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Dissertation Information for Jai H. Paik

NAME:
- Jai H. Paik

DEGREE:
- Ph.D.

DISCIPLINE:
- Psychology

SCHOOL:
- Indiana University (USA) (2005)

ADVISORS:
- Kelly S. Mix

COMMITTEE MEMBERS:
- Michael Gasser
- Robert Goldstone
- Linda B. Smith

MPACT Status: Incomplete - Not_Inspected

Title: Fraction concepts: A complex system of mappings

Abstract: Fractions are notoriously difficult for children to learn. Even after years of formal instruction, children often fail to understand even the underlying principles of fractions. I view fractions as learning a complex system of mappings among different forms of representations. I propose that children have difficulty learning fractions because they lack the ability to link certain forms of fraction representation. The present experiments examine where in the complex system of mappings children have difficulty and ways to promote such mappings.

In Experiment 1, U.S. first and second graders were given various fraction identification tasks that involved mappings between a triad of graphic representations, conventional fraction names, and numerical symbols. Results from Experiment 1 revealed that children specifically Lack the ability to link graphic and conventional representations (e.g., mapping fraction names or symbols onto pictorial representations). The results also suggested that there is systematicity in children's ability to recognize equivalent fractions-performing well when part-part reasoning was allowed while performing poorly when part-whole reasoning is required. This prediction was supported by the results from Experiment 2 and Experiment 3 where children's performance on the fraction mapping tasks varied systematically depending on whether the part-whole reasoning was necessary. In Experiment 4, I have further examined the previous claims that the explicit referent of the part-whole relations in the fraction names promotes children's ability to reason about part-whole relations. Finally, in Experiment 4, a training study shows that U.S. children were better able to understand standard fraction names (e.g., "one fourth") when they were first taught the transparent fraction names (e.g., "one of four parts").

The present study suggests that the ability to compare and link different forms of representations is essential in learning complex mathematical concepts such as those involved in fractions. The theoretical links to research on comparison processes and analogical reasoning as well as educational and instructional implications are discussed.

MPACT Scores for Jai H. Paik

A = 0
C = 0
A+C = 0
T = 0
G = 0
W = 0
TD = 0
TA = 0
calculated 2010-10-13 22:42:48

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