Constructivism and Embodied Cognition by Stephen R. Campbell
NATO ASI SERIES F COMPUTER …, Jan 1, 1995
The position advanced in the paper is derived in part from the work of Varela, Thompson and Rosch... more The position advanced in the paper is derived in part from the work of Varela, Thompson and Rosch as described in their 1991 book, The Embodied Mind: Cognitive science and human experience, which in turn draws heavily from Varela's earlier work with Maturana as found in their 1987 book, The Tree of Knowledge: The biological roots of human understanding. We begin with a brief perspective of the philosophical background which gave rise to and inspired Varela et al.'s enactive view of cognition. The major issues addressed revolve around the notion of representation and what is commonly referred to as the mind-body problem. Attempts to resolve this problem essentially define and motivate developments in cognitive science, thus affecting our understanding of mental imagery as well. It will be seen, as we subsequently present Varela et al.'s formulation of their enactive view of cognition as embodied action, that their theory is no exception in this regard. Implications of this view will eventually require a complete reconsideration of the notion of representatioin. Theories of mental imagery presupposing a representationalism must then, in some manner, be recast in terms of the immediate experiential presentations of consciousness in all of its modalities. In the final section to the paper, some of the manifest implications of this view for teaching and learning and the environments in which these occur will be discussed.
Studies in Philosophy and Education, Jan 1, 2002
The main focus of this paper is on ways in which Kantian philosophy can inform proponents and opp... more The main focus of this paper is on ways in which Kantian philosophy can inform proponents and opponents of constructivism alike. Kant was primarily concerned with reconciling natural and moral law. His approach to this general problematic was to limit and separate what we can know about things (phenomena) from things as they are in themselves (noumena), and to identify moral agency with the latter. Revisiting the Kantian problematic helps to address and resolve long standing epistemological concerns regarding constructivism as an educational philosophy in relation to issues of objectivity and subjectivity, the limits of theoretical and practical reason, and the relation between human experience and the world. It also serves to address ethical concerns regarding liberation from limited self-interests and contexts conditioned by localised beliefs and inclinations. In light of revisiting the Kantian problematic, both Glasersfeld’s radical view of constructivism and Jardine’s social critique of constructivism are found wanting. Beyond constructivism, Kant’s distinction between phenomena and noumena and the limits of reason that follow from it are briefly considered in terms of Merleau-Ponty’s novel double- embodied notion of flesh as an ontological primitive – as a matter of being both in, and of, the world – with an aim to more intimate connections between epistemology and ethics.
This chapter reports on an initiative in educational research in mathemat- ics education that is ... more This chapter reports on an initiative in educational research in mathemat- ics education that is augmenting traditional methods of educational research with methods of cognitive neuroscience and psychophysiology. Background and moti- vation are provided for this initiative—referred to here as mathematics educational neuroscience. Relations and differences between cognitive neuroscience and educa- tional neuroscience are proposed that may have some bearing as to how this area un- folds. The key role of embodied cognition as a theoretical framework is discussed in some detail, and some methodological considerations are presented and illustrated as well. Overall, mathematics educational neuroscience presents exciting new op- portunities for research in mathematics education and for educational research in general.
Modelling and Mathematics Education, ICTMA 9: …, Jan 1, 2001
... From the natural standpoint of being within the world," the living body&... more ... From the natural standpoint of being within the world," the living body" is bound to a ... serve well to define, in a programmatic manner, the kind of enactivism I have in mind. ... of double-embodiment firmly rooted in an ontology that is prior to and moves beyond Cartesian dualism. ...
Mathematical modelling: A way of life, Jan 1, 2003
22 Reconnecting Mind and World: Enacting a (New) Way of Life Stephen R. Campbell Simon Fraser Uni... more 22 Reconnecting Mind and World: Enacting a (New) Way of Life Stephen R. Campbell Simon Fraser University, Canada University of California, Irvine, USA sencael@ uci. edu; sencael@ sfu. ca A common assumption in teaching mathematical modelling and applications is ...
Towards Equity in Mathematics Education, Jan 1, 2012
What differences in gender, culture, and race can be attributed to the biological evolution of th... more What differences in gender, culture, and race can be attributed to the biological evolution of the species, and what differences in gender, culture, and race can be attributed to social interaction? Such a polarized question is well posed only if these areas of attribution, ...
