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Topic: Cognitive science of mathematics

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	Cognitive science (Site not responding. Last check: 2007-10-21)
		Cognitive science is usually defined as the scientific study either of mind or of intelligence (e.g.
		Cognitive science is usually seen as compatible with and interdependent with the physical sciences, and makes frequent use of the scientific method, as well as simulation or modeling, often comparing the output of models with aspects of human behavior.
		A cognitive scientist is likely to assert that what he says about reasoning is true at the symbolic level of abstraction, while what the neuroscientist says is true at the physical level implementing the symbolic level (much as your computer as a physical object implements a virtual machine on which your word-processor runs).
	www.1-free-software.com /en/wikipedia/c/co/cognitive_science.html (1057 words)

	Science - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-10-21)
		Science is a process for evaluating empirical knowledge (the scientific method), a global community of scholars, and the organized body of knowledge gained by this process and carried by this community (and others).
		Science is practiced in university and other scientific institutes as well as in the field; as such it is a solid vocation in academia, but has also been practiced by amateurs, who typically engage in the observational part of science.
		The term "science" is sometimes pressed into service for new and interdisciplinary fields that make use of scientific methods at least in part, and which in any case aspire to be systematic and careful explorations of their subjects, including computer science, library and information science, and environmental science.
	encyclopedia.worldsearch.com /science.htm (1610 words)

	Foundations of mathematics - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-21)
		In mathematics, foundations of mathematics is a term sometimes used for certain fields of mathematics itself, namely for mathematical logic, axiomatic set theory, proof theory, model theory, and recursion theory.
		In mathematical realism, sometimes called Platonism, the existence of a world of mathematical objects independent of humans is postulated; the truths about these objects are discovered by humans.
		Others try to create a cognitive science of mathematics, focusing on human cognition as the origin of the reliability of mathematics when applied to the "real world." These theories would propose to find foundations only in human thought, not in any "objective" outside construct.
	www.bexley.us /project/wikipedia/index.php/Foundations_of_mathematics (530 words)

	GEMS - Invited Faculty Presentation - Elizabeth Fennema (Site not responding. Last check: 2007-10-21)
		The problems of gender and mathematics were defined and documented in terms of the study of advanced mathematics courses, the learning of mathematics, and certain related variables that appeared relevant both to students' election of courses and learning of mathematics.
		Although there are many directions that scholarship on gender and mathematics could take, I would like to discuss and provide examples of research from two perspectives: cognitive science perspectives, which emphasize the irrelevance of female-male differences, and feminist perspectives, which emphasize that female-male differences are critical to the learning of mathematics.
		Brown and Borko (1992) define cognitive psychology as "the scientific study of mental events, primarily concerned with the contents of the human mind (knowledge, beliefs) and mental processes in which people engage." Central to this perspective is the idea that much of behavior is guided by mental activity or cognitions.
	www.woodrow.org /teachers/math/gender/02fennema.html (6850 words)

	Cognitive Science
		Cognitive science is the interdisciplinary study of mind and intelligence, embracing philosophy, psychology, artificial intelligence, neuroscience, linguistics, and anthropology.
		Cognitive science has unifying theoretical ideas, but we have to appreciate the diversity of outlooks and methods that researchers in different fields bring to the study of mind and intelligence.
		Cognitive science is becoming increasingly aware of the need to view the operations of mind in particular physical and social environments.
	plato.stanford.edu /entries/cognitive-science (3416 words)

	Re: Cognitive Science of Mathematics and the Syntax of Space?
		Cognitive science of mathematics has lot's of avenues that seem to branch out in various directions.
		Considering cognitive science and behavioural science we can distinguish between mathematics that is cognitive and mathematics that is behavioural.
		Cognitive thought is much more adjusted to the laws of space-time, measurement, gravity, magnetic fields etc. and derives equations that suite this phenomena.
	superstringtheory.com /forum/metaboard/messages18/351.html (988 words)

