Date of Award

Winter 12-2022

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

School

Center for Science and Math Education

Committee Chair

Dr. Julie Cwikla

Committee Chair School

Center for Science and Math Education

Committee Member 2

Dr. Rachel Gisewhite

Committee Member 2 School

Center for Science and Math Education

Committee Member 3

Dr. Anna Wan

Committee Member 3 School

Center for Science and Math Education

Committee Member 4

Dr. James Lambers

Committee Member 4 School

Mathematics and Natural Sciences

Committee Member 5

Dr. Erin Smith

Abstract

Understanding numerical quantities and applying this knowledge in practical applications is essential throughout life. A well-developed number sense comes from learning foundational skills and continuing to rely on these skills and concepts in higher mathematical education as well as in adulthood. Prior research shows that K-8 students lack a conceptual understanding of fraction, decimal, and percentage concepts (NCTM, 2009). While there is literature that identifies a deficit in these mathematical areas, there is a need to examine possible activities and interventions that can be performed throughout secondary education courses that support growth in students' conceptual understanding of rational number concepts. The purpose of this research study is to investigate how a five-day rational number sense intervention can affect students’ number sense in the subtopics of fractions, decimals, and percentages as well as their self-efficacy.

For this study, 63 students from three different math periods at the same school and taught by the same instructor participated. These 63 students were divided into three groups: a control and two intervention groups. Both intervention groups received five days of instructional activities revolving around various rational number concepts and practical applications. To collect data, a pre-assessment consisting of ten mathematical computation questions, five contextualized mathematical questions, and five self-efficacy questions was used. After the intervention was conducted, an identical post-assessment was administered. Student follow-up interviews (N=4) were conducted to gain additional insight into the effects of the intervention.

A dependent t-test compared pre-assessment results to post-assessment results for the computational items. Both intervention groups earned significantly higher scores on the post-test than on the pre-test. The control group did not display any significant score differences between pre- and post-assessment. To examine the contextualized math items, similar dependent t-tests were conducted to compare pre-and post-assessment results. There was a significant improvement in one of the two intervention classes. Analysis of the self-efficacy items showed that students had a significant increase in self-efficacy post-intervention. Implications for improvements, future research, and expanded interventions to support advancing students’ number sense are discussed.

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