Young children's intuitive solution strategies for multiplication and division word problems in a problem-centered approach.
The intention of this research was to gather and document qualitative data regarding young children's intuitive solution strategies with regard to multiplication and division word problems. In 1994, nineteen pupils from the Junior Primary Phase (i.e. Grade 1 and Grade 2), from a Durban school participated in this study, in which the instruction was generally compatible with the principles of the Problem-Centered mathematics approach proposed by Human et al (1993) and Murray et al (1992; 1993). Its basic premise is that learning is a social as well as an individual activity. The researcher's pragmatic framework has been greatly influenced by the views of Human et al (1993) and Murray et al (1992; 1993), on Socio-Constructivism and Problem-Centered mathematics. Ten problem structures, five in multiplication and five in division which were adopted from research carried out by Mulligan (1992), were presented to the pupils to solve. The children were observed while solving the problems and probing questions were asked to obtain information about their solution strategies. From an indepth analysis of the children's solution strategies conclusions on the following issues were drawn: 1. the relationship between the semantic structure of the word problems and the children's intuitive strategies, and 2. the intuitive models used by the children to solve these problems. The following major conclusions were drawn from the evidence: 1. Of the sample, 76% were able to solve the ten problem structures using a range of strategies without having received any formal instruction on these concepts and related algorithms. 2. There were few differences in the children's performance between the multiplication and division word problems, with the exception of the Factor problem type for the Grade 2 Higher Ability pupils. 3. The semantic structure of the problems had a greater impact on the children's choice of strategies than on their performance, with the exception of the Factor problems. 4. The children used a number of intuitive models. For multiplication, three models were identified, i.e. repeated addition, array, cartesian product with and without many-to-many correspondence. For division, four models were identified, i.e. sharing one-by-one, building-up (additive), building-down (subtractive), and a model for sub-dividing wholes.