A sizable body of literature exists studying various technologies and pedagogical practices for teaching secondary mathematics curriculum to students with a learning disability in mathematics. However, with the growing footprint of computer-based technologies in today's classrooms, some areas of study, such as the use of virtual manipulatives, lack sufficient exploration. Although concrete manipulatives were studied for many decades for students with a learning disability and are considered a best practice, the research base for virtual manipulatives is notably less. With a specific focus on algebraic instruction, this study sought to compare the benefits of both forms of manipulatives to assist secondary students with a learning disability in mathematics to solve single-variable linear equations using a single-subject alternating treatment design. Over the course of 30 sessions of intervention, three students exhibited over 90% average accuracy solving problems using both virtual and concrete manipulatives, while the concrete manipulative earned higher scores for two of the three students.

As researchers and practitioners have increasingly become interested in what practices are evidence based and for whom in education, different sets of quality indicators and evidence-based practice standards have emerged in the field of special education. Practices are commonly suggested as evidence based, even without a best evidence synthesis on the existing research, such as the case with the concrete–representational–abstract (CRA) instructional framework to support students with disabilities in mathematics. This study sought to support the classification of the CRA instructional framework as an evidence-based approach for students with learning disabilities by applying quality indicators and standards of evidence-based practice by Cook et al. (2014). Based on the application of the indicators and standards, the CRA instructional framework was determined to be an evidence-based practice for students with learning disabilities who struggle in mathematics relative to computational problems, such as addition, subtraction, and multiplication, largely with regrouping.

Secondary students with a learning disability in mathematics often struggle with the academic demands presented in advanced mathematics courses, such as algebra and geometry. With greater emphasis placed on problem solving and higher level thinking skills in these subject areas, students with a learning disability in mathematics often fail to keep pace with their general education peers. This study sought to address the lack of existing empirical research targeting viable interventions for learning the concepts of area and perimeter for secondary students with a learning disability in mathematics. Through the use of a multiple baseline design across three participants, virtual manipulatives were found to be an effective tool to acquire, maintain, and generalize the concepts of area and perimeter. Results from this study provide new evidence showing virtual manipulatives to be a viable and accessible technology to teach students with learning disabilities advanced mathematical concepts.

Students with autism spectrum disorder (ASD) are included in general education classes and expected to participate in general education content, such as mathematics. Yet, little research explores academically-based mathematics instruction for this population. This single subject alternating treatment design study explored the effectiveness of concrete (physical objects that can be manipulated) and virtual (3-D objects from the Internet that can be manipulated) manipulatives to teach single- and double-digit subtraction skills. Participants in this study included three elementary-aged students (ages ranging from 6 to 10) diagnosed with ASD. Students were selected from a clinic-based setting, where all participants received medically necessary intensive services provided via one-to-one, trained therapists. Both forms of manipulatives successfully assisted students in accurately and independently solving subtraction problem. However, all three students demonstrated greater accuracy and faster independence with the virtual manipulatives as compared to the concrete manipulatives. Beyond correctly solving the subtraction problems, students were also able to generalize their learning of subtraction through concrete and virtual manipulatives to more real-world applications.

Over the last two decades, the significance of academic achievement for students with disabilities in K-12 education has increased. To meet the needs of this population, educators turned to innovative strategies and technologies for instructional support in the classroom. For students with a learning disability, the need for such solutions is vital to address many of the academic struggles they face in the area of mathematics education. One evidence-based strategy shown to support instruction for students with a learning disability is the use of manipulatives. Although concrete manipulatives were extensively studied for this population, the virtual form of this technology lacks comparable research. Using a multiple probe design across three secondary students with a learning disability in mathematics, this study assessed the benefits of an instructional strategy using a virtual manipulative balance paired with explicit instruction to teach multistep linear equations. Results showed increased percent accuracy and independence scores for all three students across an intervention and maintenance phase. These findings and their broader implications for the field of mathematics education are discussed.