This is an abstract of a presentation at The 8th International Congress on Math Education (ICME 8), July 14-21, 1996 in Seville, Spain..
Nathan and Arthur, two children in our project on Children's Construction of Rational Numbers of Arithmetic, developed their operations for multiplying, dividing and simplifying fractions over a period of two years (grades 4 and 5). The two children worked with our Computer Microworlds: TIMA: Toys, Sticks and Bars. These Tools for Interactive Mathematical Activity (TIMA) were developed as part of our project in order to provide children with computer environments in which they could enact their developing operations on fractions.
The children worked with a teacher/researcher for 45 minutes a week for approximately 50 weeks (over the two year period). Each of the 50 teaching episodes were videotaped, using two cameras: one focused on the children and the other on the computer screen. Through ongoing analyses of the videotaped episodes a model of the children's development of their multiplicative operations on fractions, and their reasoning with ratios is being constructed. While the children were able to construct complex operations involving multiplication and division of fractions in the microworld environemnts, these intuitive notions of multiplication and division were different from the symbolic operations they had learned through their classroom experiences. Certain tasks that we designed using the microworlds appeared to be engendering for the children to construct their understanding of a "fraction of a fraction" and for developing a co-measure scheme for simplifying fractions.
John Olive, firstname.lastname@example.org
Additional materials have been submitted by Mr. Olive as part of the TG 19 Panel Discussion.
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