Enhancing Mathematics Fluency: Comparing the Spacing of Practice Sessions With the Number of Opportunities to Respond

Abstract

The number of opportunities to respond (OTR) and spacing (massed or distributed practice) of practice sessions are important variables to consider in instructional design. The purpose of this pilot study was to compare the impact of these variables on trajectories of mathematics fluency. Second- and third-grade students (N = 112) were randomly assigned to 1 of 4 conditions: (a) distributed practice, low OTR; (b) massed practice, low OTR; (c) distributed practice, high OTR; and (d) massed practice, high OTR. Students completed 1 practice session using cover-copy-compare for subtraction according to the group assignment. Multilevel modeling of 4 assessment time points (pretest, follow-up at 1, 4, and 7 days) was used to evaluate differences in retention (correct digits) between groups. After controlling for prior math knowledge, instructional level and OTR, but not spacing, were significant predictors of final score. These findings suggest that OTR is an important variable to consider when planning for instruction and intervention.

Keywords:

• intervention
• academic
• math
• hierarchical linear modeling

Additional information

Notes on contributors

Robin S. Codding

Robin S. Codding, PhD, BCBA-D, is an associate professor in the Department of Educational Psychology at the University of Minnesota. Her research interests focus on the intersection of intervention and implementation by developing and exploring the effectiveness of school-based interventions, the factors that contribute to student responsiveness to those interventions, and strategies to support intervention implementation. Dr. Codding's work has emphasized academic interventions and associated assessment for data-based decision making, particularly in the area of mathematics. In 2010, she was a corecipient of the Lightner Witmer Early Career Scholar Award from Division 16 (School Psychology) of the American Psychological Association. She has written more than 65 journal articles and book chapters, and she recently published a book entitled Effective Math Interventions: A Guide to Improving Whole-Number Knowledge, published by the Guilford Practical Intervention in the School Series.

Robert J. Volpe

Robert J. Volpe, PhD, is an associate professor in the Department of Applied Psychology and codirector of the Center for Research in School-Based Prevention (CRISP) at Northeastern University. His research focuses on designing academic and behavioral interventions for students with disruptive behavior disorders and feasible systems for assessing student behavior in problem-solving models. Dr. Volpe has written more than 80 journal articles, book chapters, and books, and he serves on the editorial advisory boards of the Journal of Attention Disorders, Journal of School Psychology, School Psychology Review, and School Mental Health. He is a past president of the Society for the Study of School Psychology and project director and principal investigator on Project iFAB, a grant funded by the Institute of Education Sciences to develop and evaluate a Web-based system for monitoring student social behavior.

Ryan J. Martin

Ryan J. Martin, PhD, is a research scientist at May Institute and the National Autism Center, where he currently studies school-based interventions for children with autism spectrum disorder and the dissemination of evidence-based practices. Ryan's broader research interests include mathematics intervention, home and school consultation, and methods of assessing and improving treatment fidelity.

Genevieve Krebs

Genevieve Krebs, MS, CAGS, is an intern at Devereux Children's Intellectual and Developmental Disabilities Services center. She is completing her doctoral education at Northeastern University in Boston, MA. Her research experience has been in academic intervention and play development of young children. Clinically, she is focused on evidence-based practices for social–emotional and academic success for children with autism and applied behavior analysis.