-
1
-
-
79955719641
-
An integrated theory of whole number and fractions development
-
Siegler R.S., et al. An integrated theory of whole number and fractions development. Cogn. Psychol. 2011, 62:273-296.
-
(2011)
Cogn. Psychol.
, vol.62
, pp. 273-296
-
-
Siegler, R.S.1
-
2
-
-
84863910959
-
Early predictors of high school mathematics achievement
-
Siegler R.S., et al. Early predictors of high school mathematics achievement. Psychol. Sci. 2012, 23:691-697.
-
(2012)
Psychol. Sci.
, vol.23
, pp. 691-697
-
-
Siegler, R.S.1
-
3
-
-
84866148485
-
Competence with fractions predicts gains in mathematics achievement
-
Bailey D.H., et al. Competence with fractions predicts gains in mathematics achievement. J. Exp. Child Psychol. 2012, 113:447-455.
-
(2012)
J. Exp. Child Psychol.
, vol.113
, pp. 447-455
-
-
Bailey, D.H.1
-
4
-
-
15944425784
-
Teaching and learning fraction and rational numbers: the origins and implications of whole number bias
-
Ni Y., Zhou Y-D. Teaching and learning fraction and rational numbers: the origins and implications of whole number bias. Educ. Psychol. 2005, 40:27-52.
-
(2005)
Educ. Psychol.
, vol.40
, pp. 27-52
-
-
Ni, Y.1
Zhou, Y.-D.2
-
5
-
-
13844264296
-
Understanding the structure of the set of rational numbers: a conceptual change approach
-
Vamvakoussi X., Vosniadou S. Understanding the structure of the set of rational numbers: a conceptual change approach. Learn. Instr. 2004, 14:453-467.
-
(2004)
Learn. Instr.
, vol.14
, pp. 453-467
-
-
Vamvakoussi, X.1
Vosniadou, S.2
-
6
-
-
77951261035
-
How many decimals are there between two fractions? Aspects of secondary school students' understanding of rational numbers and their notation
-
Vamvakoussi X., Vosniadou S. How many decimals are there between two fractions? Aspects of secondary school students' understanding of rational numbers and their notation. Cogn. Instr. 2010, 28:181-209.
-
(2010)
Cogn. Instr.
, vol.28
, pp. 181-209
-
-
Vamvakoussi, X.1
Vosniadou, S.2
-
7
-
-
67349256836
-
The processing and representation of fractions within the brain: an fMRI investigation
-
Ischebeck A., et al. The processing and representation of fractions within the brain: an fMRI investigation. Neuroimage 2009, 47:403-413.
-
(2009)
Neuroimage
, vol.47
, pp. 403-413
-
-
Ischebeck, A.1
-
8
-
-
84857506196
-
Relating magnitudes: the brain's code for proportions
-
Jacob S.N., et al. Relating magnitudes: the brain's code for proportions. Trends Cogn. Sci. 2012, 16:157-166.
-
(2012)
Trends Cogn. Sci.
, vol.16
, pp. 157-166
-
-
Jacob, S.N.1
-
10
-
-
0003698207
-
The Number Sense: How the Mind Creates Mathematics
-
Oxford University Press
-
Dehaene S. The Number Sense: How the Mind Creates Mathematics. Revised and Updated Edition 2011, Oxford University Press.
-
(2011)
Revised and Updated Edition
-
-
Dehaene, S.1
-
11
-
-
85066660432
-
Development of quantitative thinking
-
Oxford University Press, K.J. Holyoak, R. Morrison (Eds.)
-
Opfer J.E., Siegler R.S. Development of quantitative thinking. Oxford Handbook of Thinking and Reasoning 2012, 585-605. Oxford University Press. K.J. Holyoak, R. Morrison (Eds.).
-
(2012)
Oxford Handbook of Thinking and Reasoning
, pp. 585-605
-
-
Opfer, J.E.1
Siegler, R.S.2
-
12
-
-
34548434575
-
Development of mathematical understanding
-
John Wiley & Sons, D. Kuhn (Ed.)
-
Geary D.C. Development of mathematical understanding. Handbook of Child Psychology: Vol 2, Cognition, Perception, and Language 2006, 777-810. John Wiley & Sons. D. Kuhn (Ed.).
-
(2006)
Handbook of Child Psychology: Vol 2, Cognition, Perception, and Language
, pp. 777-810
-
-
Geary, D.C.1
-
13
-
-
44549088994
-
The generative basis of natural number concepts
-
Leslie A.M., et al. The generative basis of natural number concepts. Trends Cogn. Sci. 2008, 12:213-218.
