-
1
-
-
72449164159
-
Generalization strategies of beginning high school algebra students
-
In H. Chick & J. L. Vincent (Eds.),). Melbourne, Australia: University of Melbourne
-
Becker, J. R., & Rivera, F. (2005). Generalization strategies of beginning high school algebra students. In H. Chick & J. L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 121-128). Melbourne, Australia: University of Melbourne.
-
(2005)
Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education
, vol.4
, pp. 121-128
-
-
Becker, J.R.1
Rivera, F.2
-
2
-
-
79960303402
-
Establishing and justifying algebraic generalization at the sixth grade level
-
In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.),). Prague: Charles University
-
Becker, J. R., & Rivera, F. (2006a). Establishing and justifying algebraic generalization at the sixth grade level. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 465-472). Prague: Charles University.
-
(2006)
Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education
, vol.4
, pp. 465-472
-
-
Becker, J.R.1
Rivera, F.2
-
3
-
-
72449138791
-
Sixth graders' figural and numerical strategies for generalizing patterns in algebra
-
In S. Alatorre, J. Cortina, M. Sáiz, & A. Méndez (Eds.),). Mérida, México: Universidad Pedagógica Nacional
-
Becker, J. R., & Rivera, F. (2006b). Sixth graders' figural and numerical strategies for generalizing patterns in algebra. In S. Alatorre, J. Cortina, M. Sáiz, & A. Méndez (Eds.), Proceedings of the 28th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 95-101). Mérida, México: Universidad Pedagógica Nacional.
-
(2006)
Proceedings of the 28th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education
, vol.2
, pp. 95-101
-
-
Becker, J.R.1
Rivera, F.2
-
4
-
-
84867377340
-
Factors affecting seventh graders' cognitive perceptions of patterns involving constructive and deconstructive generalization
-
In J. Woo, K. Park, H. Sew, & D. Seo (Eds.),). Seoul, Korea: The Korea Society of Educational Studies in Mathematics
-
Becker, J. R., & Rivera, F. D. (2007). Factors affecting seventh graders' cognitive perceptions of patterns involving constructive and deconstructive generalization. In J. Woo, K. Park, H. Sew, & D. Seo (Eds.), Proceedings of the 31st conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 129-136). Seoul, Korea: The Korea Society of Educational Studies in Mathematics.
-
(2007)
Proceedings of the 31st conference of the International Group for the Psychology of Mathematics Education
, vol.4
, pp. 129-136
-
-
Becker, J.R.1
Rivera, F.D.2
-
5
-
-
18244364196
-
Linear geometric number patterns: Middle school students' strategies
-
Bishop, J. (2000). Linear geometric number patterns: Middle school students' strategies. Mathematics Education Research Journal, 12(2), 107-126.
-
(2000)
Mathematics Education Research Journal
, vol.12
, Issue.2
, pp. 107-126
-
-
Bishop, J.1
-
9
-
-
3843111596
-
Forms and means of generalization in mathematics
-
In A. Bishop, S. Mellin-Olsen, & J. van Dormolen (Eds.),. Dordrecht, Netherlands: Kluwer
-
Dörfler, W. (1991). Forms and means of generalization in mathematics. In A. Bishop, S. Mellin-Olsen, & J. van Dormolen (Eds.), Mathematical knowledge: Its growth through teaching (pp. 63-85). Dordrecht, Netherlands: Kluwer.
-
(1991)
Mathematical knowledge: Its growth through teaching
, pp. 63-85
-
-
Dörfler, W.1
-
10
-
-
0039377060
-
Seeing, believing, and knowing
-
In D. Osherson, S. M. Kosslyn, & J. Hollerback (Eds.),. Cambridge, Massachusetts: MIT Press
-
Dretske, F. (1990). Seeing, believing, and knowing. In D. Osherson, S. M. Kosslyn, & J. Hollerback (Eds.), Visual cognition and action: An invitation to cognitive science (pp. 129-148). Cambridge, Massachusetts: MIT Press.
