Implicit Learning of Arithmetic Regularities Is Facilitated by Proximal Contrast

PLoS ONE

Volumn 7, Issue 10, 2012, Pages

  Prather, Richard W ^a  

^a INDIANA UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ADULT; ARITHMETIC; ARTICLE; BRAIN FUNCTION; CONTROLLED STUDY; GRAMMAR; HUMAN; HUMAN EXPERIMENT; LANGUAGE PROCESSING; LEARNING; MENTAL TASK; NORMAL HUMAN; PROBLEM SOLVING; SCORING SYSTEM; TASK PERFORMANCE; TEMPORAL CORTEX;

ADULT; ANALYSIS OF VARIANCE; COGNITION; HUMANS; KNOWLEDGE; LEARNING; MATHEMATICS; PROBLEM SOLVING; PROBLEM-BASED LEARNING; PSYCHOMOTOR PERFORMANCE;

EID: 84868281084     PISSN: None     EISSN: 19326203     Source Type: Journal    
DOI: 10.1371/journal.pone.0048868     Document Type: Article

References (40)

1. Gelman R, Gallistel CR (1978) The Child's Understanding of Number. Cambridge, MA: Harvard University Press.
2. Dixon JA, Moore CF, (1996) The Developmental Role of Intuitive Principles in Choosing Mathematical Strategies. Developmental Psychology 32: 241-253.
3. Altmann GTM, Dienes Z, Goode A, (1995) Modality Independence of Implicitly learned grammatical knowledge. Journal of Experimental Psychology: Learning, Memory, and Cognition 21: 899-912.
4. Knowlton BJ, Squire LR, (1996) Artificial Grammar Learning Depends on Implicit Acquisition of Both Abstract and Exemplar-Specific Information. Cognition 22: 169-181.
5. Chi M, Feltovich P, Glaser R, (1982) Categorization and Representation of Physics Problems by Experts and Novices. Cognitive Science 5: 121-152.
6. Aslin RN, Saffran JR, Newport EL, (1998) Computation of conditional probability statistics by 8 month old infants. Psychological science 9: 321-324.
7. Baroody AJ, Ginsburg H (1983) Children's use of mathematical structure. Journal for Research in Mathematics Education.
8. Brush L, (1978) Preschool Children's Knowledge of Addition and Subtraction. Journal for Research in Mathematics Education 9: 44-55.
9. Canobi KH, Reeve RA, Pattison PE, (2002) Young children's understanding of addition concepts. Educational Psychology 22: 513-532.
10. Canobi KH, Reeve RA, Pattison PE, (2003) Patterns of knowledge in children's addition. Developmental Psychology 39: 521-534.
11. Cowan R, Renton E (1996) Do they know what they are doing? Children's use of economical addition strategies. Educational Psychology 16.
12. Dixon JA, Deets JK, Bangert A, (2001) The representations of the arithmetic operations include functional relationships. Memory & Cognition 29: 462-477.
13. Gilmore C, (2006) Profiles of understanding and profiles of development in early arithmetic. Sciences-New York 26: 7-12.
14. Robinson KM, Ninowski JE (2003) Adults' Understanding of Inversion Concepts: How Does Performance on Addition and Subtraction Inversion Problems Compare to Performance on Multiplication and Division Inversion Problems?: 321-330.
15. Canobi K, (2009) Concept-Procedure Interactions in addition and subtraction. Journal of Experimental Child Psychology 102: 131-149.
16. Dixon JA, Bangert AS, (2005) From regularities to concepts: the development of children's understanding of a mathematical relation. Cognitive Development 20: 65-86 doi:10.1016/j.cogdev.2004.12.001.
17. Lai M-lung, Baroody AJ, Johnson AR, (2008) Fostering Taiwanese preschoolers' understanding of the addition-subtraction inverse principle. Cognitive Development 23: 216-235 doi:10.1016/j.cogdev.2007.06.002.
18. Prather RW, Alibali MW (2011) Children's Acquisition of Arithmetic Principles: The Role of Experience. Journal of Cognition and Development 12.
