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fulltext:"Man, having within himself an imagined world of lines and numbers, operates in it with abstractions just as God in the universe, did with reality"
fulltext:"Man, having within himself an imagined world of lines and numbers, operates in it with abstractions just as God in the universe, did with reality"
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By default, Find returns all publications that contain the words in the surnames of their author, in their titles, or in their years. For example,
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Abrahamson D. & Trninic D. (2015) Bringing forth mathematical concepts: Signifying sensorimotor enactment in fields of promoted action. ZDM Mathematics Education 47(2): 295–306. https://cepa.info/6129
Abrahamson D.
&
Trninic D.
(
2015
)
Bringing forth mathematical concepts: Signifying sensorimotor enactment in fields of promoted action
.
ZDM Mathematics
Education
47(2): 295–306.
Fulltext at https://cepa.info/6129
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Inspired by Enactivist philosophy yet in dialog with it, we ask what theory of embodied cognition might best serve in articulating implications of Enactivism for mathematics
education
. We offer a blend of Dynamical Systems Theory and Sociocultural Theory as an analytic lens on micro-processes of action-to-concept evolution. We also illustrate the methodological utility of design-research as an approach to such theory development. Building on constructs from ecological psychology, cultural anthropology, studies of motor-skill acquisition, and somatic awareness practices, we develop the notion of an “instrumented field of promoted action”. Children operating in this field first develop environmentally coupled motor-action coordinations. Next, we introduce into the field new artifacts. The children adopt the artifacts as frames of action and reference, yet in so doing they shift into disciplinary semiotic systems. We exemplify our thesis with two selected excerpts from our videography of Grade 4–6 volunteers participating in task-based clinical interviews centered on the Mathematical Imagery Trainer for Proportion. In particular, we present and analyze cases of either smooth or abrupt transformation in learners’ operatory schemes. We situate our design framework vis-à-vis seminal contributions to mathematics
education
research.
Key words:
mathematics
,
education
,
motor learning
,
conceptual learning
,
motor problem
,
conceptual metaphor
Abrahamson D., Dutton E. & Bakker A. (2021) Towards an enactivist mathematics pedagogy. In: Stolz S. A. (ed.) The body, embodiment, and education: An interdisciplinary approach. Routledge, London: 156–182. https://cepa.info/7085
Abrahamson D.
,
Dutton E.
&
Bakker A.
(
2021
)
Towards an enactivist mathematics pedagogy
.
In: Stolz S. A. (ed.)
The body, embodiment, and
education
: An interdisciplinary approach
. Routledge, London: 156–182.
Fulltext at https://cepa.info/7085
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Enactivism theorizes thinking as situated doing. Mathematical thinking, specifically, is handling imaginary objects, and learning is coming to perceive objects and reflecting on this activity. Putting theory to practice, Abrahamson’s embodied-design collaborative interdisciplinary research program has been designing and evaluating interactive tablet applications centered on motor-control tasks whose perceptual solutions then form the basis for understanding mathematical ideas (e.g., proportion). Analysis of multimodal data of students’ handand eyemovement as well as their linguistic and gestural expressions has pointed to the key role of emergent perceptual structures that form the developmental interface between motor coordination and conceptual articulation. Through timely tutorial intervention or peer interaction, these perceptual structures rise to the students’ discursive consciousness as “things” they can describe, measure, analyze, model, and symbolize with culturally accepted words, diagrams, and signs – they become mathematical entities with enactive meanings. We explain the theoretical background of enactivist mathematics pedagogy, demonstrate its technological implementation, list its principles, and then present a case study of a mathematics teacher who applied her graduate-school experiences in enactivist inquiry to create spontaneous classroom activities promoting student insight into challenging concepts. Students’ enactment of coordinated movement forms gave rise to new perceptual structures modeled as mathematical content.
Abrahamson D., Nathan M. J., Williams-Pierce C., Walkington C., Ottmar E. R., Soto H. & Alibali M. W. (2020) The future of embodied design for mathematics teaching and learning. Frontiers in Education 5: 147. https://cepa.info/7086
Abrahamson D.
,
Nathan M. J.
