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Topic: Radical (mathematics)

	Radical (mathematics) - Wikipedia, the free encyclopedia
		See radical for other uses of the term.
		In mathematics, an nth root of a number a is a number b, such that b
		It was once conjectured that all roots of polynomials could be expressed in terms of radicals and elementary operations.
	en.wikipedia.org /wiki/Radical_(mathematics) (402 words)

	Intersubjectivity in Mathematics Learning (Site not responding. Last check: 2007-11-04)
		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).
		Radical constructivism is not a developmental theory, a theory of active learning, a social-cultural theory, nor even a theory of family therapy.
		Radical constructivism is no more a model of learning than it is a model of teaching even though more progress has been made in the former than in the latter case.
	s13a.math.aca.mmu.ac.uk /Chreods/Issue_13/LSteffe.html (7557 words)

	Radical - Wikipedia, the free encyclopedia
		Radical is derived from the Latin word radix, which means "root".
		Radical (mathematics), the n-th radical or root of a number 'a, written as
		Radical consonant, involves the root of the tongue
	en.wikipedia.org /wiki/Radical (187 words)

	AllRefer.com - radical, in mathematics (Mathematics) - Encyclopedia
		radical, in mathematics, symbol placed over a number or expression, called the radicand, to indicate a root of the radicand.
		The radical sign is generally taken to indicate the principal root of the radicand, although any radicand will have n different nth roots.
		The term radical is sometimes used loosely to refer to the entire expression consisting of radical sign and radicand.
	reference.allrefer.com /encyclopedia/R/radical2.html (222 words)

	The Nature of Mathematics and the State of Mathematics Education: Stuart Rowlands and Ted Graham
		Mathematics will be either reduced to the experience of the individual and his or her personal knowledge (the radical constructivist position), or to problem solving that is related in it's entirety to the narrow aspirations and social situation of the class (for example, the social constructivist position of Ernest 1991).
		Either you regard mathematics as a fixed and immutable body of objective knowledge that has certainty, and an existence that is independent of individual cognition or social acceptance, or you regard mathematics as a human creation, based on assumptions and conventions.
		Mathematics is an autonomous objective practice that creates problems the solutions to which are independent of whether anyone has found a solution and independent of whether the academic community accepts the solution.
	www.stanford.edu /~meehan/xyz/parents.html (5515 words)

	[No title]
		Indeed for radical constructivists it is difficult to see how there could be such a thing as the intersubjective construction of knowledge since, were there to be, the problem which Piaget attempted to answer through genetic epistemology would re-appear; namely, how an individual might gain access to such knowledge.
		Social settings, such as the mathematics classroom, are determined by all the actors, both present and absent, and so the intersubjectivity is a function of the time and place and the goals of the activity and the actors.
		The aim of the mathematics teacher might be seen as to assist pupils to appropriate the culture of the community of mathematicians as a further social practice.
	myweb.lsbu.ac.uk /~lermans/JRMESteve.html (8087 words)

	article8
		The central problem for the psychology of mathematics education is to provide a theory of learning mathematics that facilitates interventions in the processes of its teaching and learning.
		Radical constructivism can be described as being based on the metaphor of an evolving and adapting, but isolated organism – a cognitive alien in hostile environment.
		Lerman (1992) proposed to rescue (as he saw it) radical constructivism by replacing its Piagetian theory of mind and conceptual development with a Vygotskian theory of mind and language, in what might be seen as a form of social constructivism.
	www.people.ex.ac.uk /PErnest/pome12/article8.htm (4194 words)

	[No title]
		Consequently, the mathematics curriculum is conditioned by the social function of mathematics in society, and mathematics reforms must always be examined closely to see their relations with broader issues of power, social structure and values, and to see whose interests they serve.
		Mathematics produced in academia is also "ethno" because it is also produced in a setting--academia--with its own values, rituals and special codes in the same way as other [ethno] mathematics.
		The participants are mathematics teachers from all three phases of education and the product of the seminars has appeared in the form of papers, conferences, postgraduate programmes, and most importantly, in the development of a new conception of mathematics education through the history of mathematics.
	webdoc.sub.gwdg.de /edoc/e/pome/pome/pome6.htm (11311 words)

	Mathematics Education and Society: Peter Gates (Site not responding. Last check: 2007-11-04)
		Mathematics education plays its part in keeping the powerless in their place and the strong in positions of power.
		If the social orgainsation of mathematics teaching maintains the dominant form of social organisation - regardless of its educational effects - then that is effective insofar as this is the purpose.
		For me this is a refreshing break away from the discourses which currently permeate mathematics education with the aroma of the reasonableness and certainty of constructivism.
	s13a.math.aca.mmu.ac.uk /Chreods/Issue_11/PeterGates.html (1214 words)

