#### Title

### Overcoming Mathematics Difficulties using CRA Interventions

#### Format

Individual Presentation

#### First Presenter's Institution

Winthrop University

#### Second Presenter's Institution

University of Utah

#### Third Presenter's Institution

NA

#### Fourth Presenter's Institution

NA

#### Fifth Presenter's Institution

NA

#### Location

Harborside East & West

#### Strand #1

Academic Achievement & School Leadership

#### Relevance

Relevancy of this proposal lies in its focus on ensuring that students with disabilities and at-risk concerns succeed despite the increasing demands for mathematics learning. According to the 2015 Nations Report Card, the achievement gap in mathematics has increased since 2013 for students with disabilities, poverty, minority race / ethnicity, and even those living in rural settings for both 4^{th} and 8^{th} graders (NCES, 2016). A goal of mathematics interventions should be to close the achievement gap (Strand 1 – HEAD: Academic Achievement and Leadership). Foci for this presentation include, but are not limited to, turning around low performing schools, improving student outcomes in high poverty schools, improving mathematics instruction and intervention for the betterment of students with disabilities and at-risk concerns all through the use of empirically-validated math interventions.

#### Brief Program Description

Students with disabilities and at-risk concerns frequently experience difficulties with mathematics standards which demand conceptual reasoning along with procedural facility. One research-supported intervention strategy with a history of improving students’ outcomes is the concrete to representational to abstract sequence of instruction (CRA). In this session, participants will learn how to design and implement CRA interventions with whole and rational numbers.

#### Summary

The need for achievement in mathematics has been linked to technical degree completion (Moore & Shulock, 2010), career opportunities (University of California - Irvine, 2010), and daily living (Department of Business, Innovation, and Skills, 2012). As the importance of mathematics has been increasingly realized, so too are the emphases on graduation requirements and math standards (National Mathematics Advisory Panel, 2008). Recently, states’ standards have an increased focus on conceptual understanding and reasoning beyond rote procedural knowledge.

Despite the increased emphasis, students have not improved in their mathematics achievement, particularly students with disabilities and at-risk concerns. According to the 2015 Nations Report Card, the achievement gap in mathematics has increased since 2013 for students with disabilities, poverty, minority race / ethnicity, and even those living in rural settings for both 4^{th} and 8^{th} graders (NCES, 2016).

In order to bridge this achievement gap, students need improved instruction and intervention, particularly in areas of frequent difficulty such as computation of whole and rational numbers (Gersten et al., 2009; Hoffer et al., 2007). It is critical that students reach proficiency in these essential areas before they enroll in formal Algebra (Gersten, Clarke, & Witzel, 2007; Siegler & Pyke, 2012).

One research-supported strategy that has a history of improving mathematics outcomes of students with disabilities and at-risk concerns is the concrete to representational to abstract sequence of instruction (CRA). CRA has been featured in the National Math Panel’s Final Report (2008) and numerous IES Practice Guides (Gersten et al., 2009) as an empirically-validated method that can be adapted to critical areas of mathematics. CRA has demonstrated improved student performance for learning computational facts (Flores, Hinton, & Strozier, 2014), rational numbers (Butler, Miller, Crehan, Babbitt, & Pierce, 2003; Witzel, Riccomini, & Tiberghien, 2010) and even secondary mathematics (Witzel, 2005; Witzel, Mercer, & Miller, 2003). While CRA appears to be one of the more effective mathematics intervention strategies, it requires professional development to ensure accurate instructional steps at each learning level. In this session, participants will learn how to plan and delivery CRA interventions using examples of whole and rational numbers.

#### Evidence

- Examples and demonstrations as evidenced in the following research articles:

Flores, M. M. (2010). Using the concrete-representational-abstract sequence to teach subtraction with regrouping to students at risk for failure. *Remedial and Special Education, 31*(3), 195-207.

Flores, M. M., Hinton, V. M., & Strozier, S. D. (2014). Teaching subtraction and multiplication with regrouping using the concrete-representational-abstract sequence and strategic instruction model. *Learning Disabilities Research and Practice, 29*,75- 88.

Witzel, B. S. (2005). Using CRAto teach algebra to students with math difficulties in inclusive settings. *Learning Disabilities: A Contemporary Journal, 3*(2), 53-64.

Witzel, B. S., Mercer, C. D., & Miller, M.D. (2003). Teaching algebra to students with learning difficulties: an investigation of an explicit instruction model. *Learning Disabilities Research & Practice, 18, *121-131.