Mathematical Cognition and Learning by Stephen R. Campbell
Philosophy of Mathematics Education Journal, Jan 1, 2001
THREE PHILOSOPHICAL PERSPECTIVES ON LOGIC AND PSYCHOLOGY: IMPLICATIONS FOR MATHEMATICS EDUCATION*... more THREE PHILOSOPHICAL PERSPECTIVES ON LOGIC AND PSYCHOLOGY: IMPLICATIONS FOR MATHEMATICS EDUCATION*. ... for the subject matter in itself, the latter for it in relation to the ... what sort of correspondence exists between the structures described by logic and the ...
Philosophy of Mathematics Education Journal, Jan 1, 2004
Plato made contributions of the first rank to education in areas such as administration, cognitiv... more Plato made contributions of the first rank to education in areas such as administration, cognitive theory, curriculum development, teaching and pedagogy. I do not provide a detailed overview of these contributions here. Rather, I focus on some of his theoretical ...
Mathematics Education Research Journal, Jan 1, 2003
Educational Studies in Mathematics, Jan 1, 2002
Number theory has been a perennial topic of inspiration and importance throughout the history of ... more Number theory has been a perennial topic of inspiration and importance throughout the history of philosophy and mathematics. Despite this fact, surprisingly little attention has been given to research in learning and teaching number theory per se. This volume is an attempt to redress this matter and to serve as a launch point for further research in this area. Drawing on work from an international group of researchers in mathematics education, this volume is a collection of clinical and classroom-based studies in cognition and instruction on learning and teaching number theory. Although there are differences in emphases in theory, method, and focus area, these studies are bound through similar constructivist orientations and qualitative approaches toward research into undergraduate students' and preservice teachers' subject content and pedagogical content knowledge.
Collectively, these studies draw on a variety of cognitive, linguistic, and pedagogical frameworks that focus on various approaches to problem solving, communicating, representing, connecting, and reasoning with topics of elementary number theory, and these in turn have practical implications for the classroom. Learning styles and teaching strategies investigated involve number theoretical vocabulary, concepts, procedures, and proof strategies ranging from divisors, multiples, and divisibility rules, to various theorems involving division, factorization, partitions, and mathematical induction.
Philosophy of Mathematics Education Journal, Jan 1, 2002
Learning and teaching number theory: Research …, Jan 1, 2002
The Journal of Mathematical Behavior, Jan 1, 1996
Journal for Research in Mathematics Education, Jan 1, 1996
This study contributes to a growing body of research on teachers' content knowledge in mathematic... more This study contributes to a growing body of research on teachers' content knowledge in mathematics. The domain under investigation was elementary number theory. Our main focus concerned the con- cept of divisibility and its relation to division, multiplication, prime and composite numbers, fac- torization, divisibility rules, and prime decomposition. We used a constructivist-orientedtheoretical framework for analyzing and interpreting data acquired in clinical interviews with preservice teach- ers. Participants' responses to questions and tasks indicated pervasive dispositions toward procedural attachments, even when some degree of conceptual understanding was evident. The results of this study provide a preliminary overview of cognitive structures in elementary number theory.
Mathematical Connections, Jan 1, 2000
This book offers multiple interconnected perspectives on the largely untapped potential of elemen... more This book offers multiple interconnected perspectives on the largely untapped potential of elementary number theory for mathematics education: its formal and cognitive nature, its relation to arithmetic and algebra, its accessibility, its utility and intrinsic merits, to name just a few. Its purpose is to promote explication and critical dialogue about these issues within the international mathematics education community. The studies comprise a variety of pedagogical and research orientations by an international group of researchers that, collectively, make a compelling case for the relevance and importance of number theory in mathematics education in both pre K-16 settings and mathematics teacher education.
Topics variously engaged include:
*understanding particular concepts related to numerical structure and number theory;
*elaborating on the historical and psychological relevance of number theory in concept development;
*attaining a smooth transition and extension from pattern recognition to formative principles;
*appreciating the aesthetics of number structure;
*exploring its suitability in terms of making connections leading to aha! insights and reaching toward the learner's affective domain;
*reexamining previously constructed knowledge from a novel angle;
*investigating connections between technique and theory;
*utilizing computers and calculators as pedagogical tools; and
*generally illuminating the role number theory concepts could play in developing mathematical knowledge and reasoning in students and teachers.
Overall, the chapters of this book highlight number theory-related topics as a stepping-stone from arithmetic toward generalization and algebraic formalism, and as a means for providing intuitively grounded meanings of numbers, variables, functions, and proofs.
Number Theory in Mathematics Education: Perspectives and Prospects is of interest to researchers, teacher educators, and students in the field of mathematics education, and is well suited as a text for upper-level mathematics education courses.
