Partitioning Strategies In Children
Among the many difficult mathematical concepts for children to understand, fractions ranks as one of the most difficult. The complex concept poses a lot of problems not only for children, but for adults as well. The only way to build a conceptual understanding of fractions is to build on children’s informal knowledge of partitioning and fair share. Throughout the paper I will discuss how we can use these simpler topics as a starting point in the uphill battle to understanding this extremely difficult concept. I will identify common partitioning strategies used by children, and shed light on the way these strategies can be used to tackle the remaining four subconstructs, as well as guide in the understanding of multiplication and division
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Children also used a variety of strategies to solve problems rather than just one. “Young children’s selection of partitioning strategies depends not only on their prior knowledge and experiences but also on the context of the task, the type of analog objects being shared, the number of analog objects being shared and number of shares” (Charles & Nason, p. 216). While there is nothing wrong with using multiple strategies, students must understand three concepts in order for these strategies to work all of the time. Students need to understand that their partitioning strategy must yield equal parts that are able to be quantified accurately. In addition, the strategy they choose must clearly show a relationship between the number of people and the fraction name, as well as a relationship between the number of objects being shared and the number of parts in each share. Charles and Nason (2000) suggest that teachers use these three things to asses their students’ understanding of partitioning and fractions. Students who are using partitioning strategies which employ all three of these concepts have a deeper understanding of the content than those using only one or two of these concepts when partitioning objects and sets. This information can be used to plan and implement activities at the level the learner is functioning …show more content…
Y., & Pitta-Pantazi, D. (2007). Drawing on a theoretical model to study students’ understandings of fractions. Educational Studies in Mathematics, 64, 293-316.
Charles, K., & Nason, R. (2000). Young children’s partitioning strategies. Education Studies in Mathematics, 43, 191-222.
Mack, M. K. (2001). Building on informal knowledge through instruction in a complex content domain: Partitioning, units, and understanding multiplication of fractions. Journal for Research in Mathematics Education, 32(3). Retrieved March 14, 2007, from http://vnweb.hwwilsonweb.com/hww/results/results_single_ ftPES.jhtml
Empson, S. B. (2001). Equal sharing and the roots of fraction equivalence. Teaching Children Mathematics, 3, 421-425.
Saxe, G. B, Gearhart, M., & Nasir, N. S. (2001). Enhancing students’ understanding of mathematics: A study of three contrasting approaches to professional support. Journal of Mathematics Teacher Education, 4, 55-79.
Empson, S. B., Junk, D., Dominguez, H., & Turner, E. (2005). Fractions as the coordination of multiplicatively related quantities: A cross-sectional study of children’s thinking. Educational Studies in Mathematics, 63,
Children also used a variety of strategies to solve problems rather than just one. “Young children’s selection of partitioning strategies depends not only on their prior knowledge and experiences but also on the context of the task, the type of analog objects being shared, the number of analog objects being shared and number of shares” (Charles & Nason, p. 216). While there is nothing wrong with using multiple strategies, students must understand three concepts in order for these strategies to work all of the time. Students need to understand that their partitioning strategy must yield equal parts that are able to be quantified accurately. In addition, the strategy they choose must clearly show a relationship between the number of people and the fraction name, as well as a relationship between the number of objects being shared and the number of parts in each share. Charles and Nason (2000) suggest that teachers use these three things to asses their students’ understanding of partitioning and fractions. Students who are using partitioning strategies which employ all three of these concepts have a deeper understanding of the content than those using only one or two of these concepts when partitioning objects and sets. This information can be used to plan and implement activities at the level the learner is functioning …show more content…
Y., & Pitta-Pantazi, D. (2007). Drawing on a theoretical model to study students’ understandings of fractions. Educational Studies in Mathematics, 64, 293-316.
Charles, K., & Nason, R. (2000). Young children’s partitioning strategies. Education Studies in Mathematics, 43, 191-222.
Mack, M. K. (2001). Building on informal knowledge through instruction in a complex content domain: Partitioning, units, and understanding multiplication of fractions. Journal for Research in Mathematics Education, 32(3). Retrieved March 14, 2007, from http://vnweb.hwwilsonweb.com/hww/results/results_single_ ftPES.jhtml
Empson, S. B. (2001). Equal sharing and the roots of fraction equivalence. Teaching Children Mathematics, 3, 421-425.
Saxe, G. B, Gearhart, M., & Nasir, N. S. (2001). Enhancing students’ understanding of mathematics: A study of three contrasting approaches to professional support. Journal of Mathematics Teacher Education, 4, 55-79.
Empson, S. B., Junk, D., Dominguez, H., & Turner, E. (2005). Fractions as the coordination of multiplicatively related quantities: A cross-sectional study of children’s thinking. Educational Studies in Mathematics, 63,