-
(1990)
Visual cognition and action: An invitation to cognitive science
, pp. 129-148
-
-
Dretske, F.1
-
11
-
-
1042300390
-
Geometry from a cognitive point of view
-
In C. Mammana, & V. Villani (Eds.),. Boston: Kluwer
-
Duval, R. (1998). Geometry from a cognitive point of view. In C. Mammana, & V. Villani (Eds.), Perspectives in the teaching of geometry for the 21st century (pp. 29-83). Boston: Kluwer.
-
(1998)
Perspectives in the teaching of geometry for the 21st century
, pp. 29-83
-
-
Duval, R.1
-
12
-
-
33645709902
-
A cognitive analysis of problems of comprehension in a learning of mathematics
-
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Edcational Studies in Mathematics, 61(1 & 2), 103-131.
-
(2006)
Edcational Studies in Mathematics
, vol.61
, Issue.1-2
, pp. 103-131
-
-
Duval, R.1
-
13
-
-
33845507055
-
Introducing the variable through pattern exploration
-
English, L., & Warren, E. (1998). Introducing the variable through pattern exploration. Mathematics Teacher, 91, 166-170.
-
(1998)
Mathematics Teacher
, vol.91
, pp. 166-170
-
-
English, L.1
Warren, E.2
-
16
-
-
77957070821
-
A rational-constructivist account of early learning about numbers and objects
-
In D. Medin (Eds.),) New York: Academic
-
Gelman, R. (1993). A rational-constructivist account of early learning about numbers and objects. In D. Medin (Eds.), Learning and Motivation (Vol. 30, pp. 61-96) New York: Academic.
-
(1993)
Learning and Motivation
, vol.30
, pp. 61-96
-
-
Gelman, R.1
-
17
-
-
0001721873
-
Enabling constraints for cognitive development and learning: Domain specificity and epigenesis
-
In W. Damon, D. Kuhn, & R. Siegler (Eds.), (5th edn,). New York: Wiley
-
Gelman, R. & Williams, E. (1998). Enabling constraints for cognitive development and learning: Domain specificity and epigenesis. In W. Damon, D. Kuhn, & R. Siegler (Eds.), Cognition, perception, and language: Vol. 2 Handbook of child psychology (5th edn, pp. 575-630). New York: Wiley.
-
(1998)
Cognition, perception, and language: Vol. 2 Handbook of child psychology
, pp. 575-630
-
-
Gelman, R.1
Williams, E.2
-
18
-
-
36348980062
-
A hypothetical learning trajectory on measurement and flexible arithmetic
-
Gravemeijer, K. P. E., Bowers, J., & Stephan, M. L. (2003). A hypothetical learning trajectory on measurement and flexible arithmetic. Journal for Research in Mathematics Education, 12, 51-66.
-
(2003)
Journal for Research in Mathematics Education
, vol.12
, pp. 51-66
-
-
Gravemeijer, K.P.E.1
Bowers, J.2
Stephan, M.L.3
-
19
-
-
3843074629
-
Context problems in realistic mathematics education: A calculus course as an example
-
Gravemeijer, K. P. E., & Doorman, M. (1999). Context problems in realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics 39(1-3), 111-129.
-
(1999)
Educational Studies in Mathematics
, vol.39
, Issue.1-3
, pp. 111-129
-
-
Gravemeijer, K.P.E.1
Doorman, M.2
-
20
-
-
0000527765
-
Early understandings of numbers: Paths or barriers to the construction of new understandings?
-
Hartnett, P., & Gelman, R. (1998). Early understandings of numbers: Paths or barriers to the construction of new understandings? Learning and Instruction: The Journal of the European Association for Research in Learning and Instruction, 8(4), 341-374.
-
(1998)
Learning and Instruction: The Journal of the European Association for Research in Learning and Instruction
, vol.8
, Issue.4
, pp. 341-374
-
-
Hartnett, P.1
Gelman, R.2
-
22
-
-
52649120240
-
The cognitive and symbolic analysis of the generalization process: The comparison of algebraic signs with geometric figures
-
In E. Pehkonnen (Ed.),). Lahti, Finland
-
Iwasaki, H., & Yamaguchi, T. (1997). The cognitive and symbolic analysis of the generalization process: The comparison of algebraic signs with geometric figures. In E. Pehkonnen (Ed.), Proceedings of the 21st Annual Conference of the Psychology of Mathematics Education (Vol. 3, pp. 105-113). Lahti, Finland.
