2020
DOI: 10.1002/pits.22448
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University students' misconceptions about rational numbers: Implications for developmental mathematics and instruction of younger students

Abstract: 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 proble… Show more

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Cited by 6 publications
(5 citation statements)
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“…Students may have difficulty in learning fraction knowledge because they need to restructure their whole number understanding to accommodate new information about rational numbers (see reviews by Ni & Zhou, 2005; Siegler & Lortie-Forgues, 2017). Misconceptions about fractions can arise even when whole number knowledge is sufficient because principles and rules that apply to natural numbers are different from those that apply to fractions (Powell & Nelson, 2021; Stafylidou & Vosniadou, 2004; Vosniadou et al, 2008). Ultimately, integrating whole number and rational number skills will support students’ learning of more advanced mathematical constructs, such as algebra (Barbieri et al, 2021; Booth & Newton, 2012).…”
Section: Discussionmentioning
confidence: 99%
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“…Students may have difficulty in learning fraction knowledge because they need to restructure their whole number understanding to accommodate new information about rational numbers (see reviews by Ni & Zhou, 2005; Siegler & Lortie-Forgues, 2017). Misconceptions about fractions can arise even when whole number knowledge is sufficient because principles and rules that apply to natural numbers are different from those that apply to fractions (Powell & Nelson, 2021; Stafylidou & Vosniadou, 2004; Vosniadou et al, 2008). Ultimately, integrating whole number and rational number skills will support students’ learning of more advanced mathematical constructs, such as algebra (Barbieri et al, 2021; Booth & Newton, 2012).…”
Section: Discussionmentioning
confidence: 99%
“…For example, students who struggled when they were learning basic arithmetic will continue to face challenges when learning more complex mathematics (Empson et al, 2011). Research shows that some adults do not master arithmetic (LeFevre et al, 2017;Thompson et al, 2015) or rational number skills (Powell & Nelson, 2021), despite the importance of an understanding of the conceptual continuity from whole number arithmetic to rational numbers (Siegler, 2016;Siegler & Braithwaite, 2017). The fundamental properties of arithmetic operations and fractions form the foundations of algebra (Empson et al, 2011;Hackenberg, 2013;Mack, 1993;Nunes et al, 2016;Steffe & Olive, 2010;Thompson & Saldanha, 2003) because algebra is a more abstract, generalized version of arithmetic.…”
Section: Interpretations Of the Present Findingsmentioning
confidence: 99%
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“…Malaysian students' poor performance in algebra has been a growing concern (Teoh et al, 2020;Ying et al, 2020), but not unsurprising as research has shown that the learning of algebra is considered challenging among many students in many learning environments, even among students with positive attitudes (Poçan et al, 2023). Students' problems in algebra, such as rational numbers, arithmetic, and word problems need to be resolved as these concepts are fundamental to university mathematics (Powell & Nelson, 2021). Hence, secondary school students' algebra proficiency needs to be carefully monitored and developed (Anderson, 2021) to equip them with mathematical skills for advanced learning at tertiary level, in particular among those planning to pursue STEM careers.…”
Section: Introductionmentioning
confidence: 99%
“…However, the study of myths is not limited to behavioral science. The prevalence of myths has been studied in fields such as Education ( Ferrero, Garaizar & Vadillo, 2016 ), Medicine ( Kaufman et al, 2013 ) or public health policies ( Viehbeck, Petticrew & Cummins, 2015 ), as well as in science as a knowledge system ( McComas, 1996 ), and the practical consequences that they entail, such as those caused by the myths of mathematics in their students ( Powell & Nelson, 2021 ).…”
Section: Introductionmentioning
confidence: 99%