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61	HOW TO SOLVE IT Menna, Luigi 07 May 2012 (has links) (PDF) This work is a reflection on the results of an experimentation carried out on secondary school students of between 16 and 18 from various classes. The experimentation aims at identifying the implicit ideas they use when asked to solve a certain mathematical problem. In particular, in giving them these problems an heuristic approach was suggested, and the differences between this and a purely deductive approach were measured. Analyzing the different approaches used by the students and the difficulties they had in distinguishing between argumentative and demonstrative operations has given rise to a reflection on the use of software such as Geogebra and Excel. Problemlösung heuristische Strategien Argumentationen im Vergleich zum Beweis technologische Hilfsmittel Lehre der didaktischen Situationen problem solving heuristic strategies argumentations vs proof technological tools theory of didactical situations ddc:510 rvk:SD 2009
62	From Physical Model To Proof For Understanding Via DGS: Interplay Among Environments Osta, Iman M. 07 May 2012 (has links) (PDF) The widespread use of Dynamic Geometry Software (DGS) is raising many interesting questions and discussions as to the necessity, usefulness and meaning of proof in school mathematics. With these questions in mind, a didactical sequence on the topic “Conics” was developed in a teacher education course tailored for pre-service secondary math methods course. The idea of the didactical sequence is to introduce “Conics” using a concrete manipulative approach (paper folding) then an explorative DGS-based construction activity embedding the need for a proof. For that purpose, the DGS software serves as an intermediary tool, used to bridge the gap between the physical model and the formal symbolic system of proof. The paper will present an analysis of participants’ geometric thinking strategies, featuring proof as an embedded process in geometric construction situations. Geometrie Dynamische Geometrie Software Beweis Kegelschnitte Mathematik in der Sekundarstufe Lehramts-studierende geometrisches Denken Geometry Dynamic Geometry Software Proof Conics Secondary Mathematics Pre-Service Teachers Geometric Thinking ddc:510 rvk:SD 2009
63	Analyzing the effects of a linguistic approach to the teaching of algebra: students tell “stories of development” revealing new competencies and conceptions Cusi, Annalisa 12 April 2012 (has links) This work is part of a wide-ranging long-term project aimed at fostering students’ acquisition of symbol sense through teaching experiments on proof in elementary number theory (ENT). In this paper, in particular, we highlight the positive effects of our approach analysing the written reflections that the students involved have produced at the end of the project. These reflections testify an increased level of awareness, developed by students, about the role played by algebraic language as a tool for thinking and a positive evolution in their vision of algebra. info:eu-repo/classification/ddc/510 ddc:510
64	HOW TO SOLVE IT Menna, Luigi 07 May 2012 (has links) This work is a reflection on the results of an experimentation carried out on secondary school students of between 16 and 18 from various classes. The experimentation aims at identifying the implicit ideas they use when asked to solve a certain mathematical problem. In particular, in giving them these problems an heuristic approach was suggested, and the differences between this and a purely deductive approach were measured. Analyzing the different approaches used by the students and the difficulties they had in distinguishing between argumentative and demonstrative operations has given rise to a reflection on the use of software such as Geogebra and Excel. info:eu-repo/classification/ddc/510 ddc:510
65	From Physical Model To Proof For Understanding Via DGS:Interplay Among Environments Osta, Iman M. 07 May 2012 (has links) The widespread use of Dynamic Geometry Software (DGS) is raising many interesting questions and discussions as to the necessity, usefulness and meaning of proof in school mathematics. With these questions in mind, a didactical sequence on the topic “Conics” was developed in a teacher education course tailored for pre-service secondary math methods course. The idea of the didactical sequence is to introduce “Conics” using a concrete manipulative approach (paper folding) then an explorative DGS-based construction activity embedding the need for a proof. For that purpose, the DGS software serves as an intermediary tool, used to bridge the gap between the physical model and the formal symbolic system of proof. The paper will present an analysis of participants’ geometric thinking strategies, featuring proof as an embedded process in geometric construction situations. info:eu-repo/classification/ddc/510 ddc:510
66	Mathematical Pluralism: Constructive Mathematics and Economic Theory Steins, Stefan Arno 09 December 2021 (has links) Wir schlagen eine praxisorientierte Explikation der philosophischen Position des Mathematischen Pluralismus vor. Dieser Position zufolge existieren mehr als ein legitimes mathematisches System. Wir interpretieren 'legitim' als 'geeignet zur Realisierung wissenschaftlicher Ziele' und wenden die resultierende pluralistische Position auf die Mathematische Ökonomie an. Wir präsentieren ein begriffliches Rahmenwerk, in dem pluralistische Thesen formuliert und evaluiert werden können, stellen ein informelles System der Konstruktiven Mathematik als Alternative zur Klassischen Mathematik vor, und zeigen, dass verschiedene ökonomische Theoreme nicht konstruktiv beweisbar sind. Auf dieser Basis argumentieren wir, dass Pluralismus relativ zu Zielen mit Bezug zu Erklärung und Simplizität in der Ökonomie vorliegt. / We propose a practice-oriented explication of the philosophical position known as mathematical pluralism. According to this position there exist more than one legitimate mathematical system. We interpret 'legitimate' as 'suitable for realizing scientific goals' and apply the resultant pluralist position to mathematical economics. We present a conceptual framework within which pluralist theses can be formulated and evaluated, introduce an informal system of constructive mathematics as an alternative to classical mathematics, and point out that central theorems of economic equilibrium theory are not constructively provable. On this basis, we argue that pluralism obtains with respect to goals related to explanation and simplicity in economics. allgemeines Gleichgewicht Berechenbarkeit Bishop Brouwer Carnap Fixpunktsatz Intuitionistische Logik Konstruktive Mathematik konstruktiver Beweis LLPO LPO Mathematischer Pluralismus Mikroökonomie Ökonomische Theorie wissenschaftliche Erklärung wissenschaftliches Modell Bishop Brouwer Carnap computability constructive mathematics constructive proof economic theory fixed point theorem general equilibrium intuitionistic logic LLPO LPO mathematical pluralism microeconomics scientific explanation scientific model 510 Mathematik CC 2600 ddc:100 ddc:510

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