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Topic: Constructivism (math)

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	Constructivist epistemology - Wikipedia, the free encyclopedia
		Constructivism is a new criticism in philosophy directed against medieval realism, classical rationalism and empiricism.
		Constructivism views all of our knowledge as "constructed," it does not reflect any external "transcendent" realities, but is contingent on convention, human perception and social experience.
		One account of Social constructivism is as follows: it is a form of constructivism based on the sociological and social psychological concept of social constructionism.
	en.wikipedia.org /wiki/Social_constructivism (624 words)

	Constructivism (mathematics) - Wikipedia, the free encyclopedia
		Constructivism is often confused with intuitionism, but in fact, intuitionism is only one kind of constructivism.
		Constructivism does not, and is entirely consonant with an objective view of mathematics.
		Constructivism also rejects the use of infinite objects, such as infinite sets and sequences.
	www.wikipedia.org /wiki/Constructivism_%28math%29 (678 words)

	M.A. Boudourides: Constructivism in Education: A Shopper's Guide
		Educational constructivism, which is also labeled as psychological constructivism (Phillips, 1995), divides into personal and social constructivism, according to whether it is the individual person or a group who does the constructing or the processing of cognitive and memory structures.
		Sociological constructivism, which is called also social constructivism with the risk of being confused with the Vygotskian approach, is concerned with the public bodies of knowledge, the various disciplines of science and technology, and how they are socially constructed and interpreted in terms of changing social conditions and interests.
		Constructivism is not the only insight from psychology brought to science education by the so-called “cognitive revolution” in psychology of the 1960s.
	www.math.upatras.gr /~mboudour/articles/constr.html (5375 words)

	Mathematical constructivism : Constructivism (math) (Site not responding. Last check: 2007-10-13)
		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.termsdefined.net /co/constructivism-(math).html (311 words)

	Critical Summary of Cobb et al (Site not responding. Last check: 2007-10-13)
		The basic idea of learning in constructivism is that it is a process in which students recognize their acquired activity to solve situations that they find personally problematic.
		We can find that in constructivism theory, the change of individual belief and social norms will change their view of learning and the way they learn, which will benefit them even after they would be mixed in traditional classroom.
		Constructivism theory comes from the analysis of problems in traditional math education, and based on that theoretical analysis, there developed a systematic view of learning and instruction.
	www.msu.edu /~gulixion/cep902/cobb.htm (1009 words)

	constructivism on Encyclopedia.com
		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 and elementary preservice science teacher preparation: knowledge to application.
	www.encyclopedia.com /html/c1/construc.asp (347 words)

	Nancy Pon - E-Gallery (Site not responding. Last check: 2007-10-13)
		Constructivism is defined as "that philosophical position which holds that any so-called reality is, in the most immediate and concrete sense, the mental construction of those who believe they have discovered and investigated it" (Saunders, 1992, p.
		Constructivism, however, does not consider the zones of proximal development entailed in social constructivism, or the developmental stages of the brain involved in cognitive constructivism.
		Radical constructivism, proposed by von Glasersfeld (1987b), extends the idea of constructing knowledge to truly radical limits, stating that knowledge is totally subjective, since it is constructed in the minds of individuals based on their unique personal experiences.
	www.ucalgary.ca /~egallery/volume3/pon.html (6575 words)

	Constructivism as an `energiser for thinking'!: Anna Chronaki (Site not responding. Last check: 2007-10-13)
		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.
		Radical constructivism has enjoyed a rapid rise of followers within the maths education community in which many researchers have found hope and inspiration.
		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)

	What are they shooting at?
		Marilyn Burns is right when she points out that the problems we encounter in everyday life require mental math abilities yet the classroom remedy seems to be impose lots of similar problems to be solved with pencil and paper.
		The great Satan to the Taliban of math education is the notion that a problem might not have one solution.
		Constructivism is simply the belief that knowledge is not transmitted, but constructed by the individual based on context, motivation, negotiation, experience and interaction with others in a community of practice.
	www.stager.org /articles/mathwars.html (891 words)

	emTech - Constructivism (Site not responding. Last check: 2007-10-13)
		Constructivism is often related to the philosophies of Dewey and Rousseau, and inspired by Piaget and Vygotsky.
		Constructivism and cooperation between scientists and educators: A reply to Crowther by Thomas H. Illman.
		Constructivism and narrative psychology.- Luis Botella, Ramon Llull University.
	www.emtech.net /links/construc.htm (8622 words)

