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Advanced mathematical thinking and the computer
 In D. Tall (Ed.), Advanced Mathematical Thinking
, 1991
"... This presentation considers the developing role of the computer in advanced mathematical thinking, focusing on the learning of advanced mathematics by university students. It will consider different characteristics of advanced mathematical thinking and report research into the use of the ..."
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This presentation considers the developing role of the computer in advanced mathematical thinking, focusing on the learning of advanced mathematics by university students. It will consider different characteristics of advanced mathematical thinking and report research into the use of the
WHAT IS THE PHILOSOPHY OF MATHEMATICS EDUCATION?
"... This question (what is the philosophy of mathematics education?) provokes a number of reactions, even before one tries to answer it. Is it a philosophy of mathematics education, or is it the philosophy of mathematics education? Use of the preposition ‘a ’ suggests that what is being offered is one o ..."
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This question (what is the philosophy of mathematics education?) provokes a number of reactions, even before one tries to answer it. Is it a philosophy of mathematics education, or is it the philosophy of mathematics education? Use of the preposition ‘a ’ suggests that what is being offered is one of several such perspectives, practices or areas of study. Use of the definite article ‘the ’ suggests to some the arrogation of definitiveness to the account given. 1 In other words, it is the dominant or otherwise unique account of philosophy of mathematics education. However, an alternative reading is that ‘the ’ refers to a definite area of enquiry, a specific domain, within which one account is offered. So the philosophy of mathematics education need not be a dominant interpretation so much as an area of study, an area of investigation, and hence something with this title can be an exploratory assay into this area. This is what I intend here. Moving beyond the first word, there is the more substantive question of the reference of the term ‘philosophy of mathematics education’. There is a narrow sense that can be applied in interpreting the words ‘philosophy ’ and ‘mathematics education’. The philosophy of some area or activity can be understood as its aims or rationale. Mathematics education understood
TimeManagement, Writing, and Accounting in the EighteenthCentury English Trading Family: A Bourgeois Enlightenment
 Business and Economic History
, 1989
"... London, lay dying. As the old man moved fitfully in and out of consciousness he dreamed a dream which struck his nephew (also a businessman) so forcefully that he wrote it down in his journal:... a man came to arrest [my uncle] for debt and pushed him into a corner. "Wait " replied he, &qu ..."
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London, lay dying. As the old man moved fitfully in and out of consciousness he dreamed a dream which struck his nephew (also a businessman) so forcefully that he wrote it down in his journal:... a man came to arrest [my uncle] for debt and pushed him into a corner. "Wait " replied he, "I have money to pay you. " "Oh" said the man "that is not the thing, this debt is not to be paid with Money. " When he awoke he recounted this dream... and said that he knew well that the person who had appeared to him was Death and that his time had come [13, p. 74]. The metaphors the unconscious reaches for in its hour of distress can be deeply revealing ones, and it is reasonable to assume that Philip Eliot's dream tells us as much about his preoccupations over the course of his lifetime as it does of his coming to terms with death. This paper explore some of the particular anxieties associated with living in and attempting to profit from a society which offered little structural support for capitalist endeavor. It seeks to describe the tight and often problematic interconnection of eighteenthcentury
“But you have to remember P. J. Daniell of Sheffield”
, 2007
"... P. J. Daniell is a mysterious figure who appears at several turns in the history of mathematics in the 20th century, in the fields of integration, stochastic processes, statistics, control engineering and even in the history of English mathematical education. The main focus of this paper is on Danie ..."
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P. J. Daniell is a mysterious figure who appears at several turns in the history of mathematics in the 20th century, in the fields of integration, stochastic processes, statistics, control engineering and even in the history of English mathematical education. The main focus of this paper is on Daniell’s work in relation to the development of probability in the twentieth century. But as it seems that no survey of his work and life has been attempted for 60 years I try to consider all his contributions and place them in an appropriate historical context.
A GUIDE TO PUZZLEBASED LEARNING IN STEM SUBJECTS A GUIDE TO PUZZLEBASED LEARNING IN STEM SUBJECTS
"... ii ..."
THE PSYCHOLOGY OF SYMBOLS & SYMBOL MANIPULATORS: WHAT ARE WE DOING RIGHT?
"... Instead of saying “wow, look at the clever math I can do with my computer”, this presentation considers how mathematicians and students use symbols to think about mathematics and formulates a theory to describe how software using symbol manipulators can help and hinder the learning process. … the pr ..."
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Instead of saying “wow, look at the clever math I can do with my computer”, this presentation considers how mathematicians and students use symbols to think about mathematics and formulates a theory to describe how software using symbol manipulators can help and hinder the learning process. … the property of yielding new truths as a result of merely mechanical rearrangement of symbols […] is to be found in some form wherever a system of symbolism has been developed “to facilitate reasoning ” in a particular province of thought. The late Prof Jevons actually invented a “logical machine ” in which the exploration of the field of truth could be carried out by pulling levers and turning handles. It would probably not be impossible, if only it were worth while, to construct an “algebra machine ” which could in a similar way be made to yield from a given formula other formulae which follow from it. (T. Percy Nunn, The Teaching of Algebra, 1914, p. 15.) Symbol manipulators are reputed to “release the student from the drudgery of routine manipulation so that they can focus attention on the concepts and solving problems”.