A Long-Term Analysis of the Relationship Between Fluency and the Training and Maintenance of Complex Math Skills

Abstract

In 2 experiments, each involving different mathematical operations, we compared 2 training procedures for teaching component math skills in terms of their effects on the learning and long-term maintenance of composite skills. The dependent variables were learn units to composite task mastery and performance on the composite task 2 months later. The independent variables were instruction in math facts under (a) fluency and (b) mastery conditions . The experiments used a simultaneous treatment design in which the students were selected for participation according to prerequisite skills and instructional histories and randomly assigned to receive 1 of the 2 training procedures. Four adolescents with developmental disabilities participated in each experiment. Instructional presentations were controlled by yoked learn units during component skill instruction . Results showed that fluency instruction did not result in fewer learn units to criterion on the composite task. However, 2 months later, the fluent students performed between 83% and 100% correct on the composite task, while the mastery students performed between 17% and 83% correct. The data are discussed in terms of fluency theory and educational practice.According to behavioral fluency theorists, responses that are mastered at fast rates will result in several outcomes or benefits (Binder, 1996;Johnson & Layng, 1994, 1996. Other theorists also have a theoretical and research literature concerned with fast and accurate performance of skills, and they refer to performance of skills without "conscious attention" as automaticity

Self-Monitoring of Pace to Improve Math Fluency of High School Students with Disabilities

“…As noted previously, research has shown benefits for students who respond fluently on basic academic tasks, such as addition and subtraction problems (Singer-Dudek & Greer, 2005).…”

“…These findings are important because achieving accurate and fast responses via brief practice sessions promotes automaticity and other educational outcomes. Students who do not perform fluently on basic skills, such as math facts and sight words, frequently have difficulties with more complex skills (Carnine, 1989;Cates & Rhymer, 2003;Chiesa & Robertson, 2000;Singer-Dudek & Greer, 2005;Woodward, 2006). The gains in math fluency also appeared to be socially valid in that participants improved their math fluency more than non-participant peers.…”

“…However, some students have difficulties initiating, maintaining, and completing tasks; pacing their responses (e.g., they are quick but error-prone, or accurate but slow); and monitoring and correcting errors while responding (Woodward, 2006). Students who respond fluently, or with automaticity, are more likely to maintain the skills, resist distractions, and acquire more complex skills (Binder, 1993;Hartnedy, Mozzoni, & Fahoum, 2005;Johnson & Street, 2004;Singer-Dudek & Greer, 2005). Compared to fluent peers, students who are accurate but slow in completing problems that require basic math skills take longer to finish assignments, submit more incomplete assignments, and experience more difficulties when faced with complex math procedures for which mastery of those basic math skills is a prerequisite (Chiesa & Robertson, 2000).…”

Math Fluency: Accuracy Versus Speed in Preoperational and Concrete Operational First and Second Grade Children

“…Fewer studies have looked specifically at the development of math fluency. Those studies found correlations between fast rate instruction and each of the benefits associated with fluency theory (Singer-Dudek and Greer 2005;Binder 1996;Ivarie 1986). However, those studies focused on reading related competencies, with relatively little regard to the development and maintenance of mathematical skills, but differences do exist in children's math abilities at a young age (Floyd et al 2003).…”

“…Fluency effects have been examined in several demonstration studies; however, rarely in experimental investigations (Singer-Dudek and Greer 2005). Fewer studies have looked specifically at the development of math fluency.…”