Teaching fractions, and the concepts around them, has been proven to be a challenging task as multiple skills are required. This study examines the effectiveness of an intervention based on the “Response-to-Instruction” (RtI) model to students with math learning difficulties. The intervention was designed for teaching fractions, including both conceptual and procedural knowledge, to thirteen students with learning difficulties, attending mainstream middle schools in Greece. Its design was based on explicit instruction and on the Concrete-Representational-Abstract (CRA) strategy. The aim of this study is to evaluate the impact of the intervention and students’ intra-individual improvement, using parametric statistical t-test of dependent samples. We used Single Case Design (SCD) with multiple baseline measures type A-B as an experimental design. We found a significant positive effect on students’ performance in fractions and reliable data to monitor each student’s responsiveness. The results of the present study converge with the findings in the literature that argue that explicit instruction and CRA strategy have a significant positive effect on developing mastery about fraction concepts in students with learning difficulties.
Agaliotis, I. (2011). Teaching Mathematics in Special Education. Athens: Grigoris Publications. (In Greek)
Archer, A., & Hughes, C. (2011). Explicit Instruction: Effective and Efficient Teaching. New York: Guilford Publications.
Barbas, C., Vermeoulen, F., Kioseoglou, G., & Menexes, G. (2008). Psychometric Criterion of Mathematical Proficiency for Children and Adolescents. EPEAEK Project “Psychometric and Differential Evaluation in Children and Adolescents with Learning Disabilities”. Thessaloniki. (In Greek)
Bouck, E. C., & Park, J. (2018). A Systematic Review of the Literature on Mathematics Manipulatives to Support Students with Disabilities. Education and Treatment of Children, 41, 65-106. https://doi.org/10.1353/etc.2018.0003
Carr, J. E. (2005). Recommendations for Reporting Multiple-Baseline Designs across Participants. Behavioral Interventions, 20, 219-224. https://doi.org/10.1002/bin.191
Ennis, R. P., & Losinski, M. (2019). Interventions to Improve Fraction Skills for Students with Disabilities: A Meta-Analysis. Exceptional Children, 85, 367-386. https://doi.org/10.1177/0014402918817504
Etikan, I., Musa, S., & Alkassim, R. (2016). Comparison of Convenience Sampling and Purposive Sampling. American Journal of Theoretical and Applied Statistics, 5, 1-4. https://doi.org/10.11648/j.ajtas.20160501.11
Flores, M., Hinton, V., & Taylor, J. (2018). CRA Fraction Intervention for Fifth-Grade Students Receiving Tier Two Interventions. Preventing School Failure: Alternative Education for Children and Youth, 62, 198-213. https://doi.org/10.1080/1045988X.2017.1414027
Forbringer, L., & Fuchs, W. (2014). RtI in Math. New York: Routledge, Taylor & Francis Group, LLC. https://doi.org/10.4324/9781315852270
Fuchs, L. S., Powell, S. R., Seethaler, P. M., Fuchs, D., Hamlett, C. L., Cirino, P. T., & Fletcher, J. M. (2010). A Framework for Remediating Number Combination Deficits. Exceptional Children, 76, 135-156. https://doi.org/10.1177/001440291007600201
Gelman, R., & Williams, E. M. (1998). Enabling Constraints for Cognitive Development and Learning: Domain Specificity and Epigenesis. In W. Damon, D. Kuhn, & R. S. Siegler (Eds.), Handbook of Child Psychology: Vol. 2. Cognition, Perception, and Language (pp. 575-630). Hoboken, NJ: John Wiley & Sons Inc.
Gersten, R., Beckmann, S., Clarke, B., Foegen, A., Marsh, L., Star, J. R., & Witzel, B. (2009). Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools (NCEE 2009-4060). Washington DC: National Center for Education Evaluation and Regional Services, Institute of Education Sciences, U.S. Department of Education.
