| Summary: | 碩士 === 國立彰化師範大學 === 科學教育研究所 === 88 === Norbert Wiener：The environmental advantages of intellectual development and academic growth of a genius in mathematics
Wan-Hsiu Liao
Abstract
The purpose of this study was to study into the social environment that had to do with the nurturing of the contemporary American mathematician Norbert Wiener (1894-1964). With special emphasis on the viewpoint that "history repeats itself", this study employed a biographical case study approach to find out the evidences of critical learning experiences and processes that could account for Wiener''s metamorphosis into a mathematical genius. This finding could then be used as a reference for assessing the effectiveness of mathematics education, as well as the contents and strategies of gifted education.
So far as the methodological foundation was concerned, this study used Vygotsky''s sociocultural theory and his concept of zone of proximal development (ZPD), as well as the social constructivists'' ideas of situated learning、scaffolding and practice groups to explain for Wiener''s learning experiences and inventive activities. Moreover, by studying the reasons behind Wiener''s success in learning and invention, this study attempted to show that Vygotsky''s learning theory can be applied both to gifted students as well as to students with learning difficulties.
Based on an extensive literature review with careful cross referencing , this study arrived at several major findings that could be summarized as follows：
1. The establishment of ZPD：Norbert'' father, Leo Wiener, the British philosopher and mathematician Bertrand Russell and the British mathematician G.H.Hardy were the three major mentors of Wiener who promoted his learning in language、mathematics、philosophy and physics.
2. Lecturing and education plan：Wiener''s subsequent development had taken advantage of his father''s strict yet systematic training. Also, the useful advice from Russell, and the clear、interesting yet inspiring lectures by Hardy in mathematics held the key for his shift to mathematics.
3. Discussion group：Wiener experienced the freely discussing academic atmosphere in Cambridge University and Gottingen University and realized its importance. From thence on, he maintained that mathematics was a discipline that required discussion.
4. Practice group：Wiener made a practice of working with experts in different fields on practical problems. He absorbed the expertise from his collaborators and learned from the nature of the problem itself. He also extended his collaborators'' problem solving techniques by developing new tools and theories.
5. Particular regard：Wiener benefited from the French mathematician Jacques Hadamard''s special attention on him. His particular regard inspired Wiener, then a young novice in mathematics, to believe that he had a future in this discipline.
6. Other conditions：Wiener was born into a social surroundings with numerous academic researches. From his youth onward, his family had offered him plenty of books to study. He had been deeply influenced by the expert discussion among the friends of his father, as well as from his neighbors, who were the knowledgeable scholars of Harvard University.
Needless to say, this case study cannot offer a direct prescription for the improvement of gifted education in mathematics. However, the effect of the advantageous environment that Wiener had on his intellectual growth and academic development are well worth our attention while laying down the policies for future educational programs.
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