Date of Award

August 2020

Document Type


Degree Name

Doctor of Philosophy (PhD)


Teaching and Learning

Committee Member

Pamela M Stecker

Committee Member

Abigail A Allen

Committee Member

Catherine A Griffith

Committee Member

Sandra M Linder


Students with or at-risk of learning disabilities in mathematics often experience working memory deficits that interfere with long-term retention of facts. Fact fluency reduces the cognitive demand on working memory to allow allocation of cognitive resources for processing more complex tasks. The current study used a single-case, multiple-baseline design to investigate the effectiveness of incremental rehearsal, an evidence-based drill-and-practice strategy, in improving subtraction fact fluency among elementary students with mathematics difficulties. Participants (N = 4) were three third-grade students and one fourth-grade student either with a formal diagnosis of learning disabilities in mathematics or low performing in mathematics without an identified disability. Additionally, all participants had difficulty recalling subtraction facts fluently. Treatment involved repeated practice (unknown) target facts using flashcards with a high percentage of interspersed fluent facts, while sequentially increasing the interval between the presentation of target facts. The same set of three target facts and six fluent facts was practiced in two consecutive sessions using a ratio of one target fact to six fluent facts. Timed math probes were administered at the end of two consecutive practice sessions and were used to assess subtraction fact fluency across treatment sessions. Visual analysis and effect size calculations of student performance on timed probes revealed that incremental rehearsal was highly effective (Tau-U = 1.0) in improving subtraction fact fluency for the two participants who received treatment. Unfortunately, because of the sudden school closure due to the impact of COVID-19, this study was discontinued before introducing the intervention to the other two participants. Also, a posttest to examine fluency gains for specific facts and the social validity assessment to measure student acceptability could not be conducted. Although findings from this study provided evidence that IR is a promising strategy, results are tentative. Future research should include a direct replication of the current study. Implications for practice and additional research are discussed.



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