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In search of meaningful mathematics:...

Fiori, Nicholas.

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In search of meaningful mathematics: The role of aesthetic choice.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	In search of meaningful mathematics: The role of aesthetic choice./
作者:	Fiori, Nicholas.
面頁冊數:	256 p.
附註:	Advisers: Jo Boaler; Ray McDermott.
Contained By:	Dissertation Abstracts International68-06A.
標題:	Education, Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3267506
ISBN:	9780549060512

In search of meaningful mathematics: The role of aesthetic choice.
Fiori, Nicholas.

In search of meaningful mathematics: The role of aesthetic choice. - 256 p.

Advisers: Jo Boaler; Ray McDermott.

Thesis (Ph.D.)--Stanford University, 2007.

Mathematics offers some people an arena in which they can think, explore, and create. But others---including many students---experience it as a stifling set of restrictive rules. The contrast between the impassioned reports of those who love mathematics and the negative reactions of many students is an educational concern as critical as discrepancies in academic performance. This dissertation responds to this concern by providing an alternative lens for mathematics education.

ISBN: 9780549060512Subjects--Topical Terms:

1017588
Education, Mathematics.

In search of meaningful mathematics: The role of aesthetic choice.
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520 $a Mathematics offers some people an arena in which they can think, explore, and create. But others---including many students---experience it as a stifling set of restrictive rules. The contrast between the impassioned reports of those who love mathematics and the negative reactions of many students is an educational concern as critical as discrepancies in academic performance. This dissertation responds to this concern by providing an alternative lens for mathematics education.
520 $a Most educational and philosophical thought about mathematics focuses on the logical forms of the subject and considers mathematicians and students to be people who primarily validate statements within these systems. This project suggests that acts of discernment are as important for thinking about mathematics as acts of verification. What choices are made in mathematical work? Why are some ideas considered as more important, more essential, and more beautiful than others? Why do so few people experience mathematics as a place where such choices are possible? These questions frame mathematical systems as places where people express ideas. Like the physical media of other artistic fields, these more abstract mathematical worlds allow for a range of choices, which are, like the media of other arts, limited by certain inherent flexibilities.
520 $a People who are engaged in mathematical work inform this aesthetic lens. This study draws on published essays and statements by academic mathematicians; interviews with practicing mathematicians; interviews and video data from two summer workshops that encouraged students to pose mathematical ideas; the author's own experience as a student, teacher, and practitioner of mathematics; and important historical developments in mathematics.
520 $a From these settings, three varieties of choice in mathematical work emerge: (1) Posing single ideas, such as defining an object, proposing a conjecture, or suggesting an idea for an argument. (2) Juxtaposing multiple ideas. These acts of combination can be generative and surprising. (3) Balancing systems of ideas. Mathematicians search for frameworks that are capable of expression and yielding interesting content. These discerning acts, while indispensable to mathematics, conflict with the structures of traditional school mathematics. Throughout, this project examines the implications of this incongruity.
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