Efficacy of different concrete models for teaching the part-whole construct for fractions

Kathleen Cramer, Terry Wyberg

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


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 adding and subtracting fractions. A paper fraction chart based on a paper folding model supported students' ability to order fractions with same numerators but was 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.

Original languageEnglish (US)
Pages (from-to)226-257
Number of pages32
JournalMathematical Thinking and Learning
Issue number4
StatePublished - Oct 2009

Bibliographical note

Funding Information:
This material is based upon work supported by the National Science Foundation under Grant No. 0242704. Correspondence should be sent to Kathleen Cramer. E-mail: crame013@umn.edu


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