Students with emotional or behavioral disorders (EBD) are more likely than other students with disabilities to drop out of school (Blackorby & Wagner, 1996) and suffer societal consequences that include higher probabilities and rates of incarceration, poverty, drug abuse, homelessness, low wages, and unemployment (Bradley, Doolittle, & Bartolotta, 2008; Wagner, 1995). High school graduation is a critical factor to improve post-secondary outcomes for students with EBD; yet it is often mathematics, specifically algebra, that stands in the way of graduation (Blackorby & Wagner). Students with EBD often enter middle school lacking foundational mathematics skills, such as fractions, which sets them up to struggle with pre-algebra and ultimately fail algebra (U.S. Department of Education, 2008). The purpose of this study was to improve the ability of middle school students with EBD to access online grade-level mathematics content by providing fraction remediation to improve conceptual fraction knowledge and procedural fluency. The intervention consisted of Initial Fraction Ideas, an intervention curriculum from the Rational Number Project (RNP; Cramer, Behr, Post, & Lesh, 2009), in conjunction with three online virtual manipulatives (VM). The unique blended learning environment of this study provided the opportunity to evaluate the use of an evidence-based fraction intervention, in conjunction with VMs, in a single subject, multiple baseline across subjects design. Fluency data was gathered from daily fraction addition assessments (FAA) administered after each intervention session. A second component of the study featured a non-experimental repeated measures design that assessed student conceptual understanding of fraction equivalency through the administration of pre, post, and delayed-post Equivalent Fraction Tests (EFT). The intervention was effective in producing increases in median group fluency with high effect sizes, across three replications, establishing a functional relationship between the intervention and the dependent variable for these groups of students with EBD. In addition, all groups posted mean gains in equivalent fraction knowledge from pre to post-EFT, and maintained those gains for at least 15 days after the intervention concluded.

Virtual manipulatives are employed by both preservice and inservice teachers to enhance the instructional effectiveness of physical manipulatives and related tools by addressing limitations of access, cost, and adaptability. While research into the use of emerging technologies continues, there are several variables to consider when measuring the effects of virtual manipulative use. Research design, sampling characteristics, and the type of manipulative used may influence achievement. Variables that may influence the effectiveness of virtual manipulatives include: previous experience with computers, grade level, mathematical topic, treatment length, student attitudes toward mathematics, and computer-to-student ratio.