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

inferredcites →https://doi.org/10.2307/1175067openalex-snapshot
The Child's Understanding of Number
inferredcites →https://doi.org/10.2307/748455openalex-snapshot
The Child's Understanding of Number
inferredcites →https://doi.org/10.2307/748959openalex-snapshot
Preschool Children's Knowledge of Addition and Subtraction
inferredcites →https://doi.org/10.5951/mt.73.8.0572openalex-snapshot
Constructing Meaning for The Concept of Equation

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

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Simplified Instructional Materials (Sim): An Intervention for Improving Students’ Performance in the Factorization of Algebraic Expressions
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A Walk in Semiotics and Mathematics
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Mistakes on display: Incorrect examples refine equation solving and algebraic feature knowledge
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Psychology of Mathematical Thinking
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Does Practice Make Perfect?
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References. A Deep Sea of Luminescent Ideas
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Learning to Solve Equations in Three Swedish-Speaking Classrooms in Finland
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Argumentation in the Context of Elementary Grades: The Role of Participants, Tasks, and Tools
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Algebra Education and Digital Resources: A Long-Distance Relationship?
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Characteristics of the Learners
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Longitudinal Approaches to Investigating Arithmetic Concepts Across the Elementary and Middle School Years
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Algebra Education and Digital Resources: A Long-Distance Relationship?
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Versatile Mathematical Thinking: Making Sense of Processes and Objects
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The Relationship Between Equivalence and Equality in a Nonsymbolic Context with Regard to Algebraic Thinking in Young Children
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Early Algebra: Research into its Nature, its Learning, its Teaching
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Rethinking Algebra: A Versatile Approach Integrating Digital Technology
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Misconceptions and Learning Algebra
inferred← citeshttps://doi.org/10.1007/978-3-319-63555-2_3openalex-snapshot
Language and Cultural Issues in the Teaching and Learning of WNA
inferred← citeshttps://doi.org/10.1007/978-3-319-66811-6_4openalex-snapshot
Conceptions About System of Linear Equations and Solution
inferred← citeshttps://doi.org/10.1007/978-3-319-66811-6_6openalex-snapshot
Misconceptions About Determinants
inferred← citeshttps://doi.org/10.1007/978-3-319-68351-5_10openalex-snapshot
Generalizing Fractional Structures: A Critical Precursor to Algebraic Thinking
inferred← citeshttps://doi.org/10.1007/978-3-319-68351-5_12openalex-snapshot
Making Implicit Algebraic Thinking Explicit: Exploiting National Characteristics of German Approaches
inferred← citeshttps://doi.org/10.1007/978-3-319-68351-5_5openalex-snapshot
Cultivating Early Algebraic Thinking
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Characteristics of Korean Students’ Early Algebraic Thinking: A Generalized Arithmetic Perspective
inferred← citeshttps://doi.org/10.1007/978-3-319-68351-5_7openalex-snapshot
Function Tasks, Input, Output, and the Predictive Rule: How Some Singapore Primary Children Construct the Rule
inferred← citeshttps://doi.org/10.1007/978-3-319-68351-5_8openalex-snapshot
Algebraic Understanding of Equalities in Primary Classes
inferred← citeshttps://doi.org/10.1007/978-3-319-99861-9_10openalex-snapshot
Solving a Task with Infinitely Many Solutions: Convergent and Divergent Thinking in Mathematical Creativity
inferred← citeshttps://doi.org/10.1007/978-3-642-17735-4_14openalex-snapshot
Representational Competence and Algebraic Modeling
inferred← citeshttps://doi.org/10.1007/978-3-642-17735-4_15openalex-snapshot
Middle School Students’ Understanding of Core Algebraic Concepts: Equivalence & Variable
inferred← citeshttps://doi.org/10.1007/978-3-642-17735-4_26openalex-snapshot
A Procedural Focus and a Relationship Focus to Algebra: How U.S. Teachers and Japanese Teachers Treat Systems of Equations
inferred← citeshttps://doi.org/10.1007/978-3-642-17735-4_4openalex-snapshot
Developing Algebraic Thinking in the Context of Arithmetic
inferred← citeshttps://doi.org/10.1007/978-3-658-22616-9_3openalex-snapshot
Wie können Lehrkräfte Mathematisierungskompetenzen bei Schülerinnen und Schülern fördern und diagnostizieren?