,
Williams-Pierce C.
,
Walkington C.
,
Ottmar E. R.
,
Soto H.
&
Alibali M. W.
(
2020
)
The future of embodied design for mathematics teaching and learning
.
Frontiers in
Education
5: 147.
Fulltext at https://cepa.info/7086
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A rising epistemological paradigm in the cognitive sciences – embodied cognition – has been stimulating innovative approaches, among
education
al researchers, to the design and analysis of STEM teaching and learning. The paradigm promotes theorizations of cognitive activity as grounded, or even constituted, in goal-oriented multimodal sensorimotor phenomenology. Conceptual learning, per these theories, could emanate from, or be triggered by, experiences of enacting or witnessing particular movement forms, even before these movements are explicitly signified as illustrating target content. Putting these theories to practice, new types of learning environments are being explored that utilize interactive technologies to initially foster student enactment of conceptually oriented movement forms and only then formalize these gestures and actions in disciplinary formats and language. In turn, new research instruments, such as multimodal learning analytics, now enable researchers to aggregate, integrate, model, and represent students’ physical movements, eye-gaze paths, and verbal–gestural utterance so as to track and evaluate emerging conceptual capacity. We – a cohort of cognitive scientists and design-based researchers of embodied mathematics – survey a set of empirically validated frameworks and principles for enhancing mathematics teaching and learning as dialogic multimodal activity, and we synthetize a set of principles for
education
al practice.
Ackermann E. K. (1995) Construction and transference of meaning through form. In: Steffe L. P. & Gale J. E. (eds.) Constructivism in education. Lawrence Erlbaum Associates, Hillsdale NJ: 341–354. https://cepa.info/3064
Ackermann E. K.
(
1995
)
Construction and transference of meaning through form
.
In: Steffe L. P. & Gale J. E. (eds.)
Constructivism in
education
. Lawrence Erlbaum Associates, Hillsdale NJ: 341–354.
Fulltext at https://cepa.info/3064
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There seem to be as many definitions of constructivism as there are minds to construct them. At least this is how it felt after reading the chapters by Duit (chap. 14), Saxe (chap. 15), and Spivey (chap. 16). Or perhaps there are as many questionings of constructivist ideas as practices in the field of
education
. For example, a teacher experiences a different set of constraints than a researcher or a designer, and these constraints in turn shape theories of learning in different ways.
Ackermann E. K. (2010) Constructivism(s): Shared roots, crossed paths, multiple legacies. In: Clayson J. & Kalas I. (eds.) Constructionist approaches to creative learning, thinking and education: Lessons for the 21st century. Proceedings of Constructionism 2010. Comenius University, Bratislava: 1–9. https://cepa.info/6082
Ackermann E. K.
(
2010
)
Constructivism(s): Shared roots, crossed paths, multiple legacies
.
In: Clayson J. & Kalas I. (eds.)
Constructionist approaches to creative learning, thinking and
education
: Lessons for the 21st century. Proceedings of Constructionism 2010
. Comenius University, Bratislava: 1–9.
Fulltext at https://cepa.info/6082
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This paper examines the shared roots and crossed paths between Jean Piaget’s constructivism, what Seymour Paper refers to as “constructionism,” and socio-cultural theories as epitomized by Lev Vygotsky. We do so in the light of more situated, pragmatic, and ecological approaches to human cognition. All these views are developmental (stressing the genesis children’s interests and abilities over time), experiential (in the sense that knowledge is rooted in sensori-motor activity) and interactionist (people are seen as constructing their knowledge by transforming the world). Yet, the views also differ, each highlighting some aspects of how children grow and learn, while leaving other questions unanswered. Piaget’s main contribution was to flesh out what is common in children’s ways of thinking at different stages of their cognitive development and, more important, how consistent, robust, and generally “adapted” their views are. The theory stresses the progressive de-contextualization of knowledge (from here-and-now to then-and-there) and identifies some of the hidden mechanisms (internal reorganizations) that drive human cognitive development. Papert, in contrast, stresses how individuals learn in context and how they use their own – and other people’s – externalizations as objects to think with, especially as their convictions break down. His approach is more situated. Papert is particularly interested the role of new media in human learning. Both Papert and Vygotsky shed light on the articulations between direct and mediated experience (from action and tool-use to enactments, language, and symbol-use). Yet Vygotsky and the Russian school have paid much closer attention to the role of caring adults and peers in a child’s initiation to her culture. They remind us that it takes a whole village to raise a child. Integrating the views helps rethink how children come to make sense of their experiences, and how they find their own places – and voices – in the world. At once world-makers, world-readers, and dwellers in the world, human infants are granted from birth with the abilities to optimize exchanges with people and things by moving in and out of contexts, by shifting perspectives, and by switching roles or standpoint. They are extraordinary learners, and much can be learned from them. Lastly, while mostly inner-driven and curious, children need caring adults, secure grounds, and engaging peers and props to thrive and grow. Tools, media, and cultural artifacts are the tangible forms through which they explore their surrounds, express their thoughts, and share the fun with others – and the traces left by those who came before (cultural heritage) become a terrain for newcomers to create their paths.
