Abstract/Details

Making sense of the Fundamental Theorem of Calculus


2009 2009

Other formats: Order a copy

Abstract (summary)

This dissertation provides an elaborated examination of how a group of students, four years after first studying calculus, create an explanation of the Fundamental Theorem of Calculus for use by a figurative "novice student". The group of students studied AP Calculus in 1999, and had participated for 15 years in a longitudinal study at Rutgers University. In that study, students were invited to participate on a yearly basis in mathematical activities that asked them to justify their conclusions and make their thinking public.

The students were videotaped as they worked cooperatively on developing an explanation during two sessions one month apart. The students structured their own activity, using their own recollections, printed resource materials, and Geometer's Sketchpad sketches provided for the students' use. The students' discussions are examined with specific attention to the mathematical representations the students used, the meanings students attached to those representations, how the students decided upon those meanings.

The AP Calculus course description emphasizes "understanding the meaning" of the Fundamental Theorem from multiple perspectives, but students' understandings of the ideas of calculus have been found to be "poorly coordinated" (Judson & Nishimori, 2005; Thompson, 1994). Flexible use of representations has been suggested as a route to bring meaning to these ideas (Tall & Thomas, 1991). This dissertation illustrates in detail how students can coordinate graphical, numerical, verbal, and numerical representations to build meanings for the Fundamental Theorem of Calculus. The students' discussions provide evidence that students can develop meanings through engaging in non-evaluative dialogue where they negotiate and refine the meanings of words, symbols, and graphs.

The students, who had grown accustomed to participating in mathematical discourse (Maher, 2002), negotiated meanings in ways that may provide models for the teaching and learning of calculus in the classroom. The students' use of representations also has implications for those interested in how students might come to understand the ideas of calculus and the Fundamental Theorem in particular. The ways in which the students organized ideas serves as an example of how learners can build powerful understandings in multiple ways.

Indexing (details)


Subject
Mathematics education;
Theorems;
Calculus
Classification
0280: Mathematics education
Identifier / keyword
Education; Calculus; Fundamental theorem of calculus; Negotiation of meaning; Representation
Title
Making sense of the Fundamental Theorem of Calculus
Author
Pantozzi, Ralph S.
Number of pages
479
Publication year
2009
Degree date
2009
School code
0190
Source
DAI-A 70/08, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9781109349511
Advisor
Maher, Carolyn A.
University/institution
Rutgers The State University of New Jersey - New Brunswick
University location
United States -- New Jersey
Degree
Ed.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3373679
ProQuest document ID
304988317
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304988317
Access the complete full text

You can get the full text of this document if it is part of your institution's ProQuest subscription.

Try one of the following:

  • Connect to ProQuest through your library network and search for the document from there.
  • Request the document from your library.
  • Go to the ProQuest login page and enter a ProQuest or My Research username / password.