	[No title]
		Mathematics as we know it }{\insrsid1864167 is lim\- ited and structured by the human brain and human mental capacities.
		Question 1 is a scie}{\insrsid16348310 n}{\insrsid16348310\charrsid16348310 tific question, a question to be answered by cognitive science, t}{\insrsid16348310 he }{\insrsid16348310\charrsid16348310 interdisciplinary science of the mind.
		Cognitive science matters to mathematics b}{ \insrsid16348310 e}{\insrsid16348310\charrsid16348310 cause only cognitive science can answer this question.}{\insrsid16348310 \par }{\insrsid16348310\charrsid16348310 \par Question 1 is what this book is mostly about.
	www.math.utep.edu /Faculty/helmut/oldclass/200432_3325/ln.doc.rtf (534 words)

	GU Cognitive Science Courses (Site not responding. Last check: 2007-10-21)
		Cognitive Science is the study of the mind, i.e., of how knowledge is acquired and used.
		Cognitive Science minors who are considering undertaking a senior thesis may undertake preparatory work for the thesis during their junior year via this course.
		Students who are undertaking a senior thesis in cognitive science must enroll for this course for a minimum of four credits distributed across the two semesters of their senior year.
	www.georgetown.edu /departments/cognitivescience/courses.html (1464 words)

	Cognitive Science Lectures at Case (Site not responding. Last check: 2007-10-21)
		Cognitive science has attempted to describe these conditions, with implications for longstanding questions in ontology, epistemology and axiology.
		Research in cognitive science has shown that meta-knowledge is one of the most important preconditions of creativity, and thus this research reveals required elements of creativity while simultaneously being humanly created and constrained.
		Cognitive science as an aesthetic work finds itself informing, and informed by, the human aesthetic project that is philosophy.
	www.cwru.edu /artsci/dean/cogsci/lectures.html (683 words)

	Cognitive Science
		One major contribution of AI and cognitive science to psychology has been the information processing model of human thinking in which the metaphor of brain-as-computer is taken quite literally.
		Cognitive science is the study of the mind.
		To a philosopher of mind, cognitive science is the culmination of thousands of years of philosophical tradition.
	www.aaai.org /AITopics/html/cogsci.html (3819 words)

	Cognitive Science Courses
		Prerequisites: Cognitive Science 101A or Cognitive Science 107A.
		Prerequisites: Cognitive Science 107A or Psychology 106; Cognitive Science 101A or Psychology 105.
		Cognitive Science Seminar (4) This seminar emphasizes the conceptual basis of cognitive science, including representation, processing mechanisms, language, and the role of interaction among individuals, culture, and the environment.
	www.ucsd.edu /catalog/courses/COGS.html (4097 words)

	Articles - Cognitive science (Site not responding. Last check: 2007-10-21)
		One of the central principles in cognitive science is that (1) there are different levels of analysis (LOA) from which the brain and behavior can be studied, and (2) mental phenomena are best studied from multiple levels of analysis.
		A cognitive scientist is likely to assert that what he says about reasoning is true at the functional level of abstraction, while what the neuroscientist says is true at the physical level implementing the functional level (much like a computer as a physical object implements a virtual machine on which programs run).
		The field is usually seen as compatible with and interdependent with the physical sciences, and uses of the scientific method, as well as simulation or modeling, often comparing the output of models with aspects of human behavior.
	www.gaple.com /articles/Cognitive_Science (2159 words)

	Cognitive Science Program
		The goal of theoretical cognitive science is to determine those knowledge structures and processes that characterize organisms as biological information processing systems, to explain how these organisms come to possess this knowledge, and to account for the patterns in the breakdown of this knowledge.
		Cognitive learning strategies are grounded in theories of how children learn, think, remember, and solve problems, and are applied to knowledge domains that are included in school instruction (i.e., mathematics, science, reading, and writing).
		At the undergraduate level, there is a minor in Cognitive Science and a minor in Linguistics, plus the opportunity to pursue individualized degrees in Cognitive and Linguistic Science, Pre-Professional Speech Pathology, and Human-Computer Interaction.
	www.cis.udel.edu /cogsci/program.html (1002 words)

