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Children’s understanding of fraction and decimal symbols and the notation-specific relation to pre-algebra ability

https://doi.org/10.1016/j.jecp.2017.12.003
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1016/0010-0277(92)90049-nopenalex-snapshot
Varieties of numerical abilities
inferredcites →https://doi.org/10.1016/0010-0277(92)90050-ropenalex-snapshot
Preverbal and verbal counting and computation
inferredcites →https://doi.org/10.1016/0732-3123(95)90026-8openalex-snapshot
Algebra with numbers and arithmetic with letters: A definition of pre-algebra
inferredcites →https://doi.org/10.1016/j.actpsy.2013.01.003openalex-snapshot
Are 1/2 and 0.5 represented in the same way?
inferredcites →https://doi.org/10.1016/j.cedpsych.2012.07.001openalex-snapshot
Fractions: Could they really be the gatekeeper’s doorman?
inferredcites →https://doi.org/10.1016/j.cognition.2008.05.003openalex-snapshot
Representational change and magnitude estimation: Why young children can make more accurate salary comparisons than adults
inferredcites →https://doi.org/10.1016/j.cogpsych.2011.03.001openalex-snapshot
An integrated theory of whole number and fractions development
inferredcites →https://doi.org/10.1016/j.cogpsych.2013.01.002openalex-snapshot
Understanding decimal proportions: Discrete representations, parallel access, and privileged processing of zero
inferredcites →https://doi.org/10.1016/j.dr.2015.07.008openalex-snapshot
Why is learning fraction and decimal arithmetic so difficult?
inferredcites →https://doi.org/10.1016/j.jecp.2010.04.008openalex-snapshot
Comparing the magnitude of two fractions with common components: Which representations are used by 10- and 12-year-olds?
inferredcites →https://doi.org/10.1016/j.jecp.2013.09.001openalex-snapshot
The impact of fraction magnitude knowledge on algebra performance and learning
inferredcites →https://doi.org/10.1016/j.jecp.2015.01.013openalex-snapshot
From rational numbers to algebra: Separable contributions of decimal magnitude and relational understanding of fractions
inferredcites →https://doi.org/10.1027/1618-3169/a000086openalex-snapshot
Holistic Representation of Unit Fractions
inferredcites →https://doi.org/10.1037//0097-7403.9.3.320openalex-snapshot
A mode control model of counting and timing processes.
inferredcites →https://doi.org/10.1037/0096-3445.122.3.371openalex-snapshot
The mental representation of parity and number magnitude.
inferredcites →https://doi.org/10.1037/a0013110openalex-snapshot
Development of proportional reasoning: Where young children go wrong.
inferredcites →https://doi.org/10.1037/a0016892openalex-snapshot
A generalized fraction: An entity smaller than one on the mental number line.
inferredcites →https://doi.org/10.1037/a0018170openalex-snapshot
Representations of the magnitudes of fractions.
inferredcites →https://doi.org/10.1037/a0021334openalex-snapshot
Assessing knowledge of mathematical equivalence: A construct-modeling approach.
inferredcites →https://doi.org/10.1037/a0032916openalex-snapshot
Magnitude comparison with different types of rational numbers.
inferredcites →https://doi.org/10.1037/a0035782openalex-snapshot
Decimals are not processed automatically, not even as being smaller than one.
inferredcites →https://doi.org/10.1037/edu0000148openalex-snapshot
Conceptual knowledge of decimal arithmetic.
inferredcites →https://doi.org/10.1037/edu0000169openalex-snapshot
Working memory strategies during rational number magnitude processing.
inferredcites →https://doi.org/10.1037/xap0000036openalex-snapshot
Modeling discrete and continuous entities with fractions and decimals.
inferredcites →https://doi.org/10.1037/xge0000034openalex-snapshot
Conceptual structure and the procedural affordances of rational numbers: Relational reasoning with fractions and decimals.
inferredcites →https://doi.org/10.1037/xhp0000140openalex-snapshot
Rational-number comparison across notation: Fractions, decimals, and whole numbers.
inferredcites →https://doi.org/10.1038/2151519a0openalex-snapshot
Time required for Judgements of Numerical Inequality
inferredcites →https://doi.org/10.1080/07370001003676603openalex-snapshot
How ManyDecimalsAre There Between TwoFractions? Aspects of Secondary School Students’ Understanding of Rational Numbers and Their Notation
inferredcites →https://doi.org/10.1080/10986065.2012.625074openalex-snapshot
What Kinds of Numbers Do Students Assign to Literal Symbols? Aspects of the Transition from Arithmetic to Algebra
inferredcites →https://doi.org/10.1080/15248370701202471openalex-snapshot
The Development of Proportional Reasoning: Effect of Continuous Versus Discrete Quantities
inferredcites →https://doi.org/10.1080/17470218.2011.604785openalex-snapshot
Rapid Communication: Understanding the Real Value of Fractions and Decimals
inferredcites →https://doi.org/10.1111/1467-9280.00343openalex-snapshot
Subtracting Pigeons: Logarithmic or Linear?
