26 August 2020

References for article: Is it True That Some People Just Can’t Do Maths?

Publication: DSF Bulletin

Volume: 56 - Winter 2020

Electronic copies of the DSF Bulletin are available to DSF members. Please visit the resources page to download the publication and read the article for which these references apply.

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Estimation: Evidence for Multiple Representations of Numerical Quantity,” Psychological Science 14, no. 3 (2003): 237–243.

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21. See, for example, Robert Kail and Lynda K. Hall, “Sources of Developmental Change in Children’s Word-Problem Performance,” Journal of Educational Psychology 91, no. 4 (1999): 660–668; and H. Lee Swanson and Margaret Beebe-Frankenberger, “The Relationship between Working Memory and Mathematical Problem Solving in Children at Risk and Not at Risk for Serious Math Difficulties,” Journal of Educational Psychology 96, no. 3 (2004): 471–491.

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24. Nancy C. Jordan, Laurie B. Hanich, and David Kaplan, “Arithmetic Fact Mastery in Young Children: A Longitudinal Investigation,” Journal of Experimental Child Psychology 85, no. 2 (2003): 103–119.

25. See, for example, James Hiebert and Diana Wearne, “Instruction, Understanding, and Skill in Multidigit Addition and Subtraction,” Cognition and Instruction 14, no. 3 (1996): 251–283.

26. See, for example, Sylvia Steel and Elaine Funnell, “Learning Multiplication Facts: A Study of Children Taught by Discovery Methods in England,” Journal of Experimental Child Psychology 79, no. 1 (2001): 37–55.

27. See, for example, Hiebert and Wearne, “Instruction, Understanding, and Skill.”

28. Arthur J. Baroody, Yingying Feil, and Amanda R. Johnson, “An Alternative Reconceptualization of Procedural and Conceptual Knowledge,” Journal for Research in Mathematics Education 38, no. 2 (2007): 115–131; and Jon R. Star, “A Rejoinder Foregrounding Procedural Knowledge,” Journal for Research in Mathematics Education 38, no. 2 (2007): 132–135.

29. James P. Byrnes, “The Conceptual Basis of Procedural Learning,” Cognitive Development 7 (1992): 235–257; Katherine H. Canobi, Robert A. Reeve, and Philippa E. Pattison, “The Role of Conceptual Understanding in Children’s Addition Problem Solving,” Developmental Psychology 34, no. 5 (1998): 882–891; James A. Dixon and Colleen F. Moore, “The Developmental Role of Intuitive Principles in Choosing Mathematical Strategies,” Developmental Psychology 32, no. 2 (1996): 241–253; Hiebert and Wearne, “Instruction, Understanding, and Skill”; and Carmen Rasmussen, Elaine Ho, and Jeffrey Bisanz, “Use of the Mathematical Principle of Inversion in Young Children,” Journal of Experimental Child Psychology 85, no. 2 (2003): 89–102.

30. Douglas Frye et al., “Young Children’s Understanding of Counting and Cardinality,” Child Development 60 (1989): 1158–1171.Ask the Cognitive Scientist

31. James P. Byrnes and Barbara A. Wasik, “Role of Conceptual Knowledge in Mathematical Procedural Learning,” Developmental Psychology 27, no. 5 (1991): 777–786; Jeremy Kilpatrick, Jane Swafford, and Bradford Findell, Adding It Up: Helping Children Learn Mathematics (Washington, DC: National Academy Press, 2001); Bethany Rittle-Johnson and Martha Wagner Alibali, “Conceptual and Procedural Knowledge of Mathematics: Does One Lead to the Other?” Journal of Educational Psychology 91, no. 1 (1999): 175–189; Bethany Rittle-Johnson, Robert S. Siegler, and Martha Wagner Alibali, “Developing Conceptual Understanding and Procedural Skill in Mathematics: An Iterative Process,” Journal of Educational Psychology 93, no. 2 (2001): 346–362; and Matthew Saxton and Kadir Cakir, “Counting-On, Trading and Partitioning: Effects of Training and Prior Knowledge on Performance on Base-10 Tasks,” Child Development 77, no. 3 (2006): 767–785.

