Fraction Instruction for Students with Mathematics Disabilities: Comparing Two Teaching Sequences

Abstract.  This study investigated the effects of teaching middle school students with mathematics 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 24 students formed the RA group. The two treatment groups received carefully sequenced instruction over 10 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. Analyses of the data indicated that students in both treatment groups improved overall in their understanding of fraction equivalency from pretest to posttest. On all achievement measures, students in the CRA group had overall higher mean scores than did students in the RA group. Implications for classroom instruction and suggestions for further research are discussed.

[1]  M. Montague,et al.  Meeting the Challenge of Mathematics Reform for Students with LD , 2002 .

[2]  Joseph Calvin Gagnon,et al.  Perceptions and Application of NCTM Standards by Special and General Education Teachers , 2002 .

[3]  Mary T. Brownell,et al.  How Can I Help Students with Learning Disabilities in Algebra? , 2001 .

[4]  Charles A. Hughes,et al.  Effects of a Problem-Solving Strategy on the Introductory Algebra Performance of Secondary Students With Learning Disabilities , 2000 .

[5]  S. Miller,et al.  Teaching Multiplication to Middle School Students with Mental Retardation. , 1998 .

[6]  C. D. Mercer,et al.  Teaching Multiplication to Second Graders in Inclusive Settings. , 1998 .

[7]  Charles A. Hughes,et al.  Mathematics Interventions for Adolescents with Learning Disabilities. , 1997 .

[8]  Frederick J. Brigham.  Best Practices: Teaching Decimals, Fractions, and Percents to Students with Learning Disabilities. , 1996 .

[9]  Carolyn A. Harris.  Teaching Initial Multiplication Skills to Students with Disabilities in General Education Classrooms. , 1995 .

[10]  M. Wagner.  Outcomes for youths with serious emotional disturbance in secondary school and early adulthood. , 1995, The Future of children.

[11]  Mary M. Hatfield.  Use of Manipulative Devices: Elementary School Cooperating Teachers Self-Report , 1994 .

[12]  C. D. Mercer,et al.  CSA: Acquiring and Retaining Math Skills , 1992 .

[13]  C. D. Mercer,et al.  Teaching Students with Learning Problems in Math to Acquire, Understand, and Apply Basic Math Facts , 1992 .

[14]  Arthur J. Baroody,et al.  Meaningful Mathematics Instruction , 1991 .

[15]  D. Carnine,et al.  Making Connections in Mathematics , 1991, Journal of learning disabilities.

[16]  John F. Cawley,et al.  Cross-Sectional Comparisons of the Mathematical Performance of Children with Learning Disabilities , 1989, Journal of learning disabilities.

[17]  Walter Doyle,et al.  Work in Mathematics Classes: The Context of Students' Thinking During Instruction , 1988 .

[18]  Susan K. Peterson,et al.  Teaching Learning Disabled Students Place Value Using the Concrete to Abstract Sequence. , 1988 .

[19]  Merlyn J. Behr,et al.  Number concepts and operations in the middle grades , 1988 .

[20]  J. Hiebert.  Conceptual and procedural knowledge : the case of mathematics , 1987 .

[21]  James Hiebert,et al.  Children's Knowledge of Common and Decimal Fractions , 1985 .

[22]  Steven Pulos,et al.  Proportional reasoning: A review of the literature , 1985 .

[23]  S. W. Armstrong,et al.  Learning Disabilities in Mathematics — Skill Deficits and Remedial Approaches at the Intermediate and Secondary Level , 1982 .

[24]  A. Su,et al.  The National Council of Teachers of Mathematics , 1932, The Mathematical Gazette.