-
1
-
-
0034806994
-
Where do fractions encounter their equivalents? Can this encounter take place in elementary-school?
-
doi: 10.1023/A:1017998922475
-
Arnon, I., Nesher, P., and Nirenburg, R. (2001). Where do fractions encounter their equivalents? Can this encounter take place in elementary-school? Int. J. Comput. Math. Learn. 6, 167-214. doi: 10.1023/A:1017998922475
-
(2001)
Int. J. Comput. Math. Learn
, vol.6
, pp. 167-214
-
-
Arnon, I.1
Nesher, P.2
Nirenburg, R.3
-
2
-
-
84908959608
-
The development of adaptive expertise and flexibility: the integration of conceptual and procedural knowledge
-
eds A. J. Baroody and A. Dowker (Mahwah, NJ: Erlbaum).
-
Baroody, A. J. (2003). "The development of adaptive expertise and flexibility: the integration of conceptual and procedural knowledge," in The Development of Arithmetic Conceptsand Skills: Constructing Adaptive ExpertiseI, eds A. J. Baroody and A. Dowker (Mahwah, NJ: Erlbaum), 1-33.
-
(2003)
The Development of Arithmetic Conceptsand Skills: Constructing Adaptive ExpertiseI
, pp. 1-33
-
-
Baroody, A.J.1
-
3
-
-
0002540715
-
Rational number, ratio, and proportion
-
A. Grouws (New York, NY: Macmillan).
-
Behr, M. J., Harel, G., Post, T., and Lesh, R. (1992). "Rational number, ratio, and proportion," in Handbook of Research on Mathematics Teaching and Learning, ed D. A. Grouws (New York, NY: Macmillan), 296-333.
-
(1992)
Handbook of Research on Mathematics Teaching and Learning
, pp. 296-333
-
-
Behr, M.J.1
Harel, G.2
Post, T.3
Lesh, R.4
-
4
-
-
0003140571
-
Rational numbers concepts
-
Landau (New York, NY: Academic Press).
-
Behr, M. J., Lesh, R., Post, T. R., and Silver, E. A. (1983). "Rational numbers concepts," in Acquisition of Mathematics Concepts and Processes, eds R. Lesh and M. Landau (New York, NY: Academic Press), 91-125.
-
(1983)
Acquisition of Mathematics Concepts and Processes
, pp. 91-125
-
-
Behr, M.J.1
Lesh, R.2
Post, T.R.3
Silver, E.A.4
-
5
-
-
38349120491
-
The mental representation of numerical fractions: real or integer?
-
doi: 10.1037/0096-1523.33.6.1410
-
Bonato, M., Fabbri, S., Umiltà, C., and Zorzi, M. (2007). The mental representation of numerical fractions: real or integer? J. Exp. Psychol. Hum. Percept. Perform. 33, 1410-1419. doi: 10.1037/0096-1523.33.6.1410
-
(2007)
J. Exp. Psychol. Hum. Percept. Perform
, vol.33
, pp. 1410-1419
-
-
Bonato, M.1
Fabbri, S.2
Umiltà, C.3
Zorzi, M.4
-
6
-
-
0039264144
-
Identifying fractions on number lines
-
doi: 10.2307/749066
-
Bright, G., Behr, M., Post, T., and Wachsmuth, I. (1988). Identifying fractions on number lines, J. Res. Math. Educ. 19, 215-232. doi: 10.2307/749066
-
(1988)
J. Res. Math. Educ
, vol.19
, pp. 215-232
-
-
Bright, G.1
Behr, M.2
Post, T.3
Wachsmuth, I.4
-
8
-
-
0842333772
-
Rationals and decimals as required in the school curriculum. Part 1: rationals as measurements
-
doi: 10.1016/j.jmathb.2003.12.001
-
Brousseau, G., Brousseau, N., and Warfield, V. (2004). Rationals and decimals as required in the school curriculum. Part 1: rationals as measurements. J. Math. Behav. 23, 1-20. doi: 10.1016/j.jmathb.2003.12.001
-
(2004)
J. Math. Behav
, vol.23
, pp. 1-20
-
-
Brousseau, G.1
Brousseau, N.2
Warfield, V.3
-
10
-
-
0000973077
-
Role of conceptual knowledge in mathematical procedural learning
-
doi: 10.1037/0012-1649.27.5.777
-
Byrnes, J. P., and Wasik, B. A. (1991). Role of conceptual knowledge in mathematical procedural learning. Dev. Psychol. 27, 777-786. doi: 10.1037/0012-1649.27.5.777
-
(1991)
Dev. Psychol
, vol.27
, pp. 777-786
-
-
Byrnes, J.P.1
Wasik, B.A.2
-
11
-
-
33846799328
-
Drawing on a theoritical model to study students' understandings of fractions
-
doi: 10.1007/s10649-006-9036-2
-
Charalambous, C., and Pitta-Pantazi, D. (2007). Drawing on a theoritical model to study students' understandings of fractions. Educ. Stud. Math. 64, 293-316. doi: 10.1007/s10649-006-9036-2
-
(2007)
Educ. Stud. Math
, vol.64
, pp. 293-316
-
-
Charalambous, C.1
Pitta-Pantazi, D.2
-
12
-
-
84885409495
-
Décimaux et fractions
-
eds P. Barrouillet and V. Camos (Marseille: Solal)
-
Coquin-Viennot, D., and Camos, V. (2006). "Décimaux et fractions," in La cognition mathématique chez l'enfant, eds P. Barrouillet and V. Camos (Marseille: Solal), 145-154.
