The effect of an irrelevant number and language consistency in a word problem on pupils’ achievement and reasoning

Abstract

The adverse influence of the presence of an irrelevant number and language inconsistency in a word problem is well known. Our study focused on the combination of these two variables and on the position of the irrelevant number in the word problem for Grade 6 pupils. The study has a mixed design. Item Response Theory was used to make equally able groups and to find two-parameter models for the assigned word problem. An independent two-sample t-test was used to determine differences in the difficulty of word problems. Further insight was gained by analyzing pupils’ written solutions and complementary task-based interviews. We confirmed the influence of the variables in question on the word problem difficulty and showed that their combined influence manifests itself in further achievement drop and in the change of strategies and errors. We documented multiple ways in which an irrelevant number influences pupils’ reasoning. We showed that pupils’ insufficient familiarity with decimals may prevail over their apparent ability to mathematize a relational term with natural numbers. This shows the importance of adjusting the word problem difficulty to pupils’ knowledge and experience as the effect of a variable does not have to show itself under some circumstances.