-
(1997)
Proceedings of the 21st Annual Conference of the Psychology of Mathematics Education
, vol.3
, pp. 105-113
-
-
Iwasaki, H.1
Yamaguchi, T.2
-
23
-
-
0038361483
-
Algebra
-
In K. Hart (Ed.),. London: Murray
-
Küchemann, D. (1981). Algebra. In K. Hart (Ed.), Children's understanding of mathematics: 11-16 (pp. 102-119). London: Murray.
-
(1981)
Children's understanding of mathematics
, vol.11-16
, pp. 102-119
-
-
Küchemann, D.1
-
24
-
-
33846123777
-
Generalization and justification: The challenge of introducing algebraic reasoning through patterning activities
-
Lannin, J. (2005). Generalization and justification: The challenge of introducing algebraic reasoning through patterning activities. Mathematical Thinking and Learning, 7(3), 231-258.
-
(2005)
Mathematical Thinking and Learning
, vol.7
, Issue.3
, pp. 231-258
-
-
Lannin, J.1
-
25
-
-
33846165073
-
Recursive and explicit rules: How can we build student algebraic understanding
-
Lannin, J., Barker, D., & Townsend, B. (2006). Recursive and explicit rules: How can we build student algebraic understanding. Journal of Mathematical Behavior, 25, 299-317.
-
(2006)
Journal of Mathematical Behavior
, vol.25
, pp. 299-317
-
-
Lannin, J.1
Barker, D.2
Townsend, B.3
-
26
-
-
17144392686
-
An initiation into algebra culture through generalization activities
-
In C. Bednarz, C. Kieran, & L. Lee (Eds.),. Dordrecht, Netherlands: Kluwer
-
Lee, L. (1996). An initiation into algebra culture through generalization activities. In C. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 87-106). Dordrecht, Netherlands: Kluwer.
-
(1996)
Approaches to algebra: Perspectives for research and teaching
, pp. 87-106
-
-
Lee, L.1
-
27
-
-
14844327841
-
How "focusing phenomena" in the instructional environment support individual students' generalizations
-
Lobato, J., Ellis, A., & Muñoz, R. (2003). How "focusing phenomena" in the instructional environment support individual students' generalizations. Mathematical Thinking and Learning, 5(1), 1-36.
-
(2003)
Mathematical Thinking and Learning
, vol.5
, Issue.1
, pp. 1-36
-
-
Lobato, J.1
Ellis, A.2
Muñoz, R.3
-
28
-
-
52849122329
-
A comparison of pattern-based and equation-solving approaches to algebra
-
In B. Southwell, K. Owens, & B. Perry (Eds.),. Brisbane, Australia: MERGA
-
MacGregor, M., & Stacey, K. (1992). A comparison of pattern-based and equation-solving approaches to algebra. In B. Southwell, K. Owens, & B. Perry (Eds.), Proceedings of the Fifteenth Annual Conference of the Mathematics Education Research Group of Austalasia (pp. 362-371). Brisbane, Australia: MERGA.
-
(1992)
Proceedings of the Fifteenth Annual Conference of the Mathematics Education Research Group of Austalasia
, pp. 362-371
-
-
McGregor, M.1
Stacey, K.2
-
29
-
-
0033095839
-
Teacher questioning to promote justification and generalization in mathematics: What research practice has taught us
-
Martino, A. M., & Maher, C. A. (1999). Teacher questioning to promote justification and generalization in mathematics: What research practice has taught us. Journal of Mathematical Behavior 18(1), 53-78.
