Those Who Understand: Knowledge Growth in Teaching
Abstract
Esta investigación tiene como propósito analizar algunos referentes teóricos sobre la Filosofía de las Matemáticas (FM) y el conocimiento del profesor de Matemáticas (CPM), con el fin de presentar evidencias de la articulación e integración de la FM en los modelos del CPM en función del quehacer docente, particularmente el sugerido por Stacey (2008). Por lo anterior, se sistematizan y describen los planteamientos de algunas fuentes bibliográficas referentes a la FM y a los modelos del CPM con la intención de aportar información sobre la relación que hay entre la Didáctica de las Matemáticas (DM), la FM, y el CPM.
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PCK, as conceptualised by Shulman (1986), emphasises the transformation of subject matter knowledge into pedagogically meaningful and developmentally appropriate learning experiences.
“PCK, as conceptualised by Shulman (1986), emphasises the transformation of subject matter knowledge into pedagogically meaningful and developmentally appropriate learning experiences.”
From Teaching Science anew in the Foundation Phase: Reimagining pre-service teacher learning for Inclusive Early Pedagogy (2026) · cites this paper as Shulman (1986)
Teachers' discipline-specific knowledge is often manifested and evidenced in their practices.
“it is often manifested and evidenced in their practices (e.g., Ball et al., 2008;Shulman, 1986;Tchoshanov, 2010).”
From Preservice teachers' mathematical knowledge for teaching: Focus on lesson planning and reflection (2024) · cites this paper as Shulman, 1986
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Cheng, L., Antonenko, P. D., & Ritzhaupt, A. D. (2024) · Educational Technology Research and Development · doi:10.1007/s11423-023-10276-3 · Cited by 19 · see citing works
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Tang, X., Yuan, Z., Deng, X., & Xiang, L. (2023) · Electronic Research Archive · doi:10.3934/era.2023318 · Cited by 14 · see citing works
Coady, M., Miller, M. D., Jing, Z., Heffington, D., Lopez, M., Olszewska, A., De Jong, E., Yilmaz, T., & Ankeny, R. (2020) · TESOL Quarterly · doi:10.1002/tesq.544 · Cited by 14 · see citing works
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Nelson, P. M., Van Norman, E. R., Parker, D. C., & Cormier, D. C. (2019) · Journal of Applied School Psychology · doi:10.1080/15377903.2019.1568334 · Cited by 10 · see citing works
Wellberg, S. (2025) · Journal of Mathematics Teacher Education · doi:10.1007/s10857-024-09640-8 · Cited by 10 · see citing works
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dos Reis, K., & Braund, M. (2019) · Africa Education Review · doi:10.1080/18146627.2018.1460210 · Cited by 7 · see citing works
Computing Education Research Today
Fincher, S. A., Tenenberg, J., Dorn, B., Hundhausen, C., McCartney, R., & Murphy, L. (2019) · The Cambridge Handbook of Computing Education Research · doi:10.1017/9781108654555.003 · Cited by 7 · see citing works
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Chapter 1: Problem-based learning: A 21st-century teaching and learning strategy
Research Unit Self-Directed Learning, F. O. E., Golightly, A., Sebatana, M. J., & School of Mathematics, S. A. T. E. (2023) · NWU Self-Directed Learning Series · doi:10.4102/aosis.2023.bk409.01 · Cited by 1 · see citing works
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Santschi, S. (2026) · Teaching in Higher Education · doi:10.1080/13562517.2026.2671391 · Cited by 1 · see citing works
Dhakal, P. K., & Khanal, B. (2025) · Academic Journal of Mathematics Education · doi:10.3126/ajme.v8i1.95353
Ruswa, N., & Nhase, Z. (2026) · Journal of Education and Learning Technology · doi:10.38159/jelt.20267410
- Authors
- SHULMAN, L. S.
- Affiliations
- Stanford University (US)
- Corresponding author
- SHULMAN, LEE S.
- Venue
- Educational Researcher
- Published
- 1986-02
- Volume
- 15
- Issue
- 2
- Pages
- 4-14
- ISSN
- 0013-189X (ISSN-L)
- 1935-102X
- OpenAlex
- W2140369176
- Cited by
- 18,546
- References
- 0
- Citations by year
- 2026: 836 · 2025: 784 · 2024: 667 · 2023: 879 · 2022: 1086 · 2021: 1085 · 2020: 1109 · 2019: 1133 · 2018: 1023 · 2017: 927 · 2016: 961 · 2015: 1127 · 2014: 886 · 2013: 915 · 2012: 780
- FWCI
- 301.39
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Educational Researcher (publishedVersion)
- Topics
- Social Sciences › Education › Mathematics Education and Teaching Techniques
- Physical Sciences › Mathematics › Theoretical Computer Science › History and Theory of Mathematics
- Physical Sciences › Mathematics › Applied Mathematics › Mathematics Education and Pedagogy
- Keywords
- philosophy of mathematics, mathematical knowledge for teaching, mathematics education, teaching practice
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