inferred← citeshttps://doi.org/10.1007/978-3-662-68701-7_7openalex-snapshot
Gleichungen erforschen
inferred← citeshttps://doi.org/10.1007/978-3-8348-9836-4_3openalex-snapshot
Zeichen defizient verstehen
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Growing Possibilities: Designing Mathematical and Pedagogical Problems Using Variation
inferred← citeshttps://doi.org/10.1007/978-94-007-7560-2_19openalex-snapshot
Teaching Mathematics Using Standards-Based and Traditional Curricula: A Case of Variable Ideas
inferred← citeshttps://doi.org/10.1007/978-94-009-1465-0_16openalex-snapshot
Introduction to Section 2
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Using and Applying Mathematics in Education
inferred← citeshttps://doi.org/10.1007/978-94-009-1465-0_5openalex-snapshot
Number and Arithmetic
inferred← citeshttps://doi.org/10.1007/978-94-017-2057-1_4openalex-snapshot
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inferred← citeshttps://doi.org/10.1007/978-94-017-2211-7_13openalex-snapshot
Limitations of Iconic and Symbolic Representations of Arithmetical Concepts in Early Grades of Primary School
inferred← citeshttps://doi.org/10.1007/978-94-6209-707-0openalex-snapshot
Algebra Teaching around the World
inferred← citeshttps://doi.org/10.1007/978-94-6209-707-0_11openalex-snapshot
Teaching Algebraic Concepts in Chinese Classrooms
inferred← citeshttps://doi.org/10.1007/978-94-6209-707-0_3openalex-snapshot
Rethinking Algebra Teaching in the Light of ‘Orchestration of Signs’ – Exploring the “Equal Sign” in a Norwegian Mathematics Classroom
inferred← citeshttps://doi.org/10.1007/978-94-6300-699-6_4openalex-snapshot
Introducing Change for the Sake of Invariance
inferred← citeshttps://doi.org/10.1007/978-94-6300-782-5_8openalex-snapshot
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inferred← citeshttps://doi.org/10.1007/978-981-95-0281-3_11openalex-snapshot
Early Childhood Mathematics: Culturally Situated Pedagogies in Hong Kong
inferred← citeshttps://doi.org/10.1007/bf00302715openalex-snapshot
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inferred← citeshttps://doi.org/10.1007/bf00314722openalex-snapshot
An investigation of young children's academic arithmetic contexts
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inferred← citeshttps://doi.org/10.1007/bf01284528openalex-snapshot
A cognitive gap between arithmetic and algebra
inferred← citeshttps://doi.org/10.1007/bf02655899openalex-snapshot
Middle school students' understanding of core algebraic concepts: Equivalence & Variable1
inferred← citeshttps://doi.org/10.1007/bf03172644openalex-snapshot
Concept-referenced testing
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L’Intégration de Nouvelles Connaissances: Entre Arithmétique et Algèbre
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Sequential development of algebra knowledge: A cognitive analysis
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The case of bruce: A teacher’s model of his students’ algebraic thinking about equivalent expressions
inferred← citeshttps://doi.org/10.1007/bf03217478openalex-snapshot
Student perspectives on equation: The transition from school to university
inferred← citeshttps://doi.org/10.1007/bf03217543openalex-snapshot
Appreciating mathematical structure for all
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Schülerfehler und Lernschwierigkeiten in Algebra und Arithmetik — Theoriebildung und empirische Ergebnisse aus einer Untersuchung
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Can young students understand the mathematical concept of equality? A whole-year arithmetic teaching experiment in second grade
inferred← citeshttps://doi.org/10.1007/s10649-007-9086-0openalex-snapshot
Procedural embodiment and magic in linear equations
inferred← citeshttps://doi.org/10.1007/s10649-012-9394-xopenalex-snapshot
Young students learning formal algebraic notation and solving linear equations: are commonly experienced difficulties avoidable?