	Constructivism Bibliography
		Differentiates between psychological constructivist, sociocultural, and emergent (social constructivist) perspectives mainly with regard to the conduct of research, and to a lesser extent, teaching.
		A critique of radical constructivism, together with a common core that most mathematics education researchers today accept.
		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)

	Paul Ernest Paper
		Building on the principles of radical constructivism together with the assumption of the existence of the physical and social worlds, a social constructivist philosophy of mathematics is proposed.
		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)

	Bulletin of Academy of Sciences of Moldova. Mathematics
		For every overnilpotent radical defined on the class of all topological rings every sigma-bounded locally bounded topological ring is a subring of some radical topological ring.
		We consider the graded radicals of graded rings, and prove that any radical in the category ring graded by a group G can be defined by means of some class of graded modules.
		Radicals gamma will be studied for which the condition A[x] belongs to gamma for all nil rings A is equivalent to the positive solution of Kothe's Problem (A[x] is Jacobson radical for all nil rings A, in Krempa's formulation).
	www.math.md /imi-site/journals/Buletin/issues/iss_abst/abs04_1.shtml (504 words)

	Bulletin of Academy of Sciences of Moldova. Mathematics
		The radical class of Passman's radical assignment is the Levitzki radical class, this is used to charactarize the Levitzki radical class and its semisimple class.
		The inverse transition from the classes $\Cal L \subseteq$ Mod-$R$ to the idempotent radicals of $R$-Mod is studied.
		However it is not necessarily the case for a given ring $R$ that the radical of $R$ obtained in this way is the intersection of the radicals of $R$ corresponding to the original radical classes.
	www.math.md /buletin/issues/iss_abst/abs99_2.shtml (833 words)

	Transitivity in Action (Site not responding. Last check: 2007-11-04)
		Transitivity in mathematics is a property of relationships in which objects of a similar nature may stand to each other.
		The easiest way to see that the radical axis is perpendicular to the center line is to choose the coordinates so as to make the centers lie on the x-axis.
		Therefore, the radical axis of two intersecting circles is the straight line that passes through their points of intersection.
	www.cut-the-knot.org /triangle/remarkable.shtml (1236 words)

	Mathematics
		Fostering the ability to understand theorems and their purpose by studying selected groups of theorems in contexts that are new to the students and not part of the regular introductory courses.
		Mathematical models of spatial processes in biology including pattern formation in the embryo and during tissue differentiation, applications of traveling waves to population dynamics, epidemiology, and chemical reactions, and models for neural patterns.
		Mathematical analysis of numerical methods in linear algebra, interpolation, integration, differentiation, approximation (including least squares, Fourier analysis, and wavelets), initial- and boundary-value problems of ordinary and partial differential equations.
	www.acs.utah.edu /gencatalog/crsdesc/math.html (5215 words)

	Mathematics Classes (Site not responding. Last check: 2007-11-04)
		It is the beginning of a demanding two year study of advanced mathematical topics including functions, exponents and logarithms, trigonometry, vectors, sequences and series, limits, probability and statistics.
		This course caters to students with a strong background in mathematics and who are competent in a wide range of technical and analytical skills.
		Students are encouraged to apply their mathematical knowledge to solving problems set in a variety of meaningful contexts and to develop insight into mathematical form and structure as they continue their mathematical growth.
	aes.ac.in /aeshs/courses/math.htm (1368 words)

	Wikinfo \| Radical
		the n-th radical or root of a number a, written as √[n]a, which is a number whose n-th power is a (see radical (mathematics)).
		the Jacobson radical of a ring, which is an important ideal.
		Images, some of which are used under the doctrine of Fair use or used with permission, may not be available.
	www.wikinfo.org /wiki.php?title=Radical (248 words)

	Math Forum - Kinds of Constructivism: An Annotated Bibliography (Site not responding. Last check: 2007-11-04)
		An extension of Piagetian ideas to the learning of university level mathematics, emphasizing the "genetic decompositions of concepts," i.e., descriptions, based on empirical data and an understanding of the mathematics involved, of the constructions a student might make
		A critique, especially of Latour and Woolgar's Laboratory Life, calling SSK "an extravagant deconstructionist nihilism according to which all science is fiction and the world is said to be socially constructed by negotiation," along with the admonition that science teachers resist its findings.
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	mathforum.org /orlando/selden.orlando.html (869 words)

	radical - OneLook Dictionary Search
		Radical (radical orchiectomy) : The TCRC Glossary For Testicular Cancer and Related Conditions [home, info]
		Phrases that include radical: radical mastectomy, radical sign, radical hysterectomy, methyl radical, allyl radical, more...
		Words similar to radical: basal, base, extremist, group, radicalness, revolutionary, root, stem, theme, ultra, basic, free radical, radical sign, root word, more...
	www.onelook.com /?w=radical&ls=a (559 words)

