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.

Indian female gurus in contemporary in Hinduism : a study of central aspects and expressions of their religious leadership

Den rikt utformade och komplexa hinduiska traditionen har hittills huvudsakligen tecknats av manliga forskare och det är främst manliga religiösa strävanden som har dokumenterats. Detta förhållande och de patriarkala synsätt som styr många auktoritativa heliga texter har bidragit till att skapa intrycket att hinduiska kvinnors religiösa erfarenheter antingen saknas eller är avsevärt begränsade. Denna studie lyfter fram det faktum att ett ökande antal indiska kvinnor inom dagens hinduism axlar publika roller som religiösa ledare. Med sitt framträdande utmanar många av dessa rådande sociala uppfattningar om kvinnors underordnade ställning och främjar därmed en förnyad medvetenhet av urgamla föreställningar om Gud som kvinna. Avhandlingen utforskar fenomenet kvinnliga guruer genom att belysa sjuttio guruers andliga karriär, med särskild fokus på fyra av dem. Några av de frågor som behandlas är följande: På vilket sätt är kvinnliga guruer del av den hinduiska traditionen? Vilka förväntningar ställs på dem? Hur legitimeras deras auktoritet som guruer? Hur handskas guruerna med sina dubbla roller som kvinnor och andliga ledare? Hur återspeglas gudinnans ställning, som i indisk religiositet ofta är central, i kvinnors faktiska verklighet? Bidrar kvinnliga guruer med sitt religiösa engagemang till att nyskapa och förändra den indiska religiösa diskursen och utövningen av religion?

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.

People and the intertidal : human induced changes, biodiversity loss, livelihood implications and management in the Western Indian Ocean

Vad händer i tidvattenzonen? Var går gränsen mellan land och hav, vad händer i tidvattenzonen och vem ansvarar för detta? I västra Indiska oceanen (VIO) kan avståndet mellan den lägsta nivån för lågvattnet och den högsta nivån för högvattnet vara flera kilometer och nivåskillnaderna upp till 6 meter och detta skapar ett stort och föränderligt område. Syftet med min avhandling är att öka förståelsen för tidvattenzonen i tropiska och subtropiska västra Indiska oceanen. Sammanfattningsvis visar mina studier att det finns ett mycket stort värde i den komplexa tidvattenzonen, men också att det här området hotas från både land och hav, genom t.ex. överexploatering, erosion och föroreningar. Uttnyttjandet av tidvattenzonen är stort och min avhandling har visat att aktiviteter såsom fiske i form av plocking av musslor och andra ryggradslösa djur och hamnaktiviteter påverkar den biologiska mångfalden negativt, vilket leder till försämrad levnadsstandard för resursutnyttjande människor i regionen. För att förbättra situationen krävs det mer forskning, miljöövervakning och bättre förvaltning av tidvattenzonen. Experter i regionen har rangordnat förslag på förvaltningsstrategier som skulle kunna testas för att förbättra miljön och skapa ett mer hållbart nyttjande. Avhandlingen visar även att det är möjligt att använda fjärranalysteknik såsom satellitbildsanalys för att kvantifiera mängden sjögräsvegetation (i form av biomassa), vilket kan ha stor betydelse för att förbättra storskalig miljöövervakning av kustnära naturtyper (habitat). I avhandlingsarbetet har jag använt mig av ett multidisciplinärt tillvägagångssätt och använt metoder såsom ekologisk och biologisk provtagning, intervjuer, observationer, diskussionsgrupper, frågeformulär och fjärranalys. Resultaten presenterade i denna avhandling ger en ökad kunskap om tidvattenzonen i utvecklingsländerna inom VIO-regionen som kan användas för att initiera och fortsätta att utveckla hållbara förvaltningsstrategier av biologiska resurser.

Strategic alliances as an international entry strategy: Finnish cleantech SMEs and the Indian market

The demand for environmental technologies, also called cleantech, is growing globally but the need is especially high in emerging markets such as India where the rising economy and rapid industrialisation have led to increasing energy needs and environmental degradation. The market is of great potential also for the Finnish cleantech cluster that represents advanced expertise in several fields of environmental technologies. However, most of the Finnish companies in the field are SMEs that face challenges in their internationalisation due to their limited resources. The objective of this study was to estimate, whether strategic alliances could be an efficient entry strategy for Finnish cleantech SMEs entering the Indian market. This was done by studying what are the key factors influencing the international entry mode decision of Finnish cleantech SMEs, what are the major factors affecting the entry of Finnish cleantech SMEs to the Indian market and how do Finnish cleantech SMEs use strategic alliances in their internationalisation process. The study was realised as a qualitative multi-case study through theme interviews of Finnish cleantech SME representatives. The results indicated that Finnish cleantech SMEs prefer to enter international markets through non-equity and collaborative modes of entry. These entry modes are chosen because of the small size and limited resources of companies, but also because they want to protect their innovative technologies from property rights violations. India is an attracting market for Finnish cleantech SMEs mainly because of its size and growth, but insufficient environmental regulation and high import tariffs have hindered entry to the market. Finnish cleantech SMEs commonly use strategic alliances in their internationalisation process but the use is rather one-sided. Most of the formed strategic alliances are low-commitment, international contractual agreement in sales and distribution. Alliance partner selection receives less attention. In the future, providing Finnish cleantech SMEs with international experience and training could help in diversifying the use of strategic alliances and increase their benefits to SME internationalisation.

Ohjeita Indian moottoripyörän käyttämistä, hoitoa ja tarkistamista varten

kuv., 15 x 22 cm

Anvisningar beträffande körning, underhåll och justering av Indian motorvelocipeder

kuv., 15 x 22 cm

Indian motocycles

kuv., 16 x 24 cm