University Students' Misconceptions About Rational Numbers: Implications for Developmental Mathematics and Instruction of Younger Students

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To understand misconceptions with rational numbers (i.e., fractions, decimals, and percentages), we administered an assessment of rational numbers to 331 undergraduate students from a 4-year university. The assessment included 41 items categorized as measuring foundational understanding, calculations, or word problems. We coded each student's response and identified error patterns for items answered incorrectly. Students attempted foundational understanding and calculations problems more often than word problems, and students made fewer errors with foundational understanding and calculation items. Students demonstrated the most unique errors with calculations and word problems items. Given all items on the rational numbers assessment required elementary or middle school knowledge of rational numbers, the number and diversity of errors with a sample of university students demonstrates the persistent difficulties with rational numbers that students carry into adulthood. Elementary, secondary, and developmental mathematics educators should be aware of such errors and provide specific instruction on avoiding such errors.