Matemáticas y juego = Mathematics and games

In this article we try to look at the learning of mathematics through games in the first years of schooling. The use of game resources in the class should not be carried out in a uniquely intuitive way but rather in a manner that contains some preliminary reflections such as, what do we understand by games? Why use games as a resource in the Mathematics classroom? And what does its use imply?

¿Para qué sirven los problemas en la clase de matemáticas? = What is the use of problems in Mathematics lessons?

The results obtained in several yield tests, at an international level (mainly the famous PISA 2003 report, by the OCDE), have raised a multiplicity of performances in order to improve the students' yield regarding problem solving. In this article we set a clear guideline on how problems should be used in Mathematics lessons, not for obtaining better scores in the yield tests but for improving the development of Mathematical thinking in students. From this perspective, the author analyses, through eight reflections, how the concept of problem, transmitted both in the school and from society, influences the students

Una visión actualizada de la didáctica de la matemática en educación infantil = An up-to-date vision of pre-school mathematics teaching

This article aims to investigate pre-school mathematics teaching from an uptodate perspective. To pursue this contemporary vision we focus on four key questions: what kind of maths is being worked on, who is doing it, how it is being done, and why it is being done

Teaching mathematics and programming : new approaches with empirical evaluation

Programming and mathematics are core areas of computer science (CS) and consequently also important parts of CS education. Introductory instruction in these two topics is, however, not without problems. Studies show that CS students find programming difficult to learn and that teaching mathematical topics to CS novices is challenging. One reason for the latter is the disconnection between mathematics and programming found in many CS curricula, which results in students not seeing the relevance of the subject for their studies. In addition, reports indicate that students' mathematical capability and maturity levels are dropping. The challenges faced when teaching mathematics and programming at CS departments can also be traced back to gaps in students' prior education. In Finland the high school curriculum does not include CS as a subject; instead, focus is on learning to use the computer and its applications as tools. Similarly, many of the mathematics courses emphasize application of formulas, while logic, formalisms and proofs, which are important in CS, are avoided. Consequently, high school graduates are not well prepared for studies in CS. Motivated by these challenges, the goal of the present work is to describe new approaches to teaching mathematics and programming aimed at addressing these issues: Structured derivations is a logic-based approach to teaching mathematics, where formalisms and justifications are made explicit. The aim is to help students become better at communicating their reasoning using mathematical language and logical notation at the same time as they become more confident with formalisms. The Python programming language was originally designed with education in mind, and has a simple syntax compared to many other popular languages. The aim of using it in instruction is to address algorithms and their implementation in a way that allows focus to be put on learning algorithmic thinking and programming instead of on learning a complex syntax. Invariant based programming is a diagrammatic approach to developing programs that are correct by construction. The approach is based on elementary propositional and predicate logic, and makes explicit the underlying mathematical foundations of programming. The aim is also to show how mathematics in general, and logic in particular, can be used to create better programs.

Teachers' conceptions of literacies during and after a school library development project

Abstrakti

The mathematics of McTaggart's paradox

Mc Taggart's celebrated proof of the unreality of time is a chain of implications whose final step asserts that the A-series (i.e. the classification of events as past, present or future) is intrinsically contradictory. This is widely believed to be the heart of the argument, and it is where most attempted refutations have been addressed; yet, it is also the only part of the proof which may be generalised to other contexts, since none of the notions involved in it is specifically temporal. In fact, as I show in the first part of the paper, McTaggart's refutation of the A-series can be easily interpreted in mathematical terms; subsequently, in order to strengthen my claim, I apply the same framework by analogy to the cases of space, modality, and personal identity. Therefore, either McTaggart's proof as a whole may be extended to each of these notions, or it must embed some distinctly temporal element in one of the steps leading up to the contradiction of the A-series. I conclude by suggesting where this element might lay, and by hinting at what I believe to be the true logical fallacy of the proof.

HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS

Abstract: In this article we analyze the key concept of Hilbert's axiomatic method, namely that of axiom. We will find two different concepts: the first one from the period of Hilbert's foundation of geometry and the second one at the time of the development of his proof theory. Both conceptions are linked to two different notions of intuition and show how Hilbert's ideas are far from a purely formalist conception of mathematics. The principal thesis of this article is that one of the main problems that Hilbert encountered in his foundational studies consisted in securing a link between formalization and intuition. We will also analyze a related problem, that we will call "Frege's Problem", form the time of the foundation of geometry and investigate the role of the Axiom of Completeness in its solution.

National Library – Service Centre for All Types of Libraries in Finland

Kristiina Hormia-Poutasen esitys Jerusalemissa Israelin kansalliskirjastossa 8.9.2011

National Library and Library Network in Finland - Cooperation Being the Driving Force of Success

Kristiina Hormia-Poutasen esitys Danish Research Association -tapahtumassa Tanskassa 15.9.2011

National Library – Service Centre for All Types of Libraries in Finland

Kristiina Hormia-Poutasen esitys Jerusalemissa 8.9.2011

The Changing Nature of Library Networks - Open Data or One Big Silo?

Anders Söderbäckin esitys Kirjastoverkkopäivillä 26.10.2011 Helsingissä.

Licensing of eResources - views from Denmark's Electronic Research Library (DEFF)

Bo Öhrströmin esitys Kirjastoverkkopäivillä 27.10.2011 Helsingissä.

Library Services in a New Perspective: Unifying Resource Management

Johan Rademakersin esitys Kirjastoverkkopäivillä 26.10.2011.