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Cramer, K., & Wyberg, T. (2009). Efficacy of different concrete models for teaching the part-whole construct for fractions. Mathematical Thinking and Learning, 11 (4), 226-258.


Efficacy of Different Concrete Models for Teaching the Part-Whole Construct for Fractions

Kathleen A Cramer and Terry Wyberg


The effectiveness of different concrete and pictorial models on students’ understanding of the part-whole construct for fractions was investigated. Using interview data from fourth and fifth grade students from three different districts that adopted the Mathematics Trailblazers series, authors identified strengths and limitations of models used. Pattern blocks had limited value in aiding students’ construction of mental images for the part-whole model as well as limited value in building meaning for fraction addition and subtraction. A paper fraction chart based on paper folding model support students’ ability to order fractions with the same numerators but were less useful in helping students on estimation tasks. The dot paper model and chips did not support fifth grade students’ initial understanding of the algorithm.



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Kathleen Cramer - Associate Professor in Mathematics Education at the University of Minnesota

Terry Wyberg - Senior Lecturer in Mathematics Education at the University of Minnesota