Advanced search
Publication Cover
Educational Psychologist Volume 40, 2005 - Issue 1
Submit an article Journal homepage
3,525
Views
369
CrossRef citations to date
0
Altmetric
Original Articles

Teaching and Learning Fraction and Rational Numbers: The Origins and Implications of Whole Number Bias

Yujing Ni
&
Yong-Di Zhou
Pages 27-52 | Published online: 08 Jun 2010

Citations (369)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (45)

Pernille Ladegaard Pedersen, Pirjo Aunio, Pernille Bødtker Sunde, Mette Bjerre & Rasmus Waagepetersen. (2023) Differences in High- and Low-Performing Students’ Fraction Learning in the Fourth Grade. The Journal of Experimental Education 91:4, pages 636-654.
Read now
Margaret M. Flores, Vanessa M. Hinton, Laura Shadoan & Callye Monroe. (2023) Teaching rational number concepts and skills to students receiving tier two interventions. The Journal of Educational Research 0:0, pages 1-10.
Read now
Cecilia Björkhammer, Joakim Samuelsson, Ulf Träff & Rickard Östergren. (2023) The effects of a whole-class mathematics intervention on students’ fraction knowledge in primary school. Scandinavian Journal of Educational Research 0:0, pages 1-15.
Read now
Katja Lenz, Frank Reinhold & Gerald Wittmann. (2022) Topic specificity of students’ conceptual and procedural fraction knowledge and its impact on errors. Research in Mathematics Education 0:0, pages 1-25.
Read now
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.
Read now
Juan Manuel González-Forte, Ceneida Fernández, Jo Van Hoof & Wim Van Dooren. (2022) Profiles in understanding operations with rational numbers. Mathematical Thinking and Learning 24:3, pages 230-247.
Read now
Ofer Marmur, Ion Moutinho & Rina Zazkis. (2022) On the density of ℚ in ℝ: Imaginary dialogues scripted by undergraduate students. International Journal of Mathematical Education in Science and Technology 53:6, pages 1297-1325.
Read now
Antje Boomgaarden, Katharina Loibl & Timo Leuders. (2022) The trade-off between complexity and accuracy. Preparing for computer-based adaptive instruction on fractions. Interactive Learning Environments 0:0, pages 1-16.
Read now
Sheunghyun Yeo & Corey Webel. (2022) Elementary students’ fraction reasoning: a measurement approach to fractions in a dynamic environment. Mathematical Thinking and Learning 0:0, pages 1-27.
Read now
Terhi Vessonen, Airi Hakkarainen, Eija Väisänen, Anu Laine, Pirjo Aunio & Joseph Calvin Gagnon. (2021) Differential Effects of Virtual and Concrete Manipulatives in a Fraction Intervention on Fourth and Fifth Grade Students’ Fraction Skills. Investigations in Mathematics Learning 13:4, pages 323-337.
Read now
Jo Van Hoof, Anne-Sophie Engelen & Wim Van Dooren. (2021) How robust are learners’ misconceptions of fraction magnitude? An intervention study comparing the use of refutation and expository text. Educational Psychology 41:5, pages 524-543.
Read now
Yingying Yang & Wei He. (2021) Four- to six-year-olds’ ratio reasoning-from 2D to 3D quantities. Thinking & Reasoning 27:2, pages 212-238.
Read now
Jing Tian, Victoria Bartek, Maya Z. Rahman & Elizabeth A. Gunderson. (2021) Learning Improper Fractions with the Number Line and the Area Model. Journal of Cognition and Development 22:2, pages 305-327.
Read now
Pooja G. Sidney, Clarissa A. Thompson, Charles Fitzsimmons & Jennifer M. Taber. (2021) Children’s and Adults’ Math Attitudes Are Differentiated by Number Type. The Journal of Experimental Education 89:1, pages 1-32.
Read now
Xinchen Fu, Xiaodong Li, Ping Xu & Jie Zeng. (2020) Inhibiting the Whole Number Bias in a Fraction Comparison Task: An Event-Related Potential Study. Psychology Research and Behavior Management 13, pages 245-255.
Read now
Meghna Soni & Yukari Okamoto. (2020) Improving children’s fraction understanding through the use of number lines. Mathematical Thinking and Learning 22:3, pages 233-243.
Read now
Ofer Marmur, Xiaoheng Yan & Rina Zazkis. (2020) Fraction images: the case of six and a half. Research in Mathematics Education 22:1, pages 22-47.
Read now
Sergio Morra, Elisa Bisagno, Sara Caviola, Chiara Delfante & Irene Cristina Mammarella. (2019) Working Memory Capacity and the Development of Quantitative Central Conceptual Structures. Cognition and Instruction 37:4, pages 483-511.
Read now
Alison T. Miller Singley & Silvia A. Bunge. (2018) Eye gaze patterns reveal how we reason about fractions. Thinking & Reasoning 24:4, pages 445-468.
Read now
Der-Ching Yang. (2018) Study of fractions in elementary mathematics textbooks from Finland and Taiwan. Educational Studies 44:2, pages 190-211.
Read now
Kim A. Cheek, Nicole D. LaDue & Thomas F. Shipley. (2017) Learning About Spatial and Temporal Scale: Current Research, Psychological Processes, and Classroom Implications. Journal of Geoscience Education 65:4, pages 455-472.
Read now
Tine Degrande, Lieven Verschaffel & Wim Van Dooren. (2017) Spontaneous Focusing on Quantitative Relations: Towards a Characterization. Mathematical Thinking and Learning 19:4, pages 260-275.
Read now
Paulo Barraza, Rodrigo Avaria & Ivo Leiva. (2017) The role of attentional networks in the access to the numerical magnitude of fractions in adults / El rol de las redes atencionales en el acceso a la magnitud numérica de fracciones en adultos. Studies in Psychology 38:2, pages 495-522.
Read now
Mikko Kainulainen, Jake McMullen & Erno Lehtinen. (2017) Early Developmental Trajectories Toward Concepts of Rational Numbers. Cognition and Instruction 35:1, pages 4-19.