Key words:
Constructivism
,
Piaget
,
Papert
,
Vygotsky
,
situated learning
,
embodied cognition
,
ecology of mind
Adams P. (2006) Exploring social constructivism: Theories and practicalities. Education 34(3): 3–13. https://cepa.info/3958
Adams P.
(
2006
)
Exploring social constructivism: Theories and practicalities
.
Education
34(3): 3–13.
Fulltext at https://cepa.info/3958
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In the drive to improve standards, the collection and dissemination of numerical data still directs much contemporary
education
al policy. However, recent publications and debates seemingly attempt to reorient discussion from performance to learning. In support, constructivism is often referenced as a contributor in this endeavour. However, constructivism is not a single unified theory either of knowledge or pedagogy. This article identifies one version of constructivist thinking, social constructivism, both in terms of its underlying epistemology (theory of knowledge) and related pedagogy. Contemporary
education
al theories are then outlined to demonstrate that many practical solutions and theoretical ideas now presented as ‘good learning and teaching’ have much in common with social constructivist thinking. Finally, the article concludes by identifying two issues that require further discussion and debate if pedagogy of a social constructivist nature is to be considered.
Affifi R. R. (2011) What weston’s spider and my shorebirds might mean for bateson’s mind: Some educational wanderings in interspecies curricula. Canadian Journal of Environmental Education 16: 46–58. https://cepa.info/999
Affifi R. R.
(
2011
)
What weston’s spider and my shorebirds might mean for bateson’s mind: Some
education
al wanderings in interspecies curricula
.
Canadian Journal of Environmental
Education
16: 46–58.
Fulltext at https://cepa.info/999
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Education
has institutionalized a process that reifies cultures, ecological communities, and ultimately evolution itself. This enclosure has lessened our sensitivity to the pedagogical (eteragogical) nature of our lived relations with other people and with other living beings. By acknowledging that learning and teaching go on between species, humans can regain an eteragogical sense of the interspecies curricula within which they exist. This article explores interspecies lived curricula through a selection of ideas from ecopragmatist Anthony Weston, and cybernetician Gregory Bateson, and through lived experiences with shorebirds of Lake Ontario. Some gulls and a tern teach the author to enrich and diversify, rather than constrict, the potentiality of life. In so doing, being ecological and being educative become unified concepts.
Relevance:
The publication is concerned with the relational implications between humans and other species of Bateson’s cybernetic theory of learning.
Alhadeff-Jones M. (2013) Complexity, methodology and method: Crafting a critical process of research. Complicity: An International Journal of Complexity and Education 10(1/2): 19–44. https://cepa.info/920
Alhadeff-Jones M.
(
2013
)
Complexity, methodology and method: Crafting a critical process of research
.
Complicity: An International Journal of Complexity and
Education
10(1/2): 19–44.
