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97
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 102 (12 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
, 1998
"... 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 28 (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 21 (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
Modelling mathematical argumentation: The importance of qualification
 Educational Studies in Mathematics
, 2007
"... Abstract. In recent years several mathematics education researchers have attempted to analyse students ’ arguments using a restricted form of Toulmin’s (1958) argumentation scheme. In this paper we report data from taskbased interviews conducted with highly talented postgraduate mathematics stude ..."
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Cited by 18 (4 self)
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Abstract. In recent years several mathematics education researchers have attempted to analyse students ’ arguments using a restricted form of Toulmin’s (1958) argumentation scheme. In this paper we report data from taskbased interviews conducted with highly talented postgraduate mathematics students, and argue that a superior categorisation of genuine mathematical argumentation is provided by the use of Toulmin’s full scheme. In particular, we suggest that modal qualifiers play an important and previously unrecognised role in mathematical argumentation, and that one of the goals of instruction should be to develop students ’ abilities to appropriately match up warranttypes with modal qualifiers.
The informal logic of mathematical proof
 ASPIC2 Argumentation Service Platform with Integrated Components http://www.argumentation.org
, 2007
"... Paul Erdős famously remarked that ‘a mathematician is a machine for turning coffee into theorems ’ [9, p. 7]. The proof of mathematical theorems is central to mathematical practice and to much recent debate about the nature of mathematics. This paper is an attempt to introduce a new perspective on t ..."
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Cited by 10 (3 self)
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Paul Erdős famously remarked that ‘a mathematician is a machine for turning coffee into theorems ’ [9, p. 7]. The proof of mathematical theorems is central to mathematical practice and to much recent debate about the nature of mathematics. This paper is an attempt to introduce a new perspective on the argumentation characteristic of mathematical proof. I shall argue that this account, an application of informal logic to mathematics, helps to clarify and resolve several important philosophical difficulties. It might be objected that formal, deductive logic tells us everything we need to know about mathematical argumentation. I shall leave it to others [14, for example] to address this concern in detail. However, even the protagonists of explicit reductionist programmes—such as logicists in the philosophy of mathematics and the formal theorem proving community in computer science—would readily concede that their work is not an attempt to capture actual mathematical practice. Having said that, mathematical argumentation is certainly not inductive either. Mathematical proofs do not involve inference from particular
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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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
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 e ..."
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Cited by 7 (3 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...
Promoting Transfer by Grounding Complex Systems Principles
, 2008
"... To link to this Article: DOI: 10.1080/10508400802394898 ..."
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To link to this Article: DOI: 10.1080/10508400802394898
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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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