inferred← citeshttps://doi.org/10.1007/s10649-013-9512-4openalex-snapshot
A comparison of Korean and American secondary school textbooks: the case of quadratic equations
inferred← citeshttps://doi.org/10.1007/s10649-014-9561-3openalex-snapshot
Intertextuality and sense production in the learning of algebraic methods
inferred← citeshttps://doi.org/10.1007/s10649-018-9828-1openalex-snapshot
An assessment of the sources of the reversal error through classic and new variables
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College developmental math students’ knowledge of the equal sign
inferred← citeshttps://doi.org/10.1007/s10649-020-10000-5openalex-snapshot
Using large-scale data to determine pupils’ strategies and errors in missing value number equations
inferred← citeshttps://doi.org/10.1007/s10649-021-10092-7openalex-snapshot
Unpacking hidden views: seven ways to treat your formula
inferred← citeshttps://doi.org/10.1007/s10649-022-10158-0openalex-snapshot
Connecting characterizations of equivalence of expressions: design research in Grade 5 by bridging graphical and symbolic representations
inferred← citeshttps://doi.org/10.1007/s10649-023-10264-7openalex-snapshot
Developing the concept of task substitution and transformation by defining own equivalences
inferred← citeshttps://doi.org/10.1007/s10649-025-10419-8openalex-snapshot
Transforming equations into equivalent equations—an empirical study of the equation transformation capability as a multidimensional construct
inferred← citeshttps://doi.org/10.1007/s10649-025-10445-6openalex-snapshot
The surprising obstacle of two unknowns on the same side of the equal sign in solving equations of the type ax ± b ± cx = d and the phenomenon of ignoring the unknown
inferred← citeshttps://doi.org/10.1007/s10758-006-9107-6openalex-snapshot
Connecting the equals sign
inferred← citeshttps://doi.org/10.1007/s10763-010-9232-5openalex-snapshot
PROSPECTIVE TEACHERS’ INITIAL CONCEPTIONS ABOUT PUPILS’ DIFFICULTIES IN SCIENCE AND MATHEMATICS: A POTENTIAL RESOURCE IN TEACHER EDUCATION
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Secondary School Students’ Errors in the Translation of Algebraic Statements
inferred← citeshttps://doi.org/10.1007/s10763-016-9759-1openalex-snapshot
Making Associativity Operational
inferred← citeshttps://doi.org/10.1007/s10763-020-10144-zopenalex-snapshot
Primary School Students’ Knowledge of the Equal Sign—the Swedish Case
inferred← citeshttps://doi.org/10.1007/s10763-021-10150-9openalex-snapshot
Revisiting School Mathematics in Pre-service Secondary Teacher Education: Purposes, Opportunities and Challenges
inferred← citeshttps://doi.org/10.1007/s10763-021-10181-2openalex-snapshot
The Use of Representations when Solving Algebra Word Problems and the Sources of Solution Errors
inferred← citeshttps://doi.org/10.1007/s10763-022-10248-8openalex-snapshot
What is so Complicated in Developing Students’ Conception of the Equal Sign?
