The Effect of Context on Children's Arthmetic Problem Solving

Abstract

<p>Several studies are presented which show that the way in which a child solves an arithmetic problem on a test is influenced by the nature of the other items comprising the test, the so-called "context" problems. These context effects pose a challenge to existing models of children's arithmetic problem solving which assume that children learn and are guided by internalized procedural rules or algorithms that are exclusively applied according to the characteristics of the current to-be-solved problem. Context effects are also demonstrated for arithmetic problems at grade levels 2 through 5 and a variety of systematic computational errors. For example, at grade 2 children made significantly more algorithm errors of a particular type when the target problems (2-by-1-digit subtraction fact problems - e.g. 12-4= or 14-8=) were located in a test composed of 2-digit-by-2-digit subtraction problems (e.g. 54-21=) than when Iocated in a test composed of 1-digit-by-1-digit subtraction problems (e.g. 5-4=). Studies are also presented demonstrating context effects with 2-digit-by-1-digit addition and subtraction target problems (grade 3), 2-digit-by-2-digit multiplication problems (grade 4), and 2-digit-by-1-digit division problems (grade 5). An analysis of the relationship between the problem solving strategies used to solve the context and target problems suggests an alternative view of children's arithmetic learning and problem solving. Children solve target problems by applying procedures that are similar or analogous to procedures used to solve the context problems. That is, children's arithmetic problem solving is often governed by a contextually driven analogy mechanism, similar to that proposed in some contemporary models of reading (Glushko, 1979; Kay & Marcel, 1981) and classification (Brooks, 1978). Several studies are also presented which demonstrate that children's tendencies to error in this way is dependent upon certain kinds of arithmetic training practices commonly followed in primary school arithmetic instruction: so-called "unmixed drills" in which the practice worksheets are composed entirely of problems to be solved using the same problem solving strategy.</p>