Gersten, R., Dimino, J., & Haymond, K. (2011). Universal Screening for Students in Mathematics for the Primary Grades. The Emerging Research Base. In R. Gersten, & R. Newman-Gonchar (Eds.), Understanding RTI in Mathematics. Proven Methods and Applications (pp. 17-33). Baltimore, MD: Paul H. Brookes Publishing CO.
Gersten, R., Jordan, N. C., & Flojo, J. R. (2005). Early Identification and Interventions for Students with Mathematics Disabilities, Journal of Learning Disabilities, 38, 293-304. https://doi.org/10.1177/00222194050380040301
Kazdin, A. E. (2011). Single-Case Research Designs (2nd ed.). New York: Oxford University Press.
Koleza, E. (2000). Cognitive and Didactic Approach to Early Mathematical Concepts. Athens: Leaders Books. (In Greek)
Mertens, D. (2015). Research and Evaluation in Education and Psychology: Integrating Diversity with Quantitative, Qualitative, and Mixed Methods (4th ed., p. 332). Thousand Oaks, CA: Sage Publications, Inc.
Ministry of Education and Religious Affairs (2019). Guidelines for Teaching Mathematics at the Middle School for the School Year 2019-2020. Athens: Ministry of Education and Religious Affairs. (In Greek)
Misquitta, R. (2011). A Review of the Literature: Fraction Instruction for Struggling Learners in Mathematics. Learning Disabilities Research & Practice, 26, 109-119. https://doi.org/10.1111/j.1540-5826.2011.00330.x
National Mathematics Advisory Panel NMAP (2008). Foundations for Success: The Final Report of the National Mathematics Advisory Panel. Washington DC: U.S. Department of Education.
Papadimitriou, P., Stathopoulou, C., & Tzivinikou, S. (2015). Response to Instruction and Intervention: Development of a Tool for the Screening of Mathematics Difficulties. In D. Desli, I. Papadopoulos, & M. Tzekaki (Eds.), Mathematics with Discrimination and without Discrimination (pp. 157-166). Thessaloniki: ENEDIM. (In Greek)
Pedagogical Institute (2003). Single Cross Thematic Curriculum Framework and Compulsory Educational Curriculum. Athens: Government Gazette, Government Gazette, FEK 303B/13-03-2003, FEK 304B/13-03-2003. (In Greek)
Riley-Tillman, T., & Burns, M. (2009). Evaluating Educational Interventions, Single-Case Design for Measuring Response to Intervention. New York: Guilford Publications.
Satsangi, R., Bouck, E. C., Taber-Doughty, T., Bofferding, L., & Roberts, C. A. (2016). Comparing the Effectiveness of Virtual and Concrete Manipulatives to Learn Algebra for Secondary Students with Learning Disabilities. Learning Disability Quarterly, 39, 240-253. https://doi.org/10.1177/0731948716649754
Siegler, R. S., Thompson, C. A., & Schneider, M. (2011). An Integrated Theory of Whole Number and Fractions Development. Cognitive Psychology, 62, 273-296. https://doi.org/10.1016/j.cogpsych.2011.03.001
Spectrum K12 School Solutions (2010). Response to Intervention Adoption Survey 2010. http://sss.usf.edu/resources/presentations/2010/fasp_summer_inst2010/ Resource_SLD/RTI/2010RTIAdoptionSurveyReport.pdf
Tzivinikou, S. (2018). Fractions and Decimals (Non-Negative Rational Numbers): Learning Disabilities and Mathematics. Volos: Readnet Publications. (In Greek)
Van de Walle, J., Karp, K., & Bay-Williams, J. (2013). Elementary and Middle School Mathematics (6th ed.). Upper Saddle River, NJ: Pearson.
Witzel, B. S., Riccomini, P. J., & Schneider, E. (2008). Implementing CRA with Secondary Students with Learning Disabilities in Mathematics. Intervention in School and Clinic, 43, 270-276. https://doi.org/10.1177/1053451208314734