Teaching Algebra to Students with Learning Difficulties: An Investigation of an Explicit Instruction Model

Abstract

Thirty-four matched pairs of sixth-and seventh-grade students were selected from 358 participants in a comparison of an explicit concreteto-representational-to-abstract (CRA) sequence of instruction with traditional instruction for teaching algebraic transformation equations. Each pair of students had been previously labeled with a specific learning disability or as at risk for difficulties in algebra. Students were matched according to achievement score, age, pretest score, and class performance. The same math teacher taught both members of each matched pair, but in different classes. All students were taught in inclusive settings under the instruction of a middle school mathematics teacher. Results indicated that students who learned how to solve algebra transformation equations through CRA outperformed peers receiving traditional instruction on both postinstruction and follow-up tests. Additionally, error pattern analysis indicated that students who used the CRA sequence of instruction performed fewer procedural errors when solving for variables.Abstract thinking requires a person to work with information that is not readily represented at the concrete or pictorial level (Hawker & Cowley, 1997). To work with abstract information is to understand theoretical properties and think beyond what a person can touch or see. On a practical level, an ability to work with abstract concepts allows one to work with predictions of what may happen and expectations about what is happening elsewhere. Abstract knowledge may also be considered a conscious awareness that a symbol stands for some Requests for reprints should be sent to Bradley S. Witzel, Ph.D., Winthrop University, Richard Riley College of Education, Department of Curriculum and Instruction, Rock Hill, SC 29733. Electronic inquiries may be sent to witzelb@winthrop.edu.

Towards the Solution of Abysmal Performance in Mathematics in Junior High Schools: Comparing the Pedagogical Potential of two Designed Interventions

“…The result that DCRAI is more effective for teaching geometry and algebra is consistent with the findings (e.g. Witzel et al 2003;Witzel, 2005;Witzel et al 2008;Stricckland & Maccini, 2010) that CRA instructional approach is effective for teaching mathematics at the middle, high, and secondary schools. However, Witzelet al (2008) and Butler et al (2003) indicate that CRA instructional approach is not a simple process to apply by teachers to mathematics content.…”

“…This is reflected in the findings of Delvin (2000) that for students to understand abstract concepts more easily and solve problems in mathematics, it is important for them to learn precursor concepts in a concrete manner first. One way to simplify students' understanding of abstract concepts is to transform such complex concepts into concrete manipulations and pictorial representations (Witzel, 2003).…”

“…In a research study, Witzel, Mercer, and Miller (2003) worked with 10 general education teachers and over 350 sixth and seventh grade middle school students in inclusive mathematics education classes. The teachers delivered 19 fifty-minute lessons on algebra instruction.…”

Stemming on STEM: A STEM Education Framework for Students with Disabilities

“…Second, the arts play critical roles as scaffolds to help students with disabilities to get into an abstract world. STEM disciplines often contain abstract concepts (Brigham, Scruggs, & Mastropieri, 2011) that require understanding of theoretical properties beyond what students can manipulate on a practical level (Witzel, Mercer, & Miller, 2003). Due to the poor cognitive abilities and related skills students with disabilities have been shown to have, it is important to provide scaffolds with student-participation activities that can simplify abstract concepts in order to develop precursor concepts (Devlin, 2000).…”

A matched-pairs study of interactive computer laboratory activities in a liberal arts math course

“…For example, Lord (1997) reports on a study in which students in a constructivist biology classroom performed better than students taught by the standard approach. A matched pairs study by Witzel, Mercer and Miller (2003) showed that middle school students introduced to the concept of solving algebraic equations through concrete manipulatives outperformed students who received traditional instruction. A study of constructivist-based learning materials in social studies (Karaduman & Gültekin, 2007) shows that such activities can improve student retention of material.…”