Abstract
This article examines the conceptual problems that children experience when attempting to solve verbal problems which contain decimal numbers. After discussing the existing research, we then describe an experiment that was designed in three phases:
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1.
Exploratory interviews to discover existing conceptions and difficulties and to discover how pupils made use of diagrams, simpler numbers, and strategies. These interviews exposed difficulties with the understanding of place value, the effect of multiplying and dividing by a positive number less than one, the symbolisms of division and its noncommutative nature, the units associated with the numbers and also with familiar names for the operations. The three strategies were all found to be unfamiliar to pupils and their difficulties are discussed.
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2.
The design and administration of a diagnostic test, based on the results of these interviews, to a class of less able 14 year olds.
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3.
The preparation and use of calculator enriched teaching materials designed to remedy the identified misconceptions. From the pre- and post-test results we note the dramatic success of the teaching in improving pupils' understanding of place value, although there is a more modest improvement in enabling pupils to choose the correct operation by drawing diagrams, using easier numbers and estimating.
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Bell, A., Swan, M. & Taylor, G. Choice of operation in verbal problems with decimal numbers. Educ Stud Math 12, 399–420 (1981). https://doi.org/10.1007/BF00308139
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DOI: https://doi.org/10.1007/BF00308139