-
(2006)
La cognition mathématique chez l'enfant
, pp. 145-154
-
-
Coquin-Viennot, D.1
Camos, V.2
-
15
-
-
84864548987
-
Developing children's understanding of fractions: an intervention study
-
doi: 10.1111/j.1751-228X.2012.01149.x
-
Gabriel, F., Coché, F., Szucs, D., Carette, V., Rey, B., and Content, A. (2012). Developing children's understanding of fractions: an intervention study. Mind Brain Educ. 6, 137-146. doi: 10.1111/j.1751-228X.2012.01149.x
-
(2012)
Mind Brain Educ
, vol.6
, pp. 137-146
-
-
Gabriel, F.1
Coché, F.2
Szucs, D.3
Carette, V.4
Rey, B.5
Content, A.6
-
16
-
-
0001721873
-
Enabling constraints for cognitive development and learning: domain specificity and epigenesist
-
eds D. Kuhn and R. Siegler (New York, NY: Wiley).
-
Gelman, R., and Williams, E. M. (1997). "Enabling constraints for cognitive development and learning: domain specificity and epigenesist," in Cognitive Development, Handbook of Child Psychology, 5th Edn, eds D. Kuhn and R. Siegler (New York, NY: Wiley), 575-630.
-
(1997)
Cognitive Development, Handbook of Child Psychology, 5th Edn
, pp. 575-630
-
-
Gelman, R.1
Williams, E.M.2
-
18
-
-
68349086206
-
L'apprentissage des nombres rationnels et ses obstacles
-
ed M.-P. Noël (Marseille: Solal)
-
Grégoire, J., and Meert, G. (2005) "L'apprentissage des nombres rationnels et ses obstacles," in Les Troubles Du Calcul, ed M.-P. Noël (Marseille: Solal), 223-251.
-
(2005)
Les Troubles Du Calcul
, pp. 223-251
-
-
Grégoire, J.1
Meert, G.2
-
20
-
-
77955045797
-
Individual differences in conceptual and procedural knowledge when learning fractions
-
doi: 10.1037/a0017486
-
Hallett, D., Nunes, T., and Bryant, P. (2010). Individual differences in conceptual and procedural knowledge when learning fractions. J. Educ. Psychol. 102, 395-406. doi: 10.1037/a0017486
-
(2010)
J. Educ. Psychol
, vol.102
, pp. 395-406
-
-
Hallett, D.1
Nunes, T.2
Bryant, P.3
-
21
-
-
84859636342
-
Patterns of strengths and weaknesses in children's knowledge about fractions
-
Hecht, S. A., and Vagi, K. J. (2012). Patterns of strengths and weaknesses in children's knowledge about fractions. J. Exp. Child Psychol. 111, 212-229.
-
(2012)
J. Exp. Child Psychol
, vol.111
, pp. 212-229
-
-
Hecht, S.A.1
Vagi, K.J.2
-
22
-
-
0242635984
-
Sources of individual differences in fraction skills
-
doi: 10.1016/j.jecp.2003.08.003
-
Hecht, S. A., Close, L., and Santisi, M. (2003). Sources of individual differences in fraction skills. J. Exp. Child Psychol. 86, 277-302. doi: 10.1016/j.jecp.2003.08.003
-
(2003)
J. Exp. Child Psychol
, vol.86
, pp. 277-302
-
-
Hecht, S.A.1
Close, L.2
Santisi, M.3
-
24
-
-
0002461839
-
Conceptual and procedural knowledge in mathematics: an introductory analysis
-
ed J. Hiebert (Hillsdale, NJ: Lawrence Erlbaum Associates).