-
(2008)
Trends Cogn. Sci.
, vol.12
, pp. 213-218
-
-
Leslie, A.M.1
-
14
-
-
0036000452
-
Do infants have numerical expectations or just perceptual preferences?
-
Wynn K. Do infants have numerical expectations or just perceptual preferences?. Dev. Sci. 2002, 2:207-209.
-
(2002)
Dev. Sci.
, vol.2
, pp. 207-209
-
-
Wynn, K.1
-
17
-
-
84871712178
-
-
National Council of Teachers of Mathematics, W.G. Martin (Ed.)
-
The Learning of Mathematics, 69th NCTM Yearbook 2007, National Council of Teachers of Mathematics. W.G. Martin (Ed.).
-
(2007)
The Learning of Mathematics, 69th NCTM Yearbook
-
-
-
18
-
-
0035602865
-
Developing conceptual understanding and procedural skill in mathematics: an iterative process
-
Rittle-Johnson B., et al. Developing conceptual understanding and procedural skill in mathematics: an iterative process. J. Educ. Psychol. 2001, 93:346-362.
-
(2001)
J. Educ. Psychol.
, vol.93
, pp. 346-362
-
-
Rittle-Johnson, B.1
-
19
-
-
76949108056
-
Mathematics skills of 17-year-olds in the United States: 1978 to 2004
-
Kloosterman P. Mathematics skills of 17-year-olds in the United States: 1978 to 2004. J. Res. Math. Educ. 2010, 41:20-51.
-
(2010)
J. Res. Math. Educ.
, vol.41
, pp. 20-51
-
-
Kloosterman, P.1
-
20
-
-
84857601430
-
What community college developmental mathematics students understand about mathematics
-
Stigler J.W., et al. What community college developmental mathematics students understand about mathematics. MathAMATYC Educ. 2010, 10:4-16.
-
(2010)
MathAMATYC Educ.
, vol.10
, pp. 4-16
-
-
Stigler, J.W.1
-
21
-
-
35248889892
-
Exploring group-wise conceptual deficiences of fractions for fifth and sixth graders in Taiwan
-
Chan W-H., et al. Exploring group-wise conceptual deficiences of fractions for fifth and sixth graders in Taiwan. J. Exp. Educ. 2007, 76:26-57.
-
(2007)
J. Exp. Educ.
, vol.76
, pp. 26-57
-
-
Chan, W.-H.1
-
22
-
-
0242474792
-
Semantic domains of rational numbers and the acquisition of fraction equivalence
-
Ni Y. Semantic domains of rational numbers and the acquisition of fraction equivalence. Contemp. Educ. Psychol. 2001, 26:400-417.
-
(2001)
Contemp. Educ. Psychol.
, vol.26
, pp. 400-417
-
-
Ni, Y.1
-
23
-
-
0036401333
-
Overcoming cognitive obstacles in learning fractions: equal-partitioning and equal-whole
-
Yoshida H., Sawano K. Overcoming cognitive obstacles in learning fractions: equal-partitioning and equal-whole. Jpn. Psychol. Res. 2002, 44:183-195.
-
(2002)
Jpn. Psychol. Res.
, vol.44
, pp. 183-195
-
-
Yoshida, H.1
Sawano, K.2
-
24
-
-
0002147322
-
Learning rational numbers with understanding. The case of informal knowledge
-
Erlbaum, T.P. Carpenter (Ed.)
-
Mack N.K. Learning rational numbers with understanding. The case of informal knowledge. Rational Numbers: An Integration of Research 1993, 85-105. Erlbaum. T.P. Carpenter (Ed.).
-
(1993)
Rational Numbers: An Integration of Research
, pp. 85-105
-
-
Mack, N.K.1
-
25
-
-
34547605313
-
Ratio abstraction by 6-month-old infants
-
McCrink K., Wynn K. Ratio abstraction by 6-month-old infants. Psychol. Sci. 2007, 18:740-745.
-
(2007)
Psychol. Sci.
, vol.18
, pp. 740-745
-
-
McCrink, K.1
Wynn, K.2
-
26
-
-
0038685868
-
Origins of number sense: large-number discrimination in human infants
-
Lipton J.S., Spelke E.S. Origins of number sense: large-number discrimination in human infants. Psychol. Sci. 2003, 14:396-401.
-
(2003)
Psychol. Sci.