Read now
Sarah J. Watt & William J. Therrien. (2016) Examining a Preteaching Framework to Improve Fraction Computation Outcomes Among Struggling Learners. Preventing School Failure: Alternative Education for Children and Youth 60:4, pages 311-319.
Read now
Jessica Heather Hunt, Ron Tzur & Arla Westenskow. (2016) Evolution of Unit Fraction Conceptions in Two Fifth-Graders with a Learning Disability: An Exploratory Study. Mathematical Thinking and Learning 18:3, pages 182-208.
Read now
Anja Ischebeck, Marina Weilharter & Christof Körner. (2016) Eye movements reflect and shape strategies in fraction comparison. The Quarterly Journal of Experimental Psychology 69:4, pages 713-727.
Read now
Tim Heemsoth & Aiso Heinze. (2016) Secondary School Students Learning From Reflections on the Rationale Behind Self-Made Errors: A Field Experiment. The Journal of Experimental Education 84:1, pages 98-118.
Read now
Jessica M. Tsang, Kristen P. Blair, Laura Bofferding & Daniel L. Schwartz. (2015) Learning to “See” Less Than Nothing: Putting Perceptual Skills to Work for Learning Numerical Structure. Cognition and Instruction 33:2, pages 154-197.
Read now
Stella Vosniadou. (2014) Examining cognitive development from a conceptual change point of view: The framework theory approach. European Journal of Developmental Psychology 11:6, pages 645-661.
Read now
Jake McMullen, Minna M. Hannula-Sormunen & Erno Lehtinen. (2014) Spontaneous Focusing on Quantitative Relations in the Development of Children's Fraction Knowledge. Cognition and Instruction 32:2, pages 198-218.
Read now
Carl Bereiter. (2014) Principled Practical Knowledge: Not a Bridge but a Ladder. Journal of the Learning Sciences 23:1, pages 4-17.
Read now
Yujing Ni, Dehui Zhou, Xiaoqing Li & Qiong Li. (2014) Relations of Instructional Tasks to Teacher–Student Discourse in Mathematics Classrooms of Chinese Primary Schools. Cognition and Instruction 32:1, pages 2-43.
Read now
H. Van Steenbrugge, E. Lesage, M. Valcke & A. Desoete. (2014) Preservice elementary school teachers’ knowledge of fractions: a mirror of students’ knowledge?. Journal of Curriculum Studies 46:1, pages 138-161.
Read now
Jo Van Hoof, Tristan Lijnen, Lieven Verschaffel & Wim Van Dooren. (2013) Are secondary school students still hampered by the natural number bias? A reaction time study on fraction comparison tasks. Research in Mathematics Education 15:2, pages 154-164.
Read now
Chunhui Liu, Ziqiang Xin, Chongde Lin & Clarissa A. Thompson. (2013) Children’s mental representation when comparing fractions with common numerators. Educational Psychology 33:2, pages 175-191.
Read now
Sara Fabbri, Sara Caviola, Joey Tang, Marco Zorzi & Brian Butterworth. (2012) The role of numerosity in processing nonsymbolic proportions. The Quarterly Journal of Experimental Psychology 65:12, pages 2435-2446.
Read now
Gaëlle Meert, Jacques Grégoire, Xavier Seron & Marie-Pascale Noël. (2012) The mental representation of the magnitude of symbolic and nonsymbolic ratios in adults. The Quarterly Journal of Experimental Psychology 65:4, pages 702-724.
Read now
Meixia Ding, Xiaobao Li, Mary Margaret Capraro & Gerald Kulm. (2012) A Case Study of Teacher Responses to a Doubling Error and Difficulty in Learning Equivalent Fractions. Investigations in Mathematics Learning 4:2, pages 42-73.
Read now
Konstantinos P. Christou & Stella Vosniadou. (2012) What Kinds of Numbers Do Students Assign to Literal Symbols? Aspects of the Transition from Arithmetic to Algebra. Mathematical Thinking and Learning 14:1, pages 1-27.
Read now
Teresa Iuculano & Brian Butterworth. (2011) Understanding the real value of fractions and decimals. The Quarterly Journal of Experimental Psychology 64:11, pages 2088-2098.
Read now
GeoffreyL. Herman, Craig Zilles & MichaelC. Loui. (2011) How do students misunderstand number representations?. Computer Science Education 21:3, pages 289-312.
Read now
Xenia Vamvakoussi & Stella Vosniadou. (2010) How Many Decimals Are There Between Two Fractions? Aspects of Secondary School Students’ Understanding of Rational Numbers and Their Notation. Cognition and Instruction 28:2, pages 181-209.
Read now
Gaëlle Meert, Jacques Grégoire & Marie-Pascale Noël. (2009) Rational numbers: Componential versus holistic representation of fractions in a magnitude comparison task. The Quarterly Journal of Experimental Psychology 62:8, pages 1598-1616.
Read now
Joseph Tzelgov, Dana Ganor-Stern & Keren Maymon-Schreiber. (2009) The representation of negative numbers: Exploring the effects of mode of processing and notation. The Quarterly Journal of Experimental Psychology 62:3, pages 605-624.
Read now

Articles from other publishers (324)

Daniel Fitousi & Ran Noyman. (2024) Why fractions are difficult? Modeling optimal and sub-optimal integration strategies of numerators and denominators by educated adults. Cognition 242, pages 105656.
Crossref
Pooja G. Sidney, Julie F. Shirah, Jessica Blake & Amanda L. Kruczkowski. (2023) Adaptive variability in children’s conceptual models of division. Journal of Experimental Child Psychology 236, pages 105743.
Crossref
Karen De Keersmaeker, Jo Van Hoof & Wim Van Dooren. (2022) The relationship between primary school children’s inhibition and the processing of rational numbers. European Journal of Psychology of Education 38:4, pages 1527-1549.