	Radical Did You Mean radical
		in linguistics, a radical consonant involves the root of the tongue.
		in grammatology, it is part of a Chinese character (see radical (Chinese character)).
		If an article link referred you to this title, you might want to go back and fix it to point directly to the intended page.
	www.did-you-mean.com /Radical.html (245 words)

	[No title] (Site not responding. Last check: 2007-11-04)
		For three circles, the point at which the three radical axes of pairs of the circles intersect.
		For four spheres, the point at which the six radical planes of pairs of the spheres intersect.
		] A charged compound that has an unpaired electron; it may be either a radical cation (positively charged) or radical anion (negatively charged).
	www.accessscience.com /Dictionary/R/R3/DictR3.html (1740 words)

	Math is Radical (Site not responding. Last check: 2007-11-04)
		Teach students the who's who of mathematics, by showing them who made the discoveries that we take for granted today.
		There is a graphic of the concept or person behind the mathematical breakthrough.
		The lettering is large, focusing on the triumphs of the day.
	www.mathisradical.com (159 words)

	Radical - Questionz.net , answers to all your questions (Site not responding. Last check: 2007-11-04)
		Radical can mean: * one who advocates revolutional social movement, in sociology, often contrasted with "reformist".
		* in mathematics: o the n-th radical or root of a number a, written as [\sqrt[n]{a}], which is a number whose n-th power is a (see radical (mathematics)).
		o the Jacobson radical of a ring, which is an important ideal.
	www.questionz.net /Cancer/Radical.html (203 words)

	Radical Teacher: Preparing Mathematics and Science Teachers for Diverse Classrooms: Promising Strategies for ...
		Radical Teacher: Preparing Mathematics and Science Teachers for Diverse Classrooms: Promising Strategies for Transformative Pedagogy
		As I see it, this makes me more receptive to Preparing Mathematics and Science Teachers for Diverse Classrooms: Promising Strategies for Tranformative Pedagogy.
		The authors seek to provide not only the formats for change but also arguments that new teachers are the ones to begin this radical departure from accepted teaching norms.
	www.findarticles.com /p/articles/mi_m0JVP/is_72/ai_n13775106 (1167 words)

	Mathematics Algebra I (Site not responding. Last check: 2007-11-04)
		The Mathematics Proficiency Guide identifies the essential mathematics skills for which students in Grades K-12 will be held accountable.
		The Mathematics Proficiency Guide presents a view of mathematics teaching and learning which integrates the processes of mathematical activity and content.
		The teaching and learning of mathematics must become more discovery-oriented, inquiry-based, and problem-centered if students are to develop understandings of and about mathematics.
	www.wws.k12.in.us /cd/teachers/math/CP15478.HTM (2876 words)

	ipedia.com: Radical Article (Site not responding. Last check: 2007-11-04)
		In various fields of endeavor, it can mean: in sociology : one who advocates thoroughgoing analysis or change "at th...
		the n-th radical or root of a number a, written as, which is a number whose n-th power is a (see radical (mathematics)).
		This is a disambiguation page; that is, one that points to other pages that might otherwise have the same name.
	www.ipedia.com /radical.html (272 words)

	Mathematics - Pre-AP Algebra II (Site not responding. Last check: 2007-11-04)
		The learner will be able to translate sentences into numerical radical equations and solve for an unknown number, explain solving radical equations, find the value of an unknown variable, solve radical equations for solution sets, describe the characteristics of radical equations, and step into "teacher" roles to evaluate a sample student's work.
		The learner will be able to translate sentences into radical terms, find the product or quotient, rationalize denominators, and either reduce the answer to simplest radical form or find the approximate square root.
		The learner will be able to solve real-world application problems involving polynomials, rational algebraic expressions, radical expressions, real number exponential expressions, and logarithmic expressions, while appropriately utilizing matrices, the binomial theorem, Pascal's triangle, probability, synthetic division, polynomial factoring, and rational root theorems, as means to solving such problems.
	sps.k12.ar.us /Peggy/Web/CR16216.HTM (2007 words)

	Fictionwise eBooks: Radical Constructivism in Mathematics Education by E. von Glasersfeld
		Parents, teachers, and researchers in the field of education are well aware of this dismal situation, but their views about what causes the widespread failure and what steps should be taken to correct it have so far not come anywhere near a practicable consensus.
		The common goal is to find a better way to teach mathematics.
		The common conviction is that knowledge cannot simply be transferred ready-made from parent to child or from teacher to student, but has to be actively built up by each learner in his or her own mind.
	www.fictionwise.com /ebooks/eBook10965.htm (296 words)

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