Numerical landmarks are useful-except when they're not

Journal of Experimental Child Psychology

Volumn 120, Issue 1, 2014, Pages 39-58

  Siegler, Robert S ^a,b   Thompson, Clarissa A ^c  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b BEIJING NORMAL UNIVERSITY   (China)

^c UNIVERSITY OF OKLAHOMA   (United States)

Author keywords

Encoding; Estimation; Fractions; Landmarks; Numerical magnitudes; Verbal reports

Indexed keywords

ACHIEVEMENT; ARTICLE; CHILD; CHILD BEHAVIOR; COGNITION; CONCEPT FORMATION; EDUCATION; ENCODING; ESTIMATION; FEMALE; FRACTIONS; HUMAN; LANDMARKS; MALE; MATHEMATICS; METHODOLOGY; NUMERICAL MAGNITUDES; PHYSIOLOGY; PSYCHOLOGICAL ASPECT; STATISTICS; VERBAL REPORTS;

ENCODING; ESTIMATION; FRACTIONS; LANDMARKS; NUMERICAL MAGNITUDES; VERBAL REPORTS;

ACHIEVEMENT; CHILD; CHILD BEHAVIOR; COGNITION; CONCEPT FORMATION; EDUCATIONAL MEASUREMENT; FEMALE; HUMANS; MALE; MATHEMATICS;

EID: 84891092456     PISSN: 00220965     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jecp.2013.11.014     Document Type: Article

References (57)

