Acquiring the Skill of Identifying Fractions through the Virtual-Abstract Framework
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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.
KeywordsMathematics Manipulatives Middle school Intervention Education Technology
Compliance with Ethical Standards
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.
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.
- Agrawal, J., & Morin, L. L. (2016). Evidence-based practices: applications of concrete representational abstract framework across math concepts for students with disabilities. Learning Disabilities Research & Practice, 31, 34–44.Google Scholar
- Alberto, P., & Troutman, A. (2009). Applied behavior analysis for teachers (8th ed.). Upper Saddle River: Pearson.Google Scholar
- Bouck, E. C., Chamberlain, C., & Park, J. (2017b). Concrete and app-based manipulatives to support students with disabilities with subtraction. Education and Training in Autism and Developmental Disabilities, 52, 317–331.Google Scholar
- Bouck, E. C., Park, J., Shurr, J., Bassette, L., & Whorley, A. (2018a). Using the virtual-representational-abstract approach to support students with intellectual disability in mathematics. Focus on Autism and Developmental Disabilities. [Advanced Online Publication].Google Scholar
- Brainingcamp (2017). Fraction Tiles. Retrieved from https://itunes.apple.com/us/app/fraction-tiles-manipulative/id1111230448?mt=8.
- Browder, D. M., Jimenez, B. A., Spooner, F., Saunders, A., Hudson, M., & Bethune, K. S. (2012). Early numeracy intruction for students with moderate and severe developmental disabilities. Research & Practice for Persons with Severe Disabilities, 37, 308–320.Google Scholar
- Cass, M., Cates, D., Smith, M., & Jackson, C. (2003). Effects of manipulative instruction on solving area and perimeter problems by students with learning disabilities. Learning Disabilities Research & Practice, 18, 112–120.Google Scholar
- Collins, B. C. (2012). Systematic instruction for students with moderate and severe disabilities. Baltimore: Paul H Brookes Publishing.Google Scholar
- Common Core State Standards Initiative (2017). Retrieved from http://www.corestandards.org/.
- Doabler, C. T. & Fien, H. (2013). Explicit mathematics instruction: what teachers can do for teaching students with mathematics difficulties? Intervention for School and Clinic, 48, 276–285. https://doi.org/10.1177/1053451212473141.
- Fuchs, L. S., Schumacher, R. F., Sterba, S. K., Long, J., Namkung, J., Malone, A., et al. (2014). Does working memory moderate the effects of fraction intervention? An aptitude-treatment interaction. Journal of Educational Psychology, 106, 499–514. https://doi.org/10.1037/a0034341.CrossRefGoogle Scholar
- Gast, D. L., & Spriggs, A. D. (2014). Visual analysis of graphic data. In D. L. Gast & J. R. Ledford (Eds.), Single subject research methodology in behavioral sciences (2nd ed., pp. 176–210). New York: Routledge.Google Scholar
- Gersten, R., Chard, D. J., Jayanthi, M., Baker, S. K., Morphy, P., & Flojo, J. (2009). Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components. Review of Educational Research, 79, 1202–1242. https://doi.org/10.3102/0034654309334431.CrossRefGoogle Scholar
- Haring, N. G., & Eaton, M. D. (1978). Systematic instructional procedures: An instructional hierarchy. In N. G. Haring, T. C. Lovitt, M. D. Eaton, & C. L. Hansen (Eds.), The fourth R: Research in the classroom (pp. 23–40). Columbus: Merrill.Google Scholar
- Jordan, L., Miller, M. D., & Mercer, C. D. (1998). The effects of concrete to semiconcrete to abstract instruction in the acquisition and retention of fraction concepts and skills. Learning Disabilities, 9, 115–122.Google Scholar
- Jordan, N. C., Resnick, I., Rodrigues, J., Hansen, N., & Dyson, N. (2017). Delaware longitudinal study of fraction learning: Implications for helping children with mathematics difficulties. Journal of Learning Disabilities, 50, 621–630. https://doi.org/10.1177/0022219416662033.CrossRefPubMedGoogle Scholar
- Kellems, R. O., Frandsen, K., Hansen, B., Gabrielsen, T., Clarke, B., Simons, K., & Clements, K. (2016). Teaching multi-step math skills to adults with disabilities via video prompting. Research in Developmental Disabilities, 58, 31–44. https://doi.org/10.1016/j.ridd.2016.08.013.CrossRefPubMedGoogle Scholar
- National Center on Intensive Intervention (2016). Principles for designing intervention in mathematics. Washington, DC: Office of Special Education, U. S. Department of Education. Retrieved from http://www.intensiveintervention.org/sites/default/files/Princip_Effect_Math_508.pdf.
- Root, J. R., Browder, D. M., Saunders, A. F., & Lo, Y. Y. (2017). Schema-based instruction with concrete and virtual manipulative to teach problem solving to students with autism. Remedial and Special Education, 38, 42–52. https://doi.org/10.1177/0741932516643592.
- Satsangi, R., & Miller, B. (2017). The case for adopting virtual manipulatives in mathematics education for students with disabilities. Preventing School Failure: Alternative Education for Children and Youth. Advanced online publication. https://doi.org/10.1080/1045988X.2016.1275505.
- Shurr, J. C., Jimenez, B. A., & Bouck, E. C. (in press). Educating students with intellectual disability and autism spectrum disorder. Book1: Research-based practices and education science. Arlington: Council for Exceptional Children.Google Scholar
- Stroizer, S., Hinton, V., Flores, M., & Terry, L. (2015). An investigation of the effects of CRA instruction and students with autism spectrum disorder. Education and Training in Autism and Developmental Disabilities, 50, 223–236.Google Scholar
- Torbeyns, J., Schneider, M., Xin, Z., & Siegler, R. S. (2015). Bridging the gap: Fraction understanding is central to mathematics achievement in students from three different continents. Learning & Instruction, 37, 5–13. https://doi.org/10.1016/j.learninstruc.2014.03.002.CrossRefGoogle Scholar
- Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2016). Elementary and middle school mathematics: Teaching developmentally (9th ed.). Boston: Pearson.Google Scholar
- Watt, S. J., & Therrien, W. J. (2016). Examining a preteaching framework to improve fraction computation outcomes among struggling learners. Preventing School Failure: Alternative Education for Children and Youth, 60, 311–319. https://doi.org/10.1080/1045988X.2016.1147011.