, vol.14
, pp. 396-401
-
-
Lipton, J.S.1
Spelke, E.S.2
-
27
-
-
0002435884
-
The development of young infants' intuitions about support
-
Baillargeon R., et al. The development of young infants' intuitions about support. Early Dev. Parent. 1992, 1:69-78.
-
(1992)
Early Dev. Parent.
, vol.1
, pp. 69-78
-
-
Baillargeon, R.1
-
28
-
-
0011576081
-
Relational complexity and the development of analogical reasoning
-
Goswami U. Relational complexity and the development of analogical reasoning. Cogn. Dev. 1989, 4:251-268.
-
(1989)
Cogn. Dev.
, vol.4
, pp. 251-268
-
-
Goswami, U.1
-
29
-
-
85004763595
-
Transitive relational mappings in three- and four-year-olds: the analogy of Goldilocks and the Three Bears
-
Goswami U. Transitive relational mappings in three- and four-year-olds: the analogy of Goldilocks and the Three Bears. Child Dev. 1995, 66:877-892.
-
(1995)
Child Dev.
, vol.66
, pp. 877-892
-
-
Goswami, U.1
-
30
-
-
84989491909
-
Children's proportional judgments: the importance of 'half'
-
Spinillo A.G., Bryant P. Children's proportional judgments: the importance of 'half'. Child Dev. 1991, 62:427-440.
-
(1991)
Child Dev.
, vol.62
, pp. 427-440
-
-
Spinillo, A.G.1
Bryant, P.2
-
31
-
-
0011025448
-
Proportional reasoning in young children: Part-part comparisons about continuous and discontinuous quantity
-
Spinillo A.G., Bryant P.E. Proportional reasoning in young children: Part-part comparisons about continuous and discontinuous quantity. Math. Cogn. 1999, 5:181-197.
-
(1999)
Math. Cogn.
, vol.5
, pp. 181-197
-
-
Spinillo, A.G.1
Bryant, P.E.2
-
32
-
-
54849428511
-
Development of proportional reasoning: where young children go wrong
-
Boyer T.W., et al. Development of proportional reasoning: where young children go wrong. Dev. Psychol. 2008, 44:1478-1490.
-
(2008)
Dev. Psychol.
, vol.44
, pp. 1478-1490
-
-
Boyer, T.W.1
-
33
-
-
84855438267
-
Child proportional scaling: is 1/3 = 2/6 = 3/9 = 4/12?
-
Boyer T.W., Levine S.C. Child proportional scaling: is 1/3 = 2/6 = 3/9 = 4/12?. J. Exp. Child. Psychol. 2012, 111:516-533.
-
(2012)
J. Exp. Child. Psychol.
, vol.111
, pp. 516-533
-
-
Boyer, T.W.1
Levine, S.C.2
-
34
-
-
34447275224
-
The development of proportional reasoning: effect of continuous versus discrete quantities
-
Jeong Y., et al. The development of proportional reasoning: effect of continuous versus discrete quantities. J. Cogn. Dev. 2007, 8:237-256.
-
(2007)
J. Cogn. Dev.
, vol.8
, pp. 237-256
-
-
Jeong, Y.1
-
35
-
-
0041905329
-
Does half a pizza equal half a box of chocolates? Proportional matching in an analogy task
-
Singer-Freeman K.E., Goswami U. Does half a pizza equal half a box of chocolates? Proportional matching in an analogy task. Cogn. Dev. 2001, 16:811-829.
-
(2001)
Cogn. Dev.
, vol.16
, pp. 811-829
-
-
Singer-Freeman, K.E.1
Goswami, U.2
-
36
-
-
0034204153
-
Representing quantity beyond whole numbers: Some, none and part
-
Bialystock E., Codd J. Representing quantity beyond whole numbers: Some, none and part. Can. J. Exp. Psychol. 2000, 54:117-128.
-
(2000)
Can. J. Exp. Psychol.
, vol.54
, pp. 117-128
-
-
Bialystock, E.1
Codd, J.2
-
37
-
-
0031229698
-
When three is less than two: early developments in children's understanding of fractional quantities
-
Sophian C., et al. When three is less than two: early developments in children's understanding of fractional quantities. Dev. Psychol. 1997, 33:731-744.
-
(1997)
Dev. Psychol.
, vol.33
, pp. 731-744
-
-
Sophian, C.1
-
38
-
-
0000666784
-
Sharing and the understanding of number equivalence by young children
-
Frydman O., Bryant P.E. Sharing and the understanding of number equivalence by young children. Cogn. Dev. 1988, 3:323-339.
-
(1988)
Cogn. Dev.
