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

A research report submitted to the Faculty of Science, in partial fulfilment of the requirements for the degree of Master of Science, University of the Witwatersrand. Johannesburg, October 2016. / This research study makes an attempt at intervening in the Grade6learners’ use of models and strategies in solving addition and subtraction word problems based on Realistic Mathematics Education (RME) theory. RME theory advocates for the provision of understandable contexts that learners can relate with to support them in developing models and strategies, with specific reference to the empty number line model in assisting learners to develop an understanding of the structure of number and to work flexibly in solving addition and subtraction word problems. It is in understanding the models and strategies learners are using that we can begin to understand how the learners need to be supported in order to operate at the appropriate mathematics levels for their grade. Participants in this research study, forty boys and girls doing grade six, all with a weaker mathematical background, wrote the same tests in the form of pre test, post test and the delayed post test. After writing the pre test, the learners attended a series of six intervention lessons before writing the post tests. The intervention lessons encouraged learner engagement with word problems and the development of models as representations of problem situations and strategies which represent learner’s manipulation of models in an RME-advocated approach. Learner responses were analysed aiming at the identification of models and strategies they employed, as well as the correctness and success in solving the problems. The analysis found out that mainly there have been some improvements in the repeat sittings from predominantly using the column model with a lot of incorrect answers to using the empty number line with more correct answers. I would therefore encourage the maximum participation of teamwork amongst teachers for identifying and using efficient models and strategies in order to promote performance levels in mathematics through developing an understanding of the structure of number and working flexibly in solving addition and subtraction word problems. / LG2017

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published_or_final_version / Education / Master / Master of Education