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.


1. Ann Senghas, Sotaro Kita, and Asli Özyürek, “Children Creating Core Properties of Language: Evidence from an Emerging Sign Language in Nicaragua,” Science 305, no. 5691 (2004): 1779–1782.

2. Michiel P. van Oeffelen and Peter G. Vos, “A Probabilistic Model for the Discrimination of Visual Number,” Perception and Psychophysics 32, no. 2 (1982): 163–170; and Elise Temple and Michael I. Posner, “Brain Mechanisms of Quantity Are Similar in 5-Year-Old Children and Adults,” Proceedings of the National Academy of Sciences 95, no. 13 (1998): 7836–7841.

3. Elizabeth M. Brannon, “The Development of Ordinal Numerical Knowledge in Infancy,” Cognition 83, no. 3 (2002): 223–240; and Fei Xu and Elizabeth S. Spelke, “Large Number Discrimination in 6-Month-Old Infants,” Cognition 74, no. 1 (2000): B1–B11.

4. Elizabeth M. Brannon and Herbert S. Terrace, “Ordering of the Numerosities 1 to 9 by Monkeys,” Science 282, no. 5389 (1998): 746–749.

5. Warren H. Meck and Russell M. Church, “A Mode Control Model of Counting and Timing Processes,” Journal of Experimental Psychology: Animal Behavior Processes 9, no. 3 (1983): 320–334.

6. Lisa Feigenson, Susan Carey, and Marc Hauser, “The Representations Underlying Infants’ Choice of More: Object Files versus Analog Magnitudes,” Psychological Science 13, no. 2 (2002): 150–156.

7. Marc D. Hauser, Susan Carey, and Lilan B. Hauser, “Spontaneous Number Representation in Semi-Free-Ranging Rhesus Monkeys,” Proceedings of the Royal Society of London, B: Biological Sciences 267, no. 1445 (2000): 829–833.

8. Lana M. Trick and Zenon W. Pylyshyn, “Why Are Small and Large Numbers Enumerated Differently? A Limited-Capacity Preattentive Stage in Vision,” Psychological Review 101, no. 1 (1994): 80–102.

9. Arthur L. Benton, “Gerstmann’s Syndrome,” Archives of Neurology 49, no. 5 (1992): 445–447.

10. André Knops et al., “Recruitment of an Area Involved in Eye Movements during Mental Arithmetic,” Science 324, no. 5934 (2009): 1583–1585.

11. Daniel B. Berch et al., “Extracting Parity and Magnitude from Arabic Numerals: Developmental Changes in Number Processing and Mental Representation,” Journal of Experimental Child Psychology 74, no. 4 (1999): 286–308.

12. Stanislas Dehaene, Serge Bossini, and Pascal Giraux, “The Mental Representation of Parity and Number Magnitude,” Journal of Experimental Psychology: General 122, no. 3 (1993): 371–396.

13. Pierre Pica et al., “Exact and Approximate Arithmetic in an Amazonian Indigene Group,” Science 306, no. 5695 (2004): 499–503.

14. Stanislas Dehaene et al., “Log or Linear? Distinct Intuitions of the Number Scale in Western and Amazonian Indigene Cultures,” Science 320, no. 5880 (2008): 1217–1220.

15. Julie L. Booth and Robert S. Siegler, “Developmental and Individual Differences in Pure Numerical Estimation,” Developmental Psychology 42, no. 1 (2006): 189–201; Robert S. Siegler and Julie L. Booth, “Development of Numerical Estimation in Young Children,” Child Development 75, no. 2 (2004): 428–444; and Robert S. Siegler and John E. Opfer, “The Development of Numerical

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

16. Mark A. Changizi et al., “The Structures of Letters and Symbols throughout Human History Are Selected to Match Those Found in Objects in Natural Scenes,” American Naturalist 167, no. 5 (2006): E117–E139.

17. Stanislas Dehaene and Laurent Cohen, “Cultural Recycling of Cortical Maps,” Neuron 56, no. 2 (2007): 384–398.

18. Kerry Lee, Ee Lynn Ng, and Swee Fong Ng, “The Contributions of Working Memory and Executive Functioning to Problem Representation and Solution Generation in Algebraic Word Problems,” Journal of Educational Psychology 101, no. 2 (2009): 373–387.

19. Steven A. Hecht, “Counting on Working Memory in Simple Arithmetic When Counting Is Used for Problem Solving,” Memory and Cognition 30, no. 3 (2002): 447–455; Stuart T. Klapp et al., “Automatizing Alphabet Arithmetic: II. Are There Practice Effects after Automaticity Is Achieved?” Journal of Experimental Psychology: Learning, Memory, and Cognition 17, no. 2 (1991): 196–209; and Loel N. Tronsky, “Strategy Use, the Development of Automaticity, and Working Memory Involvement in Complex Multiplication,” Memory and Cognition 33, no. 5 (2005): 927–940.

20. Susan R. Goldman and James W. Pellegrino, “Information Processing and Educational Microcomputer Technology: Where Do We Go from Here? Journal of Learning Disabilities 20, no. 3 (1987): 144–154; and Ted S. Hasselbring, Laura Goin, and John D. Bransford, “Developing Math Automaticity in Learning Handicapped Children: The Role of Computerized Drill and Practice,” Focus on Exceptional Children 20, no. 6 (1988): 1–7.

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.

22. Ulf Andersson, “Mathematical Competencies in Children with Different Types of Learning Difficulties,” Journal of Educational Psychology 100, no. 1 (2008): 48–66; and Robert L. Russell and Herbert P. Ginsburg, “Cognitive Analysis of Children’s Mathematical Difficulties,” Cognition and Instruction 1, no. 2 (1984): 217–244.

23. James M. Royer and Loel N. Tronsky, “Addition Practice with Math Disabled Students Improves Subtraction and Multiplication Performance,” in Advances in Learning and Behavioral Disabilities, ed. Margo A. Mastropieri and Thomas E. Scruggs (Greenwich, CT: JAI Press, 1996), 12:185–217; and Nelly Tournaki, “The Differential Effects of Teaching Addition through Strategy Instruction versus Drill and Practice to Students With and Without Learning Disabilities,” Journal of Learning Disabilities 36, no. 5 (2003): 449–458.

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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