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“A Fourth is a Half of a Half”: Children’s Use of Relationships to Compare Fractions |
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Abstract:
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This study examined the interaction between the use of physical models and children’s understanding of fractions as demonstrated through their ability to compare and order fractions. Although physical models are recommended to help children developing an understanding of fraction concepts, there are multiple ideas about how to use the materials in classroom instruction and the results concerning the effectiveness of physical models have been mixed. The framework for analyzing how physical models and mathematics concepts are connected during instruction is based on Gravemeijer’s (1997) ideas of top-down or bottom-up approaches. Another part of the framework is based on the four perspectives (Parts, Components, Reference Points, and Transform) to categorize general approaches for solving order and equivalence problems identified by Smith (1995).
Classroom observations and clinical interviews were conducted over a three month period with thirteen students from a multi-level third, fourth, and fifth grade class. The analysis of the data identified the relationships students attended to when comparing and ordering fractions. These relationships were grouped into eight perspectives (Limited, Pieces, Part-Whole, Unit Fraction, Within-Fraction, Between-Fraction, Equivalence, and Transform) extending Smith’s (1995) work. Many of these perspectives were influenced by the use of physical models. Students who were able to identify, use, and extend relationships had a stronger understanding of fractions and could move between perspectives to solve problems efficiently and effectively. |
Most Common Document Word Stems:
fraction (90), student (65), relationship (52), perspect (52), use (43), mathemat (28), smith (27), piec (26), compar (23), understand (22), 1995 (21), number (21), studi (20), problem (20), part (19), equival (19), equal (19), physic (19), strategi (19), order (18), research (17), |
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Association:
Name: North American Chapter of the International Group for the Psychology of Mathematics Education
URL: http://www.pmena.org
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Citation:
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MLA Citation:
| Wenrick, Melanie. "“A Fourth is a Half of a Half”: Children’s Use of Relationships to Compare Fractions" Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Delta Chelsea Hotel, Toronto, Ontario, Canada, Oct 21, 2004 <Not Available>. 2009-05-26 <http://www.allacademic.com/meta/p117566_index.html> |
APA Citation:
| Wenrick, M. R. , 2004-10-21 "“A Fourth is a Half of a Half”: Children’s Use of Relationships to Compare Fractions" Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Delta Chelsea Hotel, Toronto, Ontario, Canada Online <.PDF>. 2009-05-26 from http://www.allacademic.com/meta/p117566_index.html |
Publication Type: Conference Paper/Unpublished Manuscript
Review Method: Peer Reviewed
Abstract: This study examined the interaction between the use of physical models and children’s understanding of fractions as demonstrated through their ability to compare and order fractions. Although physical models are recommended to help children developing an understanding of fraction concepts, there are multiple ideas about how to use the materials in classroom instruction and the results concerning the effectiveness of physical models have been mixed. The framework for analyzing how physical models and mathematics concepts are connected during instruction is based on Gravemeijer’s (1997) ideas of top-down or bottom-up approaches. Another part of the framework is based on the four perspectives (Parts, Components, Reference Points, and Transform) to categorize general approaches for solving order and equivalence problems identified by Smith (1995).
Classroom observations and clinical interviews were conducted over a three month period with thirteen students from a multi-level third, fourth, and fifth grade class. The analysis of the data identified the relationships students attended to when comparing and ordering fractions. These relationships were grouped into eight perspectives (Limited, Pieces, Part-Whole, Unit Fraction, Within-Fraction, Between-Fraction, Equivalence, and Transform) extending Smith’s (1995) work. Many of these perspectives were influenced by the use of physical models. Students who were able to identify, use, and extend relationships had a stronger understanding of fractions and could move between perspectives to solve problems efficiently and effectively. |
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| Document Type: |
.PDF |
| Page count: |
7 |
| Word count: |
3401 |
| Text sample: |
| "A FOURTH IS A HALF OF A HALF": CHILDREN'S USE OF RELATIONSHIPS TO COMPARE FRACTIONS Melanie Wenrick California State University Fresno mwenrick@csufresno.edu This study examined the interaction between the use of physical models and children's understanding of fractions as demonstrated through their ability to compare and order fractions. Clinical interviews and in-class observations and were conducted over a three month period with thirteen students from a third fourth and fifth grade class. The analysis of the data identified the |
| approach. In T. P. Carpenter E. Fennema & T. A. Romberg (Eds.) Rational numbers: An integration of research (pp. 289-325). Hillsdale NJ: Erlbaum. Thompson P. W. & Lambdin D. (1994). Concrete materials and teaching for mathematical understanding. Arithmetic Teacher 41(9) 556-558. Tzur R. (1999). An integrated study of children's construction of improper fractions and the teacher's role in promoting that learning. Journal for Research in Mathematics Education 30(4) 390-416. Vance J. H. (1986). Ordering decimals and fractions: A diagnostic |
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