, vol.3
, pp. 323-339
-
-
Frydman, O.1
Bryant, P.E.2
-
39
-
-
84855455980
-
Young children's judgments about the relative size of shared portions: the role of material type
-
Wing R.E., Beal C.R. Young children's judgments about the relative size of shared portions: the role of material type. Math. Think. Learn. 2004, 6:1-14.
-
(2004)
Math. Think. Learn.
, vol.6
, pp. 1-14
-
-
Wing, R.E.1
Beal, C.R.2
-
40
-
-
78649688226
-
Sources of group and individual differences in emerging fraction skills
-
Hecht S.A., Vagi K.J. Sources of group and individual differences in emerging fraction skills. J. Educ. Psychol 2010, 102:843-859.
-
(2010)
J. Educ. Psychol
, vol.102
, pp. 843-859
-
-
Hecht, S.A.1
Vagi, K.J.2
-
41
-
-
84884918932
-
-
doi:10.1037/a0031200 Developmental and individual differences in understanding of fractions. Dev. Psychol.
-
Siegler, R.S. and Pyke, A.A. Developmental and individual differences in understanding of fractions. Dev. Psychol. doi:10.1037/a0031200.
-
-
-
Siegler, R.S.1
Pyke, A.A.2
-
42
-
-
24644465554
-
Never getting to zero: elementary school students' understanding of the infinite divisibility of number and matter
-
Smith C.L., et al. Never getting to zero: elementary school students' understanding of the infinite divisibility of number and matter. Cogn. Psychol. 2005, 51:101-140.
-
(2005)
Cogn. Psychol.
, vol.51
, pp. 101-140
-
-
Smith, C.L.1
-
43
-
-
13844292565
-
The development of students' understanding of the numerical value of fractions
-
Stafylidou S., Vosniadou S. The development of students' understanding of the numerical value of fractions. Learn. Instr. 2004, 14:503-518.
-
(2004)
Learn. Instr.
, vol.14
, pp. 503-518
-
-
Stafylidou, S.1
Vosniadou, S.2
-
44
-
-
0032615429
-
Early fraction calculation ability
-
Mix K.S., et al. Early fraction calculation ability. Dev. Psychol. 1999, 35:164-174.
-
(1999)
Dev. Psychol.
, vol.35
, pp. 164-174
-
-
Mix, K.S.1
-
45
-
-
0000973077
-
Role of conceptual knowledge in mathematical procedural learning
-
Byrnes J.P., Wasik B.A. Role of conceptual knowledge in mathematical procedural learning. Dev. Psychol. 1991, 27:777-786.
-
(1991)
Dev. Psychol.
, vol.27
, pp. 777-786
-
-
Byrnes, J.P.1
Wasik, B.A.2
-
46
-
-
0242635984
-
Sources of individual differences in fraction skills
-
Hecht S.A., et al. Sources of individual differences in fraction skills. J. Exp. Child Psychol. 2003, 86:277-302.
-
(2003)
J. Exp. Child Psychol.
, vol.86
, pp. 277-302
-
-
Hecht, S.A.1
-
47
-
-
0345093472
-
Toward an information-processing account of individual differences in fraction skills
-
Hecht S.A. Toward an information-processing account of individual differences in fraction skills. J. Educ. Psychol. 1998, 90:545-559.
-
(1998)
J. Educ. Psychol.
, vol.90
, pp. 545-559
-
-
Hecht, S.A.1
-
48
-
-
77955045797
-
Individual differences in conceptual and procedural knowledge when learning fractions
-
Hallett D., et al. Individual differences in conceptual and procedural knowledge when learning fractions. J. Educ. Psychol. 2010, 102:395-406.
-
(2010)
J. Educ. Psychol.
, vol.102
, pp. 395-406
-
-
Hallett, D.1
-
49
-
-
0038349007
-
U.S. and Korean children's comprehension of fraction names: a reexamination of cross-national differences
-
Paik J.H., Mix K.S. U.S. and Korean children's comprehension of fraction names: a reexamination of cross-national differences. Child Dev. 2003, 74:144-154.
-
(2003)
Child Dev.
, vol.74
, pp. 144-154
-
-
Paik, J.H.1
Mix, K.S.2
-
50
-
-
0033257285
-
Language supports for children's understanding of numerical fractions: cross-national comparisons
-
Miura I.T., et al. Language supports for children's understanding of numerical fractions: cross-national comparisons. J. Exp. Child Psychol. 1999, 74:356-365.
