-
2
-
-
33947414949
-
An alternative reconceptualization of procedural and conceptual knowledge
-
Baroody, A. J., Feil, Y. and Johnson, A. R. 2007. An alternative reconceptualization of procedural and conceptual knowledge. Journal for Research in Mathematics Education, 38: 115-131.
-
(2007)
Journal for Research in Mathematics Education
, vol.38
, pp. 115-131
-
-
Baroody, A.J.1
Feil, Y.2
Johnson, A.R.3
-
3
-
-
0002540715
-
Rational number, ratio, and proportion
-
In: Grouws D., editors New York, NY, New York, NY,: Macmillan
-
Behr, M. J., Harel, G., Post, T. R. and Lesh, R. 1992. "Rational number, ratio, and proportion". In Handbook of research on mathematics teaching and learning, Edited by: Grouws, D. 296-333. New York, NY: Macmillan.
-
(1992)
Handbook of research on mathematics teaching and learning
, pp. 296-333
-
-
Behr, M.J.1
Harel, G.2
Post, T.R.3
Lesh, R.4
-
4
-
-
54649084614
-
Proportional reasoning among 7th grade students with different curricular experiences
-
Ben-Chaim, D., Fey, J. T., Benedetto, C. and Miller, J. 1998. Proportional reasoning among 7th grade students with different curricular experiences. Educational Studies in Mathematics, 46: 247-273.
-
(1998)
Educational Studies in Mathematics
, vol.46
, pp. 247-273
-
-
Ben-Chaim, D.1
Fey, J.T.2
Benedetto, C.3
Miller, J.4
-
7
-
-
84872522842
-
-
Common Core State Standards for Mathematics, Retrieved from
-
Common Core State Standards for Mathematics. 2010. Retrieved from http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf
-
(2010)
-
-
-
8
-
-
0001311877
-
Splitting, similarity, and rate of change: A new approach to multiplication and exponential functions
-
In: Harel G., Confrey J., editors Albany, NY, Albany, NY,: SUNY Press
-
Confrey, J. 1994. "Splitting, similarity, and rate of change: A new approach to multiplication and exponential functions". In The development of multiplicative reasoning in the learning of mathematics, Edited by: Harel, G. and Confrey, J. 291-331. Albany, NY: SUNY Press.
-
(1994)
The development of multiplicative reasoning in the learning of mathematics
, pp. 291-331
-
-
Confrey, J.1
-
9
-
-
84872578466
-
-
Paper presented at the Tenth Annual Meeting of the North, American Chapter of the International Group for the Psychology of Mathematics Education, De Kalb, IL
-
Confrey, J. 1988. Multiplication and splitting: Their role in understanding exponential functions, Paper presented at the Tenth Annual Meeting of the North. American Chapter of the International Group for the Psychology of Mathematics Education, De Kalb, IL.
-
(1988)
Multiplication and splitting: Their role in understanding exponential functions
-
-
Confrey, J.1
-
10
-
-
21844504051
-
Splitting, covariation, and their role in the development of exponential functions
-
Confrey, J. and Smith, E. 1995. Splitting, covariation, and their role in the development of exponential functions. Journal for Research in Mathematics Education, 26(1): 66-86.
-
(1995)
Journal for Research in Mathematics Education
, vol.26
, Issue.1
, pp. 66-86
-
-
Confrey, J.1
Smith, E.2
-
11
-
-
0008851846
-
Equal sharing and shared meaning: The development of fraction concepts in a first-grade classroom
-
Empson, S. B. 1999. Equal sharing and shared meaning: The development of fraction concepts in a first-grade classroom. Cognition and Instruction, 17(3): 283-342.
-
(1999)
Cognition and Instruction
, vol.17
, Issue.3
, pp. 283-342
-
-
Empson, S.B.1
-
12
-
-
34247584100
-
Units coordination and the construction of improper fractions: A revision of the splitting hypothesis
-
Hackenberg, A. J. 2007. Units coordination and the construction of improper fractions: A revision of the splitting hypothesis. Journal of Mathematical Behavior, 26(1): 27-47.
