Error Patterns in Ordering Fractions Among At-Risk Fourth-Grade Students

Abstract

The 3 purposes of this study were to: (a) describe fraction ordering errors among at-risk 4th-grade students; (b) assess the effect of part-whole understanding and accuracy of fraction magnitude estimation on the probability of committing errors; and (c) examine the effect of students' ability to explain comparing problems on the probability of committing errors. Students (n = 227) completed a 9-item ordering test. A high proportion (81%) of problems were completed incorrectly. Most (65% of) errors were due to students misapplying whole number logic to fractions. Fraction-magnitude estimation skill, but not part-whole understanding, significantly predicted the probability of committing this type of error. Implications for practice are discussed.

The role of domain-general cognitive abilities and decimal labels in at-risk fourth-grade students' decimal magnitude understanding

“…The ability to accurately assess magnitude is thought to be key for consolidating properties of whole numbers and rational numbers, since magnitude is a unifying property of all numbers (Siegler, Thompson, & Schneider, 2011) and rational number magnitude knowledge is related to future mathematics achievement (Bailey, Hoard, Nugent, & Geary, 2012; Booth & Siegler, 2008; DeWolf, Bassock, & Holyoack, 2015; Fazio, Bailey, Thompson, & Siegler, 2014; Rittle-Johnson, Siegler, & Alibali, 2001, 2012; Siegler & Pyke, 2013). Students at risk for mathematics difficulties demonstrate pervasive and systematic misconceptions related to estimating rational number magnitude (e.g., Jordan et al, 2016; Malone & Fuchs, 2016), but much of the research has centered on common fractions $true(\mathrm{normali}.\mathrm{normale}.,\frac{a}{b}true)$. It is unclear whether the development of decimal magnitude understanding among at-risk students, the focus of the present study, parallels that of fraction magnitude understanding.…”

Fraction errors in a digital mathematics environment: Latent class and transition analysis

“…It is important to understand both why students struggle with fractions and how they struggle with fractions. To understand how students struggle with fractions, researchers have looked at the errors students make when solving fraction problems (e.g., Ashlock, 2001;Bottge et al, 2014;Brown & Quinn, 2006;Malone & Fuchs, 2017). To do this, researchers give participants a test/activity and observe errors made.…”

“…Although this procedure is used among most fraction error researchers, there are differences in methods in terms of what skills are tested and how errors are addressed. For example, some researchers have focused on specific fraction knowledge, like ordering or adding/subtracting fractions (Bottge et al, 2014;Malone & Fuchs, 2017), whereas others have focused on a broad range of fraction knowledge (Ashlock, 2001;Brown & Quinn, 2006). Additionally, some researchers define categories of errors a priori and then examine tests to see how often students make these errors (Bottge et al, 2014;Malone & Fuchs, 2017), whereas other researchers first give tests and then code and define errors from student answers (Ashlock, 2001;Brown & Quinn, 2006).…”

“…For example, some researchers have focused on specific fraction knowledge, like ordering or adding/subtracting fractions (Bottge et al, 2014;Malone & Fuchs, 2017), whereas others have focused on a broad range of fraction knowledge (Ashlock, 2001;Brown & Quinn, 2006). Additionally, some researchers define categories of errors a priori and then examine tests to see how often students make these errors (Bottge et al, 2014;Malone & Fuchs, 2017), whereas other researchers first give tests and then code and define errors from student answers (Ashlock, 2001;Brown & Quinn, 2006). Regardless of the method used, two broad categories of fraction errors have emerged, general misunderstanding of the concepts of fractions and improper application of whole number rules to fraction problems (e.g., Ashlock, 2001;Bottge et al, 2014;Brown & Quinn, 2006;Malone & Fuchs, 2017).…”

Does initial learning about the meaning of fractions present similar challenges for students with and without adequate whole-number skill?

“…Instead, students’ prior whole-number knowledge may interfere with fractions understanding. In a recent study (Malone & Fuchs, 2017), approximately 65% of errors in ordering fractions at fourth grade were due to whole-number ordering errors, in which students misapplied whole-number properties to understand fractions magnitudes.…”