Acquiring the Skill of Identifying Fractions through the Virtual-Abstract Framework

  • Emily C. BouckEmail author
  • Jiyoon Park
  • Courtney Maher
  • Kennedy Levy
  • Katie Cwiakala


Fractions are an important component of mathematics instruction, with implications for both academics and daily living. Yet, more research is needed regarding fraction instruction for students with disabilities, including those with developmental disabilities. This study investigated the effects of using the Virtual-Abstract framework to teach sixth-grade students with developmental disabilities to identify fractions. Through a multiple probe across participants design, researchers examined if a functional relation existed between students’ acquisition of the mathematical behavior of identifying fractions and the Virtual-Abstract (VA) framework. For each student, the study involved three-to-five baseline sessions, six-to-nine intervention sessions, and two maintenance sessions. Two of the students also completed three abstract boost sessions and two additional maintenance sessions. Accuracy data reflected students’ ability to identify fractions on five problems answered independently. A functional relation existed between students’ acquisition of identifying fractions and the VA framework. Yet, two of the students failed to initially maintain their levels of accuracy. The VA framework can help students with developmental disabilities acquire mathematical behaviors, such as identifying fractions.


Mathematics Manipulatives Middle school Intervention Education Technology 


Compliance with Ethical Standards

Ethical Approval

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.

Informed Consent

The authors obtained approval to conduct the research with human participants and obtained informed consent and assent.

Conflict of Interest

The authors have no potential conflicts of interest to disclose.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Emily C. Bouck
    • 1
    Email author
  • Jiyoon Park
    • 1
  • Courtney Maher
    • 1
  • Kennedy Levy
    • 1
  • Katie Cwiakala
    • 1
  1. 1.Department of Counseling, Educational Psychology, and Special EducationMichigan State UniversityEast LansingUSA

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