	Whole Hog for Whole Math (Site not responding. Last check: 2007-10-13)
		"Whole math" is a form of instruction that has kids develop their own methods of multiplying and dividing, ask questions of one another rather than of teachers, and learn that answers that are close to correct are good enough.
		Constructivism provides the rationale for encouraging elementary school students to invent their own ways of multiplying and, when stymied, to ask other children for help.
		Math and science educators are stuck in education departments, he observes, completely cut off from math and science departments.
	www.junkscience.com /news/wholemat.htm (565 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 (12579 words)

	EJSE V2 N2 December1997 Editorial - Crowther (Site not responding. Last check: 2007-10-13)
		In that arena, the movement is called constructivism, derived from the notion that all facts are socially constructed rather than being deduced from evidence.
		Contextual Constructivism is defined by how the learner interprets phenomena and internalizes these interpretations in terms of their previous experience and culture.
		Constructivism or a constructivist view puts the students, their interests, and previous experiences and knowledge as paramount parts of understanding in designing curriculum.
	unr.edu /homepage/jcannon/ejse/ejsev2n2ed.html (3728 words)

	Constructivism, Situated Learning, and Other Learning Theories
		For example, I've been in enough high school math classes over the last five years to know that there is no developmental theory of how students learn algebra.
		We know that the brain has great plasticity, that there is a lot of brain growth after a person is born, that the brain continues to grow new neurons and new connections among neurons throughout life, that certain drugs can damage brain cells, that proper nutrition is needed for proper brain growth, and so on.
		The great majority of a person's math knowledge and skills comes from learning--learning to use parts of the brain that can learn to do math, but were not genetically designed specifically for this purpose.
	darkwing.uoregon.edu /~moursund/Math/learning-theories.htm (1142 words)

	Math Forum - Constructivism in Mathematics Education
		It's not surprising that constructivism has a strong voice in the current dialogue on math education.
		It suggests that math knowledge results from people forming models in response to the questions and challenges that come from actively engaging math problems and environments - not from simply taking in information, nor as merely the blossoming of an innate gift.
		The challenge in teaching is to create experiences that engage the student and support his or her own explanation, evaluation, communication, and application of the mathematical models needed to make sense of these experiences.
	mathforum.org /mathed/constructivism.html (647 words)

	Capital Area Science and Math Center (Site not responding. Last check: 2007-10-13)
		Math is for everyone and anyone can do it with this activity guide.
		Prentice Hall Middle Grades Math is a complete middle school mathematics series, intended to be used together as the student grows from sixth grade to eighth grade.
		Middle Grades Math is composed of four strands; algebra, geometry and measurement, data analysis, and problem solving.
	www.casmcenter.org /rlp_pd_curriculum.htm (2819 words)

	Searching For The Truth About The TIMSS 4th Grade Math Test
		Although conventionally referred to as "the TIMSS 4th grade math test", the test was targeted at nine-year-olds and actually given to 3rd and 4th graders in most countries, including the United States.
		Math was emphasized in 4 booklets, with 34, 37, 37, and 38 minutes for math.
		The TIMSS 4th grade math test was prepared in the United States and then translated from English (United States version) into 17 additional languages for the 26 participating countries.
	www.wgquirk.com /timss.html (2438 words)

	The Math Forum - Math Library - Constructivism
		Constructivism is a philosophy about learning which proposes that learners need to build their own understanding of new ideas.
		Description of a math program that uses visualization, analysis, informal deduction, and formal deduction to engage students in the study of geometry in an integrated manner.
		A discussion of math education: the intent of the NCTM Standards, reflections on the history of constructivism, classroom practices (with a link to Marilyn Burns' Math Solutions page), and a simple applet for solving linear equations.
	mathforum.org /library/ed_topics/constructivism (2240 words)

	ContraConstructivism.html
		Indeed, and in what must be one of the greater ironies, Charles Peirce's pragmatic theory of truth, which constructivists apparently believe supports their notion that we cannot know the truth, is actually a behavioral account of what we take to be true.
		And, the moment that they retreat from hegemonic intentions, and make room for other accounts, the alleged superiority of constructivism is shown to be mere hyperbole, and falls on the sword of its own proposition regarding the relativity of accounts.
		Constructivism is perhaps best seen as the anarchical utopianism of a socially privileged class (academics) fueled by fake neo-Romantic sentimentality.
	www.uncwil.edu /people/kozloffm/ContraConstructivism.html (3484 words)

	All the Information You Need on Constructivism
		Constructivism - This site is very detailed and gives a very clear understanding of Constuctivism and its learning theory.
		Constructivism as a Paradigm for Teaching and Learning - This site offers information on how Constructivism is different from traditional teaching and learning ideas.
		Math Forum-Constructivism in Mathmatics Education - This site gives a very large amount of help with Constructivism and Math.
	www.kn.pacbell.com /wired/fil/pages/listconstrucsa3.html (317 words)