Crossref
Charles J. Fitzsimmons, Lauren Woodbury, Jennifer M. Taber, Lauren K. Schiller, Marta K. Mielicki, Pooja G. Sidney, Karin G. Coifman & Clarissa A. Thompson. (2023) Visual display size and shape impact the accuracy of US adults' health‐risk estimates. Journal of Behavioral Decision Making 36:5.
Crossref
Karrie E. Godwin, Clarissa A. Thompson, Freya Kaur, Yuika Iwai, Charles J. Fitzsimmons & Jennifer M. Taber. (2023) Attending to what’s important: what heat maps may reveal about attention, inhibitory control, and fraction arithmetic performance. Frontiers in Psychology 14.
Crossref
Paul T. Cirino. (2023) Framing Executive Function as a Construct and its Relation to Academic Achievement. Mind, Brain, and Education 17:4, pages 226-237.
Crossref
Karina Hamamouche & Sara Cordes. (2023) Winning or losing: Children’s proportional reasoning across motivational contexts. Cognitive Development 68, pages 101390.
Crossref
Pooja G. Sidney & Julie F. Shirah. (2023) Surface-to-structure shifts in rational number categories. Cognitive Development 68, pages 101386.
Crossref
Lauren K. Schiller & Robert S. Siegler. (2023) Integrated knowledge of rational number notations predicts children’s math achievement and understanding of numerical magnitudes. Cognitive Development 68, pages 101380.
Crossref
Frank Reinhold, Timo Leuders & Katharina Loibl. (2023) Disentangling magnitude processing, natural number biases, and benchmarking in fraction comparison tasks: A person-centered Bayesian classification approach. Contemporary Educational Psychology 75, pages 102224.
Crossref
Juan Manuel González-Forte, Ceneida Fernández, Jo Van Hoof & Wim Van Dooren. (2022) Incorrect Ways of Thinking About the Size of Fractions. International Journal of Science and Mathematics Education 21:7, pages 2005-2025.
Crossref
Lesenia R. Fish, Lindsey Hildebrand, Nadia Chernyak & Sara Cordes. (2023) Who's the winner? Children's math learning in competitive and collaborative scenarios. Child Development 94:5, pages 1239-1258.
Crossref
Konstantinos P. Christou & Xenia Vamvakoussi. (2021) Natural number bias on evaluations of the effect of multiplication and division: the role of the type of numbers. Mathematics Education Research Journal 35:3, pages 427-443.
Crossref
Sun A. Kim, Diane P. Bryant, Brian R. Bryant, Mikyung Shin & Min Wook Ok. (2022) A Multilevel Meta-Analysis of Whole Number Computation Interventions for Students With Learning Disabilities. Remedial and Special Education 44:4, pages 332-347.
Crossref
T.M.M. Mostert & M. Hickendorff. (2023) Pizzas or no pizzas: An advantage of word problems in fraction arithmetic?. Learning and Instruction 86, pages 101775.
Crossref
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.
Crossref
Emily Bouck, Mary Bouck & Rubia D. Anderson. (2023) Teaching Fractions to Elementary Students With Learning Disabilities Using Evidence-Based Practices. Intervention in School and Clinic, pages 105345122311784.
Crossref
Megan Rojo, Sarah King, Jenna Gersib & Diane P. Bryant. (2022) Rational Number Interventions for Students With Mathematics Difficulties: A Meta-Analysis. Remedial and Special Education 44:3, pages 225-238.
Crossref
Arthur B. Powell. (2023) Enhancing students’ fraction magnitude knowledge: A study with students in early elementary education. The Journal of Mathematical Behavior 70, pages 101042.
Crossref
Roberto A. Abreu-Mendoza, Arthur B. Powell, K. Ann Renninger, Luis M. Rivera, John Vulic, Steve Weimar & Miriam Rosenberg-Lee. (2023) Middle-schoolers' misconceptions in discretized nonsymbolic proportional reasoning explain fraction biases better than their continuous reasoning: Evidence from correlation and cluster analyses. Cognitive Psychology 143, pages 101575.
Crossref
Yuan Yuan & Kuolong Chen. (2022) Whole Number Bias of Students in Fraction Number Line Tasks. International Journal of Science and Mathematics Education 21:5, pages 1433-1449.
Crossref
Parnika Bhatia, Jessica Léone, Marie-Line Gardes & Jérôme Prado. (2023) Fraction Knowledge in Adults With Persistent Mathematics Difficulties. Learning Disability Quarterly, pages 073194872311713.
Crossref
Florencia Stelzer, María Laura Andrés, Ana Comesaña, Lorena Canet-Juric & Sebastián Urquijo. (2023) Perfil cognitivo de estudiantes con diferente nivel de conocimiento de las fracciones. CES Psicología 16:2, pages 73-85.
Crossref
Jing Tian, Kexin Ren & Elizabeth A. Gunderson. (2023) Verbal labels influence children's processing of decimal magnitudes. Journal of Applied Developmental Psychology 86, pages 101537.
Crossref
Yun Pan, Jian Zhang, Changlang Zou, Mengmeng Li & Huanyu Yang. (2023) The Impact of Writing Notations and Response Types: A Spatial Representation Study on Fractions. Current Psychology 42:13, pages 10482-10497.
Crossref
Hao Wu, Yuding Zhang, Qiong Luo & Zhengzhou Zhu. (2023) The magnitude representations of fractions of Chinese students: evidence from behavioral experiment and eye-tracking. Current Psychology.
Crossref
John Ezaki, Jingxian Li & Yasemin Copur-Gencturk. (2023) Teachers’ Knowledge of Fractions, Ratios, and Proportional Relationships: the Relationship Between Two Theoretically Connected Content Areas. International Journal of Science and Mathematics Education.
Crossref
Christine Kong-Yan Tong, Eason Sai-Kit Yip & Terry Tin-Yau Wong. (2023) Examining the unique contributions and developmental stability of individual forms of relational reasoning to mathematical problem solving. Contemporary Educational Psychology 73, pages 102181.
Crossref
Megan Rojo, Sarah G. King & Christian T. Doabler. (2023) Teaching Fraction-to-Decimal Translation Using the Number Line. Intervention in School and Clinic, pages 105345122311568.
