東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Students' conceptualizations of mult...

Fisher, Brian Clifford.

FindBook

Google Book

Amazon

博客來

Students' conceptualizations of multivariable limits.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Students' conceptualizations of multivariable limits./
作者:	Fisher, Brian Clifford.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2008,
面頁冊數:	253 p.
附註:	Source: Dissertations Abstracts International, Volume: 70-05, Section: B.
Contained By:	Dissertations Abstracts International70-05B.
標題:	Mathematics education. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3320982
ISBN:	9780549751175

Students' conceptualizations of multivariable limits.
Fisher, Brian Clifford.

Students' conceptualizations of multivariable limits. - Ann Arbor : ProQuest Dissertations & Theses, 2008 - 253 p.

Source: Dissertations Abstracts International, Volume: 70-05, Section: B.

Thesis (Ph.D.)--Oklahoma State University, 2008.

Scope and method of study. The objective of this study was to describe how students with a dynamic view of limit generalize their understanding of the limit concept in a multivariable setting. This description emphasizes the type of generalization that takes place among the students (Harel and Tall, 1989) and the role of motion among students' conceptualizations. To achieve these goals, a series of task-based interviews were conducted with seven students enrolled in multivariable calculus. These interviews were analyzed and a coding scheme was developed to describe the data. This coding scheme arose from analysis of the data combined with the role of limit in formal mathematics. It emphasizes three models for understanding the limit concept, the dynamic model, the neighborhood model, and the topographical model. Findings and conclusions. After analyzing the coded data, two important interactions between the three models of limit were described. First, it was found that students superimposed dynamic imagery on top of existing topographical structures in order to understand multivariable limits, and a weak topographical understanding of multivariable limits contributed to students struggling to understand the multivariable limit concept. Second, it was found that students implementing dynamic imagery in the context of multivariable limits confronted an infinite process of analyzing motion along an infinite number of paths. It was found that students' struggles to understand the multivariable limit were connected to their struggles to understand this infinite process. Additionally, it was found that the condensation of this infinite process led several students towards the neighborhood model of limit.

ISBN: 9780549751175Subjects--Topical Terms:

641129
Mathematics education.
Subjects--Index Terms:

Calculus

Students' conceptualizations of multivariable limits.
LDR:02887nmm a2200385 4500 001 2270883
005 20201007134033.5
008 220629s2008 ||||||||||||||||| ||eng d
020 $a 9780549751175
035 $a (MiAaPQ)AAI3320982
035 $a (MiAaPQ)okstate:2859
035 $a AAI3320982
040 $a MiAaPQ $c MiAaPQ
100 1 $a Fisher, Brian Clifford. $3 3548257
245 1 0 $a Students' conceptualizations of multivariable limits.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2008
300 $a 253 p.
500 $a Source: Dissertations Abstracts International, Volume: 70-05, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Aichele, Douglas B.
502 $a Thesis (Ph.D.)--Oklahoma State University, 2008.
520 $a Scope and method of study. The objective of this study was to describe how students with a dynamic view of limit generalize their understanding of the limit concept in a multivariable setting. This description emphasizes the type of generalization that takes place among the students (Harel and Tall, 1989) and the role of motion among students' conceptualizations. To achieve these goals, a series of task-based interviews were conducted with seven students enrolled in multivariable calculus. These interviews were analyzed and a coding scheme was developed to describe the data. This coding scheme arose from analysis of the data combined with the role of limit in formal mathematics. It emphasizes three models for understanding the limit concept, the dynamic model, the neighborhood model, and the topographical model. Findings and conclusions. After analyzing the coded data, two important interactions between the three models of limit were described. First, it was found that students superimposed dynamic imagery on top of existing topographical structures in order to understand multivariable limits, and a weak topographical understanding of multivariable limits contributed to students struggling to understand the multivariable limit concept. Second, it was found that students implementing dynamic imagery in the context of multivariable limits confronted an infinite process of analyzing motion along an infinite number of paths. It was found that students' struggles to understand the multivariable limit were connected to their struggles to understand this infinite process. Additionally, it was found that the condensation of this infinite process led several students towards the neighborhood model of limit.
590 $a School code: 0664.
650 4 $a Mathematics education. $3 641129
650 4 $a Mathematics. $3 515831
650 4 $a Variables. $3 3548259
650 4 $a Students. $3 756581
653 $a Calculus
653 $a Education
653 $a Limits
653 $a Mathematics
653 $a Multivariable calculus
653 $a Multivariable limits
690 $a 0280
690 $a 0405
710 2 $a Oklahoma State University. $b Mathematics. $3 3548258
773 0 $t Dissertations Abstracts International $g 70-05B.
790 $a 0664
791 $a Ph.D.
792 $a 2008
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3320982