1. Ansari D. Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience 2008, 9:278-291.
2. Ashcraft M.H., Moore A.M. Cognitive processes of numerical estimation in children. Journal of Experimental Child Psychology 2012, 111:246-267.
3. Barth H.C., Paladino A.M. The development of numerical estimation: Evidence against a representational shift. Developmental Science 2011, 14:125-135.
4. Bastable V., Murray M., Bloomfield K., Russell S.J., Schifter D., Cochran K., et al. Investigations in number, data, and space: An innovative approach to teaching and group learning mathematics 2012, Pearson, New York.
5. Berch D.B., Foley E.J., Hill R.J., Ryan P.M. Extracting parity and magnitude from Arabic numerals: Developmental changes in number processing and mental representation. Journal of Experimental Child Psychology 1999, 74:286-308.
6. Bonato M., Fabbri S., Umiltà C., Zorzi M. The mental representation of numerical fractions: Real or integer?. Journal of Experimental Psychology: Human Perception and Performance 2007, 33:1410-1419.
7. Booth J.L., Siegler R.S. Developmental and individual differences in numerical estimation. Developmental Psychology 2006, 41:189-201.
8. Clearfield M.W. The role of crawling and walking experience in infant spatial memory. Journal of Experimental Child Psychology 2004, 89:214-241.
9. Cohen D.J., Blanc-Goldhammer D. Numerical bias in bounded and unbounded number line tasks. Psychonomic Bulletin & Review 2011, 18:331-338.
10. Cramer K., Henry A. Using manipulative models to build number sense for addition of fractions. National Council of Teachers of Mathematics 2002 yearbook: Making sense of fractions, ratios, and proportions 2002, 41-48. National Council of Teachers of Mathematics, Reston, VA.
11. de Hevia M.D., Spelke E.S. Number-space mapping in human infants. Psychological Science 2010, 21:653-660.
12. Dehaene S., Bossini S., Giraux P. The mental representation of parity and number magnitude. Journal of Experimental Psychology: General 1993, 122:371-396.
13. Dehaene S., Izard V., Spelke E., Pica P. Log or linear? Distinct intuitions of the number scale in Western and Amazonian indigene cultures. Science 2008, 320:1217-1220.
14. Fazio, L. K., DeWolfe, M. E., & Siegler, R. S. (2013). Strategy use and strategy choice in fraction magnitude comparison. Carnegie Mellon University. Unpublished manuscript.
15. Fuchs L.S., Schumacher R.F., Long J., Namkung J., Hamlett C.L., Cirino P.T., et al. Improving at-risk learners' understanding of fractions. Journal of Educational Psychology 2013, 105:683-700.
16. Geary D.C. Cognitive predictors of achievement growth in mathematics: A 5-year longitudinal study. Developmental Psychology 2011, 47:1539-1552.
17. Geary D.C., Hoard M.K., Byrd-Craven J., Nugent L., Numtee C. Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. Child Development 2007, 78:1343-1359.
18. Givvin K.B., Stigler J.W., Thompson B.J. What community college developmental mathematics students understand about mathematics: II. The interviews. MathAMATYC Educator 2011, 2(3):4-18.
19. Halberda J., Mazzocco M.M.M., Feigenson L. Individual differences in non-verbal number acuity correlate with math achievement. Nature 2008, 455:665-668.
20. Hecht S.A. Toward an information-processing account of individual differences in fraction skills. Journal of Educational Psychology 1998, 90:545-559.
21. Hecht S.A., Vagi K.J. Sources of group and individual differences in emerging fraction skills. Journal of Educational Psychology 2010, 102:843-858.
22. Hubbard E.M., Piazza M., Pinel P., Dehaene S. Interactions between number and space in parietal cortex. Nature Reviews Neuroscience 2005, 6:435-448.
23. Hubbard T.L., Ruppel S.E. Spatial memory averaging, the landmark attraction effect, and representational gravity. Psychological Research [Psychologische Forschung] 2000, 64:41-55.
24. Huttenlocher J., Newcombe N., Sandberg E. The coding of spatial location in young children. Cognitive Psychology 1994, 27:115-147.
25. Institute of Education Sciences Developing effective fractions instruction: A practice guide (IES Fractions Practice Guide, NCEE No. 2010-009) 2010, National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education, Washington, DC, Available from http://ies.ed.gov/ncee/wwc/publications/practiceguides.
26. Jordan N.C., Hansen N., Fuchs L.S., Siegler R.S., Gersten R., Micklos D. Developmental predictors of fraction concepts and procedures. Journal of Experimental Child Psychology 2013, 116:45-58.
27. Kloosterman P. Mathematics skills of 17-year-old students in the United States: 1978-2004. Journal for Research in Mathematics Education 2010, 41:20-51.
28. Laski E.V., Siegler R.S. Is 27 a big number? Correlational and causal connections among numerical categorization, number line estimation, and numerical magnitude comparison. Child Development 2007, 78:1723-1743.
29. Lew A.R. Looking beyond the boundaries: Time to put landmarks back on the cognitive map?. Psychological Bulletin 2011, 137:484-507.
30. Lew A.R., Bremner G., Lefkovitch L.P. The development of relational landmark use in six- to twelve-month-old infants in a spatial orientation task. Child Development 2000, 71:1179-1190.
31. Lourenco S.F., Longo M.R. General magnitude representation in human infants. Psychological Science 2010, 21:873-881.
32. Martin W.G., Strutchens M.E., Elliott P.C. The learning of mathematics 2007, National Council of Teachers of Mathematics, Reston, VA.
33. Mazzocco M.M.M., Devlin K.T. Parts and holes: Gaps in rational number sense in children with vs. without mathematical learning disability. Developmental Science 2008, 11:681-691.
34. Meert G., Gregoire J., Noel M.-P. Rational numbers: Componential versus holistic representation of fractions in a magnitude comparison task. Quarterly Journal of Experimental Psychology 2009, 62:1598-1616.
35. National Council of Teachers of Mathematics Second handbook of research on mathematics teaching and learning 2007, Author, Washington, DC.
36. National Mathematics Advisory Panel Foundations for success: The final report of the National Mathematics Advisory Panel 2008, U.S. Department of Education, Washington, DC.
37. Nieder A., Miller E.K. Analog numerical representations in Rhesus monkeys: Evidence for parallel processing. Journal of Cognitive Neuroscience 2004, 16:889-901.
38. Nuerk H.C., Kaufmann L., Zoppoth S., Willmes K. On the development of the mental number line: More, less, or never holistic with increasing age?. Developmental Psychology 2004, 40:1199-1211.
39. Opfer J.E., DeVries J.M. Representational change and magnitude estimation: Why young children can make more accurate salary comparisons than adults. Cognition 2008, 108:843-849.
40. Opfer J.E., Siegler R.S., Young C.J. The powers of noise-fitting: Reply to Barth and Paladino. Developmental Science 2011, 14:1194-1204.
41. Preacher, K. J. (2002). Calculation for the test of the difference between two independent correlation coefficients [computer software]. Available from http://quantpsy.org.
42. Rittle-Johnson B., Siegler R.S., Alibali M.W. Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology 2001, 93:346-362.
43. Santens S., Gevers W. The SNARC effect does not imply a mental number line. Cognition 2008, 108:263-270.
44. Schneider M., Grabner R.H., Paetsch J. Mental number line, number line estimation, and mathematical achievement: Their interrelations in Grades 5 and 6. Journal of Educational Psychology 2009, 101:359-372.
45. Schneider M., Heine A., Thaler V., Torbeyns J., De Smedt B., Verschaffel L., et al. A validation of eye movements as a measure of elementary school children's developing number sense. Cognitive Development 2008, 23:409-422.
46. Schneider M., Siegler R.S. Representations of the magnitudes of fractions. Journal of Experimental Psychology: Human Perception and Performance 2010, 36:1227-1238.
47. Siegler R.S., Booth J.L. Development of numerical estimation in young children. Child Development 2004, 75:428-444.
48. Siegler R.S., Fazio L.K., Bailey D.H., Zhou X. Fractions: The new frontier for theories of numerical development. Trends in Cognitive Science 2013, 17:13-19.
49. Siegler R.S., Opfer J. The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science 2003, 14:237-243.
50. Siegler R.S., Pyke A.A. Developmental and individual differences in understanding fractions. Developmental Psychology 2013, 49:1994-2004.
51. Siegler R.S., Thompson C.A., Schneider M. An integrated theory of whole number and fractions development. Cognitive Development 2011, 62:273-296.
52. Slusser E., Santiago R., Barth H. Developmental change in numerical estimation. Journal of Experimental Psychology: General 2013, 142:193-208.
53. Stigler J.W., Givvin K.B., Thompson B. What community college developmental mathematics students understand about mathematics. MathAMATYC Educator 2010, 1(3):4-16.
54. Tudusciuc O., Nieder A. Neuronal population coding of continuous and discrete quantity in the primate posterior parietal cortex. Proceedings of the National Academy of Sciences of the United States of America 2007, 104:14513-14518.
55. Tzelgov J., Ganor-Stern D., Maymon-Schreiber K. The representation of negative numbers: Exploring the effects of mode of processing and notation. Quarterly Journal of Experimental Psychology 2009, 62:605-624.
56. Zhou X.L., Chen Y., Chen C.S., Jiang T., Zhang H.C., Dong Q. Chinese kindergartens' automatic processing on numerical magnitude in Stroop-like tasks. Memory & Cognition 2007, 35:464-470.
57. Zorzi M., Priftis K., Umiltà C. Neglect disrupts the mental number line. Nature 2002, 417:138-139.