Crossref
Jimin Park, Soo-hyun Im & Sashank Varma. (2022) A language compatibility effect in fraction processing. Quarterly Journal of Experimental Psychology 76:3, pages 596-605.
Crossref
Kelsey J MacKay, Filip Germeys, Wim Van Dooren, Lieven Verschaffel & Koen Luwel. (2022) The structure of the notation system in adults’ number line estimation: An eye-tracking study. Quarterly Journal of Experimental Psychology 76:3, pages 538-553.
Crossref
Parnika Bhatia, Sarah Le Diagon, Emma Langlois, Melissa William, Jérôme Prado & Marie‐Line Gardes. (2022) Impact of a game‐based intervention on fraction learning for fifth‐grade students: A pre‐registered randomized controlled study. Journal of Computer Assisted Learning 39:1, pages 49-62.
Crossref
Emma Fisher & Minyi Shih Dennis. (2023) Supporting the Fraction Magnitude Understanding of Students With Significant Behavior Problems. Journal of Emotional and Behavioral Disorders, pages 106342662211493.
Crossref
Selcen ÇALIK UZUN & Selahattin ARSLAN. (2023) Modelling of Student Teachers’ Mathematical Conceptions According to Ck¢ Theory: The "Knowledge Transfer" ConceptionÖğretmen Adaylarının Matematiksel Anlayışlarının Ck¢ Teorisine Göre Modellenmesi: Bilgi Transferi Anlayışı. e-International Journal of Educational Research.
Crossref
Clarissa A. Thompson, Marta K. Mielicki, Ferdinand Rivera, Charles J. Fitzsimmons, Daniel A. Scheibe, Pooja G. Sidney, Lauren K. Schiller, Jennifer M. Taber & Erika A. Waters. (2022) Leveraging Math Cognition to Combat Health Innumeracy. Perspectives on Psychological Science 18:1, pages 152-177.
Crossref
Georgios Thoma, Julia Bahnmueller, Antero Lindstedt, Kristian Kiili, Silke M. Wortha, Korbinian Moeller & Manuel Ninaus. 2023. Game-Based Learning in Education and Health - Part A. Game-Based Learning in Education and Health - Part A 63 91 .
Sabrina M. Di Lonardo Burr, Chang Xu, Hongxia Li, Jiwei Si, Jo‐Anne LeFevre & Yangyang Wang. (2022) Fraction mapping and fraction comparison skills among grade 4 Chinese students: An error analysis. British Journal of Educational Psychology 92:4, pages 1335-1353.
Crossref
Daniel A. Scheibe, Charles J. Fitzsimmons, Marta K. Mielicki, Jennifer M. Taber, Pooja G. Sidney, Karin Coifman & Clarissa A. Thompson. (2022) Confidence in COVID problem solving: What factors predict adults’ item-level metacognitive judgments on health-related math problems before and after an educational intervention?. Metacognition and Learning 17:3, pages 989-1023.
Crossref
Ofer Marmur & Rina Zazkis. (2021) Productive ambiguity in unconventional representations: “what the fraction is going on?”. Journal of Mathematics Teacher Education 25:6, pages 637-665.
Crossref
Calliste Scheibling-Sève, Katarina Gvozdic, Elena Pasquinelli & Emmanuel Sander. (2022) Enhancing cognitive flexibility through a training based on multiple categorization: Developing proportional reasoning in primary school. Journal of Numerical Cognition 8:3, pages 443-472.
Crossref
Andreas Obersteiner, Martha Wagner Alibali & Vijay Marupudi. (2022) Comparing fraction magnitudes: Adults’ verbal reports reveal strategy flexibility and adaptivity, but also bias. Journal of Numerical Cognition 8:3, pages 398-413.
Crossref
Febe Demedts, Bert Reynvoet, Delphine Sasanguie & Fien Depaepe. (2022) Unraveling the role of math anxiety in students’ math performance. Frontiers in Psychology 13.
Crossref
Declan Devlin, Korbinian Moeller, Bert Reynvoet & Francesco Sella. (2022) A critical review of number order judgements and arithmetic: What do order verification tasks actually measure?. Cognitive Development 64, pages 101262.
Crossref
Andreas Demetriou, George Charilaos Spanoudis, Samuel Greiff, Nikolaos Makris, Rita Panaoura & Smaragda Kazi. (2022) Changing priorities in the development of cognitive competence and school learning: A general theory. Frontiers in Psychology 13.
Crossref
Jinqing Liu & Erik Jacobson. (2022) Examining US elementary students’ strategies for comparing fractions after the adoption of the common core state standards for mathematics. The Journal of Mathematical Behavior 67, pages 100985.
Crossref
Michelle A. Hurst & Susan C. Levine. (2022) Children's understanding of most is dependent on context. Cognition 225, pages 105149.
Crossref
Δημήτρης Φωκάς & Ξένια Βαμβακούση. (2022) Η κατανόηση της πυκνής διάταξης των ρητών από μαθητές Β΄ Λυκείου: ένα διδακτικό πείραμα. Psychology: the Journal of the Hellenic Psychological Society 27:1, pages 48-65.
Crossref
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.
Crossref
Rita Novita, Tatang Herman, Dadan Dasari & Mulia Putra. (2022) Analyzing Second-Year University Students’ Rational Number Understanding: A Case on Interpreting and Representing Fraction. European Journal of Educational Research 11:3, pages 1747-1762.
Crossref
Anastasia Dimakou, Aldo Antonio Sarubbi, Silvia Benavides‐Varela & Rosa Rugani. (2022) Are Rational Numbers Spontaneous? Natural Numbers Suffice all Processing by the Number Sense. Cognitive Science 46:7.
Crossref
Sangmi Park & Alena G. Esposito. (2022) Rational number conceptualization predicts mathematics achievement: Quantity matters. Cognitive Development 63, pages 101195.
Crossref
Marta K. Mielicki, Lauren K. Schiller, Charles J. Fitzsimmons, Daniel Scheibe & Clarissa A. Thompson. (2021) Perceptions of ease and difficulty, but not growth mindset, relate to specific math attitudes. British Journal of Educational Psychology 92:2, pages 707-729.
