Students' conceptual constructs involved in solving proportional reasoning problems within a computer microworld environment
Wanda King Nabors, University of Georgia, United States
University of Georgia . Awarded
Four seventh grade students participated in a constructivist teaching experiment which extended over a period of four months during the spring of 1999. The purpose of the study was to investigate the thinking processes of the students as they attempted to solve tasks which are generally perceived as involving rate, ratio and proportional reasoning. The students used manipulatives within a computer microworld in their efforts to solve such tasks. The thinking processes were analyzed from the perspective of the types of cognitive schemes of operation the students used as they engaged in the given problem situations. The students' ways of operating were interpreted, whenever possible, using schemes found through former research by Steffe and Cobb (1988), Steffe (1988, 1992, 1994, 1995), Saenz-Ludlow (1990) and Olive (1996, 1999). The students' schemes of operations were further categorized according to Kaput and West's (1994) levels of proportional reasoning, which were also analyzed in terms of the above schemes of operating.
A pretest was given before the study began and a post test was given after the teaching sessions ended. Kaput and West's levels of proportional reasoning were used to categorize the levels of schemes employed by the students in their attempts to solve the given tasks.
In the teaching experiment the students were first presented with fractional reasoning tasks that would be difficult to solve using school math rules and algorithms. They were then presented with the problems involving rate, ratio and proportional reasoning, including work problems, mixture problems, money problems and pole problems.
It was found that all of the students were able to modify their available schemes of operation to produce the schemes of operation, particularly reversible operations, considered to be necessary to solve the fractional tasks. It was also found that the students used their fractional reasoning in solving the rate, ratio and proportion problems in a manner analogous to students' use of their knowledge of whole numbers in building up their fractional knowledge as found in former research. (Saentz-Ludlow, 1990)
The results of the study give clear signals that the students who relied the most on procedural uses of their fraction knowledge were met with more severe constraints in extending their fractional schemes to the more sophisticated schemes of operating found in the solutions of the work, mixture, money and pole problems in this study. It was found that the students' fractional operations formed a basis for the schemes of operation they used in their solutions of such word problems.
Nabors, W.K. Students' conceptual constructs involved in solving proportional reasoning problems within a computer microworld environment. Ph.D. thesis, University of Georgia.
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