inferredcites →https://doi.org/10.1111/1467-9280.02438openalex-snapshot
The Development of Numerical Estimation
inferredcites →https://doi.org/10.1111/bjop.12244openalex-snapshot
A systematic investigation of the link between rational number processing and algebra ability
inferredcites →https://doi.org/10.1111/cdep.12077openalex-snapshot
An Integrative Theory of Numerical Development
inferredcites →https://doi.org/10.1177/0022219416659446openalex-snapshot
Why Learning Common Fractions Is Uncommonly Difficult: Unique Challenges Faced by Students With Mathematical Disabilities
inferredcites →https://doi.org/10.1177/0956797612440101openalex-snapshot
Early Predictors of High School Mathematics Achievement
inferredcites →https://doi.org/10.1207/s15326985ep4001_3openalex-snapshot
Teaching and Learning Fraction and Rational Numbers: The Origins and Implications of Whole Number Bias
inferredcites →https://doi.org/10.1371/journal.pone.0080016openalex-snapshot
The Development of the Mental Representations of the Magnitude of Fractions
inferredcites →https://doi.org/10.21890/ijres.61754openalex-snapshot
The Common Core State Standards for Mathematics
inferredcites →https://doi.org/10.2307/749607openalex-snapshot
Developing Children's Understanding of the Rational Numbers: A New Model and an Experimental Curriculum
inferredcites →https://doi.org/10.2307/749709openalex-snapshot
An Exploration of Aspects of Language Proficiency and Algebra Learning
inferredcites →https://doi.org/10.3758/bf03193955openalex-snapshot
Nonverbal arithmetic in humans: Light from noise
inferredcites →https://doi.org/10.3758/bf03193974openalex-snapshot
Cross-domain transfer of quantitative discriminations: Is it all a matter of proportion?
inferredcites →https://doi.org/10.3758/bf03196349openalex-snapshot
A model of exact small-number representation
inferredcites →https://doi.org/10.3758/bf03334328openalex-snapshot
Determinants of reaction time for digit inequality judgments

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Profiles of Flexibility with Fraction Arithmetic and Their Connection to Algebra Readiness
inferred← citeshttps://doi.org/10.1007/s10639-022-11453-2openalex-snapshot
Evaluation of fraction learning in authentic context using Ubiquitous Fraction App
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“Less is… more?” The influence of digit magnitude and formatting on probability weighting
inferred← citeshttps://doi.org/10.1016/j.appdev.2023.101537openalex-snapshot
Verbal labels influence children's processing of decimal magnitudes
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Does an integrated focus on fractions and decimals improve at-risk students’ rational number magnitude performance?
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Early fraction relational reasoning uniquely predicts later algebraic thinking in children: A longitudinal study
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Rational number conceptualization predicts mathematics achievement: Quantity matters
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Integrated Knowledge of Rational Number Notations Predicts Children's Math Achievement and Understanding of Numerical Magnitudes
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Winning or losing: Children’s proportional reasoning across motivational contexts
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Rational number representation, math anxiety, and algebra performance in college students
inferred← citeshttps://doi.org/10.1016/j.cognition.2023.105608openalex-snapshot
Competing numerical magnitude codes in decimal comparison: Whole number and rational number distance both impact performance
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Rational number representation by the approximate number system
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Cross-notation knowledge of fractions and decimals
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Building integrated number sense in adults and children: Comparing fractions-only training with cross-notation number line training
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Children’s estimates of equivalent rational number magnitudes are not equal: Evidence from fractions, decimals, percentages, and whole numbers
inferred← citeshttps://doi.org/10.1016/j.jecp.2024.106187openalex-snapshot
Affordances of fractions and decimals for arithmetic among middle school students in the United States and China
inferred← citeshttps://doi.org/10.1016/j.jecp.2025.106418openalex-snapshot
Early algebra knowledge predicts later fraction understanding and improves with fraction instruction
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Parental support for mathematical problem solving: Proximal and distal influences within the religious practice of tithing
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Early neural markers for individual difference in mathematical achievement determined from rational number processing
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Distributions of textbook problems predict student learning: Data from decimal arithmetic.
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Lack of integrated number sense among college students: Evidence from rational number cross-notation comparison.
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Adults systematically underestimate decimals and whole number exposure induces further magnitude-based underestimation.
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Comparing virtual and concrete manipulative on 5th grades students in fraction performance
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Structural relationships among number sense performance, fraction and decimal understanding, and mathematics achievement: Evidence from sixth-grade students in Türkiye
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Unpacking the Connections Between Fractions and Algebra: The Importance of Fraction Schemes and Units Coordination
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Perceptions of ease and difficulty, but not growth mindset, relate to specific math attitudes
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Cross‐notation knowledge of rational numbers predicts fraction arithmetic
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Predicting Middle School Profiles of Algebra Performance Using Fraction Knowledge
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Conceptual Knowledge, Procedural Knowledge, and Metacognition in Routine and Nonroutine Problem Solving
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Talking about proportion: Fraction labels impact numerical interference in non‐symbolic proportional reasoning
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The structure of the notation system in adults’ number line estimation: An eye-tracking study
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Use of Virtual Manipulatives in Addition of Fractions Among Year Four Pupils
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Students' Strategy in Connecting Fractions, Decimal, and Percent in Solving Visual Form Problems
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Using Ordering Tasks to Determine Fraction Magnitudes
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Çok Dilli Öğrencilerde Kesir Kavram İmajının İncelenmesi
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Reduction procedures in fraction arithmetic
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Fraction Symbols and their Relation to Conceptual Knowledge
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Utilization of Literature Based Math in Developing Didactic Designs for Students' Mathematical Understanding in the Decimal Concept
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Innovative teaching strategy of using the “Transcard” model in conceptualizing fraction and decimal for primary mathematics education
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Causal pathways from fractions to algebra: Integrating psychology and math education perspectives
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Peningkatan Hasil Belajar Matematika Siswa Menggunakan Model Pembelajaran Berbasis Masalah Berbantuan Multimedia Interaktif
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