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Original Article

Spontaneous Focusing on Quantitative Relations in the Development of Children's Fraction Knowledge

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Sanne Rathé, Joke Torbeyns, Bert De Smedt & Lieven Verschaffel. (2022) Spontaneous focusing on Arabic number symbols: A unique component of children’s early mathematical development?. Mathematical Thinking and Learning 24:1, pages 38-51.
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Sanne Rathé, Joke Torbeyns, Bert De Smedt & Lieven Verschaffel. (2020) Spontaneous focusing on Arabic number symbols: A unique component of children’s early mathematical development?. Mathematical Thinking and Learning 22:4, pages 281-295.
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Patricia A. Alexander, Hongyang Zhao & Yuting Sun. (2020) Spontaneous focusing on what and why? What children’s imprecise responses reveal about their mathematical thinking and relational reasoning. Mathematical Thinking and Learning 22:4, pages 332-350.
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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.
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Minna M. Hannula-Sormunen, Erno Lehtinen & Pekka Räsänen. (2015) Preschool Children’s Spontaneous Focusing on Numerosity, Subitizing, and Counting Skills as Predictors of Their Mathematical Performance Seven Years Later at School. Mathematical Thinking and Learning 17:2-3, pages 155-177.
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Articles from other publishers (30)

Anne-Sophie Supply, Nore Wijns, Wim Van Dooren & Patrick Onghena. (2022) It is probably a pattern: does spontaneous focusing on regularities in preschool predict reasoning about randomness four years later?. Educational Studies in Mathematics 112:1, pages 3-24.
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Hilma Halme, Kelly Trezise, Minna M. Hannula-Sormunen & Jake McMullen. (2022) Characterizing mathematics anxiety and its relation to performance in routine and adaptive tasks. Journal of Numerical Cognition 8:3, pages 414-429.
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Hilma Halme, Jake McMullen, Cristina E. Nanu, Anna Nyman & Minna M. Hannula-Sormunen. (2022) Mathematical skills of 11-year-old children born very preterm and full-term. Journal of Experimental Child Psychology 219, pages 105390.
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Elien Vanluydt, Lieven Verschaffel & Wim Van Dooren. (2022) The role of relational preference in word-problem solving in 6- to 7-year-olds. Educational Studies in Mathematics 110:3, pages 393-411.
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Jake McMullen, Minna M. Hannula‐Sormunen, Erno Lehtinen & Robert S. Siegler. (2021) Predicting adaptive expertise with rational number arithmetic. British Journal of Educational Psychology 92:2, pages 688-706.
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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.
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E. Vanluydt, L. Verschaffel & W. Van Dooren. (2022) The role of relational preference in early proportional reasoning. Learning and Individual Differences 93, pages 102108.
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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.
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Richard Prather. (2020) Arithmetic knowledge from the spontaneous attention to relations. Developmental Science 24:1.
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Minna Hannula-Sormunen, Jake McMullen & Erno Lehtinen. 2021. Heterogeneous Contributions to Numerical Cognition. Heterogeneous Contributions to Numerical Cognition 207 227 .
Yuan Liang, Lijin Zhang, Chunling Wang & Yujuan Liu. (2020) Performance patterns and strategy use in number line estimation among preschool children with different spontaneous focusing on numerosity tendencies. Infant and Child Development 30:1.
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Nore Wijns, Bert De Smedt, Lieven Verschaffel & Joke Torbeyns. (2019) Are preschoolers who spontaneously create patterns better in mathematics?. British Journal of Educational Psychology 90:3, pages 753-769.
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Franzis Preckel, Jessika Golle, Roland Grabner, Linda Jarvin, Aaron Kozbelt, Daniel Müllensiefen, Paula Olszewski-Kubilius, Wolfgang Schneider, Rena Subotnik, Miriam Vock & Frank C. Worrell. (2020) Talent Development in Achievement Domains: A Psychological Framework for Within- and Cross-Domain Research. Perspectives on Psychological Science 15:3, pages 691-722.
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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 .
Maria Mellone, Anna Baccaglini-Frank & Francesca Martignone. 2020. Mathematics Education in the Early Years. Mathematics Education in the Early Years 161 176 .
Jasmin Perez & Koleen McCrink. (2019) Measuring Spontaneous Focus on Space in Preschool Children. Frontiers in Psychology 10.
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Bruce Brown. (2019) Rational number understanding: The big picture, not the essence. South African Journal of Childhood Education 9:1.
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Pirjo Aunio, Markku Niemivirta & Mari Tervaniemi. 2019. Shaping Future Schools with Digital Technology. Shaping Future Schools with Digital Technology 165 178 .
Minna M. Hannula-Sormunen, Jake McMullen & Erno Lehtinen. 2019. International Handbook of Mathematical Learning Difficulties. International Handbook of Mathematical Learning Difficulties 25 42 .
Jake McMullen, Jenny Yun-Chen Chan, Michèle M. M. Mazzocco & Minna M. Hannula-Sormunen. 2019. Constructing Number. Constructing Number 69 86 .
Yingyi Liu. (2018) Fraction magnitude understanding and its unique role in predicting general mathematics achievement at two early stages of fraction instruction. British Journal of Educational Psychology 88:3, pages 345-362.
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Joanne Mulligan, Lieven Verschaffel, Anna Baccaglini-Frank, Alf Coles, Peter Gould, Shengqing He, Yunpeng Ma, Jasmina Milinković, Andreas Obersteiner, Nicole Roberts, Nathalie Sinclair, Yanling Wang, Shu Xie & Der-Ching Yang. 2018. Building the Foundation: Whole Numbers in the Primary Grades. Building the Foundation: Whole Numbers in the Primary Grades 137 167 .
Jake McMullen, Minna M. Hannula-Sormunen & Erno Lehtinen. (2017) Spontaneous focusing on quantitative relations as a predictor of rational number and algebra knowledge. Contemporary Educational Psychology 51, pages 356-365.
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Erno Lehtinen, Minna Hannula-Sormunen, Jake McMullen & Hans Gruber. (2017) Cultivating mathematical skills: from drill-and-practice to deliberate practice. ZDM 49:4, pages 625-636.
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Anna Shusterman, Pierina Cheung, Jessica Taggart, Ilona Bass, Talia Berkowitz, Julia A. Leonard & Ariel Schwartz. (2017) Conceptual correlates of counting: Children’s spontaneous matching and tracking of large sets reflects their knowledge of the cardinal principle. Journal of Numerical Cognition 3:1, pages 1-30.
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Sarah A. Gray & Robert A. Reeve. (2016) Number-specific and general cognitive markers of preschoolers’ math ability profiles. Journal of Experimental Child Psychology 147, pages 1-21.
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Ingemar Holgersson, Wolmet Barendregt, Jonas Emanuelsson, Torgny Ottosson, Elisabeth Rietz & Berner Lindström. 2016. International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives. International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives 123 145 .
Jake McMullen, Minna M. Hannula-Sormunen & Erno Lehtinen. (2015) Preschool spontaneous focusing on numerosity predicts rational number conceptual knowledge 6 years later. ZDM 47:5, pages 813-824.
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Bruce Brown. (2015) The relational nature of rational numbers. Pythagoras 36:1.
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Wim Van Dooren, Erno Lehtinen & Lieven Verschaffel. (2015) Unraveling the gap between natural and rational numbers. Learning and Instruction 37, pages 1-4.
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