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	Constructivism (mathematics) - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-07)
		Constructivism is often confused with intuitionism, but in fact, intuitionism is only one kind of constructivism.
		Constructivist mathematics use constructivist logic, which is essentially a removal of the law of the excluded middle from classical logic.
		Thus the proof of the existence of a mathematical object is tied to the possibility of its construction.
	en.wikipedia.org /wiki/Mathematical_constructivism (1291 words)

	Research Sampler: Glossary
		Constructivism is often used to refer to a teaching method, or the advocacy of a teaching method, in which students construct (invent, discover) their own mathematics.
		In contrast to this, according to the constructivism of mathematics education research, what is constructed is some kind of (personal) knowledge, i.e., a structure in an individual mind which may not even be fully describable in words and which might, or might not, arise from discovery of mathematics.
		Constructivism in mathematics is an absolutist philosophy, i.e., it is concerned with absolute truth, independent of individuals or communities, while the SSK form of constructivism is relativist, i.e., it is concerned, not with truth, but with acceptance, which is dependent on particular communities.
	www.maa.org /t_and_l/sampler/rs_glossary.html (1627 words)

	CONSTRUCTIVISM IN SCIENCE AND MATHEMATICS EDUCATION
		Constructivism is undoubtedly a major theoretical influence in contemporary science and mathematics education.
		Constructivism has done a service to science and mathematics education: by alerting teachers to the function of prior learning and extant concepts in the process of learning new material, by stressing the importance of understanding as a goal of science instruction, by fostering pupil engagement in lessons, and other such progressive matters.
		Constructivism has also done a service by making educators aware of the human dimension of science: its fallibility, its connection to culture and interests, the place of convention in scientific theory, the historicity of concepts, the complex procedures of theory appraisal, and much else.
	wwwcsi.unian.it /educa/inglese/matthews.html (8898 words)

	Mathematical constructivism : Constructive mathematics
		In the philosophy of mathematics, mathematical constructivism asserts that it is necessary to find (or "construct") a mathematical object to prove that it exists.
		Constructivism is often confused with mathematical intuitionism, but in fact, intuitionism is only one kind of constructivism.
		Constructivism doesn't, and is entirely consonant with an objective view of mathematics.
	www.fastload.org /co/Constructive_mathematics.html (143 words)

	NCTM: News & Media: President's Message: Constructivist Mathematics and Unicorns (Site not responding. Last check: 2007-10-07)
		Because the mathematics may not be taught the way they learned it, and students may not be neatly arranged in rows as they were, and teachers do not dominate the classroom conversation as they recall, these critics intentionally equate the mathematics content to the pedagogy of reform-minded teachers.
		Radical constructivism is the philosophy that knowledge cannot be provided in some final form from parent to child or from teacher to student but must be actively assembled in the mind by each learner in his or her own way.
		A type of social constructivism that applies specifically to mathematics education maintains that mathematics should be taught emphasizing problem solving; that interaction should take place (a) between teacher and students and (b) among students themselves; and that students should be encouraged to create their own strategies for solving problem situations.
	www.nctm.org /news/pastpresident/2001-0708president.htm (764 words)

	Constructivism as an `energiser for thinking'!: Anna Chronaki (Site not responding. Last check: 2007-10-07)
		Although constructivism has been severely criticised during the last two decades either in the name of Piaget or in the name of its `radical' successor von Glasersfeld, this theory of knowledge or alternatively of `knowing' is still a matter of discussion.
		We have witnessed the rise and fall of the radical perspective of constructivism advocated strongly by von Glasersfeld.
		Along similar lines, I would like to suggest that constructivism can be viewed as the contributor of a `register' for maths education research, not in the sense that it covers the needs of all researchers but of a significant community within the broader area.
	s13a.math.aca.mmu.ac.uk /Chreods/Issue_11/AnnaChronaki.html (2519 words)

	Intersubjectivity in Mathematics Learning (Site not responding. Last check: 2007-10-07)
		Lerman interprets radical constructivism as a model of learning that applies only to what he considers to be the "autonomous individual." But, contrary to his belief, intersubjectivity was an integral part of radical constructivism from its very outset (von Glasersfeld, 1995).
		Constructivism, at least as it has been applied to mathematics education, has focused almost exclusively on the process by which individual students actively construct their own mathematical realities.
		So, rather than criticize radical constructivism as being in principle incapable of doing justice "to the implications of cultural psychology" (Lerman, 1996), it would be better if Lerman criticized radical constructivists like myself who intentionally did not formulate models of mathematical interaction[20].
	s13a.math.aca.mmu.ac.uk /Chreods/Issue_13/LSteffe.html (7557 words)

	PES Yearbook: 1999: Michael R. Matthews
		There are goodies and baddies, and references to "warfare." Jeremy Kilpatrick, in his plenary address to a major international mathematics education conference in 1987, criticized the insularity and fervor of constructivists, observing that constructivism was akin to waves of religious fundamentalism that periodically sweep America.
		Constructivism is not just a banner flapping idly in the breeze, as Louis Althusser once said of the role of Marxism in the French Communist Party and as could be said of so many educational slogans.
		Rather constructivism is meant to connect with the reality of human cognitive processes and thus guide effective teaching and learning across the curriculum: in science, mathematics, literature, religion, and history.
	www.ed.uiuc.edu /EPS/PES-Yearbook/1999/matthews_body.asp (4972 words)