-
(2007)
Journal of Mathematical Behavior
, vol.26
, Issue.1
, pp. 27-47
-
-
Hackenberg, A.J.1
-
13
-
-
77958049086
-
Students' reversible multiplicative reasoning with fractions
-
Hackenberg, A. J. 2010. Students' reversible multiplicative reasoning with fractions. Cognition and instruction, 28(4): 383-432.
-
(2010)
Cognition and instruction
, vol.28
, Issue.4
, pp. 383-432
-
-
Hackenberg, A.J.1
-
14
-
-
0039625501
-
-
Vancouver, BC, Canada, Vancouver, BC,: Pacific Education Press
-
Howson, G. 1995. Mathematics textbooks: A comparative study of grade 8 texts, Vancouver, BC, Canada: Pacific Education Press.
-
(1995)
Mathematics textbooks: A comparative study of grade 8 texts
-
-
Howson, G.1
-
15
-
-
0008773679
-
Alan: A case study of knowledge of units and performance with fractions
-
Hunting, R. P. 1983. Alan: A case study of knowledge of units and performance with fractions. Journal for Research in Mathematics Education, 14(3): 182-197.
-
(1983)
Journal for Research in Mathematics Education
, vol.14
, Issue.3
, pp. 182-197
-
-
Hunting, R.P.1
-
16
-
-
0002439843
-
On the mathematical, cognitive, and instructional foundations of rational numbers
-
In: Lesh R., editors Columbus, OH, 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, Edited by: Lesh, R. 101-144. Columbus, OH: ERIC/SMEAC.
-
(1976)
Number and measurement: Papers from a research workshop
, pp. 101-144
-
-
Kieren, T.E.1
-
17
-
-
0008773680
-
The rational number construct-Its elements and mechanisms
-
In: Kieren T. E., editors Columbus, OH, Columbus, OH,: ERIC/SMEAC
-
Kieren, T. E. 1980. "The rational number construct-Its elements and mechanisms". In Recent research on number learning, Edited by: Kieren, T. E. 125-149. Columbus, OH: ERIC/SMEAC.
-
(1980)
Recent research on number learning
, pp. 125-149
-
-
Kieren, T.E.1
-
18
-
-
0003116256
-
Personal knowledge of rational numbers: Its intuitive and formal development
-
In: Hiebert J., Behr M., editors Reston, VA, Reston, VA,: NCTM
-
Kieren, T. E. 1988. "Personal knowledge of rational numbers: Its intuitive and formal development". In Number concepts and operations in the middle grades, Edited by: Hiebert, J. and Behr, M. 162-181. Reston, VA: NCTM.
-
(1988)
Number concepts and operations in the middle grades
, pp. 162-181
-
-
Kieren, T.E.1
-
19
-
-
84858625639
-
A history of algebra in the school curriculum
-
In: Greenes C., editors Reston, VA, Reston, VA,: NCTM
-
Kilpatrick, J. and Izsak, A. 2008. "A history of algebra in the school curriculum". In Algebra and algebraic thinking in school mathematics: 2008 NCTM yearbook, Edited by: Greenes, C. 3-18. Reston, VA: NCTM.
-
(2008)
Algebra and algebraic thinking in school mathematics: 2008 NCTM yearbook
, pp. 3-18
-
-
Kilpatrick, J.1
Izsak, A.2
-
20
-
-
54949096914
-
Rational numbers and proportional reasoning: Towards a theoretical framework for research
-
In: Lester F., editors Reston, VA, Reston, VA,: NCTM
-
Lamon, S. J. 2007. "Rational numbers and proportional reasoning: Towards a theoretical framework for research". In Second handbook of research on mathematics teaching and learning, Edited by: Lester, F. 629-667. Reston, VA: NCTM.
-
(2007)
Second handbook of research on mathematics teaching and learning
, pp. 629-667
-
-
Lamon, S.J.1
-
21
-
-
0017360990
-
The measurement of observer agreement for categorical data
-
Landis, J. R. and Koch, G. G. 1977. The measurement of observer agreement for categorical data. Biometrics, 33: 159-174.
-
(1977)
Biometrics
, vol.33
, pp. 159-174
-
-
Landis, J.R.1
Koch, G.G.2
-
22
-
-
84867463854
-
Conceptualizing and organizing content for teaching and learning in selected Chinese, Japanese, and U.S. mathematics textbooks: The case of fraction division
-
Li, Y., Chen, X. and An, S. 2009. Conceptualizing and organizing content for teaching and learning in selected Chinese, Japanese, and U.S. mathematics textbooks: The case of fraction division. ZDM, 41: 809-826.
