Associations of magnitude comparison and number line estimation with mathematical competence

2017 ◽  
pp. 100-119 ◽  
Author(s):  
Michael Schneider ◽  
Clarissa A. Thompson ◽  
Bethany Rittle-Johnson
Keyword(s):  
Number Line ◽  
Magnitude Comparison ◽  
Mathematical Competence ◽  
Number Line Estimation

Associations of Number Line Estimation With Mathematical Competence: A Meta-analysis

2018 ◽  
Vol 89 (5) ◽  
pp. 1467-1484 ◽  
Author(s):  
Michael Schneider ◽  
Simon Merz ◽  
Johannes Stricker ◽  
Bert De Smedt ◽  
Joke Torbeyns ◽  
...  
Keyword(s):  
Meta Analysis ◽  
Number Line ◽  
Mathematical Competence ◽  
Number Line Estimation

scholarly journals Cognitive mediators of US—China differences in early symbolic arithmetic

PLoS ONE ◽  
2021 ◽  
Vol 16 (8) ◽  
pp. e0255283
Author(s):  
John E. Opfer ◽  
Dan Kim ◽  
Lisa K. Fazio ◽  
Xinlin Zhou ◽  
Robert S. Siegler
Keyword(s):  
Standardized Tests ◽  
Number Line ◽  
Chinese Children ◽  
Numerical Magnitude ◽  
Magnitude Comparison ◽  
Cognitive Mediators ◽  
Number Line Estimation ◽  
Mathematics Knowledge ◽  
Us Children ◽  
Symbolic Number

Chinese children routinely outperform American peers in standardized tests of mathematics knowledge. To examine mediators of this effect, 95 Chinese and US 5-year-olds completed a test of overall symbolic arithmetic, an IQ subtest, and three tests each of symbolic and non-symbolic numerical magnitude knowledge (magnitude comparison, approximate addition, and number-line estimation). Overall Chinese children performed better in symbolic arithmetic than US children, and all measures of IQ and number knowledge predicted overall symbolic arithmetic. Chinese children were more accurate than US peers in symbolic numerical magnitude comparison, symbolic approximate addition, and both symbolic and non-symbolic number-line estimation; Chinese and U.S. children did not differ in IQ and non-symbolic magnitude comparison and approximate addition. A substantial amount of the nationality difference in overall symbolic arithmetic was mediated by performance on the symbolic and number-line tests.

Is a Picture Worth 1,000 Words? Investigating Fraction Magnitude Knowledge Through Analysis of Student Representations

2019 ◽  
Vol 46 (1) ◽  
pp. 27-38 ◽  
Author(s):  
Stephanie Morano ◽  
Paul J. Riccomini
Keyword(s):  
Middle School Students ◽  
Effective Area ◽  
Number Line ◽  
Students With Learning Disabilities ◽  
School Students ◽  
National Assessment ◽  
Circular Area ◽  
Magnitude Comparison ◽  
Number Line Estimation

The present study examines the features and quality of visual representations (VRs) created by middle school students with learning disabilities and difficulties in mathematics in response to a released fraction item from the National Assessment of Educational Progress (NAEP). Relations between VR quality and scores on other measures of fraction knowledge are also investigated. Results show that students used circular area models most frequently to represent the NAEP item, but used bar models most accurately. Based on results, bar models may be the most efficient and effective area model VRs for use in fractions instruction. Representation quality was associated with problem-solving accuracy, as well as with performance on fraction number line estimation and fraction magnitude comparison. Implications for practice are discussed.

scholarly journals How the Abstract Becomes Concrete: Irrational Numbers are Understood Relative to Natural Numbers and Perfect Squares

2018 ◽  
Author(s):  
Purav Patel
Keyword(s):  
Teaching And Learning ◽  
Number System ◽  
Number Line ◽  
Natural Numbers ◽  
Comparison Task ◽  
Irrational Numbers ◽  
Magnitude Comparison ◽  
Number Systems ◽  
Number Line Estimation ◽  
Perfect Squares

Mathematical cognition research has largely emphasized concepts that can be directly perceived or grounded in visuospatial referents. These include concrete number systems like natural numbers, integers, and rational numbers. Here, we investigate how a more abstract number system, the irrationals denoted by radical expressions like the square root of 2, is understood across three tasks. Performance on a magnitude comparison task suggests that people interpret irrational numbers – specifically, the radicands of radical expressions – as natural numbers. Strategy self-reports during a number line estimation task reveal that the spatial locations of irrationals are determined by referencing neighboring perfect squares. Finally, perfect squares facilitate the evaluation of arithmetic expressions. These converging results align with a constellation of related phenomena spanning tasks and number systems of varying complexity. Accordingly, we propose that the task-specific recruitment of more concrete representations to make sense of more abstract concepts (referential processing) is an important mechanism for teaching and learning mathematics.

scholarly journals Conceptual replication and extension of the relation between the number line estimation task and mathematical competence across seven studies

2021 ◽  
Vol 7 (3) ◽  
pp. 435-452 ◽  
Author(s):  
Alexa Ellis ◽  
María Inés Susperreguy ◽  
David J. Purpura ◽  
Pamela E. Davis-Kean
Keyword(s):  
Predictive Validity ◽  
Meta Analysis ◽  
Number Line ◽  
Future Research ◽  
Mathematical Competence ◽  
Developmental Progression ◽  
Number Line Estimation ◽  
The Stability ◽  
Diagnostic Importance ◽  
Poor Stability

A recent meta-analysis demonstrated the overall correlation between the number line estimation (NLE) task and children’s mathematical competence was r = .44 (positively recoded), and this relation increased with age. The goal of the current study was to conceptually replicate and extend these results by further synthesizing this correlation utilizing studies not present in the meta-analysis. Across seven studies, 954 participants, ranging from 3 to 11 years old (Age M = 6.02 years, SD = 1.57), the overall estimation-competence correlations were similar to those of the meta-analysis and ranged from r = −.40 to −.35. The current conceptual replication demonstrated that the meta-analysis captured a stable overall relation between performance on the NLE task and mathematical competence. However, the current study failed to replicate the same moderation of age group presented in the meta-analysis. Furthermore, the current study extended results by assessing the stability and predictive validity of the NLE task while controlling for covariates. Results suggested that the NLE task demonstrated poor stability and predictive validity in the seven samples present in this study. Thus, although concurrent relations replicated, the differential age moderation, lack of stability, and lack of predictive validity in these studies require a more nuanced approach to understanding the utility of the NLE task. Future research should focus on understanding the connection between children’s developmental progression and NLE measurement before further investigating the predictive and diagnostic importance of the task for broader mathematical competence.

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

2013 ◽  
Author(s):  
Julia Bahnmueller ◽  
Stefan Huber ◽  
Korbinian Moeller ◽  
Hans-Christoph Nuerk
Keyword(s):  
Number Line ◽  
Number Line Estimation ◽  
The Relationship

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

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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