Witzel, B. S., Riccomini, P. J. & Tiberghien, T. (2010). A fractions intervention in high school. *MathMate, 34*(1), 15-19.

As part of the demonstrations, we intend to use number line / linear models as evidenced in the following research:

Geary, D. C. (2011). Cognitive predictors of individual differences in achievement growth in mathematics: A five year longitudinal study. *Developmental Psychology, 47*, 1539-1552.

Kiuhara, S. A., Witzel, B., Dai, T., & Rouse, A. G. *Developing math reasoning and understanding of fractions via writing-to-learn arguments within the SRSD instructional framework*. Manuscript in preparation.

Siegler, R.S., Duncan, G.J., Davis-Kean, P.E., Duckworth, K., Claessens, A., Engel, M., Susperreguy, M.I., & Chen, M. (2012). Early predictors of high school mathematics achievement. *Psychological Science, 23*, 691–697.

The description of the concrete to representational to abstract sequence of instruction (CRA) model is based on the following policy papers and meta-analytic findings:

Gersten, R., Clarke, B., & Witzel, B. (2008). Onwards to algebra: The case for mathematics interventions for struggling students in the intermediate grades. *Compass Learning*. [Available online at http://www.compasslearning.com/files/Mathemail.pdf].

Hughes, E. M., Witzel, B. S., Riccomini, P. J., Fries, K. M., & Kanyonga, G. (2014). A meta-analysis of algebra interventions for students with learning disabilities and struggling learners. *Journal of the International Association of Special Education, 15(1), *36-47.

Since CRA builds based on mathematics language, we use the following to support our use accurate verbal reasoning within the CRA model:

Kiuhara, S. A., & Witzel, B. S. (2014). Math literacy strategies for students with learning difficulties. *Childhood Education, 90*(3), 234-238.

#### Biographical Sketch

**Bradley Witzel, Ph.D.,** is an award winning teacher and researcher who works as a full professor and program director of the MEd in Intervention at Winthrop University, the flagship education college for the state of South Carolina. As a classroom teacher he worked in multiple settings teaching mainly math and science to high achieving students with disabilities and at-risk concerns. He received his Ph.D. from the University of Florida. Dr. Witzel has authored dozens of research and practitioner articles as well as nine books, including the recently published *Bridging the Arithmetic to Algebra Gap * through the Council for Exceptional Children, *Teaching Elementary Mathematics to Struggling Learners* through Guilford Press, and the bestselling *RtI in Math* and *Building Number Sense *through Corwin Press. He is a Governing Board Member of the Southeast Regional Educational Laboratory (REL-SE), funded by the Institute of Education Sciences (IES), and a member of multiple state level MTSS and RtI governing boards. Dr. Witzel serves as the editor of *Focus on Inclusive Education* through the Association of Childhood Education International (ACEI) and recently served as an author/panelist on the IES practice guide *Assisting Students Struggling with Mathematics *as well as an invited reviewer of the National Mathematics Advisory Panel reports. Most importantly, he is a father of two, husband of an educator, and son of two educators.

**Sharlene Kiuhara, Ph.D.**, focuses her research on developing interventions that improve teaching practices and learning outcomes for K-12 students who have high incidence disabilities. Her current work investigates the effects of using the Self-Regulated Strategy Development framework (a strategic approach for developing written expression skills and self-regulation of the writing process) for constructing arguments within a multi-tiered system of instructional supports in language arts, math, and science classrooms.

#### Keyword Descriptors

Computation, Algebra, Rational numbers, Math, MTSS, RtI, Interventions, Disabilities, At-risk

#### Presentation Year

2017

#### Start Date

3-7-2017 4:00 PM

#### End Date

3-7-2017 5:30 PM

#### Recommended Citation

Witzel, Bradley Steven and Kiuhara, Sharlene A., "Overcoming Mathematics Difficulties using CRA Interventions" (2017). *National Youth Advocacy and Resilience Conference*. 128.

https://digitalcommons.georgiasouthern.edu/nyar_savannah/2017/2017/128

Overcoming Mathematics Difficulties using CRA Interventions

Harborside East & West

Students with disabilities and at-risk concerns frequently experience difficulties with mathematics standards which demand conceptual reasoning along with procedural facility. One research-supported intervention strategy with a history of improving students’ outcomes is the concrete to representational to abstract sequence of instruction (CRA). In this session, participants will learn how to design and implement CRA interventions with whole and rational numbers.