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Original Articles

Evidence for Use of Mathematical Inversion By Three-Year-Old Children

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Pages 333-344 | Published online: 05 Sep 2008

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Read on this site (7)

Koleen McCrink, Patrick Shafto & Hilary Barth. (2017) The relationship between non-symbolic multiplication and division in childhood. The Quarterly Journal of Experimental Psychology 70:4, pages 686-702.
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Meixia Ding. (2016) Opportunities to Learn: Inverse Relations in U.S. and Chinese Textbooks. Mathematical Thinking and Learning 18:1, pages 45-68.
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RebeccaP. D. Watchorn, Jeffrey Bisanz, Lisa Fast, Jo-Anne LeFevre, Sheri-Lynn Skwarchuk & BrendaL. Smith-Chant. (2014) Development of Mathematical Knowledge in Young Children: Attentional Skill and the Use of Inversion. Journal of Cognition and Development 15:1, pages 161-180.
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Marja van den Heuvel-Panhuizen & Adri Treffers. (2009) Mathe-Didactical Reflections on Young Children's Understanding and Application of Subtraction-Related Principles. Mathematical Thinking and Learning 11:1-2, pages 102-112.
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Michael Schneider & Elsbeth Stern. (2009) The Inverse Relation of Addition and Subtraction: A Knowledge Integration Perspective. Mathematical Thinking and Learning 11:1-2, pages 92-101.
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CamillaK. Gilmore & Marietta Papadatou-Pastou. (2009) Patterns of Individual Differences in Conceptual Understanding and Arithmetical Skill: A Meta-Analysis. Mathematical Thinking and Learning 11:1-2, pages 25-40.
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Jeffrey Bisanz, RebeccaP. D. Watchorn, Carley Piatt & Jody Sherman. (2009) On “Understanding” Children's Developing Use of Inversion. Mathematical Thinking and Learning 11:1-2, pages 10-24.
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Articles from other publishers (22)

Chi-Chuan Chen, Selim Jang, Manuela Piazza & Daniel C. Hyde. (2023) Characterizing exact arithmetic abilities before formal schooling. Cognition 238, pages 105481.
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Boby Ho-Hong Ching. (2023) Inhibitory control and visuospatial working memory contribute to 5-year-old children's use of quantitative inversion. Learning and Instruction 83, pages 101714.
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Dazhi Cheng, Mengyi Li, Jiaxin Cui, Li Wang, Naiyi Wang, Liangyuan Ouyang, Xiaozhuang Wang, Xuejun Bai & Xinlin Zhou. (2022) Algebra dissociates from arithmetic in the brain semantic network. Behavioral and Brain Functions 18:1.
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Amélie Lubin, Laetitia Kana, Nelly Ducloy, Florence Delteil, Hervé Perdry & Yann Mikaeloff. (2022) Do children with mathematical learning disabilities use the inversion principle to solve three-term arithmetic problems?: The impact of presentation mode. Journal of Experimental Child Psychology 216, pages 105343.
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Conilius Chagwiza, Lillias Hamufari & Gladys Sunzuma*. (2021) Exploring Zimbabwean A-Level Mathematics Learners’ Understanding of the Determinant Concept. European Journal of Mathematics and Science Education 2:2, pages 85-100.
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Boby Ho-Hong Ching & Xiaohan Wu. (2019) Concreteness fading fosters children's understanding of the inversion concept in addition and subtraction. Learning and Instruction 61, pages 148-159.
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Katherine M. Robinson. 2019. Mathematical Learning and Cognition in Early Childhood. Mathematical Learning and Cognition in Early Childhood 165 185 .
David W. Braithwaite, Jing Tian & Robert S. Siegler. (2018) Do children understand fraction addition?. Developmental Science 21:4, pages e12601.
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Jie Liu, Han Zhang, Chuansheng Chen, Hui Chen, Jiaxin Cui & Xinlin Zhou. (2017) The neural circuits for arithmetic principles. NeuroImage 147, pages 432-446.
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Nicole M. McNeil, Caroline Byrd Hornburg, Mary Wagner Fuhs & Connor D. O'Rear. 2017. Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts. Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts 167 195 .
Katherine M. Robinson. 2017. Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts. Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts 21 46 .
Adam K. Dubé & Rhonda N. McEwen. (2015) Do gestures matter? The implications of using touchscreen devices in mathematics instruction. Learning and Instruction 40, pages 89-98.
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Matthew Inglis. (2015) Review of APOS Theory: A Framework for Research and Curriculum Development in Mathematics Education, Arnon et al. (2014). New York, NY, USA: Springer-Verlag New York. eBook ISBN: 978-1-4614-7966-6, Hardcover ISBN: 978-1-4614-7965-9. International Journal of Research in Undergraduate Mathematics Education 1:3, pages 413-417.
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Amélie Lubin, Sandrine Rossi, Nicolas Poirel, Céline Lanoë, Arlette Pineau & Olivier Houdé. (2015) The Role of Self-Action in 2-Year-Old Children: An Illustration of the Arithmetical Inversion Principle before Formal Schooling. Child Development Research 2015, pages 1-7.
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Melissa M. Kibbe & Lisa Feigenson. (2015) Young children ‘solve for x ’ using the Approximate Number System . Developmental Science 18:1, pages 38-49.
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Adam K. Dubé. (2014) Adolescents' understanding of inversion and associativity. Learning and Individual Differences 36, pages 49-59.
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Noelle M. Crooks & Martha W. Alibali. (2014) Defining and measuring conceptual knowledge in mathematics. Developmental Review 34:4, pages 344-377.
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Katherine M. Robinson & Adam K. Dubé. (2013) Children's additive concepts: Promoting understanding and the role of inhibition. Learning and Individual Differences 23, pages 101-107.
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Michael Schneider. (2011) Commentary 2: knowledge integration in mathematics learning: the case of inversion. Educational Studies in Mathematics 79:3, pages 447-453.
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Katherine M. Robinson & Jo-Anne LeFevre. (2011) The inverse relation between multiplication and division: Concepts, procedures, and a cognitive framework. Educational Studies in Mathematics 79:3, pages 409-428.
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Katherine M. Robinson & Adam K. Dubé. (2009) Children’s understanding of addition and subtraction concepts. Journal of Experimental Child Psychology 103:4, pages 532-545.
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Katherine M. Robinson & Adam K. Dubé. (2009) Children's understanding of the inverse relation between multiplication and division. Cognitive Development 24:3, pages 310-321.
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