Advertisement

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

  • Emily C. BouckEmail author
  • Jiyoon Park
  • Courtney Maher
  • Kennedy Levy
  • Katie Cwiakala
ORIGINAL ARTICLE
  • 31 Downloads

Abstract

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.

Keywords

Mathematics Manipulatives Middle school Intervention Education Technology 

Notes

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.

References

  1. 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
  2. Alajmi, A. H. (2012). How do elementary textbooks address fractions? A review of mathematics textbooks in the USA, Japan, and Kuwait. Educational Studies in Mathematics, 79, 239–261.  https://doi.org/10.1007/s10649-011-9342-1.CrossRefGoogle Scholar
  3. Alberto, P., & Troutman, A. (2009). Applied behavior analysis for teachers (8th ed.). Upper Saddle River: Pearson.Google Scholar
  4. Bailey, D. H., Hoard, M. K., Nugent, L., & Geary, D. C. (2012). Competence with fractions predicts gains in mathematics achievement. Journal of Experimental Child Psychology, 113, 447–455.CrossRefGoogle Scholar
  5. Bouck, E. C., Satsangi, R., Doughty, T. T., & Courtney, W. T. (2014). Virtual and concrete manipulatives: A comparison of approaches for solving mathematics problems for students with autism spectrum disorder. Journal of Autism and Developmental Disabilities, 44, 180–193.CrossRefGoogle Scholar
  6. Bouck, E. C., Bassette, L., Shurr, J., Park, J., Kerr, J., & Whorley, A. (2017a). Teaching equivalent fractions to secondary students with disabilities via the virtual-representational-abstract instructional sequence. Journal of Special Education Technology, 32, 220–231.CrossRefGoogle Scholar
  7. 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
  8. Bouck, E. C., Park, J., Sprick, J., Shurr, J., Bassette, L., & Whorley, A. (2017c). Using the virtual-abstract instructional sequence to teach addition of fractions. Research in Developmental Disabilities, 70, 163–174.CrossRefGoogle Scholar
  9. 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
  10. Bouck, E. C., Satsangi, R., & Park, J. (2018b). The concrete-representational-abstract approach for students with learning disabilities: An evidence-based practice synthesis. Remedial and Special Education, 39, 211–228.  https://doi.org/10.1177/0741932517721712.CrossRefGoogle Scholar
  11. Butler, F. M., Miller, S. P., Crehan, K., Babbitt, B., & Pierce, T. (2003). Fraction instruction for students with mathematics disabilities: Comparing two teaching sequences. Learning Disabilities Research & Practice, 18, 99–111.CrossRefGoogle Scholar
  12. Brainingcamp (2017). Fraction Tiles. Retrieved from https://itunes.apple.com/us/app/fraction-tiles-manipulative/id1111230448?mt=8.
  13. 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
  14. 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
  15. Collins, B. C. (2012). Systematic instruction for students with moderate and severe disabilities. Baltimore: Paul H Brookes Publishing.Google Scholar
  16. Common Core State Standards Initiative (2017). Retrieved from http://www.corestandards.org/.
  17. 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.
  18. Fuchs, L. S., Schumacher, R. F., Long, J., Namkung, J., Hamlett, C. L., Cirino, P. T., et al. (2013). Improving at-risk learners’ understanding of fractions. Journal of Educational Psychology, 105, 683–700.  https://doi.org/10.1037/a0032446.CrossRefGoogle Scholar
  19. 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
  20. 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
  21. 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
  22. 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
  23. 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
  24. Jordan, N. C., Hansen, N., Fuchs, L. S., Siegler, R. S., Gersten, R., & Micklos, D. (2013). Developmental predictors of fraction concepts and procedures. Journal of Experimental Child Psychology, 116, 45–58.  https://doi.org/10.1016/j.jecp.2013.02.001.CrossRefPubMedGoogle Scholar
  25. 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
  26. 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
  27. 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.
  28. Parker, R. I., Vannest, K. J., & Brown, L. (2009). An improved effect size for single case research: Nonoverlap of all pairs (NAP). Behavior Therapy, 40, 357–367.  https://doi.org/10.1016/j.beth.2008.10.006.CrossRefPubMedGoogle Scholar
  29. Parker, R. I., Vannest, K. J., Davis, J. L., & Sauber, S. B. (2011). Combining non-overlap and trend for single case research: Tau-U. Behavior Therapy, 42, 284–299.  https://doi.org/10.1016/j.beth.2010.08.006.CrossRefPubMedGoogle Scholar
  30. Patton, J. R., Cronin, M. E., Bassett, D. S., & Koppel, A. E. (1993). A life skills approach to mathematics instruction: Preparing students with learning disabilities for the real-life math demands of adulthood. Journal of Learning Disabilities, 30, 178–187.CrossRefGoogle Scholar
  31. Powell, S. R., Fuchs, L. S., & Fuchs, D. (2013). Reaching the mountaintop: Addressing the common core standards in mathematics for students with mathematics difficulties. Learning Disabilities Research & Practice, 28, 38–48.CrossRefGoogle Scholar
  32. 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.
  33. 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.
  34. Shin, M., & Bryant, D. P. (2015). Fraction intervention for students struggling to learn mathematics: A research synthesis. Remedial and Special Education, 36, 374–387.  https://doi.org/10.1177/0741932515572910.CrossRefGoogle Scholar
  35. 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
  36. 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
  37. 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
  38. 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
  39. Vukovic, R. K., Fuchs, L. S., Geary, D. C., Jordan, N. C., Gersten, R., & Siegler, R. S. (2014). Sources of individual differences in children’s understanding of fractions. Child Development, 85, 1461–1476.  https://doi.org/10.1111/cdev.12218.CrossRefPubMedPubMedCentralGoogle Scholar
  40. 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.
  41. Zhang, D., Stecker, P., & Beqiri, K. (2017). Strategies students with and without mathematics disabilities use when estimating fractions on number lines. Learning Disability Quarterly, 40, 225–236.  https://doi.org/10.1177/0731948717704966.CrossRefGoogle Scholar

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

Personalised recommendations