%0 Journal Article
%J Journal of Mathematical Behavior
%V 6
%N 1
%P 3-40
%A Cobb, P.
%T Information-processing psychology and mathematics education: A constructivist perspective
%D 1987
%U https://cepa.info/2968
%X Discusses the implications of information processing psychology for mathematics education, with a focus on the works of schema theorists such as D. E. Rumelhart and D. A. Norman and R. Glaser and production system theorists such as J. H. Larkin, J. G. Greeno, and J. R. Anderson. Learning is considered in terms of the actor’s and the observer’s perspective and the distinction between declarative and procedural knowledge. Comprehension and meaning in mathematics also are considered. The role of abstraction and generalization in the acquisition of mathematical knowledge is discussed, and the difference between helping children to “see, ” as opposed to construct abstract relationships is elucidated. The goal of teaching is to help students modify or restructure their existing schema in predetermined ways by finding instructional representations that enable students to construct their own expert representations.
%G en
%4 PDF
%5 ok
%0 Journal Article
%J For the Learning of Mathematics
%V 9
%N 2
%P 32-42
%A Cobb, P.
%T Experiential, cognitive, and anthropological perspectives in mathematics education
%D 1989
%U https://cepa.info/6491
%X
%G en
%2 Radical Constructivism
%4 PDF
%5 ok
%0 Journal Article
%J Educational Researcher
%V 23
%N 7
%P 4
%A Cobb, P.
%T Constructivism in mathematics and science education
%D 1994
%U https://cepa.info/2951
%X
%G en
%5 ok
%0 Journal Article
%J Educational Researcher
%V 23
%N 7
%P 13-20
%A Cobb, P.
%T Where is the mind? Constructivist and sociocultural perspectives on mathematical development
%D 1994
%U https://cepa.info/3049
%X Currently, considerable debate focuses on whether mind is located in the head or in the individual-in-social-action, and whether development is cognitive self-organization or enculturation into established practices. In this article, I question assumptions that initiate this apparent forced choice between constructivist and sociocultural perspectives. I contend that the two perspectives are complementary. Also, claims that either perspective captures the essence of people and communities should be rejected for pragmatic justifications that consider the contextual relevance and usefulness of a perspective. I argue that the sociocultural perspective informs theories of the conditions far the possibility of learning, whereas theories developed from the constructivist perspective focus on what students learn and the processes by which they do so.
%G en
%4 PDF
%5 ok
%0 Book Section
%E Steffe, L. P.
%E Thompson, P.
%B Radical constructivism in action: Building on the pioneering work of Ernst von Glasersfeld
%I Falmer Press
%C London
%P 152-178
%A Cobb, P.
%T Constructivism in social context
%D 2000
%U https://cepa.info/6709
%X In this chapter, I focus on one of the aspects of constructivist theory that Glasersfeld (Ch. 1) identifies as in need of further development. This aspect of the theory involves locating students’ mathematical development in social and cultural context while simultaneously treating learning as a process of adaptive reorganization. In addressing this issue, I illustrate the approach that I and my colleagues currently take when accounting for the process of students’ mathematical learning as it occurs in the social context of the classroom. In the opening section of the chapter, I clarify why this is a significant issue for us as mathematics educators. I then outline my general theoretical orientation by discussing Glasersfeld’s constructivism and Bauersfeld’s interactionism. Against this background, I develop criteria for classroom analyses that are relevant to our interests as researchers who develop learning environments for students in collaboration with teachers. Next, I illustrate the interpretive framework that I and my colleagues currently use by presenting a sample classroom analysis. Finally, in the concluding sections of the chapter, I reflect on the sample analysis to address four more general issues. These concern the contributions of analyses of the type outlined in the illustrative example, the relationship between instructional design and classroom-based research, the role of symbols and other tools in mathematical learning, and the relation between individual students’ mathematical activity and communal classroom processes.
%G en
%4 PDF
%5 ok
%0 Book Section
%E Lester, F. K.
%B Second handbook of research on mathematics teaching and learning
%I Information Age Publishing
%C Charlotte NC
%P 3-38
%A Cobb, P.
%T Putting philosophy to work
%D 2007
%X Excerpt: In inviting me to write this chapter on philosophical issues in mathematics education, the editor has given me the leeway to present a personal perspective rather than to develop a comprehensive overview of currently influential philosophical positions as they relate to mathematics education. I invoke this privilege by taking as my primary focus an issue that has been the subject of considerable debate in both mathematics education and the broader educational research community, that of coping with multiple and frequently conflicting theoretical perspectives. The theoretical perspectives currently on offer include radical constructivism, sociocultural theory, symbolic interactionism, distributed cognition, information-processing psychology, situated cognition, critical theory, critical race theory, and discourse theory. To add to the mix, experimental psychology has emerged with a renewed vigor in the last few years. Proponents of various perspectives frequently advocate their viewpoint with what can only be described as ideological fervor, generating more heat than light in the process. In the face of this sometimes bewildering array of theoretical alternatives, the issue I seek to address in this chapter is that of how we might make and justify our decision to adopt one theoretical perspective rather than another. In doing so, I put philosophy to work by drawing on the analyses of a number of thinkers who have grappled with the thorny problem of making reasoned decisions about competing theoretical perspectives.