	What Does Research Say About Mathematics?
		In studies of mathematical problem solving, an emphasis is placed on (1) uncovering mental processes involved in expert performance within a content domain, (2) analyzing novice performance, and (3) characterizing the mental changes involved when a novice develops into an expert.
		Teachers' knowledge and beliefs about mathematics, the goals of instruction, students' learning, and the nature of instruction are critical and must be addressed as a crucial part of the reform effort.
		The transition mathematics course consolidates the arithmetic of the previous grades and prepares the student for algebra and geometry.
	www.ncrel.org /sdrs/areas/stw_esys/2math.htm (3788 words)

	Branches of Science (Site not responding. Last check: 2007-10-21)
		The major physical sciences are physics, astronomy, chemistry, and geology; the main biological sciences are botany and zoology.
		The science and study of life, from the tiniest microscopic organisms to the largest whales in the sea.
		One of the commonest applications of mathematics to science is the use of equations to fit observed data, e.g.
	kosmoi.com /Science/Branches (1625 words)

	COGS Q250 1035 Mathematics & Logic for Cognitive and Information Science (Site not responding. Last check: 2007-10-21)
		Often, however, it is not possible for the subject of study to be investigated directly and empirically, and, even when it is possible, it turns out that a very useful way to gain insights into scientific phenomena is to build models of them.
		The purpose of this course is to introduce students to some of the main mathematical and logical tools used in building models in the information and cognitive sciences.
		One of the problems with which cognitive science is deeply concerned is the relation between thought, language, and the world.
	www.indiana.edu /~deanfac/blfal99/cogs/cogs_q250_1035.html (305 words)

	Cognitive science of mathematics (Site not responding. Last check: 2007-10-21)
		This approach was long preceded by the study, in cognitive sciences proper, of human cognitive bias, especially in statistical thinking, most notably by Amos Tversky and Daniel Kahneman, including theories of measurement, risk and behavioral finance from these and other authors.
		One central claim that justifies a cognitive science of mathematics is that Euler's Identity reflects a cognitive structure unique to humans, or less specifically to a narrow range of beings similar to humans, e.g.
		This claim may or may not be necessary or central to the overall study of the subject, and there are other approaches that might come to be included as part of the study of the relationship between human cognition and formal modern mathematics.
	www.sciencedaily.com /encyclopedia/cognitive_science_of_mathematics (293 words)

	Where Mathematics Comes From: How the Embodied Mind Brings Mathematics Into Being
		As far as I can tell it is at this point (in Chapter 3 of 16) the authors leave results established by cognitive science research and move into the realm they describe as “hypothetical” and “plausible”.
		Mathematics is a product of the neural capacities of our brains, the nature of our bodies, our evolution, our environment, and our long social and cultural history.
		I recommend that the mathematical reader skip over all arguments dismissing various other philosophies of mathematics because for the most part these arguments are based on shallow summaries of what the various philosophies assert.
	www.math.cornell.edu /~dwh/papers/EmbMath/EmbMath-review-8-01.htm (2567 words)

	Revisiting Cognitive science : Exploring Essential Information, Data and Explanation.
		Cognitive science is usually defined as the scientific study either of
		Cognitive science is usually seen as compatible with and interdependent with the physical sciences, and makes frequent use of the scientific method, as well as simulation/modelling, often comparing the output of models with aspects of human behavior.
		cognitive bias and risk perception, and has been influential in the development of behavioral finance, part of economics.
	www.llpoh.org /Biology_Update/Cognitive_science.html (2488 words)

