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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
“But you have to remember P. J. Daniell of Sheffield”
"... Abstract: 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 i ..."
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Abstract: 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. Résumé: P. J. Daniell est un personnage mystérieux qui apparaît à plusieurs moments clefs de l’histoire des mathématiques du 20ème siècle, dans le domaine de l’intégration, des processus stochastiques, des statistiques, de la commande optimale et même dans l’histoire de l’éducation mathématique en Angleterre. Ce papier se concentre sur le travail de Daniell en relation avec le développement des probabilités au vingtième siècle. Comme aucune description de sa vie et de son œuvre n’a sembletil été réalisée depuis 60 ans, nous essayons de dresser un tableau de l’ensemble de ses contributions et de les placer dans un contexte historique approprié.
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
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”.