-
Hiebert, J., and Lefevre, P. (1986). "Conceptual and procedural knowledge in mathematics: an introductory analysis," in Conceptualand Procedural Knowledge: the Case of Mathematics, ed J. Hiebert (Hillsdale, NJ: Lawrence Erlbaum Associates), 1-27.
-
(1986)
Conceptualand Procedural Knowledge: the Case of Mathematics
, pp. 1-27
-
-
Hiebert, J.1
Lefevre, P.2
-
25
-
-
73649090444
-
A generalized fraction: an entity smaller than one on the mental number line
-
doi: 10.1037/a0016892
-
Kallai, A., and Tzelgov, J. (2009). A generalized fraction: an entity smaller than one on the mental number line. J. Exp. Psychol. Hum. Percept. Perform. 35, 1845-1864. doi: 10.1037/a0016892
-
(2009)
J. Exp. Psychol. Hum. Percept. Perform
, vol.35
, pp. 1845-1864
-
-
Kallai, A.1
Tzelgov, J.2
-
26
-
-
0003314423
-
Equivalent fractions: their difficulty and educational implications
-
doi: 10.1016/0732-3123(95)90035-7
-
Kamii, C., and Clark, F. B. (1995). Equivalent fractions: their difficulty and educational implications. J. Math. Behav. 14, 365-378. doi: 10.1016/0732-3123(95)90035-7
-
(1995)
J. Math. Behav
, vol.14
, pp. 365-378
-
-
Kamii, C.1
Clark, F.B.2
-
27
-
-
0010928632
-
Fractions: Children's Strategies and Errors. A Report of the Strategies and Errors in Secondary Mathematics Project
-
England: NFER-NELSON Publishing Company, Ltd.
-
Kerslake, D. (1986). Fractions: Children's Strategies and Errors. A Report of the Strategies and Errors in Secondary Mathematics Project. England: NFER-NELSON Publishing Company, Ltd.
-
(1986)
-
-
Kerslake, D.1
-
28
-
-
0002439843
-
On the mathematical, cognitive, and instructional foundations of rational numbers
-
ed R. Lesh (Columbus, OH: ERIC/SMEAC)
-
Kieren, T. E. (1976). "On the mathematical, cognitive, and instructional foundations of rational numbers," in Number and Measurement: Papers from a Research Workshop, ed R. Lesh (Columbus, OH: ERIC/SMEAC), 101-144.
-
(1976)
Number and Measurement: Papers from a Research Workshop
, pp. 101-144
-
-
Kieren, T.E.1
-
29
-
-
0003116256
-
Personal knowledge of rational numbers: its intuitive and formal development
-
eds J. Hiebert and M. Behr (Virginia: Lawrence Erlbaum)
-
Kieren, T. E. (1988) "Personal knowledge of rational numbers: its intuitive and formal development," in Research Agenda for Mathematics Education: Number Concepts and Operations in the Middle Grades, Vol. 2, eds J. Hiebert and M. Behr (Virginia: Lawrence Erlbaum), 162-181.
-
(1988)
Research Agenda for Mathematics Education: Number Concepts and Operations in the Middle Grades
, vol.2
, pp. 162-181
-
-
Kieren, T.E.1
-
30
-
-
0002358189
-
Rational and Fractional Numbers: From Quotient fields to Recursive understanding
-
eds T. P. Carpenter, E. Fennema, and T. A. Romberg (Hillsdale, NJ: Erlbaum).
-
Kieren, T. E. (1993). "Rational and Fractional Numbers: From Quotient fields to Recursive understanding," in Rational Numbers: An Integration of Research, eds T. P. Carpenter, E. Fennema, and T. A. Romberg (Hillsdale, NJ: Erlbaum), 49-84.
-
(1993)
Rational Numbers: An Integration of Research
, pp. 49-84
-
-
Kieren, T.E.1
-
31
-
-
0002929122
-
Proportional reasoning
-
eds J. Hiebert and M. Behr (Reston, VA: Lawrence Erlbaum and National Council of Teachers of Mathematics).
