Title page for ETD etd-10302005-024424

Type of Document

Dissertation

Author

Stewart, Veon

Author's Email Address

vmm6049@garnet.acns.fsu.edu

URN

etd-10302005-024424

Title

Making Sense of Students' Understanding of Fractions: An Exploratory Study of Sixth Graders' Construction of Fraction Concepts Through the use of Physical Referents and Real World Representations

Degree

Doctor of Philosophy

Department

Middle and Secondary Education, Department of

Advisory Committee

Advisor Name	Title
Elizabeth Jakubowski	Committee Chair
Florentina Bunea	Committee Member
Leslie Aspinwall	Committee Member
Maria L. Fernandez	Committee Member

Keywords

Repartitioning
Manipulatives
Middle School Mathematics
Rational Numbers
Partitioning
Unitizing

Date of Defense

2005-10-12

Availability

unrestricted

Abstract

This study was an investigative, whole class descriptive research, on the development of twenty sixth graders’ understanding of fractions as they interacted with physical referents, hands-on task-based activities and activities that model real life situations during eight weeks of a teaching sequence. The study was conducted in a metropolitan school situated in southeast Florida. The teaching sequence consisted of 12 task-based activities that spanned 20 sessions with each session lasting for approximately 60 minutes. Data was collected through audio- and video-recording, in addition to the numerous written tasks. The task-based activities that the students were involved with during this study were analyzed to gain an insight into their understanding of fractions in the context of subdividing, comparing and partitioning of continuous and discrete models and the connections they made with the fraction ideas generated through these activities. The study also examined how these students make sense of fractions and investigated how their performance differed when fractions were presented using different models. Herscovics and Bergeron’s (1988) extended model of understanding, and the partitioning strategies identified by Charles and Nason (2000) and Lamon (1996) provided the theoretical framework through which the investigation was explored.
Results from the study revealed that the participants exhibited an understanding of unit and non-unit fraction based on the components of the above-mentioned model of understanding. The students also displayed a number of different partitioning strategies.
The knowledge growth that was evident in the whole class confirms earlier studies as to the significant role that partitioning plays in the basic development of the fraction concept. Although discrete models were used by the students, a majority of the students exhibited a preference for using continuous models as forms of reference for given fractions. The students appreciated working with fractions that model real world situations. Preliminary findings from this study seem to indicate that students should be introduced to fraction concepts via partitioning activities. The partitioning activities should be introduced in grades earlier than sixth grade. Further research can be undertaken to investigate the role partitioning activities play in the development of students’ ability to add, subtract, multiply and divide fractions.

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