-
(1999)
J. Exp. Child Psychol.
, vol.74
, pp. 356-365
-
-
Miura, I.T.1
-
51
-
-
84864751016
-
Fractions: could they really be the gatekeeper's doorman?
-
Booth J.L., Newton K.J. Fractions: could they really be the gatekeeper's doorman?. Contemp. Educ. Psychol. 2012, 37:247-253.
-
(2012)
Contemp. Educ. Psychol.
, vol.37
, pp. 247-253
-
-
Booth, J.L.1
Newton, K.J.2
-
52
-
-
34249295227
-
Separating cognitive capacity from knowledge: a new hypothesis
-
Halford G.S., et al. Separating cognitive capacity from knowledge: a new hypothesis. Trends Cogn. Sci. 2007, 11:236-242.
-
(2007)
Trends Cogn. Sci.
, vol.11
, pp. 236-242
-
-
Halford, G.S.1
-
53
-
-
65249102209
-
Mental number line, number line estimation, and mathematical achievement: their interrelations in grades 5 and 6
-
Schneider M., et al. Mental number line, number line estimation, and mathematical achievement: their interrelations in grades 5 and 6. J. Educ. Psychol. 2009, 101:359-372.
-
(2009)
J. Educ. Psychol.
, vol.101
, pp. 359-372
-
-
Schneider, M.1
-
54
-
-
65549165546
-
Notation-independent representation of fractions in the human parietal cortex
-
Jacob S.N., Nieder A. Notation-independent representation of fractions in the human parietal cortex. J. Neurosci. 2009, 29:4652-4657.
-
(2009)
J. Neurosci.
, vol.29
, pp. 4652-4657
-
-
Jacob, S.N.1
Nieder, A.2
-
55
-
-
3042542187
-
Empirical validation of the triple-code model of numerical processing for complex math operations using functional MRI and group Independent Component Analysis of the mental addition and subtraction of fractions
-
Schmithorst V.J., Brown R.D. Empirical validation of the triple-code model of numerical processing for complex math operations using functional MRI and group Independent Component Analysis of the mental addition and subtraction of fractions. Neuroimage 2004, 22:1414-1420.
-
(2004)
Neuroimage
, vol.22
, pp. 1414-1420
-
-
Schmithorst, V.J.1
Brown, R.D.2
-
56
-
-
0013535126
-
Three parietal circuits for number processing
-
Dehaene S., et al. Three parietal circuits for number processing. Cogn. Neuropsychol. 2003, 20:487-506.
-
(2003)
Cogn. Neuropsychol.
, vol.20
, pp. 487-506
-
-
Dehaene, S.1
-
57
-
-
0035438182
-
Facilitating children's proportional reasoning: a model of reasoning processes and effects of intervention on strategy change
-
Fujimura N. Facilitating children's proportional reasoning: a model of reasoning processes and effects of intervention on strategy change. J. Educ. Psychol. 2001, 93:589-603.
-
(2001)
J. Educ. Psychol.
, vol.93
, pp. 589-603
-
-
Fujimura, N.1
-
58
-
-
0037410797
-
Learning for mathematical insight: a longitudinal comparative study on modeling
-
Keijzer R., Terwel J. Learning for mathematical insight: a longitudinal comparative study on modeling. Learn. Instr. 2003, 13:285-304.
-
(2003)
Learn. Instr.
, vol.13
, pp. 285-304
-
-
Keijzer, R.1
Terwel, J.2
-
59
-
-
22444453037
-
Developing children's understanding of the rational numbers: a new model and an experimental curriculum
-
Moss J., Case R. Developing children's understanding of the rational numbers: a new model and an experimental curriculum. J. Res. Math. Educ. 1999, 30:122-147.
-
(1999)
J. Res. Math. Educ.
, vol.30
, pp. 122-147
-
-
Moss, J.1
Case, R.2
-
61
-
-
68249144778
-
Iterating between lessons on concepts and procedures can improve mathematics knowledge
-
Rittle-Johnson B., Koedinger K. Iterating between lessons on concepts and procedures can improve mathematics knowledge. Br. J. Educ. Psychol. 2009, 79:483-500.
-
(2009)
Br. J. Educ. Psychol.
, vol.79
, pp. 483-500
-
-
Rittle-Johnson, B.1
Koedinger, K.2
-
62
-
-
84871716833
-
-
Improving at-risk learners' understanding of fractions. (in press)
-
Fuchs, L.S. et al. Improving at-risk learners' understanding of fractions. J. Educ. Psychol. (in press).
-
J. Educ. Psychol
-
-
Fuchs, L.S.1
|