Mathematics problem-solving skills are critical for many areas of daily life as well as for successful functioning on the job, in school, at home and in the community. However, five to ten percent of school-age children are identified as having mathematics disabilities (Fuchs, Fuchs, & Hollenbeck, 2007) and students whose math performance was ranked at or below the 20 to 35 percentile are often considered at risk for learning disabilities or for having learning difficulties in mathematics (LDM) (Bryant et al., 2011; Fuchs et al., 2007). Many students with LDM fail to acquire essential mathematics problem solving skills in their early school years (Geary 1994). Such individuals become at significant risk of failing their secondary mathematics curriculum, thereby subjecting themselves to persistent academic, life and work challenges.
According to 2013 National Assessment of Educational Progress (NAEP) mathematics assessment, 65% of Grade 8 students with disabilities scored below the basic level compared to 21% students without disabilities. From 2011 to 2013, score gains were seen in mathematics at grades four and eight for higher performing students at the 75th and 90th percentiles, but there were no significant changes over the same period for lower performing students at the 10th and 25th percentiles (NAEP, 2013). In conjunction with this lack of growth in mathematics learning among students with disabilities, expectations for all students, including those with disabilities, have been elevated in today’s educational climate. This problem is compounded by the shortage of qualified special education teachers, which is “severe, chronic, and pervasive” and presents threats to the quality of educational services provided to these students (Billingsley & McLesky, 2004).
One approach established to address mathematical challenges is the Response-to-Intervention (RtI, Fuchs & Deshler, 2007). RtI programs use benchmark assessments to identify at-risk students and then provide them with tiered intervention programs. Recent intervention programs such as Cognitive and Metacognitive Instruction, Schema-Based Instruction, and Conceptual Model-Based Instruction have shown promising effect in enhancing mathematics performance of students with LDM (Hord and Xin, 2013). Cognitive strategies relate to how to solve a problem, whereas meta-cognitive strategies relate to knowing how to solve a problem and may include self-instruction, self-questioning, and self-regulation procedures (Montague, Warger, and Morgan, 2000). Employing explicit and systematic teaching procedures as well as strategy instruction as supplements to core mathematics instruction has shown benefiting effect to students with LDM (Bryant et al., 2008, 2011). On the other hand, Schema-Based Instruction (SBI) emphasizes semantic analyses of the problem and mapping the problem into a schematic diagram (Hord & Xin, 2013). Intervention program using the “schema broadening” (Fuchs et al., 2008) strategy has also helped students see the connections between novel and familiar problems and therefore enhance skill transfer (Fuchs et al., 2002).
Most recently, Conceptual Model-Based Problem Solving instruction (COMPS, Xin, 2012) emerged as an effective intervention program (Xin, 2015). The COMPS program reflects a pedagogical shift from traditional problem-solving instruction, which focuses on the choice of operation for solution, to a mathematical model-based problem-solving that emphasizes an understanding and representation of mathematical relations in algebraic equations.
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Billingsley, S. B. & McLesky, J. (2004). Critical issues in special education teacher supply and demand: overview. The Journal of Special Education, 38(1), 2-4.
Bryant, D.P., Bryant, B.R., Gersten, R., Scammacca, N., and Chavez, M.M. (2008). Mathematics intervention for first- and second-grade students with mathematics difficulties: The effects of tier 2 intervention delivered as booster lessons. Remedial and Special Education, 29, 20-32.
Bryant, D. P., Bryant, B. R., Roberts, G., Vaughn, S., Pfannenstiel, K. H., Porterfield, J., & Gersten, R. (2011). Early numeracy intervention program for first-grade students with mathematics difficulties. Council for Exceptional Children, 78(1), 7-23.
Fuchs, D. and Deshler, D.D. (2007). What we need to know about responsiveness to intervention (and shouldn’t be afraid to ask). Learning Disabilities Research and Practice, 22, 129-136.
Fuchs, L. S., Seethaler, P. M., Powell, S. R., Fuchs, D., Hamlett, C. L., & Fletcher, J. M. (2008). Effects of preventative tutoring on the mathematical problem solving of third-grade students with math and reading difficulties. Exceptional Children, 74, 155-173.
Fuchs, L. S., Fuchs, D., Hamlett, C. L., & Appleton, A. C. (2002). Explicitly teaching for transfer: Effects on the mathematical problem-solving performance of students with mathematics disabilities. Learning Disabilities Research & Practice, 17, 90–106.
Fuchs, L. S., Fuchs, D., & K. N. Hollenbeck (2007). Expanding responsiveness to intervention to mathematics at first and third grads. Learning Disabilities Research and Practice 22(1), 13-24.
Geary, D. C. (1994). Children’s mathematical development: Research and practical applications. Washington, DC: American Psychological Association.
Hord, C. & Xin, Y. P. (2013). Intervention Research for Helping Elementary School Students with Math Learning Difficulties Understand and Solve Word Problems: 1996-2010. Learning Disabilities: A Multidisciplinary Journal, 19(1), 3-17.
Montague, M., Warger, C. & Morgan, T. H. (2000). Learning Disabilities Research & Practice, 15 (2), 110-116.
National Assessment of Educational Progress result (NEAP, 2013). Are higher and lower performing students making gains? Extracted on November 12, 2013 from http://nationsreportcard.gov/reading_math_2013/#/gains-percentiles
Xin, Y. P. (2015). Research related to modeling and problem solving: Conceptual model-based problem solving: emphasizing pre algebraic conceptualization of mathematical relations. In E. A. Silver & P. A. Kenney (Ed.) More Lessons Learned from Research: Useful and Useable Research Related to Core Mathematical Practices (pp. 235-246).
Xin, Y. P. (2012). Conceptual model-based problem solving: Teach students with learning difficulties to solve math problems. The Netherlands: Sense Publishers.