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Cramer, K. A, Post, T. R., del Mas, R. C. (2002) Initial Fraction Learning by Fourth- and Fifth-Grade Students: A Comparison of the Effects of Using Commercial Curricula With the Effects of Using the Rational Number Project Curriculum. Journal for Research in Mathematics Education. 33 (2) 111-144.

 

Initial Fraction Learning by
Fourth- and Fifth-Grade Students:
A Comparison of the Effects
of Using Commercial Curricula With
the Effects of Using the Rational
Number Project Curriculum

Kathleen A. Cramer, Thomas R. Post, and Robert C. delMas
University of Minnesota
 
NOTE --- At this time, NCTM is granting permission for this site to publish just the abstract, summary, and references for this article. It is our intention to put the complete article online when permission is obtained.
 

This study contrasted the achievement of students using either commercial curricula (CC) for initial fraction learning with the achievement of students using the Rational Number Project (RNP) fraction curriculum. The RNP curriculum placed particular emphasis on the use of multiple physical models and translations within and between modes of representation-pictorial. manipulative, verbal, real-world, and symbolic. The instructional program lasted 28-30 days and involved over 1600 fourth and fifth graders in 66 classrooms that were randomly assigned to treatment groups. Students using RNP project materials had statistically higher mean scores on the posttest and retention test and on four (of six) subscales: concepts, order, transfer, and estimation. Interview data showed differences in the quality of students' thinking as they solved order and estimation tasks involving fractions. RNP students approached such tasks conceptually by building on their constructed mental images of fractions, whereas CC students relied more often on standard, often rote, procedures when solving identical fraction tasks. These results are consistent with earlier RNP work with smaller numbers of students in several teaching experiment settings.




 

In summary, we believe RNP teachers were able to be effective because of the careful structure of the materials and the integration of information on student thinking into each lesson. We believe these students learned disproportionately well because they spent their time interacting with fraction ideas in multiple ways and were provided extended periods of time to develop an understanding of the meaning of symbols. Investing time in fostering students' understanding of rational number concepts was shown to be an effective method for developing a quantitative sense for fractions in large numbers of fourth and fifth graders. The theoretical framework and lesson structure employed here can be applied to other mathematical topics and shows promise in enabling large numbers of teachers to participate in the curriculum regeneration process and to improve student understandings.

 

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Authors

Kathleen A. Cramer, 252 Peik Hall, 159 Pillsbury Drive, University of Minnesota, Minneapolis, MN 55455; crameO13@tc.umn.edu

Thomas R. Post, 240 Peik Hall, 159 Pillsbury Drive, University of Minnesota, Minneapolis, MN 55455; postxOO1@tc.umn.edu

Robert C. delMas, 345 Appleby Hall, 128 Pleasant Street, SE, University of Minnesota, Minneapolis, MN 55455; delmaOO1@tc.umn.edu

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