Award Date


Degree Type


Degree Name

Doctor of Education (EdD)


Special Education

First Committee Member

Susan P. Miller

Number of Pages



This study investigated the effects of teaching middle-school students with mild to moderate disabilities equivalent fraction concepts and procedures using the concrete-representational-abstract (CRA) instructional sequence or the representational-abstract (RA) instructional sequence. Twenty-six students formed the CRA group, and twenty-four students formed the RA group, while sixty-five eighth-grade students without disabilities served as a contrast group. The two treatment groups received carefully sequenced instruction over ten lessons. The only difference between the two treatment groups was that the CRA group used concrete manipulative devices for the first three lessons while the RA group used representational drawings. The eighth-grade contrast group received traditional instruction using a basal text; Analyses of the data indicated that students in the treatment groups scored significantly higher than did students in the contrast group on items demonstrating conceptual knowledge, had higher scores on the attitude measure, and overall improved their understanding of fraction equivalency from pretest to posttest. Students in the treatment groups performed as well as did contrast group students on abstract problems. On word problems containing embedded fraction equivalencies, students in the CRA group had significantly higher scores than did contrast group students. On all achievement measures, students in the CRA group had overall higher mean scores than did students in the RA group although the results were not statistically significant; Some conclusions were drawn as a result of this study. First, students who used manipulative devices had a better understanding of fraction equivalency than those who did not. Second, training in the use of graphic representations had a positive effect on students' abilities to solve abstract problems and word problems. Students in both treatment groups used graphic representations to solve problems, while students in the contrast group did not. Even though students in the contrast group solved problems correctly when they were presented abstractly, they appeared not to transfer their knowledge to problems presented graphically or to word problems. Implications for classroom instruction and suggestions for further research are discussed in the last chapter.


Adolescents; Disabilities; Fraction Instruction; Learning Disabilities; Middle School Students; Sequences; Students; Teaching

Controlled Subject

Special education; Mathematics--Study and teaching; Education, Secondary

File Format


File Size

3553.28 KB

Degree Grantor

University of Nevada, Las Vegas




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