%G en
%4 PDF
%5 ok
%0 Journal Article
%J Constructivist Foundations
%V 6
%N 2
%P 157-161
%A Cobb, P.
%T Implications of Ernst von Glasersfeld’s Constructivism for Supporting the Improvement of Teaching on a Large Scale
%D 2011
%U https://cepa.info/190
%X Problem: Ernst von Glasersfeld’s radical constructivism has been highly influential in the fields of mathematics and science education. However, its relevance is typically limited to analyses of classroom interactions and students’ reasoning. Methods: A project that aims to support improvements in the quality of mathematics instruction across four large urban districts is framed as a case with which to illustrate the far-reaching consequences of von Glasersfeld’s constructivism for mathematics and science educators. Results: Von Glasersfeld’s constructivism orients us to question the standard view of policy implementation as a process of travel down through a system and to conceptualize it instead as the situated reorganization of practice at multiple levels of a system. In addition, von Glasersfeld’s constructivism orients us to understand rather than merely evaluate policies by viewing the actions of the targets of policies as reasonable from their point of view. Implications: The potential contributions of von Glasersfeld’s constructivism to mathematics and science education have been significantly underestimated by restricting the focus to classroom actions and interactions. The illustrative case of research on the application of these ideas also indicates the relevance of constructivism to researchers in educational policy and educational leadership.
%G en
%2 Radical Constructivism
%5 ok
%0 Journal Article
%J The Genetic Epistemologist
%V 13
%N 2
%P 9-15
%A Cobb, P.
%A Glasersfeld, E. von
%T Jean Piaget’s scheme and constructivism
%D 1984
%X
%F EVG-085
%G en
%2 Radical Constructivism
%4 notfound
%5 ok
%0 Journal Article
%J Journal for Research in Mathematics Education
%V 14
%N 2
%P 83-94
%A Cobb, P.
%A Steffe, L. P.
%T The constructivist researcher as teacher and model builder
%D 1983
%U https://cepa.info/2096
%X The constructivist teaching experiment is used in formulating explanations of children’s mathematical behavior. Essentially, a teaching experiment consists of a series of teaching episodes and individual interviews that covers an extended period of time – anywhere from 6 weeks to 2 years. The explanations we formulate consist of models – constellations of theoretical constructs – that represent our understanding of children’s mathematical realities. However, the models must be distinguished from what might go on in children’s heads. They are formulated in the context of intensive interactions with children. Our emphasis on the researcher as teacher stems from our view that children’s construction of mathematical knowledge is greatly influenced by the experience they gain through interaction with their teacher. Although some of the researchers might not teach, all must act as model builders to ensure that the models reflect the teacher’s understanding of the children. Relevance: Constructivist teaching experiment, Model building, Clinical interview. Teaching episode, Counting scheme, Teacher as researcher
%F LPS-1983a
%G en
%2 Radical Constructivism
%5 ok
%0 Journal Article
%J Educational Psychologist
%V 31
%N 3–4
%P 175-190
%A Cobb, P.
%A Yackel, E.
%T Constructivist, emergent, and sociocultural perspectives in the context of developmental research
%D 1996
%U https://cepa.info/4586
%X Our overall intent is to clarify relations between the psychological constructivist, sociocultural, and emergent perspectives. We provide a grounding for the comparisons in the first part of the article by outlining an interpretive framework that we developed in the course of a classroom-based research project. At this level of classroom processes, the framework involves an emergent approach in which psychological constructivist analyses of individual activity are coordinated with interactionist analyses of classroom interactions and discourse. In the second part of the article, we describe an elaboration of the framework that locates classroom processes in school and societal contexts. The perspective taken at this level is broadly sociocultural and focuses on the influence of indlividuals’ participation in culturally organized practices. In the third part of the article, we use the discussion of the framework as a backdrop against which to compare and contrast the three theoretical perspectives. We discuss how the emergent approach augments the psychological constructivist perspective by making it possible to locate analyses of individual students’ constructive activities in social context. In addition, we consider the purposes for which the emergent and sociocultural perspectives might be particularly appropriate and observe that they together offer characterizations of individual students’ activities, the classroom community, and broader communities of practice.
%G en
%2 Constructivism
%4 PDF
%5 ok