-
Lesh, R., Post, T., and Behr, M. (1988). "Proportional reasoning," in Number Concepts and Operations in the Middle Grades, eds J. Hiebert and M. Behr (Reston, VA: Lawrence Erlbaum and National Council of Teachers of Mathematics), 93-118.
-
(1988)
Number Concepts and Operations in the Middle Grades
, pp. 93-118
-
-
Lesh, R.1
Post, T.2
Behr, M.3
-
32
-
-
77951038950
-
The equivalence and ordering of fractions in part-whole and quotient situations
-
Mamede, E., Nunes, T., and Bryant, P. (2005). "The equivalence and ordering of fractions in part-whole and quotient situations," in PME CONFERENCE, Vol. 29, 3.
-
(2005)
PME CONFERENCE
, vol.29
, pp. 3
-
-
Mamede, E.1
Nunes, T.2
Bryant, P.3
-
33
-
-
84876363856
-
Limited knowledge of fraction representations differentiates middle school students with mathematics learning disability (dyscalculia) vs. low mathematics achievement
-
doi: 10.1016/j.jecp.2013.01.005
-
Mazzocco, M. M. M., Myers, G. F., Lewis, K. E., Hanich, L. B., and Murphy, M. M. (2013). Limited knowledge of fraction representations differentiates middle school students with mathematics learning disability (dyscalculia) vs. low mathematics achievement. J. Exp. Child Psychol. 115, 371-387. doi: 10.1016/j.jecp.2013.01.005
-
(2013)
J. Exp. Child Psychol
, vol.115
, pp. 371-387
-
-
Mazzocco, M.M.M.1
Myers, G.F.2
Lewis, K.E.3
Hanich, L.B.4
Murphy, M.M.5
-
35
-
-
22444453037
-
Developing children's understanding of the rational numbers: a new model and an experimental curriculum
-
doi: 10.2307/749607
-
Moss, J., and Case, R. (1999). Developing children's understanding of the rational numbers: a new model and an experimental curriculum. J. Res. Math. Educ. 30, 122-147. doi: 10.2307/749607
-
(1999)
J. Res. Math. Educ
, vol.30
, pp. 122-147
-
-
Moss, J.1
Case, R.2
-
36
-
-
84993723797
-
National Council of Teachers of Mathematics
-
Reston, VA: author
-
National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: author.
-
(2000)
Principles and Standards for School Mathematics
-
-
-
37
-
-
0242558505
-
How valid is it to use number lines to measure children's
-
doi: 10.1080/713663716
-
Ni, Y. (2000). How valid is it to use number lines to measure children's conceptual knowledge about rational number. Educ. Psychol. 20, 139-152. doi: 10.1080/713663716
-
(2000)
Educ. Psychol
, vol.20
, pp. 139-152
-
-
Ni, Y.1
-
38
-
-
0242474792
-
Semantic domains of rational numbers and the acquisition of fraction equivalence
-
doi: 10.1006/ceps.2000.1072
-
Ni, Y. (2001). Semantic domains of rational numbers and the acquisition of fraction equivalence. Contemp. Educ. Psycol. 26, 400-417. doi: 10.1006/ceps.2000.1072
-
(2001)
Contemp. Educ. Psycol
, vol.26
, pp. 400-417
-
-
Ni, Y.1
-
39
-
-
15944425784
-
Teaching and learning fraction and rational numbers: the origins and implications of whole number bias
-
doi: 10.1207/s15326985ep4001_3
-
Ni, Y., and Zhou, Y. D. (2005). Teaching and learning fraction and rational numbers: the origins and implications of whole number bias. Educ. Psychologist 40, 27-52. doi: 10.1207/s15326985ep4001_3
-
(2005)
Educ. Psychologist
, vol.40
, pp. 27-52
-
-
Ni, Y.1
Zhou, Y.D.2
-
42
-
-
0039153310
-
A review of recent research in the area of initial fraction concepts
-
doi: 10.1007/BF00163751
-
Pitkethly, A., and Hunting, R. (1996). A review of recent research in the area of initial fraction concepts. Educ. Stud. Math. 30, 5-38. doi: 10.1007/BF00163751
-
(1996)
Educ. Stud. Math
, vol.30
, pp. 5-38
-
-
Pitkethly, A.1
Hunting, R.2
-
43
-
-
0035602865
-
Developing conceptual understanding and procedural skill in mathematics: an iterative process
-
doi: 10.1037/0022-0663.93.2.346
-
Rittle-Johnson, B., Siegler, R. S., and Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: an iterative process. J. Educ. Psychol. 93, 346-362. doi: 10.1037/0022-0663.93.2.346
-
(2001)
J. Educ. Psychol
, vol.93
, pp. 346-362
-
-
Rittle-Johnson, B.1
Siegler, R.S.2
Alibali, M.W.3
-
44
-
-
0033084379
-
Conceptual and procedural knowledge of mathematics: does one lead to the other?
