How middle school students deal with rational numbers? A mixed methods research study

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YETİM S., Alkan R.

EURASIA JOURNAL OF MATHEMATICS SCIENCE AND TECHNOLOGY EDUCATION, vol.9, no.2, pp.213-221, 2013 (SSCI) identifier identifier


The aim of this study was to identify 7th grade students' common mistakes and/or misconceptions about representing rational numbers in different forms. Seventy-three 7th grade students participated in this study. We utilized a diagnostic test with 8 questions in order to determine common student mistakes. For identifying misconceptions, we conducted interviews with 25 of the participants purposefully chosen from among the ones who made mistakes more frequently. The data analysis showed that students had difficulties especially in determining rational numbers, relating rational numbers with decimals, representing rational numbers, and rational-number division. Moreover, the current study also revealed students' misconceptions about dividing by zero and division of integers (with + - signs). The results suggest that using concrete materials and multiple representations would be more beneficial for overcoming these difficulties and for a sound understanding of the abstract nature of rational numbers.