Constructivist, emergent, and sociocultural perspectives in the context of developmental research

Cobb, Paul; Yackel, Erna

doi:10.1080/00461520.1996.9653265

Cited by 351 publications

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“…Within mathematics education research, mathematics is often defined by a community with particular values and norms (socio-cultural perspective; e.g., D'Ambrosio, 1986), by particular kinds of constructions that ultimately depend upon the learner's mental activity (cognitive perspective; e.g., Tall, 2002), or some combination of the two (emergent perspective; e.g., Cobb & Yackel, 1996). The articles appearing in this special issue tend to focus on the cognitive perspective, though the article by Gutierrez, Brown, and Alibali, which investigates social interactions of pairs of students while they constructed knowledge, provides an example of an interdisciplinary team that blended these perspectives.…”

Section: Theoretical Framework and Epistemology: Problematizing Mathmentioning

confidence: 99%

Bridging frameworks for understanding numerical cognition

Norton

Nurnberger‐Haag

2018

J. Numer. Cogn.

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This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International License, CC BY 4.0 (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.This special issue represents an attempt to build bridges between research in mathematics education and psychology. Although the disciplines differ in the way they frame specific research questions, these two fields concern themselves with many of the same problems, especially problems related to mathematical learning.Too often, however, their respective communities talk past one another, not knowing how to integrate work from the other field. In a commentary published in this journal, Dan Berch (2016) voiced skepticism about whether it was even possible to do so. He cited divergent methodologies, theoretical frameworks, and epistemologies as insurmountable obstacles. Here, we present articles that provide reason for optimism while elucidating key challenges for each field.The articles presented in this issue contribute to our understanding of mathematical development in the domain of numerical cognition while integrating perspectives to various degrees. Some of the articles represent literature primarily from the authors' own discipline to call for future research and application in the other field.Other articles examine interdisciplinary research relationships themselves. In "Bridging psychology and mathematics education," Martha Alibali and Eric Knuth report on a particularly productive collaboration, which has generated several research publications and numerous insights into ways that students conceptualize mathematical equations. Additional articles-one led by educational psychologist Helena Osana and another led by mathematics educator Xenia Vamvakoussi-directly address Berch's concerns and the obstacles he identified in relation to interdisciplinary collaborations.In this editorial we elaborate on two epistemological obstacles to bridge building: differing perspectives on the nature of mathematics, and differing perspectives on research (which lead to different methodological choices).We draw upon findings from papers presented in this special issue to identify potentially productive ways to navigate these obstacles. We close with suggestions for future collaborations. Journal of Numerical Cognition jnc.psychopen.eu | 2363-8761Theoretical Frameworks and Epistemology: Problematizing MathematicsAs noted by Berch (2016) and others (e.g., Bruer, 1997), divergent frameworks and epistemologies exacerbate the challenges of interdisciplinary research. After all, theoretical frameworks frame even the way we pose questions. Here we address the challenge inherent in divergent views of mathematics itself. Davis and Hersh (1981) stated that Platonism prevails as the default epistemology of mathematics. The apparent certainty of mathematics renders it true in the minds of most people, separate from culture and cognition, s...

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Section: Theoretical Framework and Epistemology: Problematizing Mathmentioning

confidence: 99%

Bridging frameworks for understanding numerical cognition

Norton

Nurnberger‐Haag

2018

J. Numer. Cogn.

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“…To characterise this relationship, Yackel and her colleagues refer to social norms as regularities in the social interaction patterns of a classroom. Cobb and Yackel (1996) argue that the norms of a classroom environment and individual students' mathematical beliefs are deeply intertwined. In particular, individuals' beliefs can be thought of as their understanding of the normative expectancies of their mathematical environment.…”

