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European and Chinese Cognitive Styles and their Impact on Teaching Mathematics : Studies in Computational Intelligence - Filippo Spagnolo

European and Chinese Cognitive Styles and their Impact on Teaching Mathematics

Studies in Computational Intelligence

By: Filippo Spagnolo (Editor), Benedetto di Paola (Editor)

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Published: 25th March 2010
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The series Studies in Computational Intelligence (SCI) publishes new developments and advances in the various areas of computational intelligence — quickly and with a high quality. The intent is to cover the theory, applications, and design methods of computational intelligence, as embedded in the fields of engineering, computer science, physics and life science, as well as the methodologies behind them. The series contains monographs, lecture notes and edited volumes in computational intelligence spanning the areas of neural networks, connectionist systems, genetic algorithms, evolutionary computation, artificial intelligence, cellular automata, self-organizing systems, soft computing, fuzzy systems and hybrid intelligent systems. Critical to both contributors and readers are the short publication time and world-wide distribution — this permits a rapid and broad dissemination of research results.

The book provides strong evidence that research on the cognitive processes from arithmetic thought to algebraic thought should take into consideration the socio-cultural context. It is an important contribution to the literature on linguistic structure in comparative studies related to Chinese student mathematics learning.

This book not only makes a great contribution to research in mathematics education, the findings of this study also addressed insightful approaches and thoughts of understanding the development of algebraic thinking in cultural contexts for classroom teachers. Using written Chinese language from different theoretical references provided wonderful approaches for understanding student algebra cognitive development in a different way and calls educators for to pay special attention to an epistemological and linguistic view of algebraic development. The findings inform classroom teachers that the cultural context plays an important role in student learning mathematics. A typical analysis of the cognitive dimension involved in some in the historical and cultural contexts is a great resource for classroom teachers.

I really enjoyed reading this book and learned a lot from its compelling analysis. Shuhua An, Associate Professor and Director of Graduate Program in Mathematics Education, California State University, Long Beach

