Visualization and the teaching of mathematical analysis

Journal article

Fusaro Pinto, Márcia Maria and Scheiner, Thorsten. (2015). Visualization and the teaching of mathematical analysis. Educacao Matematica Pesquisa. 17(3), pp. 637-654.
AuthorsFusaro Pinto, Márcia Maria and Scheiner, Thorsten
Abstract

The teaching of mathematical analysis has been investigated and debated for

decades from different theoretical perspectives. The current and continuing debate is justified by the numerous reports of the obstacles in the teaching and learning of the subject, in its delimitation in the different curricula, in the convenience or even relevance of its study in the different courses, amongst others. Here, we intend to propose elements for the discussion on the use of visual representations in formal mathematical arguments, for the teaching and learning of mathematical analysis, presenting the notion of structural abstraction.

Keywordsvisualization; structural abstraction; mathematical argumentation; mathematics education in the tertiary level
Year2015
JournalEducacao Matematica Pesquisa
Journal citation17 (3), pp. 637-654
PublisherPontifical Catholic University of São Paulo
ISSN1983-3156
Web address (URL)https://www.proquest.com/scholarly-journals/visualização-e-ensino-de-análise-matemática/docview/1740278885/se-2?accountid=8194
Open accessPublished as ‘gold’ (paid) open access
Research or scholarlyResearch
Page range637-654
Publisher's version
License
All rights reserved
File Access Level
Open
Output statusPublished
Publication dates
Online2015
Publication process dates
Deposited09 Sep 2021
Permalink -

https://acuresearchbank.acu.edu.au/item/8wvzw/visualization-and-the-teaching-of-mathematical-analysis

Log in to edit

Download files

Publisher's version
Pinto_2015_Visualization_and_the_teaching_of_mathematical.pdf
License: All rights reserved
File access level: Open

  • 94
    total views
  • 41
    total downloads
  • 3
    views this month
  • 2
    downloads this month
These values are for the period from 19th October 2020, when this repository was created.

