Results 1  10
of
10,936
Mathematical Concepts
"... Abstract: We will discuss theoretical aspects of learning and understanding mathematics by the use of calculators or computers. We distinguish a syntactical mode of working with these machines and a semantic mode. We discuss a dualism in concept development and reflect, if this also affects the use ..."
Abstract
 Add to MetaCart
Abstract: We will discuss theoretical aspects of learning and understanding mathematics by the use of calculators or computers. We distinguish a syntactical mode of working with these machines and a semantic mode. We discuss a dualism in concept development and reflect, if this also affects
Mathematical Concepts; *Mathematical Vocabulary;
"... The purpose of this study is to contribute to an understanding of how errors could be employed in mathematics instruction so that the students use them constructively in support of their learning of mathematics. A teaching experiment was designed to create an ideal context in which the pedagogical a ..."
Abstract
 Add to MetaCart
The purpose of this study is to contribute to an understanding of how errors could be employed in mathematics instruction so that the students use them constructively in support of their learning of mathematics. A teaching experiment was designed to create an ideal context in which the pedagogical
MATHEMATICAL CONCEPTS, THEIR MEANINGS, AND
"... "Try not to think of understanding as a 'mental process ' at all. For that is the expression which confuses you. (...) In the sense in which there are processess (including mental processes) which are characteristic of understanding, understanding is not a mental process". (Witt ..."
Abstract
 Add to MetaCart
". (Wittgenstein, 1953, Philosophical Investigations, p. 61) Some key elements for developing a theory for understanding mathematical concepts are outlined. These elements are derived from the theory of mathematical objects and their meanings developed by Godino and Batanero (1994; 1996). We shall argue
Role of Mathematical Concepts in
"... by Shunichi Yamamoto* The role of mathematics in cancer research is not confined to epidemiology (population level). The expected contribution of it in various levels is exemplified stepwise. At the individual level, prediction of life expectancy of a cancer case or psychological analysis of lifet ..."
Abstract
 Add to MetaCart
, the role of mathematical concepts in cancer research was fully substantiated in the framework of epidemiology. However, they are naturally not confined to this field (population level), but also expected to function in other areas such as individual, tissue, cellular, and molecular levels of cancer
Thermodynamic and mathematical concepts of CHESS
, 1998
"... This document was prepared in A M SL ..."
Mathematical concepts of multiscale smoothing
 of Bremen, Preprint Series of the DFGSchwerpunktprogramm 1114
, 2003
"... The starting point for this paper is the well known equivalence between convolution filtering with a rescaled Gaussian and the solution of the heat equation. In the first chapters we analyze the equivalence between multiscale convolution filtering, linear smoothing methods based on continuous wavele ..."
Abstract

Cited by 11 (5 self)
 Add to MetaCart
The starting point for this paper is the well known equivalence between convolution filtering with a rescaled Gaussian and the solution of the heat equation. In the first chapters we analyze the equivalence between multiscale convolution filtering, linear smoothing methods based on continuous wavelet transforms and the solutions of linear diffusion equations. I.e. we determine a wavelet ψ, resp. a convolution filter ϕ, which is associated with a given linear diffusion equation ut = P u and vice versa. This approach has an extension to nonlinear smoothing techniques. The main result of this paper is the derivation of a differential equation, whose solution is equivalent to nonlinear multiscale smoothing based on soft shrinkage methods applied to Fourier or continuous wavelet transforms. Key Words: image smoothing, multiscale methods, wavelet transform, diffusion equation AMS Subject classification: 65K10, 42C40, 94A12, 35G25
Mathematical concepts and investigative practice
, 2011
"... In this paper I investigate two notions of concepts that have played a dominant role in 20th century philosophy of mathematics. According to the first, concepts are definite and fixed; in contrast, according to the second notion concepts are open and subject to modifications. The motivations behind ..."
Abstract
 Add to MetaCart
In this paper I investigate two notions of concepts that have played a dominant role in 20th century philosophy of mathematics. According to the first, concepts are definite and fixed; in contrast, according to the second notion concepts are open and subject to modifications. The motivations behind
The Innateness Hypothesis and Mathematical Concepts
, 2009
"... Abstract In historical claims for nativism, mathematics is a paradigmatic example of innate knowledge. Claims by contemporary developmental psychologists of elementary mathematical skills in human infants are a legacy of this. However, the connection between these skills and more formalmathematical ..."
Abstract
 Add to MetaCart
concepts andmethods remains unclear. This paper assesses the current debates surrounding nativism and mathematical knowledge by teasing them apart into two distinct claims. First, in what way does the experimental evidence from infants, nonhuman animals and neuropsychology support the nativist hypothesis
Representation of Mathematical Concepts For Inferencing And . . .
, 2004
"... Knowledge bases that represent some domain expertise for use in a formal system typically serve one of two major purposes: (1) inferencing in some problemsolving context, or (2) interfacing the system by natural language. Interfacing may be for accessing the system's functionality or for pr ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
of mathematics, we are currently developing an integrated knowledge base as part of the system WMEGA, which serves the purposes of reasoning and presentation in a coordinated way at an ambitious level of capabilities. We formulate and compare representation demands from both perspectives, sketch the current
Results 1  10
of
10,936