The DOI matches its Crossref record; 25 of the 25 references it cites were found in a registry or an index.
Local Instruction Theories as Means of Support for Teachers in Reform Mathematics Education
Abstract
This article focuses on a form of instructional design that is deemed fitting for reform mathematics education. Reform mathematics education requires instruction that helps students in developing their current ways of reasoning into more sophisticated ways of mathematical reasoning. This implies that there has to be ample room for teachers to adjust their instruction to the students' thinking. But, the point of departure is that if justice is to be done to the input of the students and their ideas built on, a well-founded plan is needed. Design research on an instructional sequence on addition and subtraction up to 100 is taken as an instance to elucidate how the theory for realistic mathematics education (RME) can be used to develop a local instruction theory that can function as such a plan. Instead of offering an instructional sequence that "works," the objective of design research is to offer teachers an empirically grounded theory on how a certain set of instructional activities can work. The example of addition and subtraction up to 100 is used to clarify how a local instruction theory informs teachers about learning goals, instructional activities, student thinking and learning, and the role of tools and imagery.
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Citations
Cites
Principles of Instructional Design
Gagné, R. M., & Briggs, L. J. (1974) · Cited by 4,467
Brown, A. L. (1992) · Journal of the Learning Sciences · doi:10.1207/s15327809jls0202_2 · Cited by 4,000
Sfard, A. (1991) · Educational Studies in Mathematics · doi:10.1007/bf00302715 · Cited by 1,852 · cited 1×
“The transition from model-of to model-for coincides with a progression from informal to more formal mathematical reasoning that involves the creation of new mathematical reality, which is thought of as consisting of mathematical objects (Sfard, 1991) within a framework of mathematical relations.”
BackgroundReconstructing Mathematics Pedagogy from a Constructivist Perspective
Simon, M. A. (1995) · Journal for Research in Mathematics Education · doi:10.2307/749205 · Cited by 1,474
Mathematics as an Educational Task
Freudenthal, H. (1972) · doi:10.1007/978-94-010-2903-2 · Cited by 1,336
Didactical Phenomenology of Mathematical Structures
(2002) · Mathematics Education Library · doi:10.1007/0-306-47235-x · Cited by 1,046
With an Eye on the Mathematical Horizon: Dilemmas of Teaching Elementary School Mathematics
Ball, D. L. (1993) · The Elementary School Journal · doi:10.1086/461730 · Cited by 1,007
Design Research: What We Learn When We Engage in Design
Edelson, D. C. (2002) · Journal of the Learning Sciences · doi:10.1207/s15327809jls1101_4 · Cited by 978
Principles and Methods of Development Research
van den Akker, J. (1999) · Design Approaches and Tools in Education and Training · doi:10.1007/978-94-011-4255-7_1 · Cited by 905
Developing realistic mathematics education
Gravemeijer, K. P. E. (1994) · TU/e Research Portal · Cited by 858
Self-citation
Cited by
Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008) · Mathematical Thinking and Learning · doi:10.1080/10986060802229675 · Cited by 1,222
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
Van der Kleij, F. M., Vermeulen, J. A., Schildkamp, K., & Eggen, T. J. H. M. (2015) · Assessment in Education: Principles, Policy & Practice · doi:10.1080/0969594x.2014.999024 · Cited by 135
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
Pittalis, M., Pitta-Pantazi, D., & Christou, C. (2018) · Mathematical Thinking and Learning · doi:10.1080/10986065.2018.1474533 · Cited by 18
Metadata
- Authors
- Gravemeijer, K.
- Venue
- Mathematical Thinking and Learning
- Publisher
- Informa UK Limited
- Published
- 2004-04
- Volume
- 6
- Issue
- 2
- Pages
- 105-128
- ISSN
- 1098-6065 (ISSN-L)
- 1532-7833
- OpenAlex
- W2100325963
- Cited by
- 337
- References
- 25
- FWCI
- 18.89
- Type
- journal article
- Language
- en
- Open access
- closed
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Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