32. David C. Geary, Peter A. Frensch, and Judith G. Wiley, “Simple and Complex Mental Subtraction: Strategy Choice and Speed-of-Processing Differences in Younger and Older Adults,” Psychology and Aging 8, no. 2 (1993): 242–256; Jo-Anne LeFevre et al., “Multiple Routes to Solution of Single-Digit Multiplication Problems,” Journal of Experimental Psychology: General 125, no. 3 (1996): 284–306; and Katherine M. Robinson et al., “Stability and Change in Children’s Division Strategies,” Journal of Experimental Child Psychology 93, no. 3 (2006): 224–238.

33. David C. Geary et al., “Computational and Reasoning Abilities in Arithmetic: Cross-Generational Change in China and the United States,” Psychonomic Bulletin and Review 4, no. 3 (1997): 425–430; and David C. Geary et al., “Contributions of Computational Fluency to Cross-National Differences in Arithmetical Reasoning Abilities,” Journal of Educational Psychology 91, no. 4 (1999): 716–719.

34. Karen C. Fuson, “Conceptual Structures for Multiunit Numbers: Implications for Learning and Teaching Multidigit Addition, Subtraction, and Place Value,” Cognition and Instruction 7, no. 4 (1990): 343–403; Anke W. Blöte, Eeke van der Burg, and Anton S. Klein, “Students’ Flexibility in Solving Two-Digit Addition and Subtraction Problems: Instructional Effects,” Journal of Educational

Psychology 93, no. 3 (2001): 627–638; and Hiebert and Wearne, “Instruction, Understanding, and Skill.”

35. Xiaobao Li et al., “Sources of Differences in Children’s Understandings of Mathematical Equality: Comparative Analysis of Teacher Guides and Student Texts in China and the United States,” Cognition and Instruction 26, no. 2 (2008): 195–217.

36. Nicole M. McNeil et al., “Middle-School Students’ Understanding of the Equal Sign: The Books They Read Can’t Help,” Cognition and Instruction 24, no. 3 (2006): 367–385; and Li et al., “Sources of Differences.”

37. Rochel Gelman, “The Epigenesis of Mathematical Thinking,” Journal of Applied Developmental Psychology 21, no. 1 (2000): 27–37.

38. David H. Uttal, Kathyrn V. Scudder, and Judy S. DeLoache, “Manipulatives as Symbols: A New Perspective on the Use of Concrete Objects to Teach Mathematics,” Journal of Applied Developmental Psychology 18, no. 1 (1997): 37–54.

39. Nicole M. McNeil et al., “Should You Show Me the Money? Concrete Objects both Hurt and Help Performance on Mathematics Problems,” Learning and Instruction 19, no. 2 (2009): 171–184.

40. Susan Carey, Conceptual Change in Childhood (Cambridge, MA: MIT Press, 1985); and Kayoko Inagaki and Giyoo Hatano, “Young Children’s Spontaneous Personification as Analogy,” Child Development 58 (1987): 1013–1020.

41. Zhe Chen, “Schema Induction in Children’s Analogical Problem Solving,” Journal of Educational Psychology 91, no. 4 (1999): 703–715; and Richard E. Mayer and Mary Hegarty, “The Process of Understanding Mathematical Problems,” in The Nature of Mathematical Thinking, ed. Robert J. Sternberg and Talia Ben-Zeev (Mahwah, NJ: Erlbaum, 1996).

42. Lindsey E. Richland, Robert G. Morrison, and Keith J. Holyoak, “Children’s Development of Analogical Reasoning: Insights from Scene Analogy Problems,” Journal of Experimental Child Psychology 94, no. 3 (2006): 249–273.

43. Lindsey E. Richland, Osnat Zur, and Keith J. Holyoak, “Cognitive Supports for Analogies in the Mathematics Classroom,” Science 316, no. 5828 (2007): 1128–1129.

44. Kho Tek Hong, Yeo Shu Mei, and James Lim, The Singapore Model Method for Learning Mathematics (Singapore: PanPac, 2009

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