Award Date


Degree Type


Degree Name

Doctor of Philosophy in Special Education


Special Education

Advisor 1

Susan Miller, Committee Chair

First Committee Member

Nancy Sileo

Second Committee Member

Pamela Campbell

Third Committee Member

Gregory Schraw

Number of Pages



This study involved an investigation of the effects of strategy instruction integrated with the concrete-representational-abstract teaching sequence on students with learning disabilities. A multiple probe design across subjects with one replication was used in this study. Two sets of data were analyzed to determine effectiveness of the independent variable (intervention lessons). The first data set consisted of pre and posttest percentage scores and the second data set consisted of baseline, intervention, and maintenance probe scores that were collected throughout the study per the parameters of a multiple probe design. The probe scores were plotted in line graph format and analyzed using visual analysis related to level, trend, and variability of the data points. A total of six fifth grade students (five males and one female) with learning disabilities participated in this study. The participants ranged in age from 10 years 10 months to 12 years 0 months. Each participant met the State of Nevada Administrative Code eligibility criteria for specific learning disabilities and failed to meet their school district's standards related to subtraction with regrouping. The six participants were divided into two triads. The students' learning disability teacher staggered the introduction of the scripted intervention lessons according to the parameters of a multiple probe design. Each intervention lesson contained pedagogically sound systematic and explicit instruction which included (a) an advance organizer, (b) a describe and model stage of instruction, (c) a guided practice stage of instruction, (d) an independent practice stage of instruction, and (e) a problem solving stage of instruction. Additionally, the lessons followed the concrete-representation-abstract teaching sequence. The principal and student investigator observed 20% of the total lessons to ensure that the learning disability teacher implemented the lessons with fidelity. The percentage of agreement between the two observers was 99% indicating a high level of implementation fidelity. Interscorer reliability was established before analyzing the data sets. The learning disability teacher scored all pre-, post-, and maintenance tests for the participants and the student investigator scored 20% of the pre-, post-, and maintenance tests. Interscorer reliability was determined to be 100%. A comparison of pre- and posttests revealed that participants' performance increased on the posttests. As a group, the participants raised their total number of correct responses from an average of 6 correct answers to 14.3 correct answers out of a total of 20 computation subtraction problems that required regrouping to solve. Participants also achieved an average of 21.6 more correct digits from pretests scores to posttest scores on a fluency measure that contained computation subtraction problems that required regrouping. Participants increased the number of correct responses on average by 4.3 on word problems that required subtraction with regrouping skills to be applied. Participants maintained these new skills over time and indicated high levels of satisfaction with regard to the mathematics intervention program. Finally, implications of the current study and suggestion for future research are discussed. With regard to the ongoing probe data, all six participants demonstrated an increase in level from baseline condition to intervention condition. This increase in level was sustained during the maintenance condition for all six participants. All six participants demonstrated a relatively stable flat trend during the intervention condition. With regard to variability, Participant 1 was the only one who demonstrated little variability during intervention condition. Participants 2,3,4,5, and 6 each demonstrated notable variability during the intervention condition and had to repeat 2 to 6 sessions in which they did not attain mastery criteria on their first try.


Addition with regrouping; Concrete-representational-abstract teaching sequence; Explicit instruction; Fifth-grade; Learning disabilities; Mathematics; Subtraction instruction; Subtraction with regrouping


Elementary Education and Teaching | Special Education and Teaching

File Format


Degree Grantor

University of Nevada, Las Vegas




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