ERIC Number: ED391660
Record Type: RIE
Publication Date: 1995-Oct
Reconstructing the Whole: A Gauge of Fraction Understanding.
Taube, Sylvia R.
This study analyzed graphical solutions of 344 students in grades 4 through college who were administered a 40-item assessment of basic fraction concepts. Of particular interest were six problems that required students to complete the whole given a fractional part presented in area contexts and set contexts. Results indicated that fourth graders frequently used the "doubling" strategy even if the fractional part showed two-thirds. In the set context, students sometimes connected the outer dots to form a rectangular unit that was totally unrelated to the given fractional part. Videotaped interviews of six fourth-grade students clearly revealed these dominant strategies. Nevertheless, there was improvement in student solution strategies as well as success in completing the unit as the grade level increased. Implied misconceptions held by both preservice teachers and elementary students include the assumption that the unit is always a regular-shaped region rather than irregular. The findings indicate the strong influence of the rectangular model often used in traditional mathematics textbooks on students' understanding of the whole. These findings support reforms in the teaching of fractions that include not only unit partitioning activities but also completing the whole using a variety of models. (Author)
Publication Type: Reports - Research; Speeches/Meeting Papers
Education Level: N/A
Authoring Institution: N/A
Note: Paper presented at the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (17th, Columbus, OH, October 1995).