Crossref
Rui Pedro Campos Bento Barros Candeias, Maria Cecília Soares de Morais Monteiro & Mária Cristina Ribeiro Correia de Almeida. (2022) Os números racionais no ensino primário em Portugal (1930-1974). Zetetike 30, pages e022011.
Crossref
Chang Xu, Hongxia Li, Sabrina Di Lonardo Burr, Jiwei Si, Jo-Anne LeFevre & Bijuan Huang. (2022) Divide and conquer: Relations among arithmetic operations and emerging knowledge of fraction notation for Chinese students in Grade 4. Journal of Experimental Child Psychology 217, pages 105371.
Crossref
Tomi Kärki, Jake McMullen & Erno Lehtinen. (2021) Improving rational number knowledge using the NanoRoboMath digital game. Educational Studies in Mathematics 110:1, pages 101-123.
Crossref
Pooja G. Sidney, Julie F. Shirah, Lauren Zahrn & Clarissa A. Thompson. (2022) Diagrams support spontaneous transfer across whole number and fraction concepts. Contemporary Educational Psychology 69, pages 102066.
Crossref
Saku Määttä, Minna Hannula-Sormunen, Hilma Halme & Jake McMullen. (2022) Guiding students’ attention towards multiplicative relations around them: A classroom intervention. Journal of Numerical Cognition 8:1, pages 36-52.
Crossref
Isabella Starling‐Alves, Matthew R. Wronski & Edward M. Hubbard. (2021) Math anxiety differentially impairs symbolic, but not nonsymbolic, fraction skills across development. Annals of the New York Academy of Sciences 1509:1, pages 113-129.
Crossref
Nathan T. T. Lau, Eric D. Wilkey, Mojtaba Soltanlou, Rebekka Lagacé Cusiac, Lien Peters, Paul Tremblay, Celia Goffin, Isabella Starling Alves, Andrew David Ribner, Clarissa Thompson, Jo Van Hoof, Julia Bahnmueller, Aymee Alvarez, Elien Bellon, Ilse Coolen, Fanny Ollivier & Daniel Ansari. (2022) Numeracy and COVID-19: examining interrelationships between numeracy, health numeracy and behaviour. Royal Society Open Science 9:3.
Crossref
Robert S. Siegler. 2022. The Cambridge Handbook of Cognitive Development. The Cambridge Handbook of Cognitive Development 361 382 .
David Muñez, Rebecca Bull, Pierina Cheung & Josetxu Orrantia. (2022) Non-symbolic Ratio Reasoning in Kindergarteners: Underlying Unidimensional Heuristics and Relations With Math Abilities. Frontiers in Psychology 13.
Crossref
Michelle A. Hurst, Alyson Wong, Raychel Gordon, Aziza Alam & Sara Cordes. (2022) Children’s gesture use provides insight into proportional reasoning strategies. Journal of Experimental Child Psychology 214, pages 105277.
Crossref
Boby Ho-Hong Ching & Kenneth Hong Cheng Kong. (2022) Development of children's informal understanding of division through sharing: Contributions of reasoning demands and problem situations. Early Childhood Research Quarterly 59, pages 228-242.
Crossref
Charles J. Fitzsimmons & Clarissa A. Thompson. (2022) Developmental differences in monitoring accuracy and cue use when estimating whole-number and fraction magnitudes. Cognitive Development 61, pages 101148.
Crossref
Paul T. Cirino, Tammy D. Tolar & Lynn S. Fuchs. (2022) Domain general and specific contributions to algebra: A sequenced longitudinal path model. Contemporary Educational Psychology 68, pages 102026.
Crossref
Robert S. Siegler & Jing Tian. 2022. 1 33 .
Antje Boomgaarden, Timo Leuders & Katharina Loibl. 2022. Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik 227 243 .
Terezinha Nunes & Peter Bryant. 2022. Quantitative Reasoning in Mathematics and Science Education. Quantitative Reasoning in Mathematics and Science Education 71 105 .
Silke M. Wortha, Andreas Obersteiner & Thomas Dresler. 2022. Handbook of Cognitive Mathematics. Handbook of Cognitive Mathematics 289 315 .
Metin BEŞALTI & Ümit KUL. (2021) Effects of a Game-Based app on Primary Students’ Self Efficacy and Achievements in Learning Fractions During Distance EducationUzaktan Eğitim Sürecinde Oyun Tabanlı Bir Uygulamanın İlkokul Öğrencilerinin Kesirleri Öğrenmede Öz-yeterlik ve Başarılarına Olan Etkisi. Türk Psikolojik Danışma ve Rehberlik Dergisi 11:63, pages 505-520.
Crossref
Ahmad Zamri Khairani & Hasni Shamsuddin. (2021) Application of Rasch Measurement Model in Developing Calibrated Item Pool for the Topic of Rational Numbers. Eurasia Journal of Mathematics, Science and Technology Education 17:12, pages em2056.
Crossref
Huomin MAO, Qin LIU, Jianxiang LÜ & Yi MOU. (2022) The relation between non-symbolic magnitude representation and symbolic fraction representation. Advances in Psychological Science 29:12, pages 2161-2171.
Crossref
Yang Jiang, Tao Gong, Luis E. Saldivia, Gabrielle Cayton-Hodges & Christopher Agard. (2021) Using process data to understand problem-solving strategies and processes for drag-and-drop items in a large-scale mathematics assessment. Large-scale Assessments in Education 9:1.
Crossref
Yunji Park & Percival G. Matthews. (2021) Revisiting and refining relations between nonsymbolic ratio processing and symbolic math achievement. Journal of Numerical Cognition 7:3, pages 328-350.
Crossref
Benjamin Shongwe. (2021) Early career teacher’s approach to fraction equivalence in Grade 4: A dialogic teaching perspective. Pythagoras 42:1.
