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34
Tragic Loss or Good Riddance? The Impending Demise of Traditional Scholarly Journals
 INTERNATIONAL JOURNAL OF HUMANCOMPUTER STUDIES
, 1995
"... Traditional printed journals are a familiar and comfortable aspect of scholarly work. They have been the primary means of communicating research results, and as such have performed an invaluable service. However, they are. ..."
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Cited by 72 (11 self)
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Traditional printed journals are a familiar and comfortable aspect of scholarly work. They have been the primary means of communicating research results, and as such have performed an invaluable service. However, they are.
Estimating Covariances of Locally Stationary Processes: Rates of Convergence of Best Basis Methods
, 1996
"... Mallat, Papanicolaou and Zhang [MPZ98] recently proposed a method for approximating the covariance of a locally stationary process by a covariance which is diagonal in a specially constructed CoifmanMeyer basis of cosine packets. In this paper we extend this approach to estimating the covariance ..."
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Cited by 20 (10 self)
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Mallat, Papanicolaou and Zhang [MPZ98] recently proposed a method for approximating the covariance of a locally stationary process by a covariance which is diagonal in a specially constructed CoifmanMeyer basis of cosine packets. In this paper we extend this approach to estimating the covariance from sampled data. Our method combines both wavelet shrinkage and cosinepacket bestbasis selection in a simple and natural way. The resulting algorithm is fast and automatic. The method has an interpretation as a nonlinear, adaptive form of anisotropic timefrequency smoothing. We introduce a new class of locally stationary processes which exhibits a form of inhomogeneous nonstationarity; our processes have covariances which typically change little from row to row, but might occasionally change abruptly. We study performance in an asymptotic setting involving triangular arrays of processes which are becoming increasingly stationary, and are able to prove rates of convergence results for our...
Cognitive growth in elementary and advanced mathematical thinking
 In D. Carraher and L. Miera (Eds.), Proceedings of PME X1X
, 1995
"... This paper addresses the development of mathematical thinking from elementary beginnings in young children to university undergraduate mathematics and on to mathematical research. It hypothesises that mathematical growth starts from perceptions of, and actions on, objects in the environment. Success ..."
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Cited by 12 (10 self)
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This paper addresses the development of mathematical thinking from elementary beginnings in young children to university undergraduate mathematics and on to mathematical research. It hypothesises that mathematical growth starts from perceptions of, and actions on, objects in the environment. Successful “perceptions of ” objects lead through a Van Hiele development in visuospatial representations with increasing verbal support to visually inspired verbal proof in geometry. Successful “actions on” objects use symbolic representations flexibly as “procepts ” — processes to do and concepts to think about — in arithmetic and algebra. The resulting cognitive structure in elementary mathematical thinking becomes advanced mathematical thinking when the concept images in the cognitive structure are reformulated as concept definitions and used to construct formal concepts that are part of a systematic body of shared mathematical knowledge. The analysis will be used to highlight the changing status of mathematical concepts and mathematical proof, the difficulties occurring in
Computers, Reasoning and Mathematical Practice
"... ion in itself is not the goal: for Whitehead [117]"it is the large generalisation, limited by a happy particularity, which is the fruitful conception." As an example consider the theorem in ring theory, which states that if R is a ring, f(x) is a polynomial over R and f(r) = 0 for every element of ..."
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Cited by 6 (2 self)
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ion in itself is not the goal: for Whitehead [117]"it is the large generalisation, limited by a happy particularity, which is the fruitful conception." As an example consider the theorem in ring theory, which states that if R is a ring, f(x) is a polynomial over R and f(r) = 0 for every element of r of R then R is commutative. Special cases of this, for example f(x) is x 2 \Gamma x or x 3 \Gamma x, can be given a first order proof in a few lines of symbol manipulation. The usual proof of the general result [20] (which takes a semester's postgraduate course to develop from scratch) is a corollary of other results: we prove that rings satisfying the condition are semisimple artinian, apply a theorem which shows that all such rings are matrix rings over division rings, and eventually obtain the result by showing that all finite division rings are fields, and hence commutative. This displays von Neumann's architectural qualities: it is "deep" in a way in which the symbol manipulati...
