Making implicit metalevel rules of the discourse on function explicit topics of reflection in the classroom to foster student learning

Güçler, Beste

doi:10.1007/s10649-015-9636-9

Cited by 21 publications

(7 citation statements)

References 22 publications

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“…For translation, this may require talking explicitly about the dynamic and static realizations of vectors and the accompanying visual mediators to support each distinct realization; and addressing how mathematical language, visual mediators, routines, and endorsed narratives differ for the objectified realization of translation as a congruence transformation compared to its realization as a process of repositioning shapes within the coordinate system. Teachers' explication of mathematical discourse and making it an explicit topic of discussion is a form of meta-level learning that has the potential to help students become aware of their teachers' and own discourses, and make communication more transparent in the classroom (Bar-Tikva, 2009;Güçler, 2016;Kjeldsen & Blomhøj, 2012). Explicating elements of mathematical discourse can also be useful for teachers in developing strategies to address student difficulties in the classroom (Güçler et al, 2015).…”

Section: Conclusion and Discussionmentioning

confidence: 99%

The Development of Two High School Students’ Discourses on Geometric Translation in Relation to the Teacher’s Discourse in the Classroom

Emre-Akdoğan

Güçler

Argün

2018

EURASIA J MATH SCI T

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Research exploring student development on geometric translation in relation to classroom teaching is scarce. We used a qualitative case study design and examined two students' development of thinking on translation in relation to the teacher's discourse in a Turkish high school classroom through a discursive framework. We examined the teacher's discourse through the video-taped classroom session in which he talked about translation. We examined the students' discursive development through three video-taped task-based interviews. Finally, we compared the students' discourses on translation with the teacher's discourse. The teacher's discourse on translation in the classroom was formal and based on an algebraic realization of the concept as an addition and a geometric transformation. The students adopted particular discursive elements used by the teacher right after instruction but later abandoned some of those and used their more established realizations of translation. The findings revealed the complexity of discursive development as the students continually and actively adjusted their discourses by taking into account the teacher's discourse while also making it compatible with their own realizations of translation. We conclude that socio-cultural and discursive approaches have the potential to shed additional light on issues regarding learning and teaching of geometric translation.

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Section: Conclusion and Discussionmentioning

confidence: 99%

The Development of Two High School Students’ Discourses on Geometric Translation in Relation to the Teacher’s Discourse in the Classroom

Emre-Akdoğan

Güçler

Argün

2018

EURASIA J MATH SCI T

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“…However, her main focus is on discrepancies between the lecturer's and the students' discourses on limits, and she emphasizes the need for making the metarules of the discourse explicit to students. In a follow-up study, Güçler (2016) investigates how such an instructional approach, focusing on the mathematical discourse of function, can help student learning, and concludes that although the students still had difficulties with the function concept they were able to identify to a greater extent the nature of these difficulties and what aspects of their discourse needed to be changed. Any such practice, however, requires an awareness on the part of the lecturer of the metarules to be conveyed, as well as of possible metarules already implicitly conveyed, and research such as that presented in this paper might be helpful in this regard.…”

Section: University Mathematics Lecturing From a Discursive Perspectivementioning

confidence: 99%

“…Perhaps if what we want students to get from lectures is not only the facts and object-level rules of the discourse, but also the more general metarules, then we need to be more explicit about these metarules. In a recent study, Güçler (2016) has tried precisely such an instructional approach with some success. Also, Oikkonen (2009), having redesigned a calculus course to focus more explicitly on displaying the thinking behind the mathematics presented, could see positive results on pass rates.…”

Section: Conclusion and Implications For Mathematics Lecturingmentioning

confidence: 99%

University Mathematics Lecturing as Modelling Mathematical Discourse

Viirman

2021

Int. J. Res. Undergrad. Math. Ed.

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The lecture format, while being the subject of much criticism, is still one of the most common formats of university mathematics teaching. This paper investigates lecturing as a means of modelling mathematical discourse, sometimes highlighted in the literature as one of its most important functions. The data analysed in the paper are taken from first-semester lectures given by seven mathematics lecturers at three Swedish universities, all concerning various aspects of the function concept. Analysis was carried out from a commognitive perspective, which distinguishes between object-level and meta-level discourse. Here I focus on two aspects of meta-level discourse: introducing new mathematical objects; and what counts as valid endorsement of a narrative. The analysis reveals a number of metarules concerning the modelling of mathematical reasoning and behaviour, both more general rules such as precision and consensus, and rules more specifically concerning construction and endorsement of narratives. The paper contributes to a small but growing body of empirical research on university mathematics teaching, and also lends empirical support to previous claims about the modelling aspect of mathematics lecturing, thus contributing to a deepened understanding of the lecture format and its potential role in future university mathematics teaching.

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“…The notion of 'reification' (Sfard, 1991) has been reconceptualised within the commognitive framework (e.g. Güçler, 2016;Sfard, 2008;Shinno, 2018)…”

Section: Notesmentioning

confidence: 99%

Characterizing how and when a way of proving develops in a primary mathematics classroom: a commognitive approach

Shinno

Fujita

2021

International Journal of Mathematical Education in Science and

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In this study we aim to characterize a way of proving which can be produced in a primary mathematics classroom and explore the factors that influence these processes and lead to changes in the way of proving. Assuming proving as a socially embedded activity, we conceptualize it as the interplay between 'construction' and 'substantiation' based on a well-established theoretical framework in mathematics education: the commognitive framework. A tangible proving task was designed, based on the idea of operative proofs, and implemented in a fifth-grade classroom in England. We analysed the construction and substantiation which fairly associated with discursive features (word use, visual mediator, narrative, and routine) during the proving process. The results show that the interplay between construction and substantiation developed progressively rather than in a straightforward manner, in which previously constructed narratives are reconstructed or substantiated in a more general context. This finding is relevant to understand the factors that might influence primary students to change the use of examples and the way of proving when used as a communicational means in proving. Our study has implications for possible continuity to proving activities in secondary schools, and thus contributes to advancing the research on proving in primary schools.

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Making implicit metalevel rules of the discourse on function explicit topics of reflection in the classroom to foster student learning

Cited by 21 publications

References 22 publications

The Development of Two High School Students’ Discourses on Geometric Translation in Relation to the Teacher’s Discourse in the Classroom

The Development of Two High School Students’ Discourses on Geometric Translation in Relation to the Teacher’s Discourse in the Classroom

University Mathematics Lecturing as Modelling Mathematical Discourse

Characterizing how and when a way of proving develops in a primary mathematics classroom: a commognitive approach

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