Crossref
Pingting Lin, Yanmei Zhu, Xinlin Zhou, Yi Bai & Haixian Wang. (2021) Neural Dissociations between Magnitude Processing of Fractions and Decimals. Neural Dissociations between Magnitude Processing of Fractions and Decimals.
Methuseli Moyo & France M. Machaba. (2021) Grade 9 learners’ understanding of fraction concepts: Equality of fractions, numerator and denominator. Pythagoras 42:1.
Crossref
Xin Lin & Sarah R. Powell. (2021) Examining the relation between whole numbers and fractions: A meta-analytic structural equation modeling approach. Contemporary Educational Psychology 67, pages 102017.
Crossref
Linsah Coulanges, Roberto A. Abreu-Mendoza, Sashank Varma, Melina R. Uncapher, Adam Gazzaley, Joaquin Anguera & Miriam Rosenberg-Lee. (2021) Linking inhibitory control to math achievement via comparison of conflicting decimal numbers. Cognition 214, pages 104767.
Crossref
Kailun Qiu & Yunqi Wang. (2020) Conceptual distinctions and preferential alignment across rational number representations. European Journal of Psychology of Education 36:3, pages 865-881.
Crossref
Clarissa A. Thompson, Jennifer M. Taber, Charles J. Fitzsimmons & Pooja G. Sidney. (2021) Math predictors of numeric health and non-health decision-making problems. Journal of Numerical Cognition 7:2, pages 221-239.
Crossref
Boby Ho-Hong Ching & Hannah Xiaohan Wu. (2021) Young children's knowledge of fair sharing as an informal basis for understanding division: A latent profile analysis. Learning and Instruction 73, pages 101460.
Crossref
Lois George & Chronoula Voutsina. (2021) Variations in Partitive Quotient Strategy Use by Children Who Have Been Taught the Part-Whole Fraction Sub-construct. Canadian Journal of Science, Mathematics and Technology Education 21:2, pages 400-423.
Crossref
Roberto A. Abreu-Mendoza, Linsah Coulanges, Kendell Ali, Arthur B. Powell & Miriam Rosenberg-Lee. (2021) From Non-symbolic to Symbolic Proportions and Back: A Cuisenaire Rod Proportional Reasoning Intervention Enhances Continuous Proportional Reasoning Skills. Frontiers in Psychology 12.
Crossref
Selami ERCAN & Döndü Gamze AKTAŞ. (2021) MATEMATİK ÖĞRETMENLERİNİN VE ÖĞRENCİLERİNİN KESİR VE RASYONEL SAYI KAVRAMINA AİT TANIMLAMALARI. Milli Eğitim Dergisi 50:230, pages 279-300.
Crossref
Jonté A. Myers, Mary T. Brownell, Cynthia C. Griffin, Elizabeth M. Hughes, Bradley S. Witzel, Nicolas A. Gage, David Peyton, Kelly Acosta & Jun Wang. (2021) Mathematics Interventions for Adolescents with Mathematics Difficulties: A Meta‐Analysis. Learning Disabilities Research & Practice 36:2, pages 145-166.
Crossref
Yunji Park, Alexandria A. Viegut & Percival G. Matthews. (2020) More than the sum of its parts: Exploring the development of ratio magnitude versus simple magnitude perception. Developmental Science 24:3.
Crossref
Emily Szkudlarek & Elizabeth M. Brannon. (2021) First and Second Graders Successfully Reason About Ratios With Both Dot Arrays and Arabic Numerals. Child Development 92:3, pages 1011-1027.
Crossref
Pernille Ladegaard Pedersen & Mette Bjerre. (2021) Two conceptions of fraction equivalence. Educational Studies in Mathematics 107:1, pages 135-157.
Crossref
Jiwon Hwang & Paul J. Riccomini. (2019) A Descriptive Analysis of the Error Patterns Observed in the Fraction-Computation Solution Pathways of Students With and Without Learning Disabilities. Assessment for Effective Intervention 46:2, pages 132-142.
Crossref
Elena Vysotskaya, Anastasia Lobanova, Iya Rekhtman & Maria Yanishevskaya. (2020) The challenge of proportion: does it require rethinking of the measurement paradigm?. Educational Studies in Mathematics 106:3, pages 429-446.
Crossref
Kexin Ren & Elizabeth A. Gunderson. (2021) The dynamic nature of children’s strategy use after receiving accuracy feedback in decimal comparisons. Journal of Experimental Child Psychology 202, pages 105015.
Crossref
Santiago Alonso-Díaz & Gabriel I. Penagos-Londoño. (2021) The numerator bias exists in millions of real-world comparisons. Acta Psychologica 213, pages 103248.
Crossref
Sarah R. Powell & Gena Nelson. (2020) University students' misconceptions about rational numbers: Implications for developmental mathematics and instruction of younger students. Psychology in the Schools 58:2, pages 307-331.
Crossref
May R. Berenbaum. (2021) On COVID-19, cognitive bias, and open access. Proceedings of the National Academy of Sciences 118:2.
Crossref
David Maximiliano Gómez. (2021) Non-symbolic and symbolic number and the approximate number system. Behavioral and Brain Sciences 44.
Crossref
Stella Vosniadou. 2021. Heterogeneous Contributions to Numerical Cognition. Heterogeneous Contributions to Numerical Cognition 95 115 .
Grégoire Borst. 2021. Heterogeneous Contributions to Numerical Cognition. Heterogeneous Contributions to Numerical Cognition 27 43 .
Miriam Rosenberg-Lee. 2021. Heterogeneous Contributions to Numerical Cognition. Heterogeneous Contributions to Numerical Cognition 143 180 .
David Maximiliano Gómez & Nicolás Morales. 2021. Mathematical Reasoning of Children and Adults. Mathematical Reasoning of Children and Adults 69 93 .
Silke M. Wortha, Andreas Obersteiner & Thomas Dresler. 2021. Handbook of Cognitive Mathematics. Handbook of Cognitive Mathematics 1 27 .
Silke M. Wortha, Andreas Obersteiner & Thomas Dresler. 2021. Handbook of Cognitive Mathematics. Handbook of Cognitive Mathematics 1 27 .