-
(2009)
ZDM
, vol.41
, pp. 809-826
-
-
Li, Y.1
Chen, X.2
An, S.3
-
23
-
-
0035610065
-
Building on informal knowledge through instruction in a complex content domain: Partitioning, units, and understanding multiplication of fractions
-
Mack, N. K. 2001. Building on informal knowledge through instruction in a complex content domain: Partitioning, units, and understanding multiplication of fractions. Journal for Research in Mathematics Education, 32(3): 267-296.
-
(2001)
Journal for Research in Mathematics Education
, vol.32
, Issue.3
, pp. 267-296
-
-
Mack, N.K.1
-
24
-
-
0041426444
-
From fractions to proportional reasoning: A cognitive schemes of operation approach
-
Nabors, W. 2003. From fractions to proportional reasoning: A cognitive schemes of operation approach. Journal of Mathematical Behavior, 22: 133-179.
-
(2003)
Journal of Mathematical Behavior
, vol.22
, pp. 133-179
-
-
Nabors, W.1
-
26
-
-
47949122887
-
Josh's operational conjectures: Abductions of a splitting operation and the construction of new fractional schemes
-
Norton, A. 2008. Josh's operational conjectures: Abductions of a splitting operation and the construction of new fractional schemes. Journal for Research in Mathematics Education, 39(4): 401-430.
-
(2008)
Journal for Research in Mathematics Education
, vol.39
, Issue.4
, pp. 401-430
-
-
Norton, A.1
-
28
-
-
70350189989
-
A quantitative analysis of children's splitting operations and fraction schemes
-
Norton, A. and Wilkins, J. L. M. 2009. A quantitative analysis of children's splitting operations and fraction schemes. Journal of Mathematical Behavior, 28(2/3): 150-161.
-
(2009)
Journal of Mathematical Behavior
, vol.28
, Issue.2-3
, pp. 150-161
-
-
Norton, A.1
Wilkins, J.L.M.2
-
31
-
-
84872567526
-
Constructions of fractions schemes: Is there an app for that, too?
-
Kalamazoo, MI, Kalamazoo, MI,: University of Western Michigan
-
Norton, A., Wilkins, J. L. M. and Boyce, S. 2012. "Constructions of fractions schemes: Is there an app for that, too?". In Proceedings of the Thirty-Third Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Kalamazoo, MI: University of Western Michigan.
-
(2012)
Proceedings of the Thirty-Third Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education
-
-
Norton, A.1
Wilkins, J.L.M.2
Boyce, S.3
-
32
-
-
0035743092
-
The construction of an iterative fractional scheme: The case of Joe
-
Olive, J. and Steffe, L. P. 2002. The construction of an iterative fractional scheme: The case of Joe. Journal of Mathematical Behavior, 20(4): 413-437.
-
(2002)
Journal of Mathematical Behavior
, vol.20
, Issue.4
, pp. 413-437
-
-
Olive, J.1
Steffe, L.P.2
-
33
-
-
32044451344
-
Making sense of instruction on fractions when a student lacks necessary fractional schemes: The case of Tim
-
Olive, J. and Vomvoridi, E. 2006. Making sense of instruction on fractions when a student lacks necessary fractional schemes: The case of Tim. Journal of Mathematical Behavior, 25(1): 18-45.
-
(2006)
Journal of Mathematical Behavior
, vol.25
, Issue.1
, pp. 18-45
-
-
Olive, J.1
Vomvoridi, E.2
-
34
-
-
0003830240
-
-
In: Trans C. Maschler, editors New York, NY, New York, NY,: Basic Books (Original work published 1968)
-
Piaget, J. 1970. Structuralism, Edited by: Trans, C. Maschler. New York, NY: Basic Books (Original work published 1968).
-
(1970)
Structuralism
-
-
Piaget, J.1
-
35
-
-
0004322907
-
-
In: Trans A. Rosin, editors New York, NY, New York, NY,: Grossman
-
Piaget, J. 1971. Psychology and epistemology, Edited by: Trans, A. Rosin. New York, NY: Grossman.
