An integrative theory of numerical development

Child Development Perspectives

Volumn 8, Issue 3, 2014, Pages 144-150

  Siegler, Robert S ^a   Lortie Forgues, Hugues ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

Fractions; Mathematical development; Negative numbers; Number line; Numerical development; Numerical magnitudes

Indexed keywords

EID: 84906243485     PISSN: 17508592     EISSN: 17508606     Source Type: Journal    
DOI: 10.1111/cdep.12077     Document Type: Article

References (42)

1. Ashcraft, M. H. (1982). The development of mental arithmetic: A chronometric approach. Developmental Review, 2, 213-236. doi:10.1016/0273-2297(82)90012-0
2. Bailey, D. H., Hoard, M. K., Nugent, L., & Geary, D. C. (2012). Competence with fractions predicts gains in mathematics achievement. Journal of Experimental Child Psychology, 113, 447-455. doi:10.1016/j.jecp.2012.06.004
3. Bailey, D. H., Siegler, R. S., & Geary, D. C. (2014). Early predictors of middle school fraction knowledge. Developmental Science. Advance online publication. doi:10.1111/desc.12155
4. Bertelletti, I., Lucangeli, D., Piazza, M., Dehaene, S., & Zorzi, M. (2010). Numerical estimation in preschoolers. Developmental Psychology, 46, 545-551. doi:10.1037/a0017887
5. Booth, J. L., & Siegler, R. S. (2006). Developmental and individual differences in pure numerical estimation. Developmental Psychology, 42, 189-201. doi:10.1037/0012-1649.41.6.189
6. Booth, J. L., & Siegler, R. S. (2008). Numerical magnitude representations influence arithmetic learning. Child Development, 79, 1016-1031. doi:10.1111/j.1467-8624.2008.01173.x
7. Chen, Q., & Li, J. (2014). Association between individual differences in non-symbolic number acuity and math performance: A meta-analysis. Acta Psychologica, 148, 163-172. doi:10.1016/j.actpsy.2014.01.016
8. De Smedt, B., Noël, M. P., Gilmore, C., & Ansari, D. (2013). How do symbolic and non-symbolic numerical magnitude processing relate to individual differences in children's mathematical skills? A review of evidence from brain and behaviour. Trends in Neuroscience and Education, 2, 48-55. doi:10.1016/j.tine.2013.06.001
9. DeWolf, M., Grounds, M. A., Bassok, M., & Holyoak, K. J. (2014). Magnitude comparison with different types of rational numbers. Journal of Experimental Psychology: Human Perception and Performance, 40, 71-82. doi:10.1037/a0032916
10. Fazio, L. K., Bailey, D. H., Thompson, C. A., & Siegler, R. S. (2014). Relations of different types of numerical magnitude representations to each other and to mathematics achievement. Journal of Experimental Child Psychology, 123, 53-72. doi:10.1016/j.jecp.2014.01.013
11. Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8, 307-314. doi:10.1016/j.tics.2004.05.002
12. Fuchs, L. S., Schumacher, R. F., Long, J., Namkung, J., Hamlett, C. L., Cirino, P. T., ... Changas, P. (2013). Improving at-risk learners' understanding of fractions. Journal of Educational Psychology, 105, 683-700. doi:10.1037/a0032446
13. Fuchs, L. S., Schumacher, R. F., Sterba, S. K., Long, J., Namkung, J., Malone, A., ... Changas, P. (2014). Does working memory moderate the effects of fraction intervention? An aptitude-treatment interaction. Journal of Educational Psychology, 106, 499-514. doi:10.1037/a0034341
14. Ganor-Stern, D., Pinhas, M., Kallai, A., & Tzelgov, J. (2010). Holistic representation of negative numbers is formed when needed for the task. Quarterly Journal of Experimental Psychology, 63, 1969-1981. doi:10.1080/17470211003721667
15. Geary, D. C., Hoard, M. K., Byrd-Craven, J., Nugent, L., & Numtee, C. (2007). Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. Child Development, 78, 1343-1359. doi:10.1111/j.1467-8624.2007.01069.x
16. Göbel, S. M., Watson, S. E., Lervåg, A., & Hulme, C. (2014). Children's arithmetic development: It is number knowledge, not the approximate number sense, that counts. Psychological Science, 25, 789-798. doi:10.1177/0956797613516471
17. Gullick, M. M., & Wolford, G. (2013). Understanding less than nothing: Children's neural response to negative numbers shifts across age and accuracy. Frontiers in Psychology, 4, 584. doi:10.3389/fpsyg.2013.00584
18. Gullick, M. M., Wolford, G., & Temple, E. (2012). Understanding less than nothing: Neural distance effects for negative numbers. Neuroimage, 62, 542-554. doi:10.1016/j.neuroimage.2012.04.058
19. Halberda, J., & Feigenson, L. (2008). Developmental change in the acuity of the "number sense": The approximate number system in 3-, 4-, 5-, and 6-year-olds and adults. Developmental Psychology, 44, 1457-1465. doi:10.1037/A0012682
