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El. knyga: Understanding in Mathematics

  • Formatas: 248 pages
  • Išleidimo metai: 11-Jan-2013
  • Leidėjas: Routledge Falmer
  • Kalba: eng
  • ISBN-13: 9781135716332
Kitos knygos pagal šią temą:
Understanding in MathematicsDidesnis paveikslėlis
  • Formatas: 248 pages
  • Išleidimo metai: 11-Jan-2013
  • Leidėjas: Routledge Falmer
  • Kalba: eng
  • ISBN-13: 9781135716332
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The concept of understanding in mathematics with regard to mathematics education is considered in this volume. The main problem for mathematics teachers being how to facilitate their students' understanding of the mathematics being taught. In combining elements of maths, philosophy, logic, linguistics and the psychology of maths education from her own and European research, Dr Sierpinska considers the contributions of the social and cultural contexts to understanding. The outcome is an insight into both mathematics and understanding.
List of Figures
vii
Acknowledgments viii
Preface by Series Editor ix
Introduction xi
Understanding and Meaning
1(26)
Understanding
1(12)
Meaning
13(14)
Components and Conditions of an Act of Understanding
27(45)
What Could Be an Act of Understanding?
28(11)
Components of an Act of Understanding
39(23)
Psychological Conditions of an Act of Understanding
62(3)
Social Conditions of an Act of Understanding
65(3)
What Understanding Is Not
68(4)
Processes of Understanding
72(40)
The Process of Understanding
72(1)
Reasonings
73(2)
Explanation and Understanding
75(13)
The Role of Example and the Medium in Which It Is Presented for Understanding
88(4)
Figure of Speech in Understanding
92(9)
The Role of Activity in Understanding
101(6)
The Question of Continuity of the Process of Understanding
107(5)
Good Understanding
112(26)
The Relativity of `Good Understanding'
112(5)
Various Approaches to Research on Understanding in Mathematics Education
117(2)
Models of Understanding
119(1)
The Historico-empirical Approach to Understanding in Mathematics
120(3)
`Good Understanding' in the Historico-empirical Approach: Significant Acts of Understanding
123(2)
The Philosophy of Epistemological Obstacles
125(3)
Epistemological Obstacles in Mathematics: The Case of the Bolzano Theorem
128(5)
The Notion of Epistemological Obstacle as a Category of Thought in Mathematics Education; Problems of Definition
133(5)
Developmental and Cultural Contraints of Understanding
138(32)
The Relationship Between Development and Culture
139(3)
The Genesis of Understanding and the Developmental Roots of Epistemological Obstacles
142(17)
The Cultural Roots of Epistemological Obstacles
159(11)
References 170(13)
Index 183
Anna Sierpinska
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