inferred← citeshttps://doi.org/10.1007/s10763-026-10731-6openalex-snapshot
Multimodal Tensions and the Foregrounding of Mathematical Content: A Textbook Analysis of Introductions to Equality and Subtraction
inferred← citeshttps://doi.org/10.1007/s10857-006-9000-1openalex-snapshot
Equivalence and relational thinking: preservice elementary teachers’ awareness of opportunities and misconceptions
inferred← citeshttps://doi.org/10.1007/s10857-009-9119-yopenalex-snapshot
How to develop mathematics-for-teaching and for understanding: the case of meanings of the equal sign
inferred← citeshttps://doi.org/10.1007/s10857-011-9178-8openalex-snapshot
Accountability conversations: mathematics teachers’ learning through challenge and solidarity
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Preparing elementary prospective teachers to teach early algebra
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The Mathematics of High School Physics
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A comparison of curricular effects on the integration of arithmetic and algebraic schemata in pre-algebra students
inferred← citeshttps://doi.org/10.1007/s11251-017-9408-2openalex-snapshot
Preservice teachers’ use of contrasting cases in mathematics instruction
inferred← citeshttps://doi.org/10.1007/s11409-019-09203-wopenalex-snapshot
Metacognitive monitoring and help-seeking decisions on mathematical equivalence problems
inferred← citeshttps://doi.org/10.1007/s11858-010-0296-zopenalex-snapshot
Imagining mathematics teaching practice: prospective teachers generate representations of a class discussion
inferred← citeshttps://doi.org/10.1007/s11858-012-0471-5openalex-snapshot
School mathematics and creativity at the elementary and middle-grade levels: how are they related?
inferred← citeshttps://doi.org/10.1007/s11858-022-01405-yopenalex-snapshot
Is a substitute the same? Learning from lessons centering different relational conceptions of the equal sign
inferred← citeshttps://doi.org/10.1007/s11858-022-01422-xopenalex-snapshot
Introducing equations in early algebra
inferred← citeshttps://doi.org/10.1007/s11858-022-01424-9openalex-snapshot
Starting points: understanding children’s pre-instructional intuitions about function tables
inferred← citeshttps://doi.org/10.1007/s11858-022-01426-7openalex-snapshot
Algebraic reasoning in years 5 and 6: classifying its emergence and progression using reverse fraction tasks
inferred← citeshttps://doi.org/10.1007/s11858-022-01435-6openalex-snapshot
The multi-dimensionality of early algebraic thinking: background, overarching dimensions, and new directions
inferred← citeshttps://doi.org/10.1007/s11858-025-01707-xopenalex-snapshot
The equal sign and equivalence: interplay between textbook research and curriculum development
inferred← citeshttps://doi.org/10.1007/s13138-024-00247-3openalex-snapshot
How Do Multiplicative and Relational Thinking Contribute to Multidigit Division?
inferred← citeshttps://doi.org/10.1007/s13394-013-0093-4openalex-snapshot
Developing learning environments which support early algebraic reasoning: a case from a New Zealand primary classroom
inferred← citeshttps://doi.org/10.1007/s13394-013-0097-0openalex-snapshot
Difficulties in initial algebra learning in Indonesia
inferred← citeshttps://doi.org/10.1007/s13394-024-00508-xopenalex-snapshot
Teacher use of multimodal signs to support kindergarten students’ developing understanding of mathematical equivalence
inferred← citeshttps://doi.org/10.1007/s13394-024-00513-0openalex-snapshot
Assessing children’s capacity for procedural flexibility with mental addition
inferred← citeshttps://doi.org/10.1007/s40574-024-00439-2openalex-snapshot
Digital artifacts in mathematics education: how can we study the learning processes they promote?
