Identifying Fraction Measures as Screeners of Mathematics Risk Status

This study investigated the accuracy of three fraction measures (i.e., fraction number line estimation accuracy, general fraction concepts, and fraction arithmetic) for screening fourth graders who might be at risk for mathematics difficulties. Receiver operating characteristic (ROC) curve analyses assessed diagnostic accuracy of the fraction measures for predicting which students would not meet state standards on the state mathematics test in fourth grade ( n = 411), fifth grade ( n = 362), and sixth grade ( n = 304). A combined measure consisting primarily of fraction number line estimation items and general fraction concept items was the most accurate screener of risk status in fourth, fifth, and sixth grades (area under the curve [AUC] = .84, .81, and .85, respectively). To maximize efficiency for classroom use, the length of the combined screener was reduced using best subset automatic linear modeling. The study highlights the importance of fraction knowledge for predicting mathematics achievement more generally and validates an effective and practical screening tool for the intermediate grades.

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Fixated in more familiar territory: Providing an explicit midpoint for typical and atypical number lines

Quarterly Journal of Experimental Psychology ◽

10.1177/1747021820967618 ◽

2020 ◽

pp. 174702182096761

Author(s):

Sabrina Di Lonardo Burr ◽

Jo-Anne LeFevre

Keyword(s):

Eye Tracking ◽

Number Line ◽

Estimation Accuracy ◽

Tracking Data ◽

Number Lines ◽

Number Line Estimation

Does providing an explicit midpoint affect adults’ performance differently for typical and atypical number line tasks? Participants ( N = 29) estimated the location of target numbers on typical (i.e., 0–10,000) and atypical (i.e., 0–7,000) number lines with either an explicitly labelled midpoint or no midpoint. For the typical number line, estimation accuracy did not differ for the explicit- and implicit-midpoint conditions. For the atypical number line, participants in the explicit-midpoint condition were more accurate than those in the implicit-midpoint condition and their pattern of error was similar to that seen for typical number lines (i.e., M-shaped). In contrast, for participants in the implicit-midpoint condition, the pattern of error on the atypical line was tent-shaped, with less accurate estimates around the midpoint and quartiles than the endpoints. Eye-tracking data showed that, for all number lines, participants used the middle of the line to guide their estimates, but participants in the explicit-midpoint condition were more likely to make their first fixation around the true midpoint than those in the implicit–midpoint condition. We conclude that adults have difficulty in estimating on atypical number lines because they incorrectly calculate the numerical value of the midpoint.

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Delaware Longitudinal Study of Fraction Learning: Implications for Helping Children With Mathematics Difficulties

Journal of Learning Disabilities ◽

10.1177/0022219416662033 ◽

2016 ◽

Vol 50 (6) ◽

pp. 621-630 ◽

Cited By ~ 29

Author(s):

Nancy C. Jordan ◽

Ilyse Resnick ◽

Jessica Rodrigues ◽

Nicole Hansen ◽

Nancy Dyson

Keyword(s):

Longitudinal Study ◽

Number Line ◽

State Standards ◽

Intermediate Grades ◽

Minimal Growth ◽

Number Magnitude ◽

Mathematics Difficulties ◽

Numerical Magnitudes ◽

And Mathematics ◽

End Of Grade

The goal of the present article is to synthesize findings to date from the Delaware Longitudinal Study of Fraction Learning. The study followed a large cohort of children ( N = 536) between Grades 3 and 6. The findings showed that many students, especially those with diagnosed learning disabilities, made minimal growth in fraction knowledge and that some showed only a basic grasp of the meaning of a fraction even after several years of instruction. Children with low growth in fraction knowledge during the intermediate grades were much more likely to fail to meet state standards on a broad mathematics measure at the end of Grade 6. Although a range of general and mathematics-specific competencies predicted fraction outcomes, the ability to estimate numerical magnitudes on a number line was a uniquely important marker of fraction success. Many children with mathematics difficulties have deep-seated problems related to whole number magnitude representations that are complicated by the introduction of fractions into the curriculum. Implications for helping students with mathematics difficulties are discussed.

