Teaching and development: Solving “missing addend” problems using subtraction

Abstract

The study presented here will examine the connection between teaching and development, focusing in particular on how children solve “missing addend” story problems. Vygotsky’s theory of development will serve as the framework. Ordinarily, when second graders are forced to solve a problem of this type by choosing an arithmetic operation (+ or −), half of them fail. The most frequent error is choosing addition. The subjects in the experiment presented here were second graders who had always been given the opportunity to use objects or drawings to “act out” (model) the actions expressed in the problem statament. They had never been in the above “forced-choice” situation. Moreover, they had been taught to use a “forward strategy” to solve subtraction problems like 42–36 (to get from 36 to 40, it takes 4; and then to get to 42, it takes 2 more) and a “backward strategy” for subtraction problems like 42–6. When given the following missing-addend problem: “Pierre has 63 pieces of candy and paul has 4. Paul wants to have the same number of pieces as Pierre. How many pieces of candy must Paul buy?” none of these children performed an addition, approximately half did a subtraction, and the others succeeded by using a breakdown strategy or a drawing. The overall success rate was 92%. The results obtained suggest a way of operationalizing the notion of “zone of proximal development” for problem solving of this type.