-
(1999)
Journal of Mathematical Behavior
, vol.18
, Issue.1
, pp. 53-78
-
-
Martino, A.M.1
Maher, C.A.2
-
30
-
-
3843109453
-
Expressing generality and roots of algebra
-
In N. Bednarz, C. Kieran, & L. Lee (Eds.),. Dordrecht, Netherlands: Kluwer
-
Mason, J. (1996). Expressing generality and roots of algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 65-86). Dordrecht, Netherlands: Kluwer.
-
(1996)
Approaches to algebra: Perspectives for research and teaching
, pp. 65-86
-
-
Mason, J.1
-
33
-
-
85186284408
-
Pictorial and practical contexts and the perception of pattern
-
In A. Orton (Ed.),. London: Cassell
-
Orton, J., Orton, A., & Roper, T. (1999). Pictorial and practical contexts and the perception of pattern. In A. Orton (Ed.), Patterns in the teaching and learning of mathematics (pp. 121-136). London: Cassell.
-
(1999)
Patterns in the teaching and learning of mathematics
, pp. 121-136
-
-
Orton, J.1
Orton, A.2
Roper, T.3
-
34
-
-
0042173905
-
Signs and meanings in students' emergent algebraic thinking: A semiotic analysis
-
Radford, L. (2000). Signs and meanings in students' emergent algebraic thinking: A semiotic analysis. Educational Studies in Mathematics 42, 237-268.
-
(2000)
Educational Studies in Mathematics
, vol.42
, pp. 237-268
-
-
Radford, L.1
-
35
-
-
33747889407
-
The historical origins of algebraic thinking
-
In R. Sutherland, T. Rojano, A. Bell, & R. Lins (Eds.),. Dordrecht: Kluwer
-
Radford, L. (2001). The historical origins of algebraic thinking. In R. Sutherland, T. Rojano, A. Bell, & R. Lins (Eds.), Perspectives in school algebra (pp. 13-63). Dordrecht: Kluwer.
-
(2001)
Perspectives in school algebra
, pp. 13-63
-
-
Radford, L.1
-
36
-
-
27944486500
-
The seen, the spoken, and the written: A Semiotic approach to the problem of objectification of mathematical knowledge
-
Radford, L. (2002). The seen, the spoken, and the written: A Semiotic approach to the problem of objectification of mathematical knowledge. For the Learning of Mathematics, 22(2), 14-23.
-
(2002)
For the Learning of Mathematics
, vol.22
, Issue.2
, pp. 14-23
-
-
Radford, L.1
-
37
-
-
29144470673
-
Gestures, speech, and the sprouting of signs: A semiotic-cultural approach to students' types of generalization
-
Radford, L. (2003). Gestures, speech, and the sprouting of signs: A semiotic-cultural approach to students' types of generalization. Mathematical Thinking and Learning, 5(1), 37-70.
-
(2003)
Mathematical Thinking and Learning
, vol.5
, Issue.1
, pp. 37-70
-
-
Radford, L.1
-
38
-
-
64949126314
-
Algebraic thinking and the generalization of patterns: A semiotic perspective
-
In S. Alatorre, J. Cortina, M. Sáiz, & A. Méndez (Eds.),). México: UPN
-
Radford, L. (2006). Algebraic thinking and the generalization of patterns: A semiotic perspective. In S. Alatorre, J. Cortina, M. Sáiz, & A. Méndez (Eds.), Proceedings of the 28th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 2-21). México: UPN.
-
(2006)
Proceedings of the 28th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education
, vol.1
, pp. 2-21
-
-
Radford, L.1
-
39
-
-
2442535873
-
Analogy use in eighth-grade mathematics classrooms
-
Richland, L., Holyoak, K., & Stigler, J. (2004). Analogy use in eighth-grade mathematics classrooms. Cognition and Instruction, 22(1), 37-60.
-
(2004)
Cognition and Instruction
, vol.22
, Issue.1
, pp. 37-60
-
-
Richland, L.1
Holyoak, K.2
Stigler, J.3
-
40
-
-
77950649494
-
The effects of figural and numerical cues on the induction processes of preservice elementary teachers
-
In N. Pateman, B. Dougherty, & J. Zilliox (Eds.),). Honolulu, HA: University of Hawaii
-
Rivera, F., & Becker, J. R. (2003). The effects of figural and numerical cues on the induction processes of preservice elementary teachers. In N. Pateman, B. Dougherty, & J. Zilliox (Eds.), Proceedings of the Joint Meeting PME and PMENA (Vol. 4, pp. 63-70). Honolulu, HA: University of Hawaii.
