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3. Conclusions

Author

Spagnolo, Filippo, Di Paola, Benedetto, Kacprzyk, Janusz, editor, Spagnolo, Filippo, and Di Paola, Benedetto

Published
2010
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10. From Arithmetical Thought to Algebraic Thought: The Role of the 'Variable'

Author

Malisani, Elsa and Spagnolo, Filippo

Abstract

The introduction of the concept of the variable represents a critical point in the arithmetic-algebraic transition. This concept is complex because it is used with different meanings in different situations. Its management depends on the particular way of using it in problem-solving. The aim of this paper was to analyse whether the notion of "unknown" interferes with the interpretation of the variable "in functional relation" and the kinds of languages used by the students in problem-solving. We also wanted to study the concept of the variable in the process of translation from algebraic language into natural language. We present two experimental studies. In the first one, we administered a questionnaire to 111 students aged 16-19 years. Drawing on the conclusions of this research we carried out the second study with two pairs of students aged 16-17 years.

Published
2009
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11. Introduction

Author

Spagnolo, Filippo, Di Paola, Benedetto, Kacprzyk, Janusz, editor, Spagnolo, Filippo, and Di Paola, Benedetto

Published
2010
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16. Introduction

Author

Regnier, Jean-Claude, Gras, Régis, Spagnolo, Filippo, Interactions, Corpus, Apprentissages, Représentations (ICAR), École normale supérieure - Lyon (ENS Lyon)-Université Lumière - Lyon 2 (UL2)-INRP-Ecole Normale Supérieure Lettres et Sciences Humaines (ENS LSH)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Informatique de Nantes Atlantique (LINA), Mines Nantes (Mines Nantes)-Université de Nantes (UN)-Centre National de la Recherche Scientifique (CNRS), Gruppo di Ricerca sull'Insegnamento delle Matematiche (GRIM), Università de Palermo, J.C. Régnier, R. Gras, F. Spagnolo, B. Di Paola, and Les auteurs remercient le LABEX ASLAN (ANR-10-LABX-0081) de l'Université de Lyon pour son soutien financier dans le cadre du programme 'Investissements d'Avenir' (ANR-11-IDEX-0007) de l'Etat Français géré par l'Agence Nationale de la Recherche (ANR).

Subjects
analyse statistique implicative, [SHS.LANGUE]Humanities and Social Sciences/Linguistics
Published
2011

23. To the beginnings of the XXI century, which possible use of neurosciences results in research in Mathematics Education ?

Author

SPAGNOLO, Filippo, DI PAOLA, Benedetto, Spagnolo, F, and Di Paola, B

Subjects
Mathematics Education, Neuroscience, Settore MAT/04 - Matematiche Complementari
Abstract

In the last 20 years we witnessed a development of research on "how" our brain works, how it processes the information, how it stores, how it links these, which are the areas appointed to a certain function and how these are interconnected with this each other etc. Then how it learn. Many people are interested to these results, first of all psychologists that are interested in the problems since long time, but also the neurophysiologists and the many categories of people who have intentions of speculative nature, but also with other kind of application. We can think to problems arising from situations of disability, related to brain injury to various types and more, etc ... In the study of the processes of teaching / learning the knowledge of the results of this field is central. Not only for the study of disorders in learning mathematics or in situations of physical disability but also for those situations that are labeled with the word "normal." Do so an innate mathematical knowledge exist? Is an understanding of natural language innate? What is the relationship between natural languages and mathematics? To all these questions, the neurophysiology of the brain begins to give tentative results. They, as scientific knowledge, can not be definitive , but they could immediately help us to "better" interpret the phenomena of teaching / learning of Mathematics. We present a general outline of this work: 1. A possible consolidated overview of the neuroscience research and learning of Mathematics: The Numeric Module, the approximation, the distance effect. 2. Does the numerical module explains everything? 3. The effects on teaching / learning of Numeric Module: discrete / continuous, etc.. A new classification of obstacles? 4. Plasticity and disability: an example of injured brain. 5. The mirror neurons: the laboratory, the processes of communication in teaching / learning, etc. 6. Fractions: the open problem of the day ... What we discuss, even if in a first approximation, in this work is to be a further study on some epistemological and educational issues related to neuroscience research and consolidate learning of Mathematics. Specifically we want to discuss some of the most significant results on key aspects of mathematics learning such as the Numeric Module, the approximation, the concept of fraction and rational number and the behaviour continuous / discrete significant for same didactical activity in scientific subject. With this objective in this work, we will discuss an appropriate analysis of the case study referred to a injured brain with cognitive difficulties in learning of the order relation, a reading of the processes of teaching learning activities through the workshop mirror neurons.

Published
2009

24. Motivating and Exciting Methods in Mathematics and Science, IT Team

Author

FAZIO, Claudio, DI PAOLA, Benedetto, LO CICERO, Maria Lucia, D'EREDITA', Giuliano, SPAGNOLO, Filippo, SPAGNOLO F., A. ULOVEC, S. CERETKOVA, A. DOCKERTY, J. MOLNAR, Fazio, C, Di Paola, B, Lo Cicero, ML, D'Eredità, G, and Spagnolo, F

Subjects
Mathematics EDucation, Science EDucation, Case study, Settore MAT/04 - Matematiche Complementari
Published
2009

28. Motivating and Exciting Methods in Mathematics Education

Author

SPAGNOLO, Filippo, Ulovec, A, Ceretkova, S, Dockerty, A, Molnar, J., Spagnolo, F, Ulovec, A, Ceretkova, S, Dockerty, A, and Molnar, J

Subjects
Mathematics EDucation, Science Education, Settore MAT/04 - Matematiche Complementari
Published
2009

40. Numer Theory

Author

SPAGNOLO, Filippo, V. BERINDE, GREGORY MAKRIDES, SPAGNOLO F, and V BERINDE

Published
2006

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