	Paul Ernest Paper
		Thus, for example, terming the weaker form of constructivism 'trivial constructivism' is a polemical move, using a value-laden, indeed pejorative term, to denigrate a position in the debate.
		First of all, the concepts of mathematics are derived by abstraction from direct experience of the physical world, from the generalisation and reflective abstraction of previously constructed concepts, by negotiating meanings with others during discourse, or by some combination of these means.
		The 'fit' of mathematical structures in areas beyond mathematics is continuously being tested, and mathematics is evolving to provide the patterns and solve the tensions that arise from this modelling enterprise.
	www.people.ex.ac.uk /PErnest/soccon.htm (2627 words)

	Applications and Misapplications
		These two schools, of situated learning and constructivism, are not identical: situated learning emphasizes that knowledge is maintained in the external, social world; constructivism argues that knowledge resides in an individual's internal state, perhaps unknowable to anyone else.
		To take an obvious example from mathematics, research on calculus instruction should be evaluated in large measure (except, possibly, for mathematics majors) by assessing the ability and propensity of students to use the calculus successfully when it is relevant in their work in physics or economics.
		Current situated and constructivist trends in mathematics education are preventing this from happening because they refuse to focus on details and precise specifications, believing that this would amount to accepting the supposedly discredited tenets of decomposition and decontextualization.
	act-r.psy.cmu.edu /papers/misapplied.html (12924 words)

	(Mis?)Constructing Constructivism (Site not responding. Last check: 2007-10-07)
		Constructivism is not the only view that argues that children learn actively or that teachers attempt to understand students' thinking.
		Constructivism is part of a distinguished intellectual history, including the work of Jean Piaget and John Dewey, and learning from that history is important.
		Constructivism is not the same as the "discovery" view promoted earlier in this century that, in one form, advised against telling students anything.
	investigations.terc.edu /relevant/MisConstructing.html (1706 words)

	Constructivism: Philosophical & Epistemological Foundations
		Mathematics and logic had an important role to play in making this knowledge manifest.
		So, while the differences between objectivism and constructivism can be clearly delineated, such is not the case for the differences between the varying perspectives on constructivism.
		For many, constructivism holds the promise of a remedy for an ailing school system and provides a robust, coherent and convincing alternative to existing paradigms.
	www.cdli.ca /~elmurphy/emurphy/cle2.html (911 words)

	CONSTRUCTIVISM IS DIFFICULT (Site not responding. Last check: 2007-10-07)
		Learning most mathematical subjects merely involves adding to one's knowledge, but learning constructivism involves modifying all aspects of one's knowledge: theorems, methods of reasoning, technical vocabulary, and even the use of everyday words that do not seem technical, such as "or".
		Constructivism is the practice of avoiding such proofs or at least pointing them out explicitly.
		There are actually several different schools of constructivism, and I do not attempt to distinguish them here; some of them are surveyed in [2].
	www.math.vanderbilt.edu /~schectex/papers/difficult.html (2004 words)

	POME 10
		Social constructivism does not mean that some or all of mathematics may be false (although Gödel's incompleteness results mean that we cannot eliminate the possibility that mathematics may generate a contradiction).
		I wish to argue that mathematical knowledge is based on contingency, due to its historical development and the inevitable impact of external forces on the resourcing and direction of mathematics, but is also based on the deliberate choices and endeavours of mathematicians, elaborated through extensive reasoning.
		Mathematics consists of language games with deeply entrenched rules and patterns that are very stable and enduring, but which always remain open to the possibility of change, and in the long term, do change.
	webdoc.sub.gwdg.de /edoc/e/pome/pome10/art22.htm (2045 words)

	Wittgenstein, Education and the Philosophy of Mathematics
		Ernest (1999) argues that the traditional absolutist (read “objectivist”) account of mathematics should be replaced by a “conceptual change” philosophy of mathematics built upon principles of radical constructivism that, nevertheless, does not deny the existence of the physical and social worlds.
		Mathematical truths arise from the definitional truths of natural language, acquired by social interaction .The truths of mathematics are defined by implicit social agreement - shared patterns of behaviour - on what constitute acceptable mathematical concepts, relationships between them, and methods of deriving new truths from old.
		To the traditional aims -- to reproduce mathematical skill and knowledge based capability, and to develop creative capabilities in mathematics - he suggests adding: to develop empowering mathematical capabilities and a critical appreciation of the social applications and uses of mathematics, and to develop an inner appreciation of mathematics: its big ideas and nature.
	theoryandscience.icaap.org /content/vol003.002/peters.html (3423 words)