inferred← citeshttps://doi.org/10.1007/s40751-015-0004-2openalex-snapshot
Improving Grade 7 Students’ Achievement in Initial Algebra Through a Technology-Based Intervention
inferred← citeshttps://doi.org/10.1007/s40751-016-0018-4openalex-snapshot
Designing Educational Software: The Case of Grid Algebra
inferred← citeshttps://doi.org/10.1007/s40751-020-00070-8openalex-snapshot
Design and Investigation of a Touch Gesture for Dividing in a Virtual Manipulative Model for Equation-solving
inferred← citeshttps://doi.org/10.1007/s40751-022-00103-4openalex-snapshot
Adapting the Balance Model for Equation Solving to Virtual Reality
inferred← citeshttps://doi.org/10.1007/s40753-022-00178-9openalex-snapshot
Sameness in Mathematics: a Unifying and Dividing Concept
inferred← citeshttps://doi.org/10.1007/s40753-024-00241-7openalex-snapshot
Student Interpretations of Eigenequations in Linear Algebra and Quantum Mechanics
inferred← citeshttps://doi.org/10.1007/s42330-019-00067-5openalex-snapshot
Context Variation and Syntax Nuances of the Equal Sign in Elementary School Mathematics
inferred← citeshttps://doi.org/10.1016/0732-3123(95)90023-3openalex-snapshot
Purpose in school algebra
inferred← citeshttps://doi.org/10.1016/b978-0-12-805086-6.00008-4openalex-snapshot
Understanding Children’s Difficulties with Mathematical Equivalence
inferred← citeshttps://doi.org/10.1016/b978-2-294-75466-1.00020-0openalex-snapshot
Les connaissances issues de la vie quotidienne et les apprentissages scolaires
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Influences of problem format and SES on preschoolers’ understanding of approximate addition
inferred← citeshttps://doi.org/10.1016/j.cogdev.2014.01.001openalex-snapshot
Organization matters: Mental organization of addition knowledge relates to understanding math equivalence in symbolic form
inferred← citeshttps://doi.org/10.1016/j.cogdev.2017.07.003openalex-snapshot
Relations between patterning skill and differing aspects of early mathematics knowledge
inferred← citeshttps://doi.org/10.1016/j.cogdev.2022.101167openalex-snapshot
Children’s confidence using incorrect strategies on mathematical equivalence problems
inferred← citeshttps://doi.org/10.1016/j.cogsci.2003.11.002openalex-snapshot
You?ll see what you mean: Students encode equations based on their knowledge of arithmetic
inferred← citeshttps://doi.org/10.1016/j.ijer.2011.12.006openalex-snapshot
Spontaneous meta-arithmetic as a first step toward school algebra
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In pursuit of knowledge: Comparing self-explanations, concepts, and procedures as pedagogical tools
inferred← citeshttps://doi.org/10.1016/j.jecp.2010.03.004openalex-snapshot
Learning about the equal sign: Does comparing with inequality symbols help?
inferred← citeshttps://doi.org/10.1016/j.jecp.2012.05.003openalex-snapshot
Substitution and sameness: Two components of a relational conception of the equals sign
inferred← citeshttps://doi.org/10.1016/j.jecp.2013.12.001openalex-snapshot
Working memory, worry, and algebraic ability
inferred← citeshttps://doi.org/10.1016/j.jecp.2017.06.002openalex-snapshot
An integrative data analysis of gender differences in children’s understanding of mathematical equivalence
inferred← citeshttps://doi.org/10.1016/j.jecp.2024.106003openalex-snapshot
Children’s confidence on mathematical equivalence and fraction problems
inferred← citeshttps://doi.org/10.1016/j.jmathb.2006.02.003openalex-snapshot
Mathematics in the home: Homework practices and mother–child interactions doing mathematics
inferred← citeshttps://doi.org/10.1016/j.jmathb.2008.08.002openalex-snapshot
Attention to meaning by algebra teachers
inferred← citeshttps://doi.org/10.1016/j.jmathb.2010.01.002openalex-snapshot
Linguistic indexicality in algebra discussions
inferred← citeshttps://doi.org/10.1016/j.jmathb.2010.11.002openalex-snapshot
Integrating algebra and proof in high school mathematics: An exploratory study
inferred← citeshttps://doi.org/10.1016/j.jmathb.2011.08.002openalex-snapshot