Section: Student Expectations and Beliefs About Their Roles As Mathemmentioning

confidence: 99%

Expanding participation in problem solving in a diverse middle school mathematics classroom

et al. 2010

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In this paper, we discuss our experiences with an after-school program in which we engaged middle-school students with low socioeconomic status from an urban community in mathematical problem solving. We document that these students participated in many aspects of problem solving, including the posing of problems, constructing justifications, developing and implementing problem-solving heuristics and strategies, and understanding and evaluating the solutions of others. We then delineate what aspects of our environment encouraged the students to take part in these activities, particularly emphasising the proactive role of the teacher, the tasks the students completed, and the social norms of our after-school sessions. Finally, we discuss the relationship between our study and the literature on equity research in mathematics education.The United States, like nearly all developed countries in the world, struggles with the issue of how to achieve equity in the mathematics classroom. Numerous studies indicate that students with low socioeconomic status (from hereon, low-SES) perform below the national average on standardised mathematics assessments and are more likely to drop out of

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“…This is because separating the output into each individual gave the false impression that insight into the children's learning processes required only data from separate individuals. One important component of a local instruction theory, however, is a description of the overarching instructional setting, which includes not only the individual children, but also the teacher, the instructional activity and materials, and the interaction between the children (Cobb & Yackel, 1996).…”

Section: Organising Datamentioning

confidence: 99%

“…In practice, it encompasses an instructional sequence, a description of the coinciding learning processes, a description of the classroom culture, and an analysis of the proactive role of the teacher. The progression should take into account both the cognitive development of the individual students, as well as the social context (i.e., the people involved, classroom culture, and type of instruction) in which the instruction experiment is to take place (Cobb & Yackel, 1996). This implies that the outcomes of the research should not be generalised beyond this particular setting.…”

Section: Brief Introduction To Design Research In Mathematics Educationmentioning

confidence: 99%

The interaction between multimedia data analysis and theory development in design research

Nes¹,

Doorman²

2010

Math Ed Res J

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Mathematics education researchers conducting instruction experiments using a design research methodology are challenged with the analysis of often complex and large amounts of qualitative data. In this paper, we present two case studies that show how multimedia analysis software can greatly support video data analysis and theory development in design research. The software can (a) act as a type of mould for organising large amounts of data; (b) contribute to improving the trackability and reliability of the research; and (c) support theory generation and validation. We propose an integrated model that elucidates the complex process of data analysis by showing how each of the components that are involved in the data analysis procedures feeds into the emerging local instruction theory. The model combines the intricate cycles of coding and analysing raw video data with the cumulative cyclic process that characterises design research in mathematics education. Our experiences with this model may support other mathematics education researchers in the development of thorough and empirically supported local instruction theories from complex qualitative analyses.Design research in mathematics education has both a theoretical and an applied purpose: theoretical in terms of coming to an understanding of mathematical thinking, teaching and learning, and applied in terms of using this understanding to improve mathematics instruction (Schoenfeld, 2000). As a result, researchers do not settle for answers that merely illustrate what works best. Instead, they use methods that both aim to understand why as well as how mathematics instruction works in practice (cf. Freudenthal, 1983;Gravemeijer, Bowers, & Stephan, 2003).What characterises the process of data analysis in design research is the interaction between data analysis and theory development. At a practical level, this interaction is illustrated in Jacobs, Kawanaka, and Stigler's (1999) cyclical process of analyzing video data. Oriented more towards theory development, Gravemeijer (2004) describes design research in terms of a cumulative cyclic process. In this paper, we propose to embed Jacobs et al.'s (1999) model into Gravemeijer's (2004) model for a more encompassing representation of the intricate interactive processes that are essential for theory development in design research. The significance of this integrated model is that it encompasses the steps that are necessary for keeping track of

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Constructivist, emergent, and sociocultural perspectives in the context of developmental research

Cited by 351 publications

References 0 publications

Bridging frameworks for understanding numerical cognition

Bridging frameworks for understanding numerical cognition

Expanding participation in problem solving in a diverse middle school mathematics classroom

The interaction between multimedia data analysis and theory development in design research

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