	Constructivism and Teaching - The socio-cultural context
		The relationship between a constructivist approach to mathematics teaching and social and cultural norms in mathematics classrooms is explored by Cobb et al.
		What I find exciting about the links between constructivism and socio-cultural theory is the potential to explain children's development of mathematical knowledge in terms of its individual and social construction under the influence of social and cultural practices.
		However, one crucial tenet of constructivism is missing from the five points, and that is the radical nature of constructivism in that it deliberately says nothing of ontology.
	www.grout.demon.co.uk /Barbara/chreods.htm (3631 words)

	Constructivism Bibliography
		It was prepared as a supplement to our talk "Constructivism in Mathematics Education -- What Does It Mean?" given at the RUMEC Conference on Research in Mathematics Education held at Central Michigan University, Sept. 5-8, 1996.
		Argues in favor of "moderate constructivism" and takes issue with radical constructivism from the viewpoint of a physicist who directs the Rutgers Center for Mathematics, Science and Computer Education.
		Six alternative paradigms of constructivism, applying to fields from mathematics education to family therapy, are considered: radical constructivism (v.
	www.maa.org /t_and_l/sampler/construct.html (1051 words)

	Díaz Muñoz: Zubiri y la matemáteca, ABSTRACT (Site not responding. Last check: 2007-10-07)
		His mathematical constructivism, which originates from the sentient intelligence and the impression of formality of reality, presupposes a "noology".
		The mathematical construction is at one and the same time, pro indiviso, to create and to sense, freedom and imposition, construction and reality, deduction and experience, construction and truth, fulfillment and encounter, and logical and historical.
		Its congruence with Gödel's new philosophy of mathematics: mathematics is the science of reality and experience, similar to physical sciences and unfeasible for a machine.
	www.zubiri.org /works/spanishworksabout/munoz/abstract.htm (446 words)

	The Math Forum - Math Library - Constructivism (Site not responding. Last check: 2007-10-07)
		A brief review of the various streams of constructivism in studies of education, society, science and technology: philosophical, cybernetic, educational, and sociological.
		Constructivism is a philosophy about learning which proposes that learners need to build their own understanding of new ideas.
		A resource for mathematics and science instructional materials that provides direct technical assistance to state education agencies, intermediate state educational units, and local school districts.
	mathforum.org /library/ed_topics/constructivism (2240 words)

	A journey into Constructivism - Martin Dougiamas
		Constructivism is a theory, a tool, a lens for examining educational practices.
		Constructivism has been said to be post-epistemological, meaning that it is not another epistemology, or a way of knowing.
		Despite the very fluid nature of constructivism and it's many faces, I now believe that attempting to understand it while simultaneously applying that understanding in a reflective manner promotes the development of influential mental constructs that are useful in the pursuit of more effective communications, teaching and learning.
	dougiamas.com /writing/constructivism.html (13153 words)

	constructivism
		However, beginning in 1921, constructivism (and all modern art movements) were officially disparaged as unsuitable for mass propaganda purposes.
		Implications of constructivism for teaching math to students with moderate to mild disabilities.
		Constructivism: a naturalistic methodolgy for nursing inquiry.(Methods of Clinical Inquiry) (Advances in Nursing Science)
	www.infoplease.com /ce6/ent/A0813351.html (178 words)

	Tony McCullers' Journal Article Collection
		The author analyzes learner-centered education trends and applies constructivism in the theory analysis.
		Simon, M. Reconstructing mathematics pedagogy from a constructivist perspective.
		This research proves to be a solid study to hang my hat upon connecting constructivism in the mathematics classroom.
	www.arches.uga.edu /~tonymc/JournalArticles/ArticleCollection.htm (1325 words)

	ref
		The Impact of Computing Technology on School Mathematics: Report of an NCTM Conference.
		Proceedings of the Twentieth Conference of the International Group for the Psychology of Mathematics Education XX, 1, 21-34.
		The Union of Technology, Constructivism, and Teacher Education.
	www.cdli.ca /~tsharpe/6390/ref.html (202 words)

	Essays on constructivism and education
		The Role of Representations in Learning an Interdisciplinary Mathematics and Physics University Course by: Gilli Shama and John Layman, Maryland Collaborative for Teacher Preparation
		On Constructivism (21 Kbytes) by: Susan Hanley, Maryland Collaborative for Teacher Preparation
		Cognitive Flexibility, Constructivism, and Hypertext by: Rand J. Spiro, et.
	www.towson.edu /csme/mctp/Essays.html (787 words)

	Constructivism
		Ernest Social Constructivism as a Philosophy of Mathematics: Radical Constructivism Rehabilitated?
		Matthews (1998) Constructivism in Science and Mathematics Education
		Otaola (2003) Constructivism across the borders of Russia, Switzerland, and the US Evoluiton, Coincidences, and Differences
	carbon.cudenver.edu /~mryder/itc_data/constructivism.html (311 words)

	Maryland Collaborative for Teacher Preparation (Site not responding. Last check: 2007-10-07)
		for Elementary and Middle School Science and Mathematics
		cthornton@towson.edu), Center for Science and Mathematics Education, Towson University.
		Thanks to Tom O'Haver, Professor Emeritus, The University of Maryland at College Park, for creating this site and maintaining it until April 2001.
	www.towson.edu /csme/mctp/home.html (105 words)

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