Export as

Related outputs

Addressing equity, diversity and inclusion in academic publishing : key initiatives from JMTE
Scheiner, Thorsten, Brodie, Karin, Planas, Núria, Darragh, Lisa, Halai, Anjum, Potari, Despina, Santos-Trigo, Manuel and Walkoe, Janet. (2024). Addressing equity, diversity and inclusion in academic publishing : key initiatives from JMTE. Journal of Mathematics Teacher Education. pp. 1-11. https://doi.org/10.1007/s10857-024-09636-4
Embracing local insights for global advancement
Scheiner, Thorsten. (2024). Embracing local insights for global advancement. Journal of Mathematics Teacher Education. 27, pp. 547-550. https://doi.org/10.1007/s10857-024-09645-3
Longitudinal Studies on Video-based Interventions for Mathematics Teacher Noticing
Santagata, Rossella, Liu, Jinqing, Scheiner, Thorsten, König, Johannes and Kaiser, Gabriele Agnes Hildegard. (2024). Longitudinal Studies on Video-based Interventions for Mathematics Teacher Noticing . In In Blikstad-Balas, Marte and Staal Jenset, Inga (Ed.). Using Video to Foster Teacher Development : Improving Professional Practice through Adaptation and Reflection pp. 113 Routledge. https://doi.org/10.4324/9781003427414-11
Exploring prospective teachers’ stances in making sense of students’ mathematical ideas
Scheiner, Thorsten and Montes, Miguel A.. (2024). Exploring prospective teachers’ stances in making sense of students’ mathematical ideas. Journal of Mathematics Teacher Education. pp. 1-25. https://doi.org/10.1007/s10857-024-09639-1
Innovative research approaches to mathematics teacher noticing
Kaiser, Gabriele and Scheiner, Thorsten. (2023). Innovative research approaches to mathematics teacher noticing. 46th Conference of the International Group for the Psychology of Mathematics Education. Haifa, Israel 16 - 21 Jul 2023 Israel: International Group for the Psychology of Mathematics. pp. 103-104
Mathematical knowledge for teaching and mathematics didactic knowledge : A comparative study
Scheiner, Thorsten, Buchholtz, Nils and Kaiser, Gabriele. (2023). Mathematical knowledge for teaching and mathematics didactic knowledge : A comparative study. Journal of Mathematics Teacher Education. pp. 1-22. https://doi.org/10.1007/s10857-023-09598-z
On the relationship between school mathematics and university mathematics : A comparison of three approaches
Scheiner, Thorsten and Bosch, Marianna. (2023). On the relationship between school mathematics and university mathematics : A comparison of three approaches. ZDM Mathematics Education. 55, pp. 767-778. https://doi.org/10.1007/s11858-023-01499-y
Shifting the ways prospective teachers frame and notice student mathematical thinking : From deficits to strengths
Scheiner, Thorsten. (2023). Shifting the ways prospective teachers frame and notice student mathematical thinking : From deficits to strengths. Educational Studies in Mathematics. pp. 1-27. https://doi.org/10.1007/s10649-023-10235-y
Problematizing the metaphors of unpacking, deconstructing, and decompressing mathematics
Scheiner, Thorsten and Bowers, David. (2023). Problematizing the metaphors of unpacking, deconstructing, and decompressing mathematics. For the Learning of Mathematics. 43(1), pp. 9-13.
Measuring teacher noticing : A scoping review of standardized instruments
Weyers, Jonas, König, Johannes, Santagata, Rossella, Scheiner, Thorsten and Kaiser, Gabriele. (2023). Measuring teacher noticing : A scoping review of standardized instruments. Teaching and Teacher Education. 122, p. Article 103970. https://doi.org/10.1016/j.tate.2022.103970
On mathematical learning processes and their epistemological, conceptual and cognitive functions
Pinto, Márcia M. F. and Scheiner, Thorsten. (2022). On mathematical learning processes and their epistemological, conceptual and cognitive functions. Bolema: Boletim De Educação Matemática. 36(72), pp. 495-514. https://doi.org/10.1590/1980-4415v36n72a22
Sense-making in learning mathematics : An act of comprehension or creation?
Scheiner, Thorsten and Pinto, Marcia M. F.. (2022). Sense-making in learning mathematics : An act of comprehension or creation? For the Learning of Mathematics. 42(3), pp. 16-20.
Pedagogical content knowledge oder fachdidaktisches wissen?
Scheiner, Thorsten and Buchholtz, Nils. (2022). Pedagogical content knowledge oder fachdidaktisches wissen? In In Buchholtz, Nils, Schwarz, Björn and Vorhölter, Katrin (Ed.). Initiationen mathematikdidaktischer Forschung : Festschrift zum 70. Geburtstag von Gabriele Kaiser pp. 267-286 Springer Spektrum. https://doi.org/10.1007/978-3-658-36766-4_14
Teacher noticing : A systematic literature review on conceptualizations, research designs, and findings on learning to notice
König, Johannes, Santagata, Rosella, Scheiner, Thorsten, Adleff, Ann-Kristin, Yang, Xinrong and Kaiser, Gabriele. (2022). Teacher noticing : A systematic literature review on conceptualizations, research designs, and findings on learning to notice. Educational Research Review. 36, p. Article 100453. https://doi.org/10.1016/j.edurev.2022.100453
On metaphors in thinking about preparing mathematics for teaching : In memory of José (“Pepe”) Carrillo Yáñez (1959–2021)
Scheiner, Thorsten, Godino, Juan D., Montes, Miguel A., Pino-Fan, Luis R. and Climent, Nuria. (2022). On metaphors in thinking about preparing mathematics for teaching : In memory of José (“Pepe”) Carrillo Yáñez (1959–2021). Educational Studies in Mathematics. 111(2), pp. 253-270. https://doi.org/10.1007/s10649-022-10154-4
Examining assumptions about the need for teachers to transform subject matter into pedagogical forms accessible to students
Scheiner, Thorsten. (2021). Examining assumptions about the need for teachers to transform subject matter into pedagogical forms accessible to students. Teachers and Teaching. 28(1), pp. 1-11. https://doi.org/10.1080/13540602.2021.2016688
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
Dealing with opposing theoretical perspectives : Knowledge in structures or knowledge in pieces?
Scheiner, Thorsten. (2020). Dealing with opposing theoretical perspectives : Knowledge in structures or knowledge in pieces? Educational Studies in Mathematics: An international journal. 104, pp. 127-145. https://doi.org/10.1007/s10649-020-09950-7
Using conflicts, tensions, and paradoxes for theory building: the case of conceptual change
Scheiner, Thorsten. (2020). Using conflicts, tensions, and paradoxes for theory building: the case of conceptual change. Annual meeting of the American Educational Research Association (AERA). Institute for Learning Sciences and Teacher Education, Australian Catholic University. pp. 1-11
Problematizing pedagogical content knowledge
Scheiner, Thorsten. (2019). Problematizing pedagogical content knowledge. American Educational Research Association Annual Meeting Program. Toronto, Canada 05 - 09 Apr 2019 American Educational Research Association. pp. 1-6 https://doi.org/10.302/1429187
Toward a model of teacher noticing
Scheiner, Thorsten. (2019). Toward a model of teacher noticing. American Educational Research Association Annual Meeting Program. Toronto, Canada 05 - 09 Apr 2019 American Educational Research Association. pp. 1-5 https://doi.org/10.302/1429207
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
Problematizing knowledge for teaching
Scheiner, Thorsten. (2018). Problematizing knowledge for teaching. The Fifth Africa Regional Congress of ICMI on Mathematical Education (AFRICME 5). Salama House, Aga Khan University, Dar es Salaam, Tanzania 29 - 31 Aug 2018 International Commission on Mathematical Instruction. pp. 116-120
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. 41st Conference of the International Group for the Psychology of Mathematics Education. Singapore, Singapore: International Group for the Psychology of Mathematics. 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
New light on old horizon: Constructing mathematical concepts, underlying abstraction processes, and sense making strategies
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
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