-
(1971)
Psychology and epistemology
-
-
Piaget, J.1
-
36
-
-
0039153310
-
A review of recent research in the area of initial fraction concepts
-
Pitkethly, A. and Hunting, R. 1996. A review of recent research in the area of initial fraction concepts. Educational Studies of Mathematics, 30(1): 5-38.
-
(1996)
Educational Studies of Mathematics
, vol.30
, Issue.1
, pp. 5-38
-
-
Pitkethly, A.1
Hunting, R.2
-
38
-
-
84872554944
-
The emergence of the splitting metaphor in a fourth grade classroom
-
In: Owens D., Reed M., Millsaps G., editors Columbus, OH, Columbus, OH,: The ERIC Clearinghouse for Science, Mathematics, and Environmental Education
-
Sáenz-Ludlow, A. 1995. "The emergence of the splitting metaphor in a fourth grade classroom". In The Proceedings of the Seventh Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Edited by: Owens, D., Reed, M. and Millsaps, G. Vol. 1, 152-157. Columbus, OH: The ERIC Clearinghouse for Science, Mathematics, and Environmental Education.
-
(1995)
The Proceedings of the Seventh Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education
, vol.1
, pp. 152-157
-
-
Sáenz-Ludlow, A.1
-
39
-
-
0347569337
-
Metaphor and numerical diagrams in the arithmetical activity of a fourth-grade class
-
Sáenz-Ludlow, A. 2004. Metaphor and numerical diagrams in the arithmetical activity of a fourth-grade class. Journal for Research in Mathematics Education, 35: 34-56.
-
(2004)
Journal for Research in Mathematics Education
, vol.35
, pp. 34-56
-
-
Sáenz-Ludlow, A.1
-
40
-
-
0003761866
-
-
New York, NY, New York, NY,: McGraw-Hill
-
Siegel, S. and Castellan, N. J. Jr. 1988. Nonparametric statistics for the behavioral sciences (2nd ed.), New York, NY: McGraw-Hill.
-
(1988)
Nonparametric statistics for the behavioral sciences
-
-
Siegel, S.1
Castellan Jr., N.J.2
-
41
-
-
21844488292
-
Reconstructing mathematics pedagogy from a constructivist perspective
-
Simon, M. A. 1995. Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2): 114-145.
-
(1995)
Journal for Research in Mathematics Education
, vol.26
, Issue.2
, pp. 114-145
-
-
Simon, M.A.1
-
42
-
-
33746186990
-
Explicating the role of mathematical tasks in conceptual learning: An elaboration of the hypothetical learning trajectory
-
Simon, M. A. and Tzur, R. 2004. Explicating the role of mathematical tasks in conceptual learning: An elaboration of the hypothetical learning trajectory. Mathematical Thinking and Learning, 6: 91-104.
-
(2004)
Mathematical Thinking and Learning
, vol.6
, pp. 91-104
-
-
Simon, M.A.1
Tzur, R.2
-
43
-
-
0035729603
-
A new hypothesis concerning children's fractional knowledge
-
Steffe, L. P. 2002. A new hypothesis concerning children's fractional knowledge. Journal of Mathematical Behavior, 20(3): 267-307.
-
(2002)
Journal of Mathematical Behavior
, vol.20
, Issue.3
, pp. 267-307
-
-
Steffe, L.P.1
-
44
-
-
34247566085
-
On the construction of learning trajectories of children: The case of commensurate fractions
-
Steffe, L. P. 2004. On the construction of learning trajectories of children: The case of commensurate fractions. Mathematical Thinking and Learning, 6(2): 129-162.
-
(2004)
Mathematical Thinking and Learning
, vol.6
, Issue.2
, pp. 129-162
-
-
Steffe, L.P.1
-
45
-
-
78650940017
-
The partitioning and fraction schemes
-
In: Steffe L. P., Olive J., editors New York, NY, New York, NY,: Springer
-
Steffe, L. P. 2010. "The partitioning and fraction schemes". In Children's fractional knowledge, Edited by: Steffe, L. P. and Olive, J. 315-340. New York, NY: Springer.
