-
1
-
-
77951238231
-
Middle school mathematics teachers' knowledge of students' understanding of core algebraic concepts: equal sign and variable
-
Asquith P., Stephens A.C., Knuth E.J., Alibali M.W. Middle school mathematics teachers' knowledge of students' understanding of core algebraic concepts: equal sign and variable. Mathematical Thinking and Learning 2007, 9:249-272. 10.1080/10986060701360910.
-
(2007)
Mathematical Thinking and Learning
, vol.9
, pp. 249-272
-
-
Asquith, P.1
Stephens, A.C.2
Knuth, E.J.3
Alibali, M.W.4
-
2
-
-
84866148485
-
Competence with fractions predicts gains in mathematics achievement
-
Bailey D.H., Hoard M.K., Nugent L., Geary D.C. Competence with fractions predicts gains in mathematics achievement. Journal of Experimental Child Psychology 2012, 113:447-455. 10.1016/j.jecp.2012.06.004.
-
(2012)
Journal of Experimental Child Psychology
, vol.113
, pp. 447-455
-
-
Bailey, D.H.1
Hoard, M.K.2
Nugent, L.3
Geary, D.C.4
-
4
-
-
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?. Contemporary Educational Psychology 2012, 37:247-253. 10.1016/j.cedpsych.2012.07.001.
-
(2012)
Contemporary Educational Psychology
, vol.37
, pp. 247-253
-
-
Booth, J.L.1
Newton, K.J.2
-
5
-
-
41349101642
-
How students interpret literal symbols in algebra: a conceptual change approach
-
Lawrence Erlbaum Associates, Stresa, Italy, B.G. Bara, L. Barsalou, M. Bucciarelli (Eds.)
-
Christou K.P., Vosniadou S. How students interpret literal symbols in algebra: a conceptual change approach. Proceedings of the XXVII annual conference of the Cognitive Science Society 2005, 453-458. Lawrence Erlbaum Associates, Stresa, Italy. B.G. Bara, L. Barsalou, M. Bucciarelli (Eds.).
-
(2005)
Proceedings of the XXVII annual conference of the Cognitive Science Society
, pp. 453-458
-
-
Christou, K.P.1
Vosniadou, S.2
-
6
-
-
84855981462
-
What kinds of numbers do students assign to literal symbols? Aspects of the transition from arithmetic to algebra
-
Christou K.P., Vosniadou S. What kinds of numbers do students assign to literal symbols? Aspects of the transition from arithmetic to algebra. Mathematical Thinking and Learning 2012, 14:1-27. 10.1080/10986065.2012.625074.
-
(2012)
Mathematical Thinking and Learning
, vol.14
, pp. 1-27
-
-
Christou, K.P.1
Vosniadou, S.2
-
7
-
-
23044533336
-
Initial fraction learning by fourth- and fifth-grade students: a comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum
-
Cramer K.A., Post T.R., delMas R.C. Initial fraction learning by fourth- and fifth-grade students: a comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum. Journal for Research in Mathematics Education 2002, 33(2):111-144.
-
(2002)
Journal for Research in Mathematics Education
, vol.33
, Issue.2
, pp. 111-144
-
-
Cramer, K.A.1
Post, T.R.2
delMas, R.C.3
-
8
-
-
33646802601
-
Automatic-heuristic and executive-analytic processing in reasoning: chronometric and dual task considerations
-
De Neys W. Automatic-heuristic and executive-analytic processing in reasoning: chronometric and dual task considerations. Quarterly Journal of Experimental Psychology 2006, 59:1070-1100. 10.1080/02724980543000123.
-
(2006)
Quarterly Journal of Experimental Psychology
, vol.59
, pp. 1070-1100
-
-
De Neys, W.1
-
9
-
-
85139490904
-
The whole number bias in fraction magnitude comparisons with adults
-
Cognitive Science Society, Austin, TX, L. Carlson, C. Hoelscher, T.F. Shipley (Eds.)
-
DeWolf M., Vosniadou S. The whole number bias in fraction magnitude comparisons with adults. Proceedings of the 33rd annual conference of the Cognitive Science Society 2011, 1751-1756. Cognitive Science Society, Austin, TX. L. Carlson, C. Hoelscher, T.F. Shipley (Eds.).
-
(2011)
Proceedings of the 33rd annual conference of the Cognitive Science Society
, pp. 1751-1756
-
-
DeWolf, M.1
Vosniadou, S.2
-
11
-
-
0001230906
-
The role of implicit models in solving problems in multiplication and division
-
Fischbein E., Deri M., Nello M., Marino M. The role of implicit models in solving problems in multiplication and division. Journal for Research in Mathematics Education 1985, 16(1):3-17.
