Using a Virtual Manipulative Intervention Package to Support Maintenance in Teaching Subtraction with Regrouping to Students with Developmental Disabilities

Adapting a virtual manipulative-based instructional sequence to target maintenance

The ability to maintain mathematical skills learned is critical for students to successfully engage in advanced mathematics and promote independence in daily living skills. The purpose of this study was to evaluate the effectiveness of a graduated manipulative sequence consisting of virtual, representational, abstract, and an extended abstract phase (VRAEa) to teach various types of mathematical problems to three students with autism and mild intellectual disability using a multiple probe across behavior single case design. This study extended previous research on the virtual, representational, abstract sequence (VRA) to address deficiency in maintenance results through incorporating the extended abstract phase. The results indicate the intervention was effective, however, maintenance was variable. Implications for practice and ideas for future research to support the learning needs of students with developmental disabilities are discussed.

Teacher-delivered virtual manipulative mathematics intervention to individuals with extensive support needs

While mathematics is foundational to further academic learning and post-school outcomes for students with disabilities, research and practice specifically for those students has not received significant attention. Moreover, an insufficient number of studies have sought to verify the effectiveness of interventions delivered by teachers who work directly with students with extensive support needs (ESN). The purpose of this study was to explore the effectiveness of an intervention-the virtual manipulatives-based instructional sequence-in teaching equivalent fractions delivered by the special education teacher who worked regularly with the students. Among three students aged from 15 to 17, all acquired the skill and one of the three maintained the skill up to eight weeks later. With additional strategy (i.e., self-monitoring), the other two students maintained the skill. The study also addressed limitations and future directions.

Exploring the Virtual-Representational-Abstract Instructional Sequence Across the Learning Stages for Struggling Students

In recent years, virtual manipulatives have been explored and used as an alternative to concrete manipulatives in mathematics for students on their own and as part of manipulative-based instructional sequences. Researchers examining virtual manipulative-based instructional sequences tend to focus on students documented with disabilities, as opposed to students at-risk or struggling with mathematics, as well as students’ acquisition of the target skill, despite students experiencing learning in four stages: acquisition, fluency, maintenance, and generalization. This study explored the virtual-representational-abstract (VRA) instructional sequence across four stages of learning for three elementary students struggling in mathematics. In the single-case design study, researchers found a functional relationship between the VRA instructional sequence delivered online via explicit instruction and students’ computational accuracy in their targeted area of mathematics need. Researchers also found limited influence on fluency rate or generalization to word problem accuracy but that students did maintain.

Cognitive factors and educational placement affecting mathematical attainment in middle school students with mild intellectual disability

The study investigated the relationship between mathematics achievement, cognitive and motor skills, and general intellectual ability among seventy 10-12 years old students with mild intellectual disability (MID) attending regular school (n = 30) and special school (n = 40). The purpose of the study was to identify the critical deficits teachers need to consider when teaching mathematics at the secondary school level. The students attending regular schools had significantly higher fluid intelligence scores (p = 0.036), but we found no difference in the total score of the math achievement test. Special school students were more eager to use assistance and aids when solving math problems (p = 0.040). The study indicated significant associations between basic mathematical skills, verbal and visuospatial processing, and motor skills. Thus, it is essential to compensate for the delay of students' cognitive development to improve their basic mathematical skills and, in general, mathematical performance. The educational placement affects the willingness or ability to seek academic help when solving mathematical problems.

Mathematics Learning Through Online Video-Based Instruction for an Autistic Child

The purpose of this study was to examine the effectiveness of a video modeling (VM) intervention package (including virtual manipulatives and error correction) delivered via synchronous, virtual environment to teach the mathematics skills of addition, number comparison, and subtraction to a five-year old autistic child. Using a multiple probe across skills design of a single-case experimental design, we examined whether a causal relation existed between the intervention and the child’s improved accuracy of mathematics problem-solving. Following the intervention, the autistic child showed improved accuracy across all three skills and continued to solve problems with 100% accuracy during the generalization phase, which also served as the immediate maintenance phase.

Online Delivery of a Manipulative-Based Intervention Package for Finding Equivalent Fractions

Mathematics education for students with and at-risk for a disability is important and high-quality, research-supported practices should be used for online teaching-whether intentional or as a result of a global pandemic. This single-case design multiple probe replicated across participants study explored the online delivery of an intervention package consisting of the virtual-abstract instructional sequence-taught via modified explicit instruction-and the system of least prompts to three upper elementary students with a disability or at-risk in solving equivalent fractions. Researchers determined a functional relation existed between the intervention package and student accuracy. Researchers also found students were independent and able to maintain accuracy when instruction did not proceed either following the intervention or with the support of boost sessions. Implications for providing mathematical interventions to students with disabilities or at-risk online exist. Further, the study lends support to virtual manipulative-based instructional sequences, as the setting, population, and implementation of explicit instruction differed in this study as compared to previous research.

Maintenance in Mathematics for Individuals with Intellectual Disability: A Systematic Review of Literature

Despite the growing attention being paid to teaching mathematics for students with disabilities, the existing research tends to focus on mathematical skill acquisition, but not on skill maintenance. The researchers in this study reviewed all studies from 1975 to 2018 that involved teaching mathematics to individuals with intellectual disability. A total of 135 studies met inclusion criteria, but only 53 studies involved a maintenance phase (39.2%). Among the 53 studies, only 22 were included for the final analysis, after evaluating their methodological rigor. In those 22 studies, there was no consensus among researchers on the standards for conducting a maintenance phase (i.e., latency between intervention and maintenance phases, length of maintenance phase, number of maintenance sessions). Further, in the studies which included a maintenance phase, the most widely taught mathematical content was numbers and operations. All studies employed intervention packages which included more than one instructional method and/or materials and the most widely used instructional method was prompting while the most widely used instructional materials were visual supports and manipulatives. The results suggest that prompting is an evidence-based practice for individuals with intellectual disability in supporting maintenance, while explicit instruction, time delay, feedback, and instructional sequence (e.g., the virtual-representational-abstract instructional sequence) are potentially evidence-based practice for individuals with intellectual disability.