Fulltext at https://cepa.info/920
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This paper defines a theoretical framework aiming to support the actions and reflections of researchers looking for a “method” in order to critically conceive the complexity of a scientific process of research. First, it starts with a brief overview of the core assumptions framing Morin’s “paradigm of complexity” and Le Moigne’s “general system theory.” Distinguishing “methodology” and “method,” the framework is conceived based on three moments, which represent recurring stages of the spiraling development of research. The first moment focuses on the definition of the research process and its sub-systems (author, system of ideas, object of study and method) understood as a complex form of organization finalized in a specific environment. The second moment introduces a matrix aiming to model the research process and nine core methodological issues, according to a programmatic and critical approach. Using the matrix previously modeled, the third moment suggests conceiving of the research process following a strategic mindset that focuses on contingencies, in order to locate, share and communicate the path followed throughout the inquiry.
Relevance:
This paper provides the readers with a constructivist methodology of research inspired by Morin’s paradigm of complexity and Le Moigne’s general system theory.
Alkove L. D. & McCarty B. J. (1992) Plain talk: Recognizing positivism and constructivism in practice. Action in Teacher Education 14(2): 16–22. https://cepa.info/7077
Alkove L. D.
&
McCarty B. J.
(
1992
)
Plain talk: Recognizing positivism and constructivism in practice
.
Action in Teacher
Education
14(2): 16–22.
Fulltext at https://cepa.info/7077
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Excerpt:
The first challenge we face in this endeavor is to define two philosophies which provide the basis for most teaching practices: positivism and || constructivism. Next, we intend to familiarize teachers with the influences these philosophies have had on teacher
education
programs and the classroom. Our final task is to help teachers identify these philosophies within their own practice so they may determine whether or not their teaching style actually reflects their personal beliefs.
Amoonga T. (2010) The use of constructivism in teaching mathematics for understanding: A study of the challenges that hinder effective teaching of mathematics for understanding. In: L. G. C. D. M. B. & I. C. T. (eds.) EDULEARN10 Proceedings CD: Second International Conference on Education and New Learning Technologies, 5–7 July 2010, Barcelona, Spain. International Association of Technology. Education and Development (IATED), Valencia: 5010–5019.
Amoonga T.
(
2010
)
The use of constructivism in teaching mathematics for understanding: A study of the challenges that hinder effective teaching of mathematics for understanding
.
In: L. G. C. D. M. B. & I. C. T. (eds.)
EDULEARN10 Proceedings CD: Second International Conference on
Education
and New Learning Technologies, 5–7 July 2010, Barcelona, Spain. International Association of Technology
. Education and Development (IATED), Valencia: 5010–5019.
Copy Citation
The major purpose of this study was to investigate factors and challenges that hindered effective teaching of mathematics for understanding in senior secondary schools in the Omusati
Education
Region in Namibia. The study investigated how the participants dealt with identified challenges in the mathematics classrooms in selected senior secondary schools. Further, the study attempted to establish necessary support and / or training opportunities that mathematics teachers might need to ensure effective application of teaching mathematics for understanding in their regular classrooms. The sample was made up of eight senior secondary schools out of the population of 12 senior secondary schools in the Omusati
Education
Region. The schools were selected from the school circuits using maximum variation and random sampling techniques. Twenty out of 32 mathematics teachers from eight selected senior secondary schools in the Omusati
Education
Region responded to the interviews and two lessons per participant were observed. Interviews and observations were used to collect data from the 20 senior secondary school mathematics teachers with respect to teaching mathematics for understanding. Frequency tables, pie charts and bar graphs were used to analyze the data collected. The results indicated that teaching for understanding was little observed in mathematics classrooms. Part of the challenges identified were, overcrowded classrooms, lack of teaching and learning resources, lack of support from advisory teachers, and automatic promotions, among others. Mathematics teachers needed induction programmes, in-service training opportunities, and advisory services amongst others in order to be able to teach mathematics effectively. The study recommended that teaching for understanding should be researched in all subjects in Namibian classrooms and should be made clearly understood by all teachers in order to be able to use and apply it during their teaching. New teachers should be provided with induction programmes to give them support and tools at the beginning of their teaching careers. Further research on teaching for understanding should be conducted in other school subjects in Namibia in order to ensure teaching for understanding across the curriculum.
Key words:
teaching
,
understanding.
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