-
(2003)
Proceedings of the Joint Meeting PME and PMENA
, vol.4
, pp. 63-70
-
-
Rivera, F.1
Becker, J.R.2
-
41
-
-
34547764196
-
Abduction-induction (generalization) processes of elementary majors on figural patterns in algebra
-
Rivera, F., & Becker, J. R. (2007). Abduction-induction (generalization) processes of elementary majors on figural patterns in algebra. Journal of Mathematical Behavior, 140-155.
-
(2007)
Journal of Mathematical Behavior
, pp. 140-155
-
-
Rivera, F.1
Becker, J.R.2
-
43
-
-
52849137145
-
Factors influencing students' generalization thinking processes
-
In O. Zaslavsky (Ed.),). Haifa: Israel Institute of Technology
-
Sasman, M., Olivier, A., & Linchevski, L. (1999). Factors influencing students' generalization thinking processes. In O. Zaslavsky (Ed.), Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 161-168). Haifa: Israel Institute of Technology.
-
(1999)
Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education
, vol.4
, pp. 161-168
-
-
Sasman, M.1
Olivier, A.2
Linchevski, L.3
-
44
-
-
33845507053
-
The development of algebra: Confronting historical and psychological perspectives
-
Sfard, A. (1995). The development of algebra: Confronting historical and psychological perspectives. Journal of Mathematical Behavior 12, 353-383.
-
(1995)
Journal of Mathematical Behavior
, vol.12
, pp. 353-383
-
-
Sfard, A.1
-
45
-
-
84867392585
-
-
Chicago, Illinois: Encyclopaedia Brittanica, Inc
-
Spence, M., Simon, A., & Pligge, M. (2006). Patterns and Figures. Chicago, Illinois: Encyclopaedia Brittanica, Inc.
-
(2006)
Patterns and Figures
-
-
Spence, M.1
Simon, A.2
Pligge, M.3
-
46
-
-
1842768042
-
Finding and using patterns in linear generalizing problems
-
Stacey, K. (1989). Finding and using patterns in linear generalizing problems. Educational Studies in Mathematics, 20, 147-164.
-
(1989)
Educational Studies in Mathematics
, vol.20
, pp. 147-164
-
-
Stacey, K.1
-
47
-
-
33846136539
-
Curriculum reform and approaches to algebra
-
In R. Sutherland, T. Rojano, A. Bell, & R. Lins (Eds.),. Dordrecht, Netherlands: Kluwer
-
Stacey, K., & MacGregor, M. (2001). Curriculum reform and approaches to algebra. In R. Sutherland, T. Rojano, A. Bell, & R. Lins (Eds.), Perspectives on school algebra (pp. 141-154). Dordrecht, Netherlands: Kluwer.
-
(2001)
Perspectives on school algebra
, pp. 141-154
-
-
Stacey, K.1
McGregor, M.2
-
48
-
-
8644227820
-
A schematic-theoretic view of problem solving and development of algebraic thinking
-
Steele, D., & Johanning, D. (2004). A schematic-theoretic view of problem solving and development of algebraic thinking. Educational Studies in Mathematics, 57, 65-90.
-
(2004)
Educational Studies in Mathematics
, vol.57
, pp. 65-90
-
-
Steele, D.1
Johanning, D.2
-
49
-
-
22844453992
-
Grade 6 students' preinstructional use of equations to describe and represent problem situations
-
Swafford, J., & Langrall, C. (2000). Grade 6 students' preinstructional use of equations to describe and represent problem situations. Journal for Research in Mathematics Education, 31(1), 89-112.
-
(2000)
Journal for Research in Mathematics Education
, vol.31
, Issue.1
, pp. 89-112
-
-
Swafford, J.1
Langrall, C.2
|