Educational Neuroscience by Stephen R. Campbell
Online Submission, Jan 1, 2009
A widely recognized concern in elementary school mathematics education is that teachers'... more A widely recognized concern in elementary school mathematics education is that teachers' understanding of the mathematical curricular content generally appears quite fragmented, sparsely connected, and procedurally oriented. This pilot study applies methods of educational ...
meeting of the American Educational Research …, Jan 1, 2005
Proceedings of the 28th Annual Meeting of the North …, Jan 1, 2006
Uploads
Constructivism and Embodied Cognition by Stephen R. Campbell
Mathematical Cognition and Learning by Stephen R. Campbell
Collectively, these studies draw on a variety of cognitive, linguistic, and pedagogical frameworks that focus on various approaches to problem solving, communicating, representing, connecting, and reasoning with topics of elementary number theory, and these in turn have practical implications for the classroom. Learning styles and teaching strategies investigated involve number theoretical vocabulary, concepts, procedures, and proof strategies ranging from divisors, multiples, and divisibility rules, to various theorems involving division, factorization, partitions, and mathematical induction.
Topics variously engaged include:
*understanding particular concepts related to numerical structure and number theory;
*elaborating on the historical and psychological relevance of number theory in concept development;
*attaining a smooth transition and extension from pattern recognition to formative principles;
*appreciating the aesthetics of number structure;
*exploring its suitability in terms of making connections leading to aha! insights and reaching toward the learner's affective domain;
*reexamining previously constructed knowledge from a novel angle;
*investigating connections between technique and theory;
*utilizing computers and calculators as pedagogical tools; and
*generally illuminating the role number theory concepts could play in developing mathematical knowledge and reasoning in students and teachers.
Overall, the chapters of this book highlight number theory-related topics as a stepping-stone from arithmetic toward generalization and algebraic formalism, and as a means for providing intuitively grounded meanings of numbers, variables, functions, and proofs.
Number Theory in Mathematics Education: Perspectives and Prospects is of interest to researchers, teacher educators, and students in the field of mathematics education, and is well suited as a text for upper-level mathematics education courses.
Educational Neuroscience by Stephen R. Campbell
Collectively, these studies draw on a variety of cognitive, linguistic, and pedagogical frameworks that focus on various approaches to problem solving, communicating, representing, connecting, and reasoning with topics of elementary number theory, and these in turn have practical implications for the classroom. Learning styles and teaching strategies investigated involve number theoretical vocabulary, concepts, procedures, and proof strategies ranging from divisors, multiples, and divisibility rules, to various theorems involving division, factorization, partitions, and mathematical induction.
Topics variously engaged include:
*understanding particular concepts related to numerical structure and number theory;
*elaborating on the historical and psychological relevance of number theory in concept development;
*attaining a smooth transition and extension from pattern recognition to formative principles;
*appreciating the aesthetics of number structure;
*exploring its suitability in terms of making connections leading to aha! insights and reaching toward the learner's affective domain;
*reexamining previously constructed knowledge from a novel angle;
*investigating connections between technique and theory;
*utilizing computers and calculators as pedagogical tools; and
*generally illuminating the role number theory concepts could play in developing mathematical knowledge and reasoning in students and teachers.
Overall, the chapters of this book highlight number theory-related topics as a stepping-stone from arithmetic toward generalization and algebraic formalism, and as a means for providing intuitively grounded meanings of numbers, variables, functions, and proofs.
Number Theory in Mathematics Education: Perspectives and Prospects is of interest to researchers, teacher educators, and students in the field of mathematics education, and is well suited as a text for upper-level mathematics education courses.
* Encourages interdisciplinary perspectives in educational neuroscience
* Contributions from leading researchers examine key issues relating to educational neuroscience and mind, brain, and education more generally
* Promotes a theoretical and empirical base for the subject area
* Explores a range of methods available to researchers
* Identifies agencies, organizations, and associations facilitating development in the field
* Reveals a variety of on-going efforts to establish theories, models, methods, ethics, and a common language
(This volume) provides an overview of a wide range of recent initiatives in educational neuroscience implicating and pertaining to mind, brain, and education. Contributions from top researchers in the field examine a variety of concerns, issues, and directions pertaining and relating to educational neuroscience and mind, brain, and education more generally, focusing on three main areas:
* motivations, aims, and prospects
* theories, methods, and collaborations
* challenges, results, and implications
Chapters promote interdisciplinary perspectives and further establishment of theoretical and empirical bases for research and scholarship bridging Education and the Neurosciences. Though not exhaustive, these chapters identify various parties, agencies, organizations, and initiatives involved in facilitating and furthering development in the field, providing a compendium of on-going efforts to help establish theories, models, methods, ethics, and common language.