-
(1985)
Journal for Research in Mathematics Education
, vol.16
, Issue.1
, pp. 3-17
-
-
Fischbein, E.1
Deri, M.2
Nello, M.3
Marino, M.4
-
12
-
-
0002694829
-
The epigenesis of mathematical thinking
-
Gelman R. The epigenesis of mathematical thinking. Journal of Applied Developmental Psychology 2000, 21:27-37. 10.1016/S0193-3973(99)00048-9.
-
(2000)
Journal of Applied Developmental Psychology
, vol.21
, pp. 27-37
-
-
Gelman, R.1
-
13
-
-
64349084004
-
Dual processes in the psychology of mathematics education and cognitive psychology
-
Gillard E., Van Dooren W., Schaeken W., Verschaffel L. Dual processes in the psychology of mathematics education and cognitive psychology. Human Development 2009, 52:95-108. http://dx.doi.org/10.1159/000202728.
-
(2009)
Human Development
, vol.52
, pp. 95-108
-
-
Gillard, E.1
Van Dooren, W.2
Schaeken, W.3
Verschaffel, L.4
-
14
-
-
13844262803
-
The growth of mathematics through conceptual restructuring
-
Greer B. The growth of mathematics through conceptual restructuring. Learning & Instruction 2004, 14:541-548. 10.1016/j.learninstruc.2004.06.018.
-
(2004)
Learning & Instruction
, vol.14
, pp. 541-548
-
-
Greer, B.1
-
15
-
-
0013467151
-
On difficulties with fractions
-
Hasemann C. On difficulties with fractions. Educational Studies in Mathematics 1981, 12:171-187. 10.1007/BF00386047.
-
(1981)
Educational Studies in Mathematics
, vol.12
, pp. 171-187
-
-
Hasemann, C.1
-
16
-
-
85135996149
-
Research on the learning and teaching of algebra: A broadening of sources of meaning
-
Sense Publishers, Rotterdam, The Netherlands, A. Gutiérrez, P. Boero (Eds.)
-
Kieran C. Research on the learning and teaching of algebra: A broadening of sources of meaning. Handbook of research on the psychology of mathematics education: Past, present and future 2006, 11-49. Sense Publishers, Rotterdam, The Netherlands. A. Gutiérrez, P. Boero (Eds.).
-
(2006)
Handbook of research on the psychology of mathematics education: Past, present and future
, pp. 11-49
-
-
Kieran, C.1
-
17
-
-
77649173768
-
Longitudinal data analysis using generalized linear models
-
Liang K.Y., Zeger S.L. Longitudinal data analysis using generalized linear models. Biometrika 1986, 73:13-22. 10.1093/biomet/73.1.13.
-
(1986)
Biometrika
, vol.73
, pp. 13-22
-
-
Liang, K.Y.1
Zeger, S.L.2
-
18
-
-
77951038950
-
The equivalence and ordering of fractions in part-whole and quotient situations
-
PME, Melbourne, Australia
-
Mamede E., Nunes T., Bryant P. The equivalence and ordering of fractions in part-whole and quotient situations. Proceedings of the 29th conference of the International Group for the Psychology of Mathematics Education 2005, Vol. 3:281-288. PME, Melbourne, Australia.
-
(2005)
Proceedings of the 29th conference of the International Group for the Psychology of Mathematics Education
, vol.3
, pp. 281-288
-
-
Mamede, E.1
Nunes, T.2
Bryant, P.3
-
19
-
-
49549099008
-
Parts and 'holes': gaps in rational number sense among children with vs. without mathematical learning disabilities
-
Mazzocco M.M.M., Devlin K.T. Parts and 'holes': gaps in rational number sense among children with vs. without mathematical learning disabilities. Developmental Science 2008, 11:681-691. 10.1111/j.1467-7687.2008.00717.x.
-
(2008)
Developmental Science
, vol.11
, pp. 681-691
-
-
Mazzocco, M.M.M.1
Devlin, K.T.2
-
20
-
-
77954758096
-
Comparing the magnitude of two fractions with common components: which representations are used by 10- and 12-year-olds?
-
Meert G., Grégoire J., Noël M.-P. Comparing the magnitude of two fractions with common components: which representations are used by 10- and 12-year-olds?. Journal of Experimental Child Psychology 2010, 107:244-259. 10.1016/j.jecp.2010.04.008.
-
(2010)
Journal of Experimental Child Psychology
, vol.107
, pp. 244-259
-
-
Meert, G.1
Grégoire, J.2
Noël, M.-P.3
-
21
-
-
13844264286
-
Number concept and conceptual change: towards a systemic model of the processes of change
-
Merenluoto K., Lehtinen E. Number concept and conceptual change: towards a systemic model of the processes of change. Learning and Instruction 2004, 14:519-534. 10.1016/j.learninstruc.2004.06.016.