An exploration of the role natural language and idiosyncratic representations in teaching how to convert among fractions, decimals, and percents
inferred← citeshttps://doi.org/10.1016/j.jmathb.2012.06.001openalex-snapshot
Prospective middle grade mathematics teachers’ knowledge of algebra for teaching
inferred← citeshttps://doi.org/10.1016/j.jmathb.2013.02.001openalex-snapshot
Equation structure and the meaning of the equal sign: The impact of task selection in eliciting elementary students’ understandings
inferred← citeshttps://doi.org/10.1016/j.jmathb.2013.04.001openalex-snapshot
Decoding a proof of Fermat's Little Theorem via script writing
inferred← citeshttps://doi.org/10.1016/j.jmathb.2013.04.003openalex-snapshot
The role of problem representation and feature knowledge in algebraic equation-solving
inferred← citeshttps://doi.org/10.1016/j.jmathb.2013.06.004openalex-snapshot
Flexible thinking and met-befores: Impact on learning mathematics
inferred← citeshttps://doi.org/10.1016/j.jmathb.2013.07.002openalex-snapshot
Prerequisite algebra skills and associated misconceptions of middle grade students: A review
inferred← citeshttps://doi.org/10.1016/j.jmathb.2013.12.003openalex-snapshot
Evolving a three-world framework for solving algebraic equations in the light of what a student has met before
inferred← citeshttps://doi.org/10.1016/j.jmathb.2014.10.003openalex-snapshot
Disappearing x: When solving does not mean finding the solution set
inferred← citeshttps://doi.org/10.1016/j.jmathb.2016.10.002openalex-snapshot
Moving in and out of contexts in collaborative reasoning about equations
inferred← citeshttps://doi.org/10.1016/j.jmathb.2017.05.003openalex-snapshot
Zimbabwean in-service mathematics teachers’ understanding of matrix operations
inferred← citeshttps://doi.org/10.1016/j.jmathb.2017.11.001openalex-snapshot
An investigation of an undergraduate student’s reasoning with zero-divisors and the zero-product property
inferred← citeshttps://doi.org/10.1016/j.jmathb.2021.100871openalex-snapshot
From “You have to have three numbers and a plus sign” to “It’s the exact same thing”: K–1 students learn to think relationally about equations
inferred← citeshttps://doi.org/10.1016/j.jmathb.2022.100935openalex-snapshot
An initial framework for analyzing students’ reasoning with equivalence across mathematical domains
inferred← citeshttps://doi.org/10.1016/j.jmathb.2022.100951openalex-snapshot
Handling a language to think together in the classroom: The case of the notion of equivalence
inferred← citeshttps://doi.org/10.1016/j.jmathb.2022.101011openalex-snapshot
Future teachers’ use of co-occurrence and same extent perspectives when generating linear equations
inferred← citeshttps://doi.org/10.1016/j.jmathb.2024.101174openalex-snapshot
Preparing elementary pre-service teachers to teach early algebra: A conceptual replication study
inferred← citeshttps://doi.org/10.1016/j.jmathb.2024.101193openalex-snapshot
Snapshots of sameness: Characterizations of mathematical sameness across student groups
inferred← citeshttps://doi.org/10.1016/j.jmathb.2025.101258openalex-snapshot
The semiotic potential of pseudo-random numbers for the idea of indeterminacy in algebra
inferred← citeshttps://doi.org/10.1016/j.jmathb.2025.101285openalex-snapshot
Students’ productive use of equivalence transformations
inferred← citeshttps://doi.org/10.1016/j.learninstruc.2012.11.002openalex-snapshot
Using example problems to improve student learning in algebra: Differentiating between correct and incorrect examples
inferred← citeshttps://doi.org/10.1016/j.lindif.2015.01.001openalex-snapshot
A specific misconception of the equal sign acts as a barrier to children's learning of early algebra
inferred← citeshttps://doi.org/10.1016/j.lindif.2018.02.007openalex-snapshot
Patterns of anxiety in algebraic problem solving: A three-step latent variable analysis
inferred← citeshttps://doi.org/10.1016/j.lindif.2018.04.013openalex-snapshot
