Expanding the numerical central conceptual structure : first graders' understanding of integers

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In working with integers, students have difficulties that may extend into middle school and even adulthood. However, even young children can display insights into negative numbers well before receiving formal instruction. Using a pre-test, instruction, post-test design, this study explores how 61 first graders reason about negative number properties and operations and how their understanding changes depending on the instruction they receive. Results of the study indicate that children build on their existing whole number understanding to develop a central conceptual structure for integers. Furthermore, the process by which they extend their numerical central conceptual structure differs among students; their initial schemas, together with the form of the integer instruction, influence how they reason about and solve integer addition and subtraction problems. These results highlight the need to revisit the placement, duration, and content of integer instruction in curricula.


Type of resource text
Form electronic; electronic resource; remote
Extent 1 online resource.
Publication date 2011
Issuance monographic
Language English


Associated with Bofferding, Laura Christine
Associated with Stanford University, School of Education.
Primary advisor Murata, Aki
Thesis advisor Murata, Aki
Thesis advisor Goldman, Shelley V
Thesis advisor Okamoto, Yukari
Thesis advisor Schwartz, Daniel L
Advisor Goldman, Shelley V
Advisor Okamoto, Yukari
Advisor Schwartz, Daniel L


Genre Theses

Bibliographic information

Statement of responsibility Laura Christine Bofferding.
Note Submitted to the School of Education.
Thesis Thesis (Ph.D.)--Stanford University, 2011.
Location electronic resource

Access conditions

© 2011 by Laura Christine Bofferding
This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

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