Date of Award:

2016

Document Type:

Dissertation

Degree Name:

Doctor of Philosophy (PhD)

Department:

Education

Advisor/Chair:

Patricia S. Moyer-Packenham

Abstract

Instruction for developing students' number sense is a critical area of research in mathematics education because of the role number sense plays in early mathematics learning. Specifically, number system knowledge has been identified as a key cognitive mechanism in number sense development. The purpose of this mixed methods study was to explore variations in second-grade students' number sense development as they engaged in a counting-focused instructional treatment, geared towards developing number system knowledge, for differing amounts of time. Sixty second-grade students participated in number sense assessments and two students participated in in-depth, task-based interviews to provide quantitative and qualitative data to investigate the change and development of students' number sense during the instructional treatment.

A generalized estimating equations (GEE) analysis showed an associated average increase in test scores for students participating int 9 weeks of the instructional treatment as compared to students participating in 3 weeks of the instructional treatment. This indicated that the counting-focused instructional treatment influenced and changed students' number sense. An important implication of this result is that it highlights the importance of number sense developing over time with multiple, connected experiences.

The in-depth analyses of two cases showed learning growth from pretest to posttest for a low-achieving and high-achieving student. However, the two students' number sense developed in different ways and their access of number system knowledge varied. Shifts in learning mainly occurred after 6 weeks of the instructional treatment and depended on the student's existing use of number sense. The implication of this result is that the multiple access points and the high-ceiling of the instructional treatment benefited low- and high-achieving students in this study.

Findings from the study showed that the counting-focused instructional treatment provided number sense learning opportunities for students from a wide range of abilities and backgrounds within the classroom setting. For many teachers, it is difficult to orchestrate differentiated, whole-class mathematics instructional activities due to their students' wide ranging mathematics abilities. This study identifies a promising instructional practice for elementary mathematics teachers that can facilitate opportunities for students to develop their number sense during whole-class mathematics instruction.

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