20. Halberda, J., Mazzocco, M. M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlates with math achievement. Nature, 455, 665-668. doi:10.1038/Nature07246
21. Ischebeck, A., Schocke, M., & Delazer, M. (2009). The processing and representation of fractions within the brain: An fMRI investigation. NeuroImage, 47, 403-413. doi:10.1016/S1053-8119(09)70693-7
22. Jacob, S. N., & Nieder, A. (2009). Notation-independent representation of fractions in the human parietal cortex. Journal of Neuroscience, 29, 4652-4657. doi:10.1523/jneurosci.0651-09.2009
23. Le Corre, M., Van de Walle, G., Brannon, E. M., & Carey, S. (2006). Re-visiting the competence/performance debate in the acquisition of the counting principles. Cognitive Psychology, 52, 130-169. doi:10.1016/j.cogpsych.2005.07.002
24. Lemaire, P., & Siegler, R. S. (1995). Four aspects of strategic change: Contributions to children's learning of multiplication. Journal of Experimental Psychology: General, 124, 83-97. doi:10.1037/0096-3445.124.1.83
25. Libertus, M., Feigenson, L., & Halberda, J. (2011). Preschool acuity of the approximate number system correlates with school math ability. Developmental Science, 14, 1292-1300. doi:10.1111/j.1467-7687.2011.01080.x
26. Mazzocco, M. M., Feigenson, L., & Halberda, J. (2011). Preschoolers' precision of the approximate number system predicts later school mathematics performance. PLoS One, 6, e23749. doi:10.1371/journal.pone.0023749
27. McCrink, K., & Wynn, K. (2007). Ratio abstraction by 6-month-old infants. Psychological Science, 18, 740-745. doi:10.1111/j.1467-9280.2007.01969.x
28. Meert, G., Grégoire, J., & Noël, M.-P. (2009). Rational numbers: Componential versus holistic representation of fractions in a magnitude comparison task. Quarterly Journal of Experimental Psychology, 62, 1598-1616. doi:10.1080/17470210802511162
29. Moyer, R. S., & Landauer, T. K. (1967). Time required for judgments of numerical inequality. Nature, 215, 1519-1520. doi:10.1038/2151519a0
30. Piazza, M., Facoetti, A., Trussardi, A. N., Berteletti, I., Conte, S., Lucangeli, D., ... Zorzi, M. (2010). Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition, 116, 33-41. doi:10.1016/j.cognition.2010.03.012
31. Piazza, M., Pinel, P., Le Bihan, D., & Dehaene, S. (2007). A magnitude code common to numerosities and number symbols in human intraparietal cortex. Neuron, 53, 293-305. doi:10.1016/j.neuron.2006.11.022
32. Ramani, G. B., & Siegler, R. S. (2008). Promoting broad and stable improvements in low-income children's numerical knowledge through playing number board games. Child Development, 79, 375-394. doi:10.1111/j.1467-8624.2007.01131.x
33. Schaeffer, B., Eggleston, V. H., & Scott, J. L. (1974). Number development in young children. Cognitive Psychology, 6, 357-379. doi:10.1016/0010-0285(74)90017-6
34. Schneider, M., & Siegler, R. S. (2010). Representations of the magnitudes of fractions. Journal of Experimental Psychology: Human Perception and Performance, 36, 1227-1238. doi:10.1037/a0018170
35. Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75, 428-444. doi:10.1111/j.1467-8624.2004.00684.x
36. Siegler, R. S., & Opfer, J. (2003). The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14, 237-243. doi:10.1111/1467-9280.02438
37. Siegler, R. S., & Pyke, A. A. (2013). Developmental and individual differences in understanding fractions. Developmental Psychology, 49, 1994-2004. doi:10.1037/a0031200
38. Siegler, R. S., & Ramani, G. B. (2009). Playing linear number board games-but not circular ones-improves low-income preschoolers' numerical understanding. Journal of Educational Psychology, 101, 545-560. doi:10.1037/a0014239
39. Siegler, R. S., Thompson, C. A., & Schneider, M. (2011). An integrated theory of whole number and fractions development. Cognitive Psychology, 62, 273-296. doi:10.1016/j.cogpsych.2011.03.001
40. Starr, A., Libertus, M. E., & Brannon, E. M. (2013). Number sense in infancy predicts mathematical abilities in childhood. Proceedings of the National Academy of Sciences of the United States of America, 110, 18116-18120. doi:10.1073/pnas.1302751110
41. VanMarle, K., Chu, F. W., Li, Y., & Geary, D. C. (2014). Acuity of the approximate number system and preschoolers' quantitative development. Developmental Science. Advance online publication. doi:10.1111/desc.12143
42. Wood, J. N., & Spelke, E. S. (2005). Infants' enumeration of actions: Numerical discrimination and its signature limits. Developmental Science, 8, 173-181. doi:10.1111/j.1467-7687.2005.00404.x