# Mathematics cognition reconsidered: On ascribing meaning

Conference item

Scheiner, Thorsten. (2018). Mathematics cognition reconsidered: On ascribing meaning. United States of America: Research in Undergraduate Mathematics Education. pp. 1234 - 1239

Authors | Scheiner, Thorsten |
---|---|

Abstract | In contrast to the common assumption that mathematics cognition involves the attempt to recognize a previously unnoticed meaning of a concept, here mathematics cognition is reconsidered as a process of ascribing meaning to the objects of one’s thinking. In this paper, the attention is focused on three processes that are convoluted in the complex dynamics involved when individuals ascribe meaning to higher mathematical objects: contextualizing, complementizing, and complexifying. The aim is to discuss emerging perspectives of these three processes in more detail that speak to the complex dynamics in mathematics cognition. |

Keywords | complexifying; complementizing; contextualizing; mathematics cognition; sensemaking |

Year | 2018 |

Journal | Proceedings of the 21st annual conference on research in undergraduate mathematics education |

Publisher | Research in Undergraduate Mathematics Education |

Open access | Open access |

Publisher's version | |

Page range | 1234 - 1239 |

Research Group | Institute for Learning Sciences and Teacher Education (ILSTE) |

Place of publication | United States of America |

Permalink -

https://acuresearchbank.acu.edu.au/item/88qz5/mathematics-cognition-reconsidered-on-ascribing-meaning

## Download files

##### 162

total views##### 69

total downloads##### 2

views this month##### 3

downloads this month

*These values are for the period from 19th October 2020, when this repository was created.*

## Export as

## Related outputs

##### 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

##### 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

##### Visualization and the teaching of mathematical analysis

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

##### 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