Understanding the process of advanced mathematical thinking. An invited
 ICMI lecture at the International Congress of Mathematicians
, 1994
"... In preparing successive generations of mathematicians to think in a creative mathematical way, it is difficult to convey the personal thought processes which mathematicians use themselves. So many students, unable to cope with the complexity, resort to rotelearning to pass examinations. In this pap ..."
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Cited by 4 (2 self)
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In preparing successive generations of mathematicians to think in a creative mathematical way, it is difficult to convey the personal thought processes which mathematicians use themselves. So many students, unable to cope with the complexity, resort to rotelearning to pass examinations. In this paper I shall consider the growth of mathematical
The polymath project: lessons from a successful online collaboration in mathematics
 In Proc. CHI ’11. ACM
, 2011
"... Although science is becoming increasingly collaborative, there are remarkably few success stories of online collaborations between professional scientists that actually result in real discoveries. A notable exception is the Polymath Project, a group of mathematicians who collaborate online to solve ..."
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Cited by 3 (0 self)
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Although science is becoming increasingly collaborative, there are remarkably few success stories of online collaborations between professional scientists that actually result in real discoveries. A notable exception is the Polymath Project, a group of mathematicians who collaborate online to solve open mathematics problems. We provide an indepth descriptive history of Polymath, using data analysis and visualization to elucidate the principles that led to its success, and the difficulties that must be addressed before the project can be scaled up. We find that although a small percentage of users created most of the content, almost all users nevertheless contributed some content that was highly influential to the task at hand. We also find that leadership played an important role in the success of the project. Based on our analysis, we present a set of design suggestions for how future collaborative mathematics sites can encourage and foster newcomer participation. Author Keywords largescale collaboration, online collaborative mathematics, online collaborative science, online communities
Mathematical Intuition vs. Mathematical Monsters
, 1998
"... Geometrical and physical intuition, both untutored and cultivated, is ubiquitous in the research, teaching, and development of mathematics. A number of mathematical “monsters”, or pathological objects, have been produced which⎯according to some mathematicians⎯seriously challenge the reliability of ..."
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Cited by 3 (1 self)
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Geometrical and physical intuition, both untutored and cultivated, is ubiquitous in the research, teaching, and development of mathematics. A number of mathematical “monsters”, or pathological objects, have been produced which⎯according to some mathematicians⎯seriously challenge the reliability of intuition. We examine several famous geometrical, topological and settheoretical examples of such monsters in order to see to what extent, if at all, intuition is undermined in its everyday roles.
A well grounded education: The role of perception in science and mathematics
 In M. de Vega, A. Glenberg, & A. Graesser (Eds.), Symbols, embodiment, and meaning (pp
, 2008
"... One of the most important applications of grounded cognition theories is to science and mathematics education, where the primary goal is to foster knowledge and skills that are widely transportable to new situations. This presents a challenge to those grounded cognition theories that tightly tie kno ..."
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Cited by 3 (0 self)
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One of the most important applications of grounded cognition theories is to science and mathematics education, where the primary goal is to foster knowledge and skills that are widely transportable to new situations. This presents a challenge to those grounded cognition theories that tightly tie knowledge to the specifics of a single situation. In this
CDM: Teaching discrete mathematics to computer science majors
, 2005
"... CDM, for Computational Discrete Mathematics, is a course that attempts to teach a number of topics in discrete mathematics to computer science majors. The course abandons the classical definitiontheoremproof model and instead relies heavily on computation, as a source of motivation and also for ex ..."
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Cited by 2 (0 self)
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CDM, for Computational Discrete Mathematics, is a course that attempts to teach a number of topics in discrete mathematics to computer science majors. The course abandons the classical definitiontheoremproof model and instead relies heavily on computation, as a source of motivation and also for experimentation and illustration. The emphasis on computational issues is particularly attractive to computer science majors and increases their involvement and participation.