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Fong, H. K. (1999). Strategic models for solving ratio and proportion problems. The Mathematics Educator, 4(1), 34-51.
This paper is concerned with the investigation of children's knowledge and
their methods of organising it in solving ratio and proportion problems. Strategic
models which represent pupils' approaches in solving different types of ratio and
proportion problems and a generic model which explains the essential information
for solving a set of ratio and proportion problems were identified. A total number of
499 children at an average age of ll years sat for a ratio and proportion test.
Analysis of their responses was carried out in 3 stages: (1)examining and recording
different strategies used by problem solvers, (2)classifying the identified strategies in terms of techniques and methods used and the different steps in arriving at the answers and (3)linking procedural knowledge and conceptualising (a)an overall strategic model used for solving ratio and proportion problems and (b)a schematic model for solving each ratio and proportion problem. The results of the study
revealed the various types of strategies used by these children and the different
levels of thinking employed in solving the problems. The models are presented to show the path of each strategy by connecting sets of skills of the problem solvers. The study confirms that problem solver requires bodies of essential knowledge and well organised structure to solve mathematical problems.
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