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.

A key complication facing teachers who seek to integrate technology in their teaching is the fact that most technologies are not designed for educational purposes. Making a tool an educational technology requires creative input from the teacher to redesign , or maybe even subvert the original intentions of the designer. The learning technology by design (LT/D) framework has been proposed as being an effective instructional technique to develop deeper understanding of technological pedagogical content knowledge. In this paper we expand our description of the LT/D technique to develop what we call a deep-play model for teacher professional development. The deep-play model integrates: a pedagogy for key 21st century learning skills b content that cuts across disciplines with trans-disciplinary cognitive tools c technology by the creative repurposing of tools for pedagogical purposes.

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.