What is a number?

The concept of number is an abstract concept. Numbers do not exist itself in the nature. On the other hand, they carry a wide variety of significant information about the environment and are present in the life of human being in almost all fields. The origins of numbers as well as its nature were considered in numerous ways by mathematicians, philosophers, psychologists etc. The classical theories of number are briefly discussed and opposed to the psychological and neuroscientific findings regarding number representations. It seems that the ability use information carried by number is not exclusive to educated human mind, contrary its origins are innate and common to humans and several other species

What is a number?: production, circulation and appropriation of a New Math for children

This study addresses content changes to be taught in the first years of elementary school. In particular, it considers the teaching of mathematics with a focus on the emergence of Modern Mathematics in Brazil. In a specific way, it examines the concept of number. It considers as a theoretical and methodological foundation studies originally from cultural history. The analysis considers the pedagogical movement prior to what is known as the Modern Mathematics Movement: traditional education, intuitive teaching and progressive era in education. It then takes into account the emergence, dissemination and appropriation of a new mathematics for schools in the [mid-20th Century / 1940s]. The article is guided by the following question: what changes does the concept of number undergo in the mathematics for schools in the late 1950s? As a result the study reveals how the production, distribution and appropriation of new mathematics content for children of elementary school took place.O estudo aborda as mudanças nos conteúdos a serem ensinados nos primeiros anos da escola elementar. Em particular, considera o ensino de matemática. Atém-se, sobretudo, à emergência da Matemática Moderna no Brasil. De forma específica, analisa o conceito de número. Leva em consideração, como base teórico-metodológica, estudos vindos da História Cultural. Na análise realizada trata de movimentos pedagógicos anteriores ao que fica conhecido como Movimento da Matemática Moderna: o ensino tradicional, o ensino intuitivo e o escolanovismo. Em seguida, leva em conta a emergência, divulgação e apropriação de uma nova matemática escolar a partir de finais da primeira metade do século XX. O artigo orienta-se pela seguinte questão: que alterações o conceito de número sofre, na matemática escolar brasileira, em finais da década de 1950? Como resultado do estudo revela-se como se dá o processo de produção, de circulação e de apropriação de novos conteúdos elementares da matemática escolar para crianças.Universidade Federal de São Paulo (UNIFESP)UNIFESPSciEL

The ontology of number

What is a number? Answering this will answer questions about its philosophical foundations - rational numbers, the complex numbers, imaginary numbers. If we are to write or talk about something, it is helpful to know whether it exists, how it exists, and why it exists, just from a common-sense point of view [Quine, 1948, p. 6]. Generally, there does not seem to be any disagreement among mathematicians, scientists, and logicians about numbers existing in some way, but currently, in the mainstream arena only definitions, descriptions of properties, and effects are presented as evidence. Enough historical description of numbers in history provides an empirical basis of number, although a case can be made that numbers do not exist by themselves empirically. Correspondingly, numbers exist as abstractions. All the while, though, these "descriptions" beg the question of what numbers are ontologically. Advocates for numbers being the ultimate reality have the problem of wrestling with the nature of reality. I start on the road to discovering the ontology of number by looking at where people have talked about numbers as already existing: history. Of course, we need to know not only what ontology is but the problems of identifying one, leading to the selection between metaphysics and provisional approaches. While we seem to be dimensionally limited, at least we can identify a more suitable bootstrapping ontology than mere definitions, leading us to the unity of opposites. The rest of the paper details how this is done and modifies Peano's Postulates

Barnes Hospital Record

https://digitalcommons.wustl.edu/bjc_barnes_record/1065/thumbnail.jp

Mathematics primary teacher training in the context of the european higher education area

The future implementation of the European Higher Education Area requires thorough reflection on how to design and develop teacher training courses. In this reflection, it is important to reconsider, among other issues, (a) the role of prospective teachers in their own learning process and (b) the professional competencies that they must develop in the course of their higher education. Since 2003, the University of Granada has undertaken the development of pilot experiences to adapt some degree programs to this new framework. One of these degrees is Teacher in Primary Education degree, which includes several courses that focus on promoting prospective teachersÕ development of mathematical and pedagogical knowledge. In this paper how to organize future teachersÕ learning through practical activities in one of these courses is described. Firstly, the general process of adapting the course is analysed. Secondly, its theoretical and practical structure, with some examples of practical activities, are described. Finally, some results of the implementation are discussed