Differences between how Undergraduate Students Define Geometric Solids and what their Lecturers Expect from them through the Lens of the Theory of Commognition

Martín-Molina, Verónica; González-Regaña, Alfonso J.; Toscano, Rocío; Izquierdo, José María Gavilán

doi:10.29333/ejmste/9159

Cited by 6 publications

(3 citation statements)

References 21 publications

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“…Understanding the definitions of the concepts in the subjects helps to avoid simple memorization and visual learning. Thus, the definition process, essential for transparent mathematics education, must be encouraged (Erdem & Man, 2018;Martín-Molina et al, 2020).…”

Section: Concept Definition (Cd)mentioning

confidence: 99%

Middle school mathematics teachers’ concept definitions of geometric objects

ERDEM,

MAN

2024

IJMTL

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The aim of this study is to examine middle school mathematics teachers’ concept definitions of five geometric objects (prism, pyramid, cone, cylinder, and sphere). The study was carried out with the participation of 99 mathematics teachers who have been working in middle schools located in three different provinces and districts. The data were gathered through a form consisting of six open-ended questions, which were prepared to reveal the participants’ Concept Definition (CD) of Geometric Objects (GOs). Via content analysis technique, codes from the data and categories from the codes were obtained. Results showed that some of the participants could not make the CDs of GOs correctly, that they generally drew the square or rectangular forms and only included the vertical states of the GOs objects. It was found that participants generally could not establish a relation between “cylinder and prism” and “cone and pyramid”. Evidence was also found that some of the participants saw themselves as inadequate in defining the GOs. On the other hand, it can be said from their explanations and drawings that the teachers’ professional experiences do not have much effect on defining those concepts.

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Section: Concept Definition (Cd)mentioning

confidence: 99%

Middle school mathematics teachers’ concept definitions of geometric objects

ERDEM,

MAN

2024

IJMTL

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“…Communicative Cognitive Theory questions Descartes’ dual ontological epistemology of body and schizophrenia ( Sfard, 2020 ). It is proposed that discourse in communication is the mirror of thinking ( Lu et al, 2019 ), and discourse becomes the main object of communication cognitive theory ( Martín-Molina et al, 2020 ). Considering discourse analysis as a fundamental research method and discourse learning and discourse development as conceptual tools for analyzing teaching activities ( Bebell and O’Dwyer, 2010 ), the development of mathematical discourse can be conceived at the object level or the meta-level ( Sfard, 2020 ; Shinno and Fujita, 2021 ), which is a breakthrough and innovation in research methods in the field of social culture.…”

Section: Research Reviewmentioning

confidence: 99%

Visualizing Commognitive Responsibility Shift in Collaborative Problem-Solving During Computer-Supported One-to-One Math Tutoring

Tuo

Feng

et al. 2022

Front. Psychol.

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The aim of this study is to use a commognitive responsibility framework to visualize responsibility shift in collaborative problem solving (CPS) during computer-supported one-to-one tutoring. Commognitive responsibility shift means that individuals’ cognitive responsibility shift can be reflected by the discourse in communication. For our sample, we chose a 15-year-old Chinese boy and his mathematics teacher with 6 years of teaching experience, both of whom have experienced computer-supported learning and teaching mathematics, respectively. We collected four tutoring videos (each 60–90 min; in total, more than 330 min) online, and a 45-min interview video from the teacher. We found that the third type of commognitive responsibility shift in both the teacher’s and student’s CPS behavior online is not only teacher–student comparison but also alternating-led, which includes teacher–student-led (TS) and student–teacher-led (ST).

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“…Several researchers have recently used commognition to characterize teachers' and students' discursive activity (Emre-Akdoğan et al, 2018;Güçler, 2013;Martín-Molina et al, 2020;Park, 2011Park, , 2015Tasara, 2018;Viirman, 2014). They conclude that the differences between discourses frequently cause difficulties in the teaching and learning processes.…”

Section: Introductionmentioning

confidence: 99%

How an Upper Secondary School Teacher Provides Resources for the Transition to University: A Case Study

Gallego

Izquierdo

2021

INT ELECT J MATH ED

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This paper analyzes the discursive activity of an upper secondary school teacher on the topic of the derivative. Specifically, we focus on the discursive activity when introducing the three essential concepts related to this topic: the average rate of change, the derivative at a point, and the derivative function. The theoretical framework used is the theory of commognition (Sfard, 2008). Using this framework, we identify different types of visual mediators (symbols, graphs, gestures) and routines (mainly construction and substantiation ones, with various subtypes). The analysis of these visual mediators and routines allows us to examine some resources students will have in their transition to university discourse. We also draw some other conclusions and present implications for teaching in this stage.

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Differences between how Undergraduate Students Define Geometric Solids and what their Lecturers Expect from them through the Lens of the Theory of Commognition

Cited by 6 publications

References 21 publications

Middle school mathematics teachers’ concept definitions of geometric objects

Middle school mathematics teachers’ concept definitions of geometric objects

Visualizing Commognitive Responsibility Shift in Collaborative Problem-Solving During Computer-Supported One-to-One Math Tutoring

How an Upper Secondary School Teacher Provides Resources for the Transition to University: A Case Study

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