Introductionp. 1
A General Framework and Theoretical Referencesp. 3
Principal Objective of the Bookp. 3
The Experimental Epistemology of the Mathematics as Paradigma of Referencep. 3
The Differences and the Analogies of the Carrying Cultural Coordinatesp. 4
What the References with the Mathematics, with to Deduce and to Conjecture (and to Conceptualize)p. 5
Experimental Epistemology of Mathematics, Didactics of Mathematics, Communication of Mathematics, Semiotics: Theoretical Possible Interpretationp. 6
Conclusionsp. 10
The Chinese Written Language as Tool for a Possible Historical and Epistemological Reflections on the Mathematics and the Impact of Teaching/Learning of Mathematicsp. 13
The Written Chinese Language as Possible Tool to Acquire Algebraic Competences in Mathematicsp. 13
The Point of View of the Neurosciencesp. 14
Origin and Development of the Chinese Writing: Some Fundamental Stepp. 15
The Pinyin and the Chinese Language in the Chinese Schoolp. 17
Observations Cognitive on the Chinese Languagep. 19
Chinese Language and Mathematicsp. 22
Rules of Composition of a Chinese Characterp. 24
The Classification of the Chinese Charactersp. 25
Constitutions of Ideograms and Algebraic Thoughtp. 27
The Research of the Characters on the Dictionaryp. 30
The Parametric Structure of the Written Chinese Languagep. 30
The Meta-rules of the Language and the Mathematicsp. 32
Can the Natural Language Influence the Educational System of the Area Logical-Mathematics? Which Is the Impact in the Teaching of the Mathematics?p. 34
Contents and Objectives in the Historical Evolution of the Teaching of the Mathematics in the Chinese School: A Brief Panningp. 34
The Teaching of the Mathematics in the Today's Didactic Practicep. 39
A Resume Chart on the Relationship Natural Language Mathematicsp. 44
The Meta-rules between Natural Language and History of Mathematicsp. 47
The Algebra between the History and the Didactics, a Variety of Perspectivesp. 47
The Algebraic Tradition in Antiquity: An Overviewp. 52
The Elements of Euclid as a Canon of Reference for the Western Mathematical Traditionp. 57
An Initial Comparison between the "Elements" of Euclid and the "Jiuzhang Suanshu"p. 58
One Possible Comparison between Diofanto and Babyloniansp. 59
The Algebraic Tradition among the Arabs and the Indiansp. 60
Significant Developments for the Symbolic Algebrap. 69
A Look at the Ancient Chinese Mathematicsp. 73
The Historical-Culturalp. 73
The Jiuzhang Suanshup. 75
The Rule of Fangcheng as Meta-rule for the Chinese Algebrap. 80
Argue, and Demonstrate in Conjecturing Jiuzhang Suanshu an Example through the Algebrap. 84
Conclusionp. 87
How to Summarize the Role of History?p. 89
Common Sense and Fuzzy Logicp. 91
Fuzzy Logic, Fuzzy Thinking and Linguistic Approachp. 91
Fuzzy Sets and Their Representationsp. 92
The Representative Point of View of Koskop. 95
Some Epistemological Reflections on the Approaches to the Fuzzy Logicp. 98
Some Experimental Observations on Common Sense and Fuzzy Logicp. 99
Common Sense and Fuzzy Logicp. 99
Fuzzy Logic and Complexityp. 100
The Hypothesisp. 101
The Assignment a Computer Science Activityp. 102
A Priori Analysisp. 103
Implicative Analysis using the Chic Programp. 104
From the Pupil Recordsp. 105
A Possible Interpretation Keyp. 106
Conclusionsp. 107
Open Problemsp. 108
Conclusionsp. 117
The Experimental Epistemology as a Tool to Observe and Preview Teaching/Learning Phenomenap. 119
The Experimental Contextp. 119
Choice of the Problematic Situations in Accordance with the Theoretical Framework and the Hypotheses of Researchp. 119
The First Experimental Investigation: "Sudoku Magic Box"p. 127
A Priori Analysisp. 130
Quantitative and Qualitative Analyses of the Datap. 131
Second Experimental Investigation: "The Problem of Fermat", "Varying Questionnaire and Parameter in Different Semiotic Context"p. 136
A Priori Analysis: "Fermat Problem"p. 145
Quantitative and Quantitative Analysis: "Fermat Problem"p. 146
A Priori Analysis: "Questionnaire Variable and Parameter in Different Semiotic Context"p. 151
Quantitative and Qualitative Analysis: "Questionnaire Variable and Parameter in Different Semiotic Context"p. 154
Third Experimental Investigation: "The Sequence", "The Grid of Numbers"p. 165
A Priori Analysis "The Sequence"p. 170
Quantitative and Qualitative Analysis of "The Sequence"p. 171
A Priori Analysis of "The Grid of Numbers"p. 174
Qualitative Analysis of "The Grid of Numbers"p. 174
From Natural Languages to Logical Linguistic Aspects: Cognitive Styles of European and Chinese Studentsp. 185
Some Reflections on "Arguing, Conjecturing and Demonstrating" in Chinese Culture with Relation to Occidental Culturep. 186
The Algorithm as Fundamental Element of Arguing and Demonstrating?p. 186
What are the Stable Reasoning Patterns in Chinese Culture?p. 187
How were the Situations/Problems Chosen?p. 189
The a Priori Analysis of the Situations. We Report the a Priori Analysis of the Hypothesized Behavioursp. 190
Presentation of the Experimental Work in the Italian Classesp. 191
The Quantitative Analysis: Implicative and Factorialp. 191
Implicative and Similarities Analysisp. 192
General Considerations on Factorial Analysis, Implicative Analysis and Similaritiesp. 193
Interviews with Two Chinese: Qualitative Considerationsp. 194
The Experience in the Chinese Classesp. 195
Factorial Analysisp. 196
Supplementary Variablesp. 196
Considerations on the Analysis of the Data Relative to the Chinese Samplep. 197
General Conclusions and Future Perspectivesp. 197
Strategy and Tactics in the Chinese and European Culture: Chess and Weich'Ip. 201
Introductionp. 201
Strategy and Tacticsp. 203
Notes on the Conceptions of Strategy and Tactics in the Orient and the Occidentp. 205
Historical Games of Strategy in the Orient and Occident: Chess, Wei-ch'i and the Different Conceptions of Strategy and Tacticsp. 206
Connection to Didactics and Open Problemsp. 211
Conclusionsp. 212
Referencesp. 212
Rhythm and Natural Language in the Chinese and European Culturep. 219
Rhythm and Natural Language in the Westp. 219
Rhythm and Natural Language in Chinap. 222
Conclusionsp. 227
Referencesp. 227
Conclusionsp. 229
The Conclusions of the Experimental Workp. 229
Topics such as Research Agreements?p. 230
The Experimental Epistemology of Mathematics: Concluding Observations on the Experimental Investigations Discussedp. 231
The First Experimental Investigationp. 232
The Second Experimental Investigationp. 234
Conclusions and Open Problems Related to "Strategy and Tactics"p. 238
Links with Educationp. 239
Conclusions and Open Problems Related to Musicp. 240
The References to Mathematics, the Reasoning and the Conceptualisationp. 240
Referencesp. 243
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9783642116797
ISBN-10: 3642116795
Series: Studies in Computational Intelligence
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 300
Published: 25th March 2010
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.5 x 15.5  x 1.91
Weight (kg): 0.65