New light on old horizon: Constructing mathematical concepts, underlying abstraction processes, and sense making strategies

Journal article


Scheiner, Thorsten. (2016) New light on old horizon: Constructing mathematical concepts, underlying abstraction processes, and sense making strategies. Educational Studies in Mathematics: An international journal. 91(2), pp. 165 - 183. https://doi.org/10.1007/s10649-015-9665-4
AuthorsScheiner, Thorsten
Abstract

The initial assumption of this article is that there is an overemphasis on abstraction-from-actions theoretical approaches in research on knowing and learning mathematics. This article uses a critical reflection on research on students’ ways of constructing mathematical concepts to distinguish between abstraction-from-actions theoretical approaches and abstraction-from-objects theoretical approaches. Acknowledging and building on research on knowing and learning processes in mathematics, this article presents a theoretical framework that provides a new perspective on the underlying abstraction processes and a new approach for interpreting individuals’ ways of constructing concepts on the background of their strategies to make sense of a mathematical concept. The view taken here is that the abstraction-from-actions and abstraction-from-objects approaches (although different) are complementary (rather than opposing) frameworks. The article is concerned with the theoretical description of the framework rather than with its use in empirical investigations. This article addresses the need for more advanced theoretical work in research on mathematical learning and knowledge construction.

KeywordsCognition; Learner types; Reflective abstraction; Reflectural abstraction; Sense making strategies; Structural abstraction; Theory development
Year2016
JournalEducational Studies in Mathematics: An international journal
Journal citation91 (2), pp. 165 - 183
PublisherSpringer International Publishing
ISSN0013-1954
Digital Object Identifier (DOI)https://doi.org/10.1007/s10649-015-9665-4
Scopus EID2-s2.0-84953638432
Page range165 - 183
Research GroupInstitute for Learning Sciences and Teacher Education (ILSTE)
Publisher's version
File Access Level
Controlled
Place of publicationNetherlands
Permalink -

https://acuresearchbank.acu.edu.au/item/85444/new-light-on-old-horizon-constructing-mathematical-concepts-underlying-abstraction-processes-and-sense-making-strategies

Restricted files

Publisher's version

  • 12
    total views
  • 0
    total downloads
  • 0
    views this month
  • 0
    downloads this month
These values are for the period from 19th October 2020, when this repository was created.

