The effect of number size and ordering of data on the difficulty of selected arithmetic word problems

Kieley, Mary Sharon (1983) The effect of number size and ordering of data on the difficulty of selected arithmetic word problems. Masters thesis, Memorial University of Newfoundland.

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Abstract

The purpose of this study was to investigate the effects of number size and ordering of data on the difficulty of arithmetic word problems. The study was conducted at level one of the senior high school system in Newfoundland with 220 students enrolled in the practical mathematics course at that level. The students were randomly selected and each was asked to complete one of six tests in a 30 minute time period. Each test consisted of 12 two-step word problems incorporating the operations of multiplication - addition; division - addition; multiplication - subtraction; division - subtraction, with three items per instrument testing each set of operations. The tests were designed as follows: (1) small numbers with ordered data; (2) large numbers with ordered data; (3) small numbers and large numbers with ordered data; (4) small numbers with unordered data; (5) large numbers with unordered data; (6) small numbers and large numbers with unordered data. -- It was concluded that there was no significant interaction effect between number size and ordering of data, but there was a significant effect for the number size variable and for the order variable. Whether the data was ordered or unordered, problems containing large numbers as data were the most difficult for students in the practical level of mathematics at level one of the senior high school; problems containing a combination of small numbers and large numbers were of intermediate difficulty, and problems containing small numbers were the least difficult. Also, whether the numbers were small, large, or a combination of small and large problems containing unordered data were more difficult than problems containing ordered data. -- Implications for teaching were discussed and recommendations for future research in arithmetic word problems were proposed.

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