Lessons Learned From a Rural Classroom Study: Transitioning From Concrete to Virtual Manipulatives to Teach Math Fact Fluency to Students With Learning Disabilities

Jiwon Hwang,Jiyung Hwang,Matthew Kabel

doi:10.46303/jcsr.2021.7

Abstract

As the use of technology has become more prevalent within the educational environment over the past decade, the emergence of the use of virtual manipulatives to support student learning in math has made transitioning to technology-infused math instruction unavoidable. Students in rural areas, however, have tended to receive far less technology-infused instruction due to the many challenges faced by rural schools that can adversely affect academic opportunities and disrupt equity in learning and teaching. In the current paper, we report on a classroom study conducted to examine whether the previously proven effects of concrete manipulatives can carry over into those of virtual manipulatives when teaching math fact fluency in multiplication and explored the potential for virtual manipulatives in rural classrooms from the teacher’s perspective. Quantitative and qualitative results both indicated a promising potential for usage of virtual manipulatives, with meaningful implications for practitioners. The educational implications for designing and planning effective instruction incorporating virtual manipulatives are discussed.

Highlights

Mathematics has long been known to be a notoriously difficult subject for students with learning disabilities (LD) because of many contributing factors including standards-based spiral nature of mathematics where topics increase in complexity and build upon previous learning, neuropsychological and academic characteristics of learning disability, and lack of instructional strategies or support (Fletcher & Grigorenko, 2017; Becker et al, 2009; Jayanthi et al, 2008)
While the use of both virtual and concrete manipulatives increased the performance of all students’ math fact fluency and accuracy, students demonstrated a greater rate of increase and long-lasting effect when using virtual manipulatives than they did when using concrete manipulatives
While all eight students demonstrated positive trends in that their performance on one-digit by one-digit multiplication facts when using virtual manipulatives changed in a therapeutic direction, only three students demonstrated positive trends with the use of concrete manipulatives

Summary

Introduction

Mathematics has long been known to be a notoriously difficult subject for students with learning disabilities (LD) because of many contributing factors including standards-based spiral nature of mathematics where topics increase in complexity and build upon previous learning, neuropsychological and academic characteristics of learning disability, and lack of instructional strategies or support (Fletcher & Grigorenko, 2017; Becker et al, 2009; Jayanthi et al, 2008). Hwang and Riccomini (2016) identified three main instructional approaches—heuristic, semantic, and authentic—that categorize math interventions with relative focus among the five strands Among these three instructional approaches, math interventions that use a heuristic approach (e.g., mnemonic, meta-cognitive, and cover-copy-comparison strategies) concentrate more on promoting procedural fluency by teaching students’ skills to carry out the problemsolving process more flexibly and efficiently (Kelley, 2008; Ramos-Christian et al, 2008). While both mathematical understanding and procedural skill are important (Common Core State Standards Initiative, 2010), increasing math fact fluency, the basic skill of procedural fluency, has gained a lot of attention when teaching students with LD. Math fact fluency has often been defined by speed and accuracy in solving basic mathematical facts (i.e., the number of problems correctly solved per minute)

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Conclusion