Search results for "mathematical practice"
showing 4 items of 4 documents
Branch Points of Algebraic Functions and the Beginnings of Modern Knot Theory
1995
Many of the key ideas which formed modern topology grew out of “normal research” in one of the mainstream fields of 19th-century mathematical thinking, the theory of complex algebraic functions. These ideas were eventually divorced from their original context. The present study discusses an example illustrating this process. During the years 1895-1905, the Austrian mathematician, Wilhelm Wirtinger, tried to generalize Felix Klein's view of algebraic functions to the case of several variables. An investigation of the monodromy behavior of such functions in the neighborhood of singular points led to the first computation of a knot group. Modern knot theory was then formed after a shift in mat…
For a Philosophy of Mathematical Practice
2010
It is a fact that of the logicist, the intuitionist, and Hilbert's programmes, the classical programmes set up to establish mathematics on safe foundations, some have failed, whereas others have long since lost their propulsive force. Two of the consequences of the crisis of the classical programmes in the foundations of mathematics were: a widespread scepticism towards the possibility of establishing the certainty of mathematical methods, and a new attention paid to mathematical practice. The main aim of this article is that of individuating some directions of research along which to develop a tenable philosophy of mathematical practice.
Tools and Mathematics in the Real World
2016
This chapter considers, with special regard to tool use, mathematics in out-of-school practices and attempts to replicate these practices in school mathematics. Both foci are important and problematic issues in mathematics education. This chapter has four sections. The two central sections address the two main foci. The opening section sets the scene with an historical account of ways that mathematics has been subdivided with regard to its application(s). The last section considers problem issues.
Kindergarten teachers’ accounts of their developing mathematical practice
2012
Published version of an article in the journal: ZDM. Also available from the publisher at: http://dx.doi.org/10.1007/s11858-012-0422-1 This study explores kindergarten teachers’ accounts of their developing mathematical practice in the context of their participation in a developmental research project. Observations and interviews were analysed to elaborate the accounts as regards orchestrating mathematical activities in the kindergarten. A co-learning agreement was established as collaboration between the kindergarten teachers and researchers. The study reveals that the kindergarten teachers argue that they have been empowered in developing an inquiry stance towards mathematics and mathemat…