19. Prather RW, Alibali MW, (2008) Understanding and using principles of arithmetic: operations involving negative numbers. Cognitive Science 32: 445-457 doi:10.1080/03640210701864147.
20. Siegler RS, Stern E, (1998) Conscious and unconscious strategy discoveries: A microgenetic analysis. Journal of Experimental Psychology-General 127: 377-397.
21. Seger CA, (1994) Implicit learning. Psychological Bulletin 115: 163-296.
22. Gomez R, Schvaneveldt R, (1994) What is learned from Artificial Grammars? Transfer Test of Simple Association. Journal of experimental psychology Learning, memory, and cognition 20: 396-410.
23. Servan-Schreiber E, Anderson JR, (1990) Learning Artificial Grammars With Competitive Chunking. Cognition 16: 592-608.
24. Tunney RJ, Altmann GTM (2001) Two Modes of Transfer in Articifical Grammar learning. Journal of Experimental Psychology: Learning, Memory, and Cognition 27.
25. Saffran JR, (2002) Constraints on Statistical Language Learning. Journal of Memory and Language 196: 172-196 doi:10.1006/jmla.2001.2839.
26. Rittle-Johnson B, Star JR (2007) Does comparison solution methods facilitate conceptual and procedural knowledge? Journal of Educational Psychology: 1-43.
27. Gentner D, Loewenstein J, Thompson L, (2003) Learning and transfer: A general role for analogical encoding. Journal of Educational Psychology 95: 393-408.
28. Karmiloff-Smith A (1992) Beyound Modularity. Cambridge, MA: MIT press.
29. Larkin J, Simon H (1987) Why a Diagram is (Sometimes) Worth Ten Thousand Words. Cognitive Science 11: 65-100. Available:http://linkinghub.elsevier.com/retrieve/pii/S0364021387800265.
30. Mcneil NM, Alibali MW, (2004) You'll see what you mean: Students encode equations based on their knowledge of arithmetic. Cognitive Science 28: 451-466.
31. Siegler RS (1976) Three aspects of cognitive development. Cognitive Psychology 8: 481-520. Available:http://linkinghub.elsevier.com/retrieve/pii/0010028576900165.
32. Landy DH, Goldtone RL, (2010) Proximity and Precedence in Arithmetic. Quarterly journal of experimental psychology 63: 1953-1968.
33. Rittle-Johnson B, Alibali MW, (1999) Conceptual and procedural knowledge of mathematics: Does one lead to the other. Journal of Educational Psychology 91: 175-189.
34. Chase WG, Simon HA, (1973) Perception in Chess. Cognitive Psychology 4: 55-81.
35. Canobi KH, (2005) Children's profiles of addition and subtraction understanding. Journal of Experimental Child Psychology 92: 220-246 doi:10.1016/j.jecp.2005.06.001.
36. Canobi KH, Reeve RA, Pattison PE, (1996) The Role of Conceptual Understanding in Children's Addition Problem Solving. Developmental Psychology 34: 882-891.
37. Cohen J, Macwhinney B, Flatf MHEW, Provost J (1993) PsyScope/: An interactive graphic system for designing and controlling experiments in the psychology laboratory using Macintosh computers. 25.
38. Bisanz J, Lefevre Joanne (1992) Understanding Elementary Mathematics. In: Campbell JID, editor. The Nature and Origins of Mathematical Skills. Elsevier. p. 113.
39. Prather RW, Alibali MW (2009) The development of arithmetic principle knowledge: How do we know what learners know? Developmental Review 29: 221-248. Available:http://linkinghub.elsevier.com/retrieve/pii/S027322970900029X.
40. Hattikudur S, Alibali MW (2010) Learning about the equal sign: does comparing with inequality symbols help? Journal of experimental child psychology 107: 15-30. Available:http://www.ncbi.nlm.nih.gov/pubmed/20488452. Accessed 2 July 2010.