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A Fraction Sense Intervention for Sixth Graders With or At Risk for Mathematics Difficulties

Remedial and Special Education ◽

10.1177/0741932518807139 ◽

2018 ◽

Vol 41 (4) ◽

pp. 244-254 ◽

Cited By ~ 2

Author(s):

Nancy I. Dyson ◽

Nancy C. Jordan ◽

Jessica Rodrigues ◽

Christina Barbieri ◽

Luke Rinne

Keyword(s):

At Risk ◽

Intervention Group ◽

Deep Understanding ◽

Sixth Graders ◽

Number Line ◽

Control Group ◽

General Measure ◽

Mathematics Difficulties ◽

Number Line Estimation ◽

Meaningful Context

The efficacy of a research-based fraction sense intervention for sixth graders with or at risk for mathematics difficulties ( N = 52) was examined. The intervention aimed to build understanding of fraction magnitudes on the number line. Key concepts were taught with a narrow range of denominators to develop deep understanding. The intervention was centered on a visual number line in the meaningful context of a color run race. Students were randomly assigned to the fraction sense intervention ( n = 25) or a business-as-usual control group ( n = 27). Students in the intervention condition received 21 lessons in small groups (45 min each) during their regular mathematics intervention period. Students in the intervention group performed significantly better than those in the control group on a measure of fraction number line estimation and a more general measure of fraction concepts, both at immediate posttest and delayed posttest, with large effect sizes; lesser effects were shown for fraction arithmetic.

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The relationship between number line estimation and arithmetic competencies depends on age, operation and skill

PsycEXTRA Dataset ◽

10.1037/e636952013-354 ◽

2013 ◽

Author(s):

Julia Bahnmueller ◽

Stefan Huber ◽

Korbinian Moeller ◽

Hans-Christoph Nuerk

Keyword(s):

Number Line ◽

Number Line Estimation ◽

The Relationship

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The Development of the Mental Representation of Numbers 0-10 in Elementary School Children

10.31234/osf.io/z5t4b ◽

2020 ◽

Author(s):

Anat Feldman ◽

Michael Shmueli ◽

Dror Dotan ◽

Joseph Tzelgov ◽

Andrea Berger

Keyword(s):

Sixth Grade ◽

Number Line ◽

Number Representation ◽

Large Numbers ◽

Position Task ◽

Sigmoidal Curve ◽

Anchor Points ◽

The Right ◽

Line P ◽

Best Fit

In recent years, there has been growing interest in the development of mental number line (MNL) representation examined using a number-to-position task. In the present study, we investigated the development of number representation on a 0-10 number line using a computerized version of the number-to-position task on a touchscreen, with restricted response time; 181 children from first through sixth grade were tested. We found that the pattern of estimated number position on the physical number line was best fit by the sigmoidal curve function–which was characterized by underestimation of small numbers and overestimation of large numbers–and that the breakpoint changed with age. Moreover, we found that significant developmental leaps in MNL representation occurred between the first and second grades and again between the second and third grades, which was reflected in the establishment of the right endpoint and the number 5 as anchor points, yielding a more accurate placement of other numbers along the number line.

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Improving Struggling Fifth-Grade Students’ Understanding of Fractions: A Randomized Controlled Trial of an Intervention That Stresses Both Concepts and Procedures

Council review ◽

10.1177/00144029211008851 ◽

2021 ◽

pp. 001440292110088

Author(s):

Madhavi Jayanthi ◽

Russell Gersten ◽

Robin F. Schumacher ◽

Joseph Dimino ◽

Keith Smolkowski ◽

...

Keyword(s):

Randomized Controlled Trial ◽

Explicit Instruction ◽

Controlled Trial ◽

Number Line ◽

Randomized Controlled ◽

Fifth Grade Students ◽

Linear Representations ◽

Mathematical Explanations ◽

Grade 5 ◽

Number Line Estimation

Using a randomized controlled trial, we examined the effect of a fractions intervention for students experiencing mathematical difficulties in Grade 5. Students who were eligible for the study ( n = 205) were randomly assigned to intervention and comparison conditions, blocked by teacher. The intervention used systematic, explicit instruction and relied on linear representations (e.g., Cuisenaire Rods and number lines) to demonstrate key fractions concepts. Enhancing students’ mathematical explanations was also a focus. Results indicated that intervention students significantly outperformed students from the comparison condition on measures of fractions proficiency and understanding ( g = 0.66–0.78), number line estimation ( g = 0.80–1.08), fractions procedures ( g = 1.07), and explanation tasks ( g = 0.68–1.23). Findings suggest that interventions designed to include explicit instruction, along with consistent use of the number line and opportunities to explain reasoning, can promote students’ proficiency and understanding of fractions.

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