-
(2004)
Learning and Instruction
, vol.14
, pp. 519-534
-
-
Merenluoto, K.1
Lehtinen, E.2
-
22
-
-
33750161942
-
Pipes, tubes, and beakers: new approaches to teaching the rational-number system
-
National Academic Press, Washington, DC, M.S. Donovan, J.D. Bransford (Eds.)
-
Moss J. Pipes, tubes, and beakers: new approaches to teaching the rational-number system. How students learn: Mathematics in the classroom 2005, 121-162. National Academic Press, Washington, DC. M.S. Donovan, J.D. Bransford (Eds.).
-
(2005)
How students learn: Mathematics in the classroom
, pp. 121-162
-
-
Moss, J.1
-
23
-
-
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. Educational Psychologist 2005, 40:27-52. 10.1207/s15326985ep4001_3.
-
(2005)
Educational Psychologist
, vol.40
, pp. 27-52
-
-
Ni, Y.1
Zhou, Y.-D.2
-
24
-
-
70449358329
-
Rational numbers and intensive quantities: challenges and insights to pupils' implicit knowledge
-
Nunes T., Bryant P. Rational numbers and intensive quantities: challenges and insights to pupils' implicit knowledge. Anales de Psicologia 2008, 24(2):262-270.
-
(2008)
Anales de Psicologia
, vol.24
, Issue.2
, pp. 262-270
-
-
Nunes, T.1
Bryant, P.2
-
25
-
-
84879747887
-
The natural number bias and magnitude representation in fraction comparison by expert mathematicians
-
Obersteiner A., Van Dooren W., Van Hoof J., Verschaffel L. The natural number bias and magnitude representation in fraction comparison by expert mathematicians. Learning and Instruction 2013, 28:64-72. http://dx.doi.org/10.1016/j.learninstruc.2013.05.003.
-
(2013)
Learning and Instruction
, vol.28
, pp. 64-72
-
-
Obersteiner, A.1
Van Dooren, W.2
Van Hoof, J.3
Verschaffel, L.4
-
26
-
-
0001974117
-
Conceptual bases of arithmetic errors: the case of decimal fractions
-
Resnick L.B., Nesher P., Leonard F., Magone M., Omanson S., Peled I. Conceptual bases of arithmetic errors: the case of decimal fractions. Journal for Research in Mathematics Education 1989, 20(1):8-27.
-
(1989)
Journal for Research in Mathematics Education
, vol.20
, Issue.1
, pp. 8-27
-
-
Resnick, L.B.1
Nesher, P.2
Leonard, F.3
Magone, M.4
Omanson, S.5
Peled, I.6
-
27
-
-
84871712336
-
Fractions: the new frontier for theories of numerical development
-
Siegler R.S., Fazio L.K., Bailey D.H., Zhou X. Fractions: the new frontier for theories of numerical development. Trends in Cognitive Sciences 2012, 17:13-19. 10.1016/j.tics.2012.11.004.
-
(2012)
Trends in Cognitive Sciences
, vol.17
, pp. 13-19
-
-
Siegler, R.S.1
Fazio, L.K.2
Bailey, D.H.3
Zhou, X.4
-
28
-
-
79955719641
-
An integrated theory of whole number and fractions development
-
Siegler R.S., Thompson C.A., Schneider M. An integrated theory of whole number and fractions development. Cognitive Psychology 2011, 62:273-296. 10.1016/j.cogpsych.2011.03.001.
-
(2011)
Cognitive Psychology
, vol.62
, pp. 273-296
-
-
Siegler, R.S.1
Thompson, C.A.2
Schneider, M.3
-
29
-
-
24644465554
-
Never getting to zero: elementary school students' understanding of the infinite divisibility of number and matter
-
Smith C.L., Solomon G.E.A., Carey S. Never getting to zero: elementary school students' understanding of the infinite divisibility of number and matter. Cognitive Psychology 2005, 51:101-140. 10.1016/j.cogpsych.2005.03.001.
-
(2005)
Cognitive Psychology
, vol.51
, pp. 101-140
-
-
Smith, C.L.1
Solomon, G.E.A.2
Carey, S.3
-
30
-
-
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. Learning and Instruction 2004, 14:503-518. 10.1016/j.learninstruc.2004.06.015.
-
(2004)
Learning and Instruction
, vol.14
, pp. 503-518
-
-
Stafylidou, S.1
Vosniadou, S.2
-
31
-
-
85019250789
-
Bridging the gap: fraction understanding is central to mathematics achievement in students from three different continents
-
Torbeyns J., Schneider M., Xin Z., Siegler R.S. Bridging the gap: fraction understanding is central to mathematics achievement in students from three different continents. Learning and Instruction 2014.
