| Summary: | This study was aimed at discovering the differences in how children responded to word problems involving an operation in which they had received formal instruction (subtraction) and word problems involving an operation in which they have not received formal instruction. Nineteen children were individually interviewed and were asked to attempt to solve 6 subtraction and 6 division word problems. Their solution strategies were recorded, and analysed with respect to whether or not they were appropriate, as to whether or not they modeled the structure of the problem, and as to how consistent the strategies were, within problem types.
It was found that children tended to model division problems more often than subtraction problems, and also that the same types of errors were made on problems of both operations. It was also found that children were more likely to keep the strategies for the different interpretations separate for the operation in which they had not been instructed (division) than for the operation in which they had been instructed (subtraction). For division problems, the strategies used to solve one type of problem were seldom, if ever used to solve the other type of problem. For subtraction problems, children had more of a tendency to use the strategies for the various interpretations interchangeably.
In addition, some differences in the way children deal with problems involving the solution of a basic fact, and those involving the subtraction of 2-digit numbers, were found. The 2-digit open addition problems were solved using modeling strategies about half as often as any other problem type. The same types of errors were made for both the basic fact and the 2-digit problems, but there were more counting errors and more inappropriate strategy errors for the 2-digit problems, and more incorrect operations for the basic fact problems.
Finally, some differences were noted in the problem-solving behaviour of children who performed well on the basic fact tests and those who did not. The children in the low group made more counting errors, used more modeling strategies, and used fewer incorrect operations than children in the high group.
These implications for instruction were stated: de-emphasize drill of the basic facts in the primary grades, delay the formal instruction of the operations until children have had a lot of exposure to word problem situations involving these concepts, use the problem situations to introduce the operations instead of the other way around, and leave comparison subtraction word problems until after the children are quite familiar with take away and open addition problems. === Education, Faculty of === Curriculum and Pedagogy (EDCP), Department of === Graduate
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