Cognitive Versus Behavioral Models: Promoting Competency in Mathematics Fluency

1. Cognitive Versus Behavioral Models: Promoting Competency in Mathematics Fluency Jennifer Lytle, M.S., Jeremy O’Neal, M.S., Kallie Pitcock, M.S., & Carlen Henington, Ph.D. Mississippi State University INTRODUCTION The role of the School Psychologist is ever evolving. With the advent of Response to Intervention, more emphasis is placed on pre-referral interventions. The goal is to provide support at the secondary level of prevention in tier II. A number of students who do not qualify for special education are lagging behind academically. The use of classroom-friendly interventions should boost achievement for all students, as well as those who require a greater level of support. The use of self-instruction, in which sequential steps are followed to teach students to use covert self-speech, has been suggested as an effective intervention to improve academic function for a multitude of students for a multitude of academic problems. Results from Wood, Rosenberg, and Curran (1993) adds to the body of literature supporting the use of self-instruction for teaching mathematics (Wood et al., 1993). Additionally, the Wood and colleagues results imply that such a method can be time and cost effective, freeing the teacher to spend more time teaching students with special needs. Moreover, Hux, Reid, and Lugert (1994) suggested that strategy instruction may be a promising intervention for some students with acquired neurological injuries (Hux, Reid, & Lugert, 1994, p. 267). Mickler (1984) stated that the self-instruction steps promote the development of a self-appraised understanding of the nature of the task, the necessary steps to complete the task, the determination of success or failure, and if failure, a reappraisal of the nature and appropriate steps of the task (Mickler, 1984). • Independent Variables • Cognitive-Based Intervention Sequence: • 1. Interventionist models solving the math probe written and aloud. • 2. Interventionist solves math probe aloud as the student follows along writing. • 3. Student speaks aloud and writes as they solve the math probe with immediate corrective feedback from the interventionist. • 4. The student completes the math probe written and aloud. • 5. Student completes the math probe using private speech (silently). • 6. The interventionist gives summative feedback and graphs the results of DCPM (results from step 5) with non-contingent reinforcement. • Behavioral- Based Intervention Sequence: • 1. Interventionist models solving the math probe written and silently. • 2. Student uses repeated practice on 1 min. math probes four times with immediate corrective feedback (ICF). On fourth probe the interventionist does not offer ICF (ex: "No that is not correct, the answer is X“) • The interventionist gives summative feedback and graphs the results of DCPM (results from 4th repeated practice) with non-contingent reinforcement. • Integrity & IOA Data • Treatment Integrity/Intervention compliance was obtained for 33% of the sessions with 98% integrity. • IOA was obtained for 33% of complete probes with 100% agreement. • Dependent Variables • Digits Correct Per Minute: • The number of digits recorded correctly in 1 minute (DCPM). • Errors Per Minute: • The number of errors committed in 1 minute (EPM). EPM Intervention Baseline Behavioral Intervention • RESULTS • Kelly obtained her highest DCPM in the behavioral intervention (M = 21.20, Mdn = 23.0) compared to her DCPM under the Cognitive Intervention (M = 16.0, Mdn = 18.0). Based on this divergence, only the behavioral intervention was continued during the remainder of the academic clinic. • Zack obtained his highest DCPM two times, both in the cognitive intervention (M = 23.57, Mdn = 24.0). • Jessie obtained her highest DCPM under the behavior intervention (M = 22.0, Mdn = 22.5) compared to her DCPM under the cognitive intervention (M = 19.0, Mdn=18). Based on this divergence, only the behavioral intervention was continued during the final week of intervention. • For one student, the final intervention session was conducted on the final day of the clinic (i.e., during the end of the summer celebration). This data point was significantly lower than previous data points during intervention. • There were no overlapping data points for baseline or treatment conditions across all participants. DISCUSSION This study showed that all three students improved under both conditions. Two of the three students performed the best under the behavioral condition. Zack performed well and obtained his highest data points in the cognitive conditions. The lower data points achieved by one student on the final day of the clinic indicate the susceptibility of mathematics skills to environmental conditions. It is noteworthy that interventionists should always attempt to determine that the student is healthy and prepared to engage during intervention; otherwise, the students performance may appear variable and poor decisions regarding the responsiveness to the intervention may result. The poor achievement may be due to motivational factors (i.e., performance deficits), rather than a lack of ability (i.e., skill deficit). Limitationsand Future Research • A number of limitations should be considered for this study: (a) the interventions were implemented for a limited time only; (b) the summer academic clinic is laboratory-based and may not resemble a school setting; (c) the amount of time required for the cognitive-based intervention may make it difficult to implement on a school-wide level; and (d) the small, relatively heterogeneous sample may have produced results that may not generalize to other populations/settings. Future Research: Applying the interventions to the classroom setting, more specifically interventions at Tier II & III. Also, the cognitive-based intervention could prove useful to older students as a metacognitive strategy. Previous research utilized self-instruction with students with ADHD. References Hux, Reid, and Lugert (1994) Mickler (1984). Wood, Rosenberg, & Carran (1993). METHOD Participants & Setting Three African American students (2 females, 1 male) in grades 2 and 3 were participants, based on their attendance at a 4-week summer academic clinic. Procedure Instructional level was determined using curriculum-based assessment using DIBELs multi-skill math probes, and baseline was established following a stable or decreasing trend with no more than six days of baseline (due to the limited time allotted for the clinic). Interventions (e.g., cognitive, behavioral) were implemented by a trained interventionist. Students were randomly assigned to a schedule of interventions based on an alternating treatments design (ATD) in which no student received more than two consecutive days of the same intervention. Students attended the summer clinic four days a week and received 5-10 min. for behavioral intervention or 10-15 min. for cognitive interventions. Progress was graphed. Assessment phase: The interventionists conducted CBM to determine instructional level on DIBLES multi-skill math probes. After instructional level was established. At least three probes were given to establish baseline within six days. Intervention Phase: Once a students’ data displayed clear divergence the child was moved to the most effective intervention for that individual. Daily pre-intervention multi-skill grade level probes were given to establish generalization of the skills learned in intervention. DCPM