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Mathematical Thinking and Learning Volume 14, 2012 - Issue 1
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Articles

What Kinds of Numbers Do Students Assign to Literal Symbols? Aspects of the Transition from Arithmetic to Algebra

Konstantinos P. Christou Department of Philosophy and History of Science, National and Kapodistrian University of Athens
&
Stella Vosniadou Department of Philosophy and History of Science, National and Kapodistrian University of AthensCorrespondence[email protected]
Pages 1-27 | Published online: 09 Jan 2012

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Konstantinos P. Christou, Despoina Ioanna Kyrvei & Xenia Vamvakoussi. (2022) Interpreting literal symbols in algebra under the effects of the natural number bias. Mathematical Thinking and Learning 0:0, pages 1-14.
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J. Matt Switzer. (2018) U.S. grade 4–6 students’ rational-number substitutions for odd-sum unknown addend tasks. Investigations in Mathematics Learning 10:1, pages 33-53.
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Ian Whitacre, Jessica Pierson Bishop, Lisa L. Lamb, Randolph A. Philipp, Spencer Bagley & Bonnie P. Schappelle. (2015) ‘Negative of my money, positive of her money’: secondary students’ ways of relating equations to a debt context. International Journal of Mathematical Education in Science and Technology 46:2, pages 234-249.
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Articles from other publishers (28)

Xiaodong Li, Ping Xu, Ronghuan Jiang & Shuang Chen. (2023) The role of inhibition in overcoming arithmetic natural number bias in the Chinese context: Evidence from behavioral and ERP experiments. Learning and Instruction 86, pages 101752.
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Ulises Xolocotzin, Ana M. Medrano-Moya & Teresa Rojano. (2022) Starting points: understanding children’s pre-instructional intuitions about function tables. ZDM – Mathematics Education 54:6, pages 1363-1376.
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Κωνσταντίνος Π. Χρήστου. (2022) Παρανοήσεις των μαθητών στις αριθμητικές πράξεις μέσα από την προσέγγιση της εννοιολογικής αλλαγής. Psychology: the Journal of the Hellenic Psychological Society 27:1, pages 32-47.
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Stella Vosniadou. 2021. Heterogeneous Contributions to Numerical Cognition. Heterogeneous Contributions to Numerical Cognition 95 115 .
Pinar YILDIZ, Azime ATAY & S. Koza ÇİFTÇİ. (2020) Preservice Middle School Mathematics Teachers’ Definitions of Algebraic Expression and Equation. International Journal of Contemporary Educational Research 7:2, pages 156-164.
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Michelle Ann Hurst, Marisa Massaro & Sara Cordes. (2020) Fraction magnitude: Mapping between symbolic and spatial representations of proportion. Journal of Numerical Cognition 6:2, pages 204-230.
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Konstantinos P. Christou, Courtney Pollack, Jo Van Hoof & Wim Van Dooren. (2020) Natural number bias in arithmetic operations with missing numbers – A reaction time study. Journal of Numerical Cognition 6:1, pages 22-49.
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Lhachimi Mohamed Younes, Mamouni My Ismail & Achtaich Naceur. (2020) A Didactic Balance to Solve Equations. Advances in Science, Technology and Engineering Systems Journal 5:5, pages 288-294.
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Dina Tirosh & Pessia Tsamir. 2020. Encyclopedia of Mathematics Education. Encyclopedia of Mathematics Education 428 433 .
Peter A. Edelsbrunner, Lennart Schalk, Ralph Schumacher & Elsbeth Stern. (2018) Variable control and conceptual change: A large-scale quantitative study in elementary school. Learning and Individual Differences 66, pages 38-53.
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Xenia Vamvakoussi, Konstantinos P. Christou & Stella Vosniadou. (2018) Bridging psychological and educational research on rational number knowledge. Journal of Numerical Cognition 4:1, pages 84-106.
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Michelle A. Hurst & Sara Cordes. (2018) Children’s understanding of fraction and decimal symbols and the notation-specific relation to pre-algebra ability. Journal of Experimental Child Psychology 168, pages 32-48.
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Michelle Hurst & Sara Cordes. (2018) A systematic investigation of the link between rational number processing and algebra ability. British Journal of Psychology 109:1, pages 99-117.
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Jessica P. Bishop, Lisa L. Lamb, Randolph A. Philipp, Ian Whitacre & Bonnie P. Schappelle. 2018. Exploring the Integer Addition and Subtraction Landscape. Exploring the Integer Addition and Subtraction Landscape 47 71 .
Jo Van Hoof, Lieven Verschaffel, Pol Ghesquière & Wim Van Dooren. (2017) The natural number bias and its role in rational number understanding in children with dyscalculia. Delay or deficit?. Research in Developmental Disabilities 71, pages 181-190.
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Christopher M. Walick & Matthew K. Burns. (2017) A Proposed Algebra Assessment for Use in a Problem-Analysis Framework. Assessment for Effective Intervention 42:3, pages 150-159.
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Jo Van Hoof, Xenia Vamvakoussi, Wim Van Dooren & Lieven Verschaffel. 2017. Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts. Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts 101 123 .
David C. Geary, Daniel B. Berch, Robert J. Ochsendorf & Kathleen Mann Koepke. 2017. Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts. Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts 1 18 .
Andreas Obersteiner, Jo Van Hoof, Lieven Verschaffel & Wim Van Dooren. (2016) Who can escape the natural number bias in rational number tasks? A study involving students and experts. British Journal of Psychology 107:3, pages 537-555.
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Craig Pournara, Jeremy Hodgen, Yvonne Sanders & Jill Adler. (2016) Learners’ errors in secondary algebra: Insights from tracking a cohort from Grade 9 to Grade 11 on a diagnostic algebra test. Pythagoras 37:1.
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Spencer Bagley & Jeffrey M. Rabin. (2015) Students’ Use of Computational Thinking in Linear Algebra. International Journal of Research in Undergraduate Mathematics Education 2:1, pages 83-104.
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Konstantinos P. Christou. (2015) Natural number bias in operations with missing numbers. ZDM 47:5, pages 747-758.
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Xenia Vamvakoussi. (2015) The development of rational number knowledge: Old topic, new insights. Learning and Instruction 37, pages 50-55.
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Melissa DeWolf & Stella Vosniadou. (2015) The representation of fraction magnitudes and the whole number bias reconsidered. Learning and Instruction 37, pages 39-49.
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Jo Van Hoof, Jolien Vandewalle, Lieven Verschaffel & Wim Van Dooren. (2015) In search for the natural number bias in secondary school students' interpretation of the effect of arithmetical operations. Learning and Instruction 37, pages 30-38.
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Kelly Trezise & Robert A. Reeve. (2014) Working memory, worry, and algebraic ability. Journal of Experimental Child Psychology 121, pages 120-136.
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Jessica Pierson Bishop, Lisa L. Lamb, Randolph A. Philipp, Ian Whitacre, Bonnie P. Schappelle & Melinda L. Lewis. (2014) Obstacles and Affordances for Integer Reasoning: An Analysis of Children's Thinking and the History of Mathematics. Journal for Research in Mathematics Education 45:1, pages 19-61.
Crossref
Dina Tirosh & Pessia Tsamir. 2014. Encyclopedia of Mathematics Education. Encyclopedia of Mathematics Education 325 330 .

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