction (Cooper, Heirdsfield, & Irons, 1996a). This paper reports on a series of three studies on young children's understanding of mental addition and subtraction and describes the mental architecture of a proficient mental computer. The first of these studies charted children's proficiency with and use of mental strategies with respect to instruction (Cooper, Heirdsfield, & Irons, 1996b; Heirdsfield & Cooper, 1996). The second and third related knowledge of mental computation to knowledge of number and numeration, concepts of addition and subtraction, basic facts, computational estimation, and mental representations of number and operation (Heirdsfield, 1996; Heirdsfield, in preparation). Analysis of the first study showed that children's strategy use is idiosyncratic, but influenced by instructional emphases, experience and presentation forms; particularly in relation to the strategies underlying pen-and-paper algorithm procedures. Analysis of the second study identified a relationship between proficiency in mental computation, number fact knowledge and computational estimation. Initial analysis of the third study, which involves detailed construction of mental models, is indicating a more complex interaction.