	Lesson I
		Some of my students are very accurate in their math, but don't understand when to use what to solve a problem.
		This is the same principle of constructivism that instructors use to teach new experiences and concepts to their students.
		The most important ideas that I found about Constructivism that I would use in teaching include; giving more independence and choices to the learners, using the learners' prior knowledge and experiences, teaching meaningful experiences through lessons, and that learning is an active process.
	www.eiu.edu /~edtech/lesson_04/sturespond.htm (2993 words)

	everydaymath2
		Although the new math program does have some merit, such as the use of hands-on manipulatives, it is very weak and incomplete in its coverage, and it will not prepare high school students to take college math courses upon entering college without first taking a heavy dose of remedial math courses.
		A survey of students from both schools was solicited and their achievements in college math courses were also analyzed as to their readiness in taking college math courses in a university environment with their high school math preparation.
		The trouble with the new math approach is that that’s all it uses and 2000 years of mathematical rigor is to be reinvented by the students themselves through self-discovery and hands-on trial-and-error manipulations.
	www.lit.net /orschools/everydaymath2.htm (3275 words)

	Cut The Knot!
		The ascendant philosophy of mathematical education in the United States is constructivism, a mixture of Piaget's psychology with counterculture and postmodernist ideology.
		Being thus loaded, the term "constructivism" may not be a good choice of word to describe the current pedagogical thinking.
		One possible explanation is that parental involvement with children is an important factor in early math education.
	www.maa.org /editorial/knot/reform.html (2704 words)

	Constructivism: Math 20 Student Lessons Project
		In general many of the students achieved on par with how they do in the regular course, however the writing aspect allowed those linguistic students to flourish.
		Also, those students who are intimidated by math were able to find a deferent outlet that allowed them to feel more at ease with some topics.
		As well students improved their use of math terminology.
	www.saskschools.ca /curr_content/constructivism/where/martin/math20/studentlessons/reflect.html (280 words)

	Investigations in Number, Data, and Space
		According to a recent Boston Globe article on math education, the percentage of Boston fourth-graders scoring proficient or advanced on the math MCAS—the highest categories—increased from 14 percent to 22 percent between 2000 and 2004, and the percentage failing decreased from nearly half of the students to about a third.
		The approach demonstrates the student's knowledge of math facts and his ability to apply them appropriately to solve the problem quickly.
		Part of the teacher's role is to help students consolidate their strategies and procedures and build on their strong mathematical foundation to become fluent.
	investigations.terc.edu (557 words)

	Constructivism -- Encyclopædia Britannica
		Between 1912 and 1914 there emerged an antisculptural movement, called Constructivism, that attacked the false seriousness and hollow moral ideals of academic art.
		The movement began with the relief fabrications of Vladimir Tatlin in 1913.
		Covers radical constructivism, discovery learning, the role of social interaction, and implications for teaching.
	www.britannica.com /eb/article-9026019 (707 words)

	Critics Say Math Curriculum Doesn't Add Up [TERC Investigations and Connected Mathematics Program]
		The 'constructivist' math curriculum for elementary and middle school students has been given the pejorative name "fuzzy math" by critics.
		Board members said they have been receiving numerous complaints from local parents, who are worried that their children aren't learning the basics of mathematics, such as multiplication tables.
		Sharply criticized by parents for the departure from rote learning, 'constructivism' dives into conceptualized learning allowing students to explore a number of answers and how to achieve them, instead of just memorizing, said Ron Feinstein, the district's new math director.
	www.nychold.com /art-rp-020328.html (1041 words)

	OTRNet: Web links to Sites on Constructivism
		An introduction and series of links on the relevance of Constructivism in maths education.
		This paper represents a collaborative effort of two teacher educators to articulate a constructivist approach to "designing for learning" rather than planning for teaching.
		Builds an understanding of constructivism and includes a section on developing Geometry through a constructivist approach.
	www.otrnet.com.au /Pedagogy/constructivism.html (220 words)

	Cornell Math - Math Education Web Sites
		The Math Forum at Drexel — Many links to articles on mathematics education.
		Famous Problems in the History of Mathematics — Problems of the week are in each of a variety of categories (including math fundamentals, pre-algebra, algebra, geometry, and pre-calculus).
		Math Challenges for Families — Interactive mathematics miscellany and puzzles
	www.math.cornell.edu /Undergraduate/Teaching/websites.html (183 words)

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