Christophe Lembregts & Jorge Pena‐Marin. (2020) Numbers and Units Affect Goal Pursuit Organization and Motivation. Journal of Consumer Psychology 31:1, pages 37-54.
Crossref
Robert S. Siegler, Soo-hyun ImLauren K. SchillerJing TianDavid W. Braithwaite. (2020) The Sleep of Reason Produces Monsters: How and When Biased Input Shapes Mathematics Learning. Annual Review of Developmental Psychology 2:1, pages 413-435.
Crossref
Sabrina M. Di Lonardo Burr, Heather Douglas, Maria Vorobeva & Kasia Muldner. (2020) Refuting misconceptions: Computer tutors for fraction arithmetic. Journal of Numerical Cognition 6:3, pages 355-377.
Crossref
Jennifer A. Kaminski & Vladimir M. Sloutsky. (2020) The use and effectiveness of colorful, contextualized, student-made material for elementary mathematics instruction. International Journal of STEM Education 7:1.
Crossref
Silke M. Wortha, Johannes Bloechle, Manuel Ninaus, Kristian Kiili, Antero Lindstedt, Julia Bahnmueller, Korbinian Moeller & Elise Klein. (2020) Neurofunctional plasticity in fraction learning: An fMRI training study. Trends in Neuroscience and Education 21, pages 100141.
Crossref
Hyewon Chang. (2020) A Study on the Method of Introducing Improper Fractions and Mixed Numbers Using Additions. Journal of Educational Research in Mathematics 30:4, pages 733-750.
Crossref
Frank Reinhold, Sarah Isabelle Hofer, Stefan Hoch, Bernhard Werner, Jürgen Richter-Gebert & Kristina Reiss. (2020) Digital support principles for sustained mathematics learning in disadvantaged students. PLOS ONE 15:10, pages e0240609.
Crossref
Jo Van Hoof, Lieven Verschaffel, Wim De Neys & Wim Van Dooren. (2020) Intuitive errors in learners’ fraction understanding: A dual-process perspective on the natural number bias. Memory & Cognition 48:7, pages 1171-1180.
Crossref
Nadia Chernyak, Vanessa Turnbull, Raychel Gordon, Paul L. Harris & Sara Cordes. (2020) Counting promotes proportional moral evaluation in preschool-aged children. Cognitive Development 56, pages 100969.
Crossref
Pooja G. Sidney. (2020) Children’s learning from implicit analogies during instruction: Evidence from fraction division. Cognitive Development 56, pages 100956.
Crossref
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.
Crossref
Yingyi Liu & Terry Tin‐Yau Wong. (2019) The growth rates of dot enumeration ability predict mathematics achievements: A 5‐year longitudinal study. British Journal of Educational Psychology 90:3, pages 604-617.
Crossref
Emily C. Bouck, Jiyoon Park, Katie Cwiakala & Abbie Whorley. (2019) Learning Fraction Concepts Through the Virtual-Abstract Instructional Sequence. Journal of Behavioral Education 29:3, pages 519-542.
Crossref
Juan Manuel González-Forte, Ceneida Fernández, Jo Van Hoof & Wim Van Dooren. (2019) Various ways to determine rational number size: an exploration across primary and secondary education. European Journal of Psychology of Education 35:3, pages 549-565.
Crossref
Lu Zhang, Junjie Shang, Tim Pelton & Leslee Francis Pelton. (2020) Supporting primary students' learning of fraction conceptual knowledge through digital games. Journal of Computer Assisted Learning 36:4, pages 540-548.
Crossref
Charles J. Fitzsimmons, Clarissa A. Thompson & Pooja G. Sidney. (2020) Confident or familiar? The role of familiarity ratings in adults’ confidence judgments when estimating fraction magnitudes. Metacognition and Learning 15:2, pages 215-231.
Crossref
Mihwa Park, Minju Yi, Raymond Flores & Bangtam Nguyen. (2020) Informal Formative Assessment Conversations in Mathematics: Focusing on Preservice Teachers’ Initiation, Response and Follow-up Sequences in the Classroom. Eurasia Journal of Mathematics, Science and Technology Education 16:10, pages em1884.
Crossref
Nancy I. Dyson, Nancy C. Jordan, Jessica Rodrigues, Christina Barbieri & Luke Rinne. (2018) A Fraction Sense Intervention for Sixth Graders With or At Risk for Mathematics Difficulties. Remedial and Special Education 41:4, pages 244-254.
Crossref
Wu-Yuin Hwang, Ika Qutsiati Utami, Siska Wati Dewi Purba & Holly S. L. Chen. (2020) Effect of Ubiquitous Fraction App on Mathematics Learning Achievements and Learning Behaviors of Taiwanese Students in Authentic Contexts. IEEE Transactions on Learning Technologies 13:3, pages 530-539.
Crossref
Priya B. Kalra, John V. Binzak, Percival G. Matthews & Edward M. Hubbard. (2020) Symbolic fractions elicit an analog magnitude representation in school-age children. Journal of Experimental Child Psychology 195, pages 104844.
Crossref
Priya B. Kalra, Edward M. Hubbard & Percival G. Matthews. (2020) Taking the relational structure of fractions seriously: Relational reasoning predicts fraction knowledge in elementary school children. Contemporary Educational Psychology 62, pages 101896.
Crossref
Safa ÖZALTUN, Dönsel DANACI & Keziban ORBAY. (2020) Altıncı Sınıf Öğrencilerinin Kesirler Konusundaki Kavram Yanılgılarını Belirleme Testi ve Bir Uygulaması. Uluslararası Alan Eğitimi Dergisi 6:1, pages 175-200.
Crossref
Nicolás Morales, Pablo Dartnell & David Maximiliano Gómez. (2020) A Study on Congruency Effects and Numerical Distance in Fraction Comparison by Expert Undergraduate Students. Frontiers in Psychology 11.
Crossref
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.
Crossref
Vana A. Avgerinou & Andrew Tolmie. (2019) Inhibition and cognitive load in fractions and decimals. British Journal of Educational Psychology 90:S1, pages 240-256.