	Cognitive Science Home Page (Site not responding. Last check: 2007-10-21)
		Cognitive science studies the human mind viewed as a computational process.
		It lies at the confluence of psychology, linguistics, anthropology, computer science, educational and cognitive development, neuroscience, neurobiology, philosophy, and certain areas of mathematics.
		Cognitive science has arguably been the most important development in the study of human thinking in the past twenty years; its influence can be seen across a wide variety of disciplines, from logic to communication disorders.
	www.ling.udel.edu /cogsci (101 words)

	Math Forum: Learning and Mathematics: Cognitive Apprenticeship - Collins, et al.
		For cognitive domains this implies sequencing of lessons so students have a chance to apply a set of skills in constructing an interesting problem solution before they are required to generate or remember those skills.
		"Drawing students into a culture of expert practice in cognitive domains involves teaching them how to 'think like experts.' The focus of much current cognitive research is to understand better what is really meant by such a goal and to find ways to communicate more effectively about the processes involved" (p.
		In A. Schoenfeld (Ed.), Cognitive science and mathematics education (pp.
	mathforum.org /~sarah/Discussion.Sessions/Collins.html (729 words)

	Learning_to_think_Math (Site not responding. Last check: 2007-10-21)
		Proceedings of the second international seminar on misconceptions and educational strategies in science and mathematics.
		Pollak, H. Cognitive science and mathematics education: A mathematician's perspective.
		On mathematics as sense-making: An informal attack on the unfortunate divorce of formal and informal mathematics.
	www-gse.berkeley.edu /faculty/ahschoenfeld/LearningToThink/Learning_to_think_Math11.html (1044 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		Nowadays, however, theoretical and experimental advances in cognitive science (the scientific interdisciplinary study of the mind) have made some important contributions to approach these questions.
		The view that comes out from these findings is that mathematics with all its beauty and complexity, does not transcend the nature of the human primate.
		Mathematics is the result of a very sophisticated creation of the human mind based on a precise coordination of already existing ordinary cognitive mechanisms which are highly efficient, flexible, and rich in inferential structure (e.g., conceptual metaphors).
	math.la.asu.edu /~kaz/colloquium/03s/nunez.txt (270 words)

	Discussion Questions 9-3
		Schoenfeld, A. Cognitive Science and Mathematics Education: An Overview, In Cognitive Science and Mathematics Education, 1-31.
		In the section on the cognitive science approach, notice the assumption that all thinking can be modeled by a computer program.
		Schoenfeld notes that evidence and argument in mathematics education research are different than in mathematics.
	math.la.asu.edu /~oehrtman/mte598-fall2002/DQ9-3.html (602 words)

	Encyclopedia article on Cognitive science [EncycloZine] (Site not responding. Last check: 2007-10-21)
		Institute for Research in Cognitive Science, University of Pennsylvania (http://www.ircs.upenn.edu/)
		Department of Cognitive Science, University of California, San Diego (http://www.cogsci.ucsd.edu/)
		School of Informatics, University of Edinburgh (http://www.inf.ed.ac.uk/) (Centre for Cognitive Science has been merged into this school)
	encyclozine.com /Cognitive_science (1255 words)

	Institute for Research in Cognitive Science
		For further information on the minor in cognitive science, contact the Director of the Cognitive Science program, Prof.
		Although these areas are patterned after those in the major, the sixth breadth area of the Cognitive Science major, Mathematics, does not apply to the minor.
		Finally, the minor requires two credits drawn from a single concentration, as defined for the specialized tracks of the Cognitive Science major.
	www.ircs.upenn.edu /education/minor-cogsci.shtml (231 words)

	Cognitive science
		A cognitive scientist is likely to assert that what he says about reasoning is true at the symbolic level of abstraction, while what the neuroscientist says is true at the physical level implementing the symbolic level (much like a computer as a physical object implements a virtual machine on which a word-processor runs).
		• Institute for Research in Cognitive Science, University of Pennsylvania (http://www.ircs.upenn.edu/)
		• Department of Cognitive Science, University of California, San Diego (http://cogsci.ucsd.edu/cogsci/)
	www.v72.org /mind_cognitive_science.htm (1158 words)

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