Arithmetic practice that includes relational words promotes understanding of symbolic equations
inferred← citeshttps://doi.org/10.1016/j.ssaho.2024.101019openalex-snapshot
Analyses of algebra knowledge and difficulties among Ghanaian Junior High School learners: Insights from standard-based mathematics curriculum implementation
inferred← citeshttps://doi.org/10.1016/j.stueduc.2021.101046openalex-snapshot
Mathematical equivalence assessment: Measurement invariance across six countries
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Conceptual knowledge of the associativity principle: A review of the literature and an agenda for future research
inferred← citeshttps://doi.org/10.1016/s0065-2407(05)80005-9openalex-snapshot
Mechanisms of change in the development of mathematical reasoning
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Children's understanding of the commutative law of addition
inferred← citeshttps://doi.org/10.1023/a:1003473509628openalex-snapshot
The roles of reification and reflective abstraction in the development of abstract thought: Transitions from arithmetic to algebra
inferred← citeshttps://doi.org/10.1023/a:1004091631981openalex-snapshot
Collaborative action research on the learning and teaching of algebra: a story of one mathematics teacher's development
inferred← citeshttps://doi.org/10.1023/a:1020229023965openalex-snapshot
The balance model: Hindrance or support for the solving of linear equations with one unknown
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Conceptual and procedural knowledge of mathematics: Does one lead to the other?
inferred← citeshttps://doi.org/10.1037/0012-1649.43.3.687openalex-snapshot
U-shaped development in math: 7-year-olds outperform 9-year-olds on equivalence problems.
inferred← citeshttps://doi.org/10.1037/a0013156openalex-snapshot
Equivalence in symbolic and nonsymbolic contexts: Benefits of solving problems with manipulatives.
inferred← citeshttps://doi.org/10.1037/a0018447openalex-snapshot
Contribution of equal-sign instruction beyond word-problem tutoring for third-grade students with mathematics difficulty.
inferred← citeshttps://doi.org/10.1037/a0021334openalex-snapshot
Assessing knowledge of mathematical equivalence: A construct-modeling approach.
inferred← citeshttps://doi.org/10.1037/a0028389openalex-snapshot
The effects of feedback during exploratory mathematics problem solving: Prior knowledge matters.
inferred← citeshttps://doi.org/10.1037/a0028997openalex-snapshot
It pays to be organized: Organizing arithmetic practice around equivalent values facilitates understanding of math equivalence.
inferred← citeshttps://doi.org/10.1037/a0037687openalex-snapshot
Arithmetic practice can be modified to promote understanding of mathematical equivalence.
inferred← citeshttps://doi.org/10.1037/edu0000053openalex-snapshot
Feedback both helps and hinders learning: The causal role of prior knowledge.
inferred← citeshttps://doi.org/10.1037/edu0000208openalex-snapshot
Assessing formal knowledge of math equivalence among algebra and pre-algebra students.
inferred← citeshttps://doi.org/10.1037/edu0000337openalex-snapshot
Improving children’s understanding of mathematical equivalence via an intervention that goes beyond nontraditional arithmetic practice.
inferred← citeshttps://doi.org/10.1037/edu0000747openalex-snapshot
Factors associated with children’s understanding of mathematical equivalence: An investigation across six countries.
inferred← citeshttps://doi.org/10.1063/1.4941165openalex-snapshot
Learning algebra on screen and on paper: The effect of using a digital tool on students’ understanding
inferred← citeshttps://doi.org/10.1063/5.0102778openalex-snapshot
Algebra ideas in early grades
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An Overview of the Calculus Curriculum Reform Effort: Issues for Learning, Teaching, and Curriculum Development
inferred← citeshttps://doi.org/10.1080/0020739x.2017.1293856openalex-snapshot
Will learning to solve one-step equations pose a challenge to 8th grade students?
