Understanding children's construction of rational number knowledge is important to both mathematics educators and researchers. The study presented investigated how children's concepts of units might influence their construction of rational numbers. The research questions addressed are: (1) What is the nature of a child's concepts of one as a composite whole, that is, divisible whole? (2) How does a child's experiences such as sharing influence this construction? / Four second graders participated in the study. Each child was interviewed individually four times. Additionally, the children were paired and each group participated in four problem solving sessions. / The analyses of the data showed that children's schemes to coordinate units play an important role in their understanding of fractional quantities. Four schemes to coordinate units were identified: one-as-one, one-as-many, many-as-one, and many-as-many. The one-as-one scheme is the most basic scheme involved in counting. When a child considers a unitary item as a multiplicity of another unit, he/she is considered to have the one-as-many scheme. The many-as-one scheme coordinates a multiplicity of a unit with another unit. Finally, the many-as-many scheme coordinates a multiplicity of a unit with a multiplicity of another unit. / These schemes form a basis for the levels of sophistication in a child's ability to coordinate units. In level one, the child has not constructed relationships between units, and his/her coordination scheme is limited to one-as-one. Level two is divided into two sub-levels. In sub-level one, the child's coordination schemes include one-as-many and/or many-as-one. In sub-level two, the child is able to coordinate many-as-many. / The many-as-many coordination scheme is conjectured to influence children's construction of multiplicative understanding, including proportional reasoning and rational numbers. Furthermore, the many-as-many scheme is conjectured to be a prerequisite for construction of abstract fractional units. / Source: Dissertation Abstracts International, Volume: 52-10, Section: A, page: 3550. / Major Professor: Grayson H. Wheatley. / Thesis (Ph.D.)--The Florida State University, 1991.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_76515 |
| Contributors | Watanabe, Tadanobu., Florida State University |
| Source Sets | Florida State University |
| Language | English |
| Detected Language | English |
| Type | Text |
| Format | 234 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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