The DOI matches its Crossref record; 28 of the 28 references it cites were found in a registry or an index.
Explicating the Role of Mathematical Tasks in Conceptual Learning: An Elaboration of the Hypothetical Learning Trajectory
Abstract
Simon's (1995) development of the construct of hypothetical learning trajectory (HLT) offered a description of key aspects of planning mathematics lessons. An HLT consists of the goal for the students' learning, the mathematical tasks that will be used to promote student learning, and hypotheses about the process of the students' learning. However, the construct of HLT provided no framework for thinking about the learning process, the selection of mathematical task, or the role of the mathematical tasks in the learning process. Such a framework could contribute significantly to the generation of useful HLTs. In this article we demonstrate how an elaboration of reflective abstraction (i.e., reflection on activity-effect relationships), postulated by Simon, Tzur, Heinz, and Kinzel (in press), can provide such a framework and thus a theoretical elaboration of the HLT construct.
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Citations
Cites
National Council of Teachers of Mathematics
(1979) · The Mathematics Teacher · doi:10.5951/mt.72.8.0637 · Cited by 8,499
The Construction Of Reality In The Child
Piaget, J. (2013) · Routledge eBooks · doi:10.4324/9781315009650 · Cited by 4,568
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Sfard, A. (1991) · Educational Studies in Mathematics · doi:10.1007/bf00302715 · Cited by 1,852 · cited 1×
“Consistent with the work of others (e.g., Dubinsky, 1991; Piaget, 1954; Pirie & Kieren, 1994; Sfard, 1991), our empirical work has led to distinctions among stages of conceptual learning.”
ResultReconstructing Mathematics Pedagogy from a Constructivist Perspective
Simon, M. A. (1995) · Journal for Research in Mathematics Education · doi:10.2307/749205 · Cited by 1,474
Self-citationTheory of didactical situations in mathematics
Brousseau, G. (1997) · Cited by 1,212
The equilibration of cognitive structures : the central problem of intellectual development
Piaget, J., Brown, T., & Thampy, K. J. (1985) · University of Chicago Press eBooks · Cited by 901
Developing realistic mathematics education
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Reflective Abstraction in Advanced Mathematical Thinking
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Cited by
Developing a hypothetical multi‐dimensional learning progression for the nature of matter
Stevens, S. Y., Delgado, C., & Krajcik, J. S. (2010) · Journal of Research in Science Teaching · doi:10.1002/tea.20324 · Cited by 265
Facilitating the Transition from Empirical Arguments to Proof
Stylianides, G. J., & Stylianides, A. J. (2009) · Journal for Research in Mathematics Education · doi:10.5951/jresematheduc.40.3.0314 · Cited by 198
Fonger, N. L., Stephens, A., Blanton, M., Isler, I., Knuth, E., & Gardiner, A. M. (2018) · Cognition and Instruction · doi:10.1080/07370008.2017.1392965 · Cited by 46
Youth and Video Games: Exploring Effects on Learning and Engagement
Evans, M. A., Norton, A., Chang, M., Deater-Deckard, K., & Balci, O. (2013) · Zeitschrift für Psychologie · doi:10.1027/2151-2604/a000135 · Cited by 29
Metadata
- Authors
- Simon, M. A., & Tzur, R.
- Venue
- Mathematical Thinking and Learning
- Publisher
- Informa UK Limited
- Published
- 2004-04
- Volume
- 6
- Issue
- 2
- Pages
- 91-104
- ISSN
- 1098-6065 (ISSN-L)
- 1532-7833
- OpenAlex
- W1977340441
- Cited by
- 411
- References
- 28
- FWCI
- 18.89
- Type
- journal article
- Language
- en
- Open access
- closed
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