-
(2010)
Children's fractional knowledge
, pp. 315-340
-
-
Steffe, L.P.1
-
46
-
-
0030305056
-
Symbolizing as a constructive activity in a computer microworld
-
Steffe, L. P. and Olive, J. 1996. Symbolizing as a constructive activity in a computer microworld. Journal of Educational Computing Research, 14: 113-138.
-
(1996)
Journal of Educational Computing Research
, vol.14
, pp. 113-138
-
-
Steffe, L.P.1
Olive, J.2
-
47
-
-
84891426172
-
-
New York, NY, New York, NY,: Springer
-
Steffe, L. P. and Olive, J. 2010. Children's fractional knowledge, New York, NY: Springer.
-
(2010)
Children's fractional knowledge
-
-
Steffe, L.P.1
Olive, J.2
-
48
-
-
0002182058
-
Teaching experiment methodology: Underlying principles and essential elements
-
In: Kelly A. E., Lesh R. A., editors Mahwah, NJ, Mahwah, NJ,: Lawrence Erlbaum Associates
-
Steffe, L. P. and Thompson, P. W. 2000. "Teaching experiment methodology: Underlying principles and essential elements". In Handbook of research design in mathematics and science education, Edited by: Kelly, A. E. and Lesh, R. A. 267-306. Mahwah, NJ: Lawrence Erlbaum Associates.
-
(2000)
Handbook of research design in mathematics and science education
, pp. 267-306
-
-
Steffe, L.P.1
Thompson, P.W.2
-
49
-
-
0004158641
-
-
New York, NY, New York, NY,: Summit
-
Stevenson, H. and Stigler, J. 1992. The learning gap, New York, NY: Summit.
-
(1992)
The learning gap
-
-
Stevenson, H.1
Stigler, J.2
-
51
-
-
8644246924
-
Fractions and multiplicative reasoning
-
In: Kilpatrick J., Martin W. G., Schifter D., editors Reston, VA, Reston, VA,: National Council of Teachers of Mathematics
-
Thompson, P. W. and Saldanha, L. A. 2003. "Fractions and multiplicative reasoning". In Research companion to the principles and standards for school mathematics, Edited by: Kilpatrick, J., Martin, W. G. and Schifter, D. 95-113. Reston, VA: National Council of Teachers of Mathematics.
-
(2003)
Research companion to the principles and standards for school mathematics
, pp. 95-113
-
-
Thompson, P.W.1
Saldanha, L.A.2
-
53
-
-
22644452255
-
An integrated study of children's construction of improper fractions and the teacher's role in promoting that learning
-
Tzur, R. 1999. An integrated study of children's construction of improper fractions and the teacher's role in promoting that learning. Journal for Research in Mathematics Education, 30(4): 390-416.
-
(1999)
Journal for Research in Mathematics Education
, vol.30
, Issue.4
, pp. 390-416
-
-
Tzur, R.1
-
55
-
-
84870372828
-
Initial treatment of fractions in Japanese textbooks
-
Watanabe, T. 2007. Initial treatment of fractions in Japanese textbooks. Focus on Learning Problems in Mathematics, 29(2): 41-60.
-
(2007)
Focus on Learning Problems in Mathematics
, vol.29
, Issue.2
, pp. 41-60
-
-
Watanabe, T.1
-
57
-
-
84872551529
-
Validating a written instrument for assessing students' fractions schemes and operations
-
(in press)
-
Wilkins, J. L. M., Norton, A. and Boyce, S. Validating a written instrument for assessing students' fractions schemes and operations. The Mathematics Educator, (in press)
-
The Mathematics Educator
-
-
Wilkins, J.L.M.1
Norton, A.2
Boyce, S.3
-
58
-
-
84865374056
-
Comparing the development of fractions in the fifth- and sixth-graders' textbooks of Singapore, Taiwan, and the USA
-
Yang, D, Reys, R. T. and Wu, L. 2010. Comparing the development of fractions in the fifth- and sixth-graders' textbooks of Singapore, Taiwan, and the USA. School Science and Mathematics, 110(3): 118-127.
-
(2010)
School Science and Mathematics
, vol.110
, Issue.3
, pp. 118-127
-
-
Yang, D.1
Reys, R.T.2
Wu, L.3
|