Export as

Related outputs

Mathematics teacher learning to notice : A systematic review of studies of video-based programs
Santagata, Rossella, König, Johannes, Scheiner, Thorsten, Nguyen, Ha, Adleff, Ann-Kristin, Yang, Xinrong and Kaiser, Gabriele. (2021) Mathematics teacher learning to notice : A systematic review of studies of video-based programs. ZDM Mathematics Education. 53(1), pp. 119-134. https://doi.org/10.1007/s11858-020-01216-z
Towards a more comprehensive model of teacher noticing
Scheiner, Thorsten. (2021) Towards a more comprehensive model of teacher noticing. ZDM. 53, pp. 85-94. https://doi.org/10.1007/s11858-020-01202-5
What makes mathematics teacher knowledge specialized? Offering alternative views
Scheiner, Thorsten, Montes, Miguel A., Godino, Juan D., Carrillo, José and Pino-Fan, Luis R.. (2019) What makes mathematics teacher knowledge specialized? Offering alternative views. International Journal of Science and Mathematics Education. 17(1), pp. 153 - 172. https://doi.org/10.1007/s10763-017-9859-6
If we want to get ahead, we should transcend dualisms and foster paradigm pluralism
Scheiner, Thorsten. (2019) If we want to get ahead, we should transcend dualisms and foster paradigm pluralism. In In G. Kaiser and N. Presmeg (Ed.). Compendium for Early Career Researchers in Mathematics Education pp. 511 - 531 SpringerOpen. https://doi.org/10.1007/978-3-030-15636-7_27
Emerging perspectives in mathematical cognition: Contextualizing, complementizing, and complexifying
Scheiner, Thorsten and Pinto, Marcia M. F.. (2019) Emerging perspectives in mathematical cognition: Contextualizing, complementizing, and complexifying. Educational Studies in Mathematics: An international journal. 101(3), pp. 357 - 372. https://doi.org/10.1007/s10649-019-9879-y
Mathematics cognition reconsidered: On ascribing meaning
Scheiner, Thorsten. (2018) Mathematics cognition reconsidered: On ascribing meaning. United States of America: Research in Undergraduate Mathematics Education. pp. 1234 - 1239
Theoretical advances in mathematical cognition
Scheiner, Thorsten and Pinto, Marcia M. F.. (2018) Theoretical advances in mathematical cognition. Chile: The International Group for the Psychology of Mathematics Education. pp. 97 - 104
Sense-making in mathematics: Towards a dialogical framing
Scheiner, Thorsten. (2018) Sense-making in mathematics: Towards a dialogical framing. New Zealand: MERGA. pp. 669 - 676
Conception to concept or concept to conception? From being to becoming
Scheiner, Thorsten. (2017) Conception to concept or concept to conception? From being to becoming. In B. Kaur, W. K. Ho and T. L. Toh and B. H. Choy (Ed.). 41st Conference of the International Group for the Psychology of Mathematics Education. Singapore: National Institute of Education, Nanyang Technological University. pp. 145 - 152
Emerging insights from the evolving framework of structural abstraction
Scheiner, Thorsten and Pinto, Márcia M. F.. (2017) Emerging insights from the evolving framework of structural abstraction. In A. Weinberg, C. Rasmussen and J. Rabin, M. Wawro and S. Brown (Ed.). 20th Annual Conference on Research in Undergraduate Mathematics Education, San Diego, California. San Diego, California: Research in Undergraduate Mathematics Education. pp. 274 - 284
Crossing the boundaries of our historical ways of thinking in conceptualizing teachers' knowledge
Scheiner, Thorsten. (2016) Crossing the boundaries of our historical ways of thinking in conceptualizing teachers' knowledge. 2016 Annual Meeting of the American Educational Research Association. Washington, D.C., United States of Amreica 08 - 12 Apr 2016 American Educational Research Association. pp. 1-5
Images of abstraction in mathematics education: Contradictions, controversies, and convergences
Scheiner, Thorsten and Pinto, Márcia M. F.. (2016) Images of abstraction in mathematics education: Contradictions, controversies, and convergences. In C. Csíkos, A. Rausch and J. Szitányi (Ed.). 40th Conference of the International Group for Psychology of Mathematics Education. Szeged, Hungary: International Group for the Psychology of Mathematics. pp. 155 - 162
Making sense of students' sense making through the lens of the structural abstraction framework
Pinto, Márcia M. F. and Scheiner, Thorsten. (2016) Making sense of students' sense making through the lens of the structural abstraction framework. In E. Nardi, C. Winsløw and T. Hausberger (Ed.). First Conference of the International Network for Didactic Research in University Mathematics. Montpellier, France: University of Montpellier and INDRUM. pp. 474 - 483
Teacher noticing: Enlightening or blinding?
Scheiner, Thorsten. (2016) Teacher noticing: Enlightening or blinding? ZDM: The International Journal on Mathematics Education. 48(1 - 2), pp. 227 - 238. https://doi.org/10.1007/s11858-016-0771-2
Lessons we have (not) learned from past and current conceptualizations of mathematics teachers' knowledge
Scheiner, Thorsten. (2015) Lessons we have (not) learned from past and current conceptualizations of mathematics teachers' knowledge. In K. Krainer and N. Vondrová (Ed.). Ninth Congress of the European Society for Research in Mathematics Education (CERME9, 4-8 February 2015). Prague, Czech Republic: Charles University in Prague. pp. 3248 - 3253
Theorising about mathematics teachers' professional knowledge: The content, form, nature, and source of teachers' knowledge
Scheiner, Thorsten. (2015) Theorising about mathematics teachers' professional knowledge: The content, form, nature, and source of teachers' knowledge. In M. Marshman, V. Geiger and A. Bennison (Ed.). 38th annual conference of the Mathematics Education Research Group of Australasia. Australia: Mathematics Education Research Group of Australasia. pp. 563 - 570
Shifting the emphasis toward a structural description of (mathematics) teachers' knowledge
Scheiner, Thorsten. (2015) Shifting the emphasis toward a structural description of (mathematics) teachers' knowledge. In K. Beswick, T. Muir and J. Fielding-Wells (Ed.). 39th Conference of the International Group for the Psychology of Mathematics Education. Hobart, Australia: Uniprint, University of Tasmania. pp. 129 - 136
Cognitive processes underlying mathematical concept construction: The missing process of structural abstraction
Scheiner, Thorsten and Pinto, Márcia M. F.. (2014) Cognitive processes underlying mathematical concept construction: The missing process of structural abstraction. In C. Nicol, S. Oesterle and P. Liljedahl and D. Allen (Ed.). 38th Conference of the International Group for the Psychology of Mathematics Education and 36th Conference of the North American Chapter of the Psychology of Mathematics Education. Vancouver, Canada: The International Group for the Psychology of Mathematics Education. pp. 105 - 112