Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Mathematics: Mathematics Education

First Advisor

Jeffrey E. Barrett

Second Advisor

Craig J. Cullen


Children's conceptions of length measurement has been the focus of research that has built on the work of Piaget and his colleagues to produce developmental accounts for the acquisition of conceptual and procedural knowledge. Prior research focused on children's developing conceptions of length measurement for straight or rectilinear paths; however, little is known about how these conceptions grow beyond the elementary grades. The present study increased the scope of this research beyond elementary grades to include middle and secondary level students, exploring the development of students' intuitive and analytical thinking for determining the length of a curved path across a wide span of development. Finally, this study extends a hypothetical learning trajectory (LT), to include intuitions for path length.

I administered a written LT-based length assessment to 82 students in Grades 4, 6, 8, and 10, which I coded using a length LT. Based on this assessment, I selected four participants from each of Grades 4, 6, 8, and 10 as representatives of four levels of the LT. I conducted two individual task-based interviews (Goldin, 2000) with each of the 16

participants, which I analyzed using codes from research on path length intuition (Chiu, 1996) and emergent codes generated through a constant comparative method. I then tracked the frequency of each code to explore developmental patterns.

Results suggest that the tasks included in this study effectively differentiated students' thinking at different LT levels. These findings are consistent with Fischbein's theory of intuition (1987), which describes intuition as a developmental phenomenon. Participants who exhibited different levels of sophistication, measured by the length LT, exhibited different ways of evoking intuitions in terms of (a) intuitions and analytical strategies overall, (b) each individual intuition, and (c) analytical strategies with embedded intuitions. Furthermore, findings confirm conjectured concepts and processes outlined in the LT


Imported from ProQuest Eames_ilstu_0092E_10312.pdf


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