inferred← citeshttps://doi.org/10.1080/00313831.2025.2516437openalex-snapshot
Learning from errors: co-clustering students’ answer types in a digital learning environment to verify task design on linear equations
inferred← citeshttps://doi.org/10.1080/02619760802208429openalex-snapshot
Prospective teachers' initial conceptions about pupils' understanding of science and mathematics
inferred← citeshttps://doi.org/10.1080/03057267.2017.1248627openalex-snapshot
Representational competence: towards a distributed and embodied cognition account
inferred← citeshttps://doi.org/10.1080/03640210701863933openalex-snapshot
Trade‐Offs Between Grounded and Abstract Representations: Evidence From Algebra Problem Solving
inferred← citeshttps://doi.org/10.1080/07370000801980845openalex-snapshot
Sources of Differences in Children's Understandings of Mathematical Equality: Comparative Analysis of Teacher Guides and Student Texts in China and the United States
inferred← citeshttps://doi.org/10.1080/08957347.2021.1890744openalex-snapshot
Examining Three Learning Progressions in Middle-school Mathematics for Formative Assessment
inferred← citeshttps://doi.org/10.1080/09650792.2012.727644openalex-snapshot
Teacher–researcher collaboration in a Grade Four mathematics classroom: restoring equality to students’ usage of the ‘=’ sign
inferred← citeshttps://doi.org/10.1080/10288457.2006.10740593openalex-snapshot
Revisiting the equal sign: Some Grade 8 and 9 learners' interpretations
inferred← citeshttps://doi.org/10.1080/10288457.2012.10740752openalex-snapshot
Some South African mathematics Teachers' concept images of the equation concept
inferred← citeshttps://doi.org/10.1080/10288457.2014.930980openalex-snapshot
‘We won't know it since we don't teach it’: Interactions between Teachers' Knowledge and Practice
inferred← citeshttps://doi.org/10.1080/10508400903191912openalex-snapshot
Meta-Representation in an Algebra I Classroom
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Directionality of the Equals Sign: A Case Study Using Logarithmic Properties
inferred← citeshttps://doi.org/10.1080/10824669.2014.986674openalex-snapshot
Design-Based Research Within the Constraints of Practice: AlgebraByExample
inferred← citeshttps://doi.org/10.1080/10986060701360902openalex-snapshot
A Longitudinal Examination of Middle School Students' Understanding of the Equal Sign and Equivalent Equations
inferred← citeshttps://doi.org/10.1080/10986060701360910openalex-snapshot
Middle School Mathematics Teachers' Knowledge of Students' Understanding of Core Algebraic Concepts: Equal Sign and Variable
inferred← citeshttps://doi.org/10.1080/10986060701818644openalex-snapshot
Mother and Child Emotions during Mathematics Homework
inferred← citeshttps://doi.org/10.1080/10986065.2012.657956openalex-snapshot
Integrating Algebra and Proof in High School: Students' Work with Multiple Variables and a Single Parameter in a Proof Context
inferred← citeshttps://doi.org/10.1080/10986065.2018.1474534openalex-snapshot
Exploring Kindergarten Students’ Early Understandings of the Equal Sign
inferred← citeshttps://doi.org/10.1080/10986065.2020.1700587openalex-snapshot
Features of a pan balance that may support students’ developing understanding of mathematical equivalence
inferred← citeshttps://doi.org/10.1080/10986065.2020.1740857openalex-snapshot
Curricular approaches to algebra in Estonia, Finland and Sweden – a comparative study
inferred← citeshttps://doi.org/10.1080/10986065.2020.1777364openalex-snapshot
Students’ opposing conceptions of equations with two equal signs
inferred← citeshttps://doi.org/10.1080/10986065.2020.1779012openalex-snapshot
Exploring the intersection of algebraic and computational thinking
inferred← citeshttps://doi.org/10.1080/10986065.2020.1793055openalex-snapshot
The role of balance scales in supporting productive thinking about equations among diverse learners
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