Learning Fractions with a Virtual Manipulative Based Graduated Instructional Sequence

Fractions are foundational concepts for more advanced mathematics as well as used throughout daily living, for all students, including students with disabilities. This study explored the virtual-abstract (VA) instructional sequence with regard to the acquisition and maintenance of fraction behaviors for three middle school students with mild intellectual disability and/or autism. Through a multiple probe across participants design, students received a minimum of three sessions using the app-based manipulative (i.e., virtual portion of the VA instructional sequence) and a minimum of five sessions using numerical strategies (i.e., abstract portion of the VA instructional sequence). A functional relation was found between the independent variable–the VA instructional sequence—and the dependent variable (i.e., accuracy in finding equivalent fractions or adding fractions with unlike denominators, depending on the student).