-
(2014)
Learning and Instruction
-
-
Torbeyns, J.1
Schneider, M.2
Xin, Z.3
Siegler, R.S.4
-
32
-
-
79960050993
-
What fills the gap between discrete and dense? Greek and Flemish students' understanding of density
-
Vamvakoussi X., Christou K.P., Mertens L., Van Dooren W. What fills the gap between discrete and dense? Greek and Flemish students' understanding of density. Learning and Instruction 2011, 21:676-685. http://dx.doi.org/10.1016/j.learninstruc.2011.03.005.
-
(2011)
Learning and Instruction
, vol.21
, pp. 676-685
-
-
Vamvakoussi, X.1
Christou, K.P.2
Mertens, L.3
Van Dooren, W.4
-
33
-
-
84862993778
-
Naturally biased? In search for reaction time evidence for a natural number bias in adults
-
Vamvakoussi X., Van Dooren W., Verschaffel L. Naturally biased? In search for reaction time evidence for a natural number bias in adults. The Journal of Mathematical Behavior 2012, 31:344-355. http://dx.doi.org/10.1016/j.jmathb.2012.02.001.
-
(2012)
The Journal of Mathematical Behavior
, vol.31
, pp. 344-355
-
-
Vamvakoussi, X.1
Van Dooren, W.2
Verschaffel, L.3
-
34
-
-
84872498745
-
Educated adults are still affected by intuitions about the effect of arithmetical operations: evidence from a reaction-time study
-
Vamvakoussi X., Van Dooren W., Verschaffel L. Educated adults are still affected by intuitions about the effect of arithmetical operations: evidence from a reaction-time study. Educational Studies in Mathematics 2013, 82:323-330. http://dx.doi.org/10.1007/s10649-012-9432-8.
-
(2013)
Educational Studies in Mathematics
, vol.82
, pp. 323-330
-
-
Vamvakoussi, X.1
Van Dooren, W.2
Verschaffel, L.3
-
35
-
-
84977507829
-
Greek and Flemish students' interpretation of the literal symbols as variables
-
PME, Belo Horizonte, Brazil, M. Pinto, T. Kawasaki (Eds.)
-
Van Dooren W., Vamvakoussi X. Greek and Flemish students' interpretation of the literal symbols as variables. Proceedings of the 34th Conference of the International Group for the Psychology in Mathematics Education 2010, Vol. 4:257-264. PME, Belo Horizonte, Brazil. M. Pinto, T. Kawasaki (Eds.).
-
(2010)
Proceedings of the 34th Conference of the International Group for the Psychology in Mathematics Education
, vol.4
, pp. 257-264
-
-
Van Dooren, W.1
Vamvakoussi, X.2
-
36
-
-
85011729736
-
Searching for a whole number bias in secondary school student - A reaction time study on fraction comparison
-
PME, Taipei, Taiwan
-
Van Dooren W., Van Hoof J., Lijnen T., Verschaffel L. Searching for a whole number bias in secondary school student - A reaction time study on fraction comparison. Proceedings of the 36th Conference of the International Group for the Psychology in Mathematics Education 2012, Vol. 4:187-194. PME, Taipei, Taiwan.
-
(2012)
Proceedings of the 36th Conference of the International Group for the Psychology in Mathematics Education
, vol.4
, pp. 187-194
-
-
Van Dooren, W.1
Van Hoof, J.2
Lijnen, T.3
Verschaffel, L.4
-
37
-
-
84879643447
-
Are secondary school students still hampered by the natural number bias? - A reaction time study on fraction comparison tasks
-
Van Hoof J., Lijnen T., Verschaffel L., Van Dooren W. Are secondary school students still hampered by the natural number bias? - A reaction time study on fraction comparison tasks. Research in Mathematics Education 2013, 15(2):154-164.
-
(2013)
Research in Mathematics Education
, vol.15
, Issue.2
, pp. 154-164
-
-
Van Hoof, J.1
Lijnen, T.2
Verschaffel, L.3
Van Dooren, W.4
-
38
-
-
85019191128
-
The representation of fraction magnitudes and the whole number bias reconsidered
-
Vosniadou S., DeWolf M. The representation of fraction magnitudes and the whole number bias reconsidered. Learning and Instruction 2014.
-
(2014)
Learning and Instruction
-
-
Vosniadou, S.1
DeWolf, M.2
-
39
-
-
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. Learning and Instruction 2004, 14:453-467. 10.1016/j.learninstruc.2004.06.013.
-
(2004)
Learning and Instruction
, vol.14
, pp. 453-467
-
-
Vamvakoussi, X.1
Vosniadou, S.2
|