Date of Award

Spring 6-10-2025

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Education

First Advisor/Committee Member

Dr. Nalline Baliram

Second Advisor/Committee Member

Dr. Roger Howe

Third Advisor/Committee Member

Dr. David Denton

Fourth Advisor/Committee Member

Dr. Julie Antilla

Keywords

rational numbers, mathematics education, conceptual understanding, teacher professional development, educational equity, middle school math

Abstract

Mathematical literacy is critical in an increasingly data-driven society, yet many students struggle with rational number concepts due to the prevalence of decontextualized algorithmic instruction. This study investigates the impact of targeted professional development (PD) on sixth-grade teachers’ instructional strategies and their students’ rational number achievement. The research examines whether explicit, conceptually grounded teaching of rational number operations improves student understanding compared to traditional algorithm-based instruction. Using a mixed-methods approach, the study collected quantitative and qualitative data from students at two middle schools. The intervention was statistically significant at School A, where students in the intervention group demonstrated greater achievement gains than their control group peers. Conceptual fraction division emerged as a key predictor of overall rational number achievement, highlighting the importance of instructional methods that contextualize algorithms. Findings suggest that while procedural fluency can lead to correct answers, it often lacks conceptual backing, which can impede the transition between natural and rational number reasoning. At School B, the intervention did not yield statistically significant differences in achievement gains, potentially due to a lack of readiness to receive sixth-grade math instruction. This research contributes to the discourse on math education reform by demonstrating that shifting instructional focus toward rigorous conceptual understanding can enhance students' long-term mathematical proficiency. Implications for curriculum development, teacher training, and future research on rational number instruction are discussed.

Keywords: rational numbers, natural number bias, teacher professional development, fraction division, conceptual rigor

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