Teaching Rate of Change and Problem Solving to High School Students With High Incidence Disabilities at Tier 3

Abstract

Implementing an integrated sequence of concrete-representational-abstract depictions of mathematics concepts (CRA-I) can improve the mathematics achievement of students with disabilities, and explicit instructional strategies involving problem-solving heuristics and student verbalizations can help facilitate students’ conceptual understanding of mathematics. Combining CRA-I and explicit instructional strategies may increase students’ conceptual understanding and ability to express mathematical reasoning through writing. This study included three ninth-grade students with disabilities, and employed a multiple-probe design across-participants to investigate a functional relation between an explicit instructional strategy within a CRA-I framework and high school students’ with disabilities proficiency in solving rate of change problems. Results showed that all three students improved their mathematics scores (combined Tau-U effect size = 0.77, p < .001) and maintained improvements during a 1- to 7-week post-instruction phase. Implications for research and practice related to mathematics instruction and intervention specifically for students with learning disabilities are discussed.

Reporting Quality of Single–Case Research Published in Learning Disabilities Journals

“…Thus, some studies included participants with LD and other disabilities. For example, Bundock et al (2021) included two students with LD, one student with autism, and one student with Other Health Impairment. Analyses including additional special education journals and disabilities would help to deepen our understanding of overall reporting quality in the special education field, including comparisons across design standards that continue to evolve and be updated.…”

Dyslexia in higher education

“…According to some estimates, up to 15% of students enrolled in higher education have an LD (Bundock et al, 2019;Lipka and Hess, 2016;McMorris et al, 2019). Some studies show extraordinarily little difference in completion rates, but this may be the result of many students with disabilities self-selecting out of the endeavor before ever enrolling.…”

Using the Concrete–Representational–Abstract Sequence to Teach Conceptual Understanding of Place Value, Rounding, and Expanded Notation

“…The CRA sequence has been used successfully to teach students with LD single-digit operations (Mercer & Miller, 1992), place value (Mercer & Miller, 1992;Peterson et al, 1988), operations with regrouping (Flores, Requests for reprints should be sent to M. M. Flores, Auburn University. Electronic inquiries should be sent to mmf0010@auburn.edu 2009; Flores et al, 2019;Flores & Hinton, 2022;Mancl et al, 2012), and algebra (Bundock et al, 2021;Strickland & Maccini, 2013;Witzel, 2005).…”

“…An explicit approach to mathematics using multiple representations is the concrete–representational–abstract sequence (CRA). The CRA sequence has been used successfully to teach students with LD single–digit operations (Mercer & Miller, 1992), place value (Mercer & Miller, 1992; Peterson et al, 1988), operations with regrouping (Flores, 2009; Flores et al, 2019; Flores & Hinton, 2022; Mancl et al, 2012), and algebra (Bundock et al, 2021; Strickland & Maccini, 2013; Witzel, 2005).…”

“…The first stage of CRA is concrete. In previous research, at this stage, students learned a mathematics concept and/or completed a task using manipulative items such as counters (Mercer & Miller, 1992), base-10 blocks (Flores, 2009;Flores et al, 2019;Flores & Hinton, 2022;Mancl et al, 2012;Peterson et al, 1988), interlocking centimeter cubes (Bundock et al, 2021), or algebra tiles (Strickland & Maccini, 2013;Witzel, 2005). The second stage is representational, in which manipulative items are replaced by pictures and drawings.…”