Crossref
Eve Kikas, Kaja Mädamürk & Anu Palu. (2019) What role do comprehension‐oriented learning strategies have in solving math calculation and word problems at the end of middle school?. British Journal of Educational Psychology 90:S1, pages 105-123.
Crossref
Andreas Obersteiner, Martha Wagner Alibali & Vijay Marupudi. (2020) Complex fraction comparisons and the natural number bias: The role of benchmarks. Learning and Instruction 67, pages 101307.
Crossref
John V. Binzak & Edward M. Hubbard. (2020) No calculation necessary: Accessing magnitude through decimals and fractions. Cognition 199, pages 104219.
Crossref
Shaun O'Grady & Fei Xu. (2019) The Development of Nonsymbolic Probability Judgments in Children. Child Development 91:3, pages 784-798.
Crossref
Frank Reinhold, Andreas Obersteiner, Stefan Hoch, Sarah Isabelle Hofer & Kristina Reiss. (2020) The Interplay Between the Natural Number Bias and Fraction Magnitude Processing in Low-Achieving Students. Frontiers in Education 5.
Crossref
Terry Tin-Yau Wong. (2020) Are the acuities of magnitude representations of different types and ranges of numbers related? Testing the core assumption of the integrated theory of numerical development. Cognitive Development 54, pages 100888.
Crossref
Hea-Jin Lee & Irina Boyadzhiev. (2020) Underprepared College Students’ Understanding of and Misconceptions with Fractions. International Electronic Journal of Mathematics Education 15:3.
Crossref
Y Yulia, E Musdi, J Afriadi & I Wahyuni. (2020) Developing a hypothetical learning trajectory of fraction based on RME for junior high school. Journal of Physics: Conference Series 1470:1, pages 012015.
Crossref
Frank Reinhold, Stefan Hoch, Bernhard Werner, Jürgen Richter-Gebert & Kristina Reiss. (2020) Learning fractions with and without educational technology: What matters for high-achieving and low-achieving students?. Learning and Instruction 65, pages 101264.
Crossref
Jake McMullen & Jo Van Hoof. (2020) The role of rational number density knowledge in mathematical development. Learning and Instruction 65, pages 101228.
Crossref
Justin K. Dimmel & Eric A. Pandiscio. 2020. Borders in Mathematics Pre-Service Teacher Education. Borders in Mathematics Pre-Service Teacher Education 21 45 .
Lieven Verschaffel, Sanne Rathé, Nore Wijns, Tine Degrande, Wim van Dooren, Bert De Smedt & Joke Torbeyns. 2020. Mathematics Education in the Early Years. Mathematics Education in the Early Years 23 42 .
Sandrine Rossi, Julie Vidal, Marie Letang, Olivier Houdé & Grégoire Borst. (2019) Adolescents and adults need inhibitory control to compare fractions. Journal of Numerical Cognition 5:3, pages 314-336.
Crossref
Armando Paulino Preciado Babb. 2019. Handbook of Research on Integrating Computer Science and Computational Thinking in K-12 Education. Handbook of Research on Integrating Computer Science and Computational Thinking in K-12 Education 45 68 .
Veena Paliwal & Angela C. Fain. 2019. Special Education Design and Development Tools for School Rehabilitation Professionals. Special Education Design and Development Tools for School Rehabilitation Professionals 1 20 .
Jessica Rodrigues, Nancy C. Jordan & Nicole Hansen. (2019) Identifying Fraction Measures as Screeners of Mathematics Risk Status. Journal of Learning Disabilities 52:6, pages 480-497.
Crossref
Taajah Felder Witherspoon. (2019) Fifth graders’ understanding of fractions on the number line. School Science and Mathematics 119:6, pages 340-352.
Crossref
Bruce Brown. (2019) Rational number understanding: The big picture, not the essence. South African Journal of Childhood Education 9:1.
Crossref
Jiwon Hwang & Paul J. Riccomini. (2019) Investigating the relationship between solution pathway preference and accuracy of adding fractions for students with learning disabilities. British Journal of Special Education 46:3, pages 361-378.
Crossref
Lillian Ham & Elizabeth A. Gunderson. (2019) Utilizing analogical reasoning to aid children’s proportional reasoning understanding. Journal of Numerical Cognition 5:2, pages 140-157.
Crossref
Stephanie Morano, Paul J. Riccomini & Joo‐Young Lee. (2019) Accuracy of Area Model and Number Line Representations of Fractions for Students with Learning Disabilities. Learning Disabilities Research & Practice 34:3, pages 133-143.
Crossref
Katharina Loibl & Timo Leuders. (2019) How to make failure productive: Fostering learning from errors through elaboration prompts. Learning and Instruction 62, pages 1-10.
Crossref
David W. Braithwaite, Elena R. Leib, Robert S. Siegler & Jake McMullen. (2019) Individual differences in fraction arithmetic learning. Cognitive Psychology 112, pages 81-98.
Crossref
David Maximiliano Gómez & Pablo Dartnell. (2018) Middle Schoolers’ Biases and Strategies in a Fraction Comparison Task. International Journal of Science and Mathematics Education 17:6, pages 1233-1250.
Crossref
Marie Björk. (2019) Transforming a practice-based problem into research questions. International Journal for Lesson and Learning Studies 8:3, pages 244-255.
Crossref
Stephanie Denison & Fei Xu. (2019) Infant Statisticians: The Origins of Reasoning Under Uncertainty. Perspectives on Psychological Science 14:4, pages 499-509.
Crossref
Michelle A. Hurst & Sara Cordes. (2019) Talking about proportion: Fraction labels impact numerical interference in non‐symbolic proportional reasoning. Developmental Science 22:4.
Crossref
Xu Hua Sun. (2018) Bridging whole numbers and fractions: problem variations in Chinese mathematics textbook examples. ZDM 51:1, pages 109-123.
Crossref

Displaying 200 of 369 citing articles. Use the download link below to view the full list of citing articles.

Download full citations list

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.