Cognition as Communication: Rethinking Learning-by-Talking Through Multi-Faceted Analysis of Students' Mathematical Interactions

Sfard, Anna; Kieran, Carolyn

doi:10.1207/s15327884mca0801_04

Cited by 221 publications

(136 citation statements)

References 18 publications

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“…Developing our understanding of this relationship should help us develop strategies to fully maximise the use of metacognitive interventions in group mathematical problem-solving. This is particularly relevant within the teaching and learning of mathematics (Sfard & Kieran, 2001) because the verbal interaction skills required for successful mathematical problem-solving in collaborative settings rarely develop alone.…”

Section: Discussionmentioning

confidence: 99%

“…Sfard & Kieran, 2001), it is important that researchers are able to understand the nature of group interactions, together with mediating factors. Research in the area of collaborative problem-solving suggests that there is a relationship between metacognitive talk and collaborative talk, but this relationship has not been fully explored.…”

Section: Collaborative Metacognition: Methodological Progress and Limmentioning

confidence: 99%

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Exploring the relationship between metacognitive and collaborative talk during group mathematical problem-solving – what do we mean bycollaborativemetacognition?

Smith

Mancy

2018

Research in Mathematics Education

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The purpose of this study was to enhance our understanding of the relationship between collaborative talk and metacognitive talk during group mathematical problem-solving. Research suggests that collaborative talk may mediate the use of metacognitive talk, which in turn is associated with improved learning outcomes. However, our understanding of the role of group work on the individual use of metacognition during problem-solving has been limited because research has focused on either the individual or the group as a collective. Here, primary students (aged nine to 10) were video-recorded in a naturalistic classroom setting during group mathematical problem-solving sessions. Student talk was coded for metacognitive, cognitive and social content, and also for collaborative content. Compared with cognitive talk, we found that metacognitive talk was more likely to meet the criteria to be considered collaborative, with a higher probability of being both preceded by and followed by collaborative talk. Our results suggest that collaborative metacognition arises from combined individual and group processes.ARTICLE HISTORY

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Section: Discussionmentioning

confidence: 99%

Section: Collaborative Metacognition: Methodological Progress and Limmentioning

confidence: 99%

Exploring the relationship between metacognitive and collaborative talk during group mathematical problem-solving – what do we mean bycollaborativemetacognition?

Smith

Mancy

2018

Research in Mathematics Education

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“…Examples of such frameworks and analytic schemas emphasized the reasoning process in social interaction processes (Sawyer and Berson 2004;Sfard and Kieran 2001), (collaborative) argumentation and meaning making (Baker 1999;Weinberger and Fischer 2006), procedural and relational aspects of interaction (Barron 2003;Rummel and Spada 2005), or deictic aspects of conversation (Lindwall and Lymer 2011). Productive interactions, inter alia, not only comprise these constructive, discursive, and procedural aspects but also refer to something outside this conversational space.…”

Section: An Integrative Analytic Frameworkmentioning

confidence: 99%

The multi-layered nature of small-group learning: Productive interactions in object-oriented collaboration

Damşa

2014

Intern. J. Comput.-Support. Collab. Learn.

112

100

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This article presents a study of small-group interaction in the context of collaborative learning in undergraduate education. The student groups participated in collaborative projects, which involved setting-up, conducting, and reporting on empirical research studies. This study sheds light on the nature of productive interactions, the joint efforts to co-construct knowledge and the shared epistemic agency expected to emerge when groups are addressing ill-structured, complex problems in a collaboration over time. In-depth qualitative analysis and descriptive statistics were used to analyze and interpret interaction data and developing knowledge objects (i.e., research reports) collected during a 20-week project period. The findings show that productive interactions can take different forms, with discourse-based and object-oriented being the most relevant patterns arising. In the latter case, the emergent knowledge objects also influence the course and productivity of the interaction. Finally, groups manifesting shared epistemic agency produce knowledge objects more complex and suitable to the problems addressed. These findings contribute to a better understanding of the collaborative learning process that includes work on knowledge objects over time. The implications for the educational practice and further research point towards the need for a better understanding of the way groups function when challenged to address complex problems and to participate in knowledge production, how these processes can benefit learning, and what is needed in terms of pedagogical and technological support, to enable students to be more than mere coursetakers, but also producers of knowledge.Keywords Knowledge co-construction . Knowledge objects . Learning in higher education . Productive interaction . Shared epistemic agency . Small-group collaboration In the context of emerging changes in the knowledge-based society, students in higher education are expected to be able to address ill-structured and open-ended problems, conceive new ideas, show inquiring attitudes and proactive behavior, and capitalize on collective expertise (Goodyear and Zenios 2007). Learning in small groups that focuses on solving open-ended problems and on managing the collaborative process has been proposed as a wayIntern.

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“…Addressing notation rather than the ideas referred to by the notation renders mathematical discourse superficial and disconnected. As Sfard and Kieran (2001) caution: "In mathematical communication, in which there are no familiar visible objects likely to serve as a basis for an attended focus, people avail themselves of symbolic artefacts as a replacement. As communication mediators, however, the symbolic substitutes are not as readily effective as the familiar objects used in everyday discourse" (p. 72).…”

Section: Language and Mathematical Notationmentioning

confidence: 99%

How Does Language Impact the Learning of Mathematics? Let Me Count the Ways

Boulet

2007

Journal of Teaching and Learning

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The role that language plays in the teaching and learning of mathematics is one of some importance in the current literature in mathematics education. In this paper, I give particular attention to the manner in which teachers engage students in the exploration of mathematical concepts and procedures with the goal of revealing how language impacts students' learning. Through a series of examples of language commonly used in the mathematics classroom, I address specific issues pertaining to language used to describe mathematical processes, to read and interpret notation, and to define mathematical terms. Considering that communication is a key factor in the building of understanding, it is hoped that these examples will motivate teachers to examine and adapt their own practices in order to cultivate productive and meaningful mathematical discourse in their classrooms.

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Cognition as Communication: Rethinking Learning-by-Talking Through Multi-Faceted Analysis of Students' Mathematical Interactions

Cited by 221 publications

References 18 publications

Exploring the relationship between metacognitive and collaborative talk during group mathematical problem-solving – what do we mean bycollaborativemetacognition?

Exploring the relationship between metacognitive and collaborative talk during group mathematical problem-solving – what do we mean bycollaborativemetacognition?

The multi-layered nature of small-group learning: Productive interactions in object-oriented collaboration

How Does Language Impact the Learning of Mathematics? Let Me Count the Ways

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