-
doi: 10.1037/0022-0663.91.1.175
-
Rittle-Johnson, B., and Alibali, M. W. (1999). Conceptual and procedural knowledge of mathematics: does one lead to the other? J. Educ. Psychol. 91, 175-189. doi: 10.1037/0022-0663.91.1.175
-
(1999)
J. Educ. Psychol
, vol.91
, pp. 175-189
-
-
Rittle-Johnson, B.1
Alibali, M.W.2
-
47
-
-
76449121435
-
The developmental relations between conceptual and procedural knowledge: a multimethod approach
-
doi: 10.1037/a0016701
-
Schneider, M., and Stern, E. (2010). The developmental relations between conceptual and procedural knowledge: a multimethod approach. Dev. Psychol. 46, 178-192. doi: 10.1037/a0016701
-
(2010)
Dev. Psychol
, vol.46
, pp. 178-192
-
-
Schneider, M.1
Stern, E.2
-
48
-
-
79955719641
-
An integrated theory of whole number and fractions development
-
doi: 10.1016/j.cogpsych.2011.03.001
-
Siegler, R. S., Thompson, C. A., and Schneider, M. (2011). An integrated theory of whole number and fractions development. Cogn. Psychol. 62, 273-296. doi: 10.1016/j.cogpsych.2011.03.001
-
(2011)
Cogn. Psychol
, vol.62
, pp. 273-296
-
-
Siegler, R.S.1
Thompson, C.A.2
Schneider, M.3
-
49
-
-
0041905329
-
Does half a pizza equal half a box of chocolates?: proportional matching in an analogy task
-
doi: 10.1016/S0885-2014(01)00066-1
-
Singer-Freeman, K. E., and Goswami, U. (2001). Does half a pizza equal half a box of chocolates?: proportional matching in an analogy task. Cogn. Dev. 16, 811-829. doi: 10.1016/S0885-2014(01)00066-1
-
(2001)
Cogn. Dev
, vol.16
, pp. 811-829
-
-
Singer-Freeman, K.E.1
Goswami, U.2
-
50
-
-
84989491909
-
Children's proportional judgments: The importance of "half"
-
doi: 10.1111/j.1467-8624.1991.tb01542.x
-
Spinillo, A. G., and Bryant, P. (1991). Children's proportional judgments: The importance of "half". Child Dev. 62, 427-440. doi: 10.1111/j.1467-8624.1991.tb01542.x
-
(1991)
Child Dev
, vol.62
, pp. 427-440
-
-
Spinillo, A.G.1
Bryant, P.2
-
51
-
-
13844292565
-
The development of students' understanding of the numerical value of fractions
-
doi: 10.1016/j.learninstruc.2004.06.015
-
Stafylidou, S., and Vosniadou, S. (2004). The development of students' understanding of the numerical value of fractions. Learn. Instr. 14, 503-518. doi: 10.1016/j.learninstruc.2004.06.015
-
(2004)
Learn. Instr
, vol.14
, pp. 503-518
-
-
Stafylidou, S.1
Vosniadou, S.2
-
52
-
-
22644452255
-
An integrated study of children's construction of improper fractions and the teacher's role in promoting that learning
-
doi: 10.2307/749707
-
Tzur, R. (1999). An integrated study of children's construction of improper fractions and the teacher's role in promoting that learning. J. Res. Math. Educ. 30, 390-416. doi: 10.2307/749707
-
(1999)
J. Res. Math. Educ
, vol.30
, pp. 390-416
-
-
Tzur, R.1
-
53
-
-
13844264296
-
Understanding the structure of the set of rational numbers: a conceptual change approach
-
doi: 10.1016/j.learninstruc.2004.06.013
-
Vamvakoussi, X., and Vosniadou, S. (2004). Understanding the structure of the set of rational numbers: a conceptual change approach, Learn. Instr. 14, 453-467. doi: 10.1016/j.learninstruc.2004.06.013
-
(2004)
Learn. Instr
, vol.14
, pp. 453-467
-
-
Vamvakoussi, X.1
Vosniadou, S.2
|