Efficacy of Two Mathematics Interventions for Enhancing Fluency with Elementary Students

An alternating treatments design was used to evaluate two curriculum-based mathematics interventions designed to enhance fluency with three elementary school students. Results indicate that both the Math to Mastery (MTM) intervention and the Cover, Copy, Compare (CCC) intervention were effective at increasing mathematics fluency, as measured by digits correct per min, for all students. However, MTM was more effective than CCC for two of the three students. Follow-up data taken 6 and 18 days following termination of the intervention phase indicated that all participants achieving mastery performance maintained mastery levels across both interventions.     

Prescriptive Analysis: Further Individualization of Hypothesis Testing in Brief Experimental Analysis of Reading Fluency

Brief experimental analyses (BEA) have been used to identify effective individualized interventions for improving reading fluency with school-age children. Interventions involving incentives, modeling, repeated reading, and error correction are most often tested in a BEA. However, these interventions are rarely modified according to individual student needs. The current study examined the effects of varied levels of modeling (passage, sentence, word) and varied contingencies (tracking and fluency) on fluency in non-treated high-word overlap passages and general outcome measure passages. BEA-identified interventions were effective for improving reading fluency on non-treated passages for both second grade students and the third grade student. Notably, the effects reversed when intervention was withdrawn with one of the second grade students. Results are discussed in terms of considerations in the application of BEA technology in the schools.     

Comparing Brief Experimental Analysis and Teacher Judgment for Selecting Early Reading Interventions

The purpose of this study was to examine the use of brief experimental analysis (BEA) to identify early reading interventions for students in the primary grades and to compare teachers’ judgments about their students’ early reading intervention needs to BEA results. In addition, the research was conducted to explore how teachers make decisions regarding early reading intervention selection and evaluation. Three teachers and three elementary students (two kindergarten and one second grade) participated in the study. A BEA using a multielement design with mini-reversals was used to test the effects of four different interventions. Each teacher selected an intervention that she judged to be the most promising for her student. An extended analysis using an alternating treatments design compared the relative effects of the BEA-identified intervention and the teacher-identified intervention across time. The teachers were interviewed before and after selecting and implementing the interventions. The extended analysis results showed that the BEA-identified intervention was more effective than the teacher-identified intervention for all participants. Initial and final interview findings revealed that the teachers reported using data to make intervention decisions, but with limited specificity and in some cases, misjudgments. The results are discussed in regard to limitations and future research.     

An Application of Brief Experimental Analysis with Early Writing

Students’ poor performance on national assessments of writing suggests that educators need effective approaches to assess and intervene with writing problems. Brief experimental analysis (BEA) has supporting evidence for identifying interventions in reading, but little research has investigated BEA with writing. Early writing is an especially important period for students, and the current study sought to extend BEA research in early writing. Results showed that BEAs for 3 first grade students identified promising writing interventions, and extended analyses showed improved performance for each student following implementation of the interventions. Implications for future research in direct assessment and intervention are discussed.     

Increasing Elementary-aged Students’ Reading Fluency with Small-group Interventions: A Comparison of Repeated Reading, Listening Passage Preview, and Listening Only Strategies

Although reading fluency is one of the five essential early-reading skills students must develop, many elementary-aged students in the United States do not read age-appropriate material fluently. As such, small-group interventions are practical and often more time efficient than individualized interventions aimed to address this problem. However, few small-group interventions targeting students’ reading fluency have been empirically evaluated. The primary purpose of this study was to examine three small-group reading interventions that have been used to improve students’ reading fluency (repeated reading, listening passage preview, and listening only). Using an alternating-treatments design, the effects of each intervention were evaluated with four-second-grade students with average to below average reading skills. Students’ words read correctly per minute (immediately following and 2 days after intervention) served as the outcome measures. Results supported the repeated reading intervention, followed by listening passage preview, as most effective. Findings also suggested that improvements from each intervention remained 2 days later.     

Brief Experimental Analysis of Written Letter Formation: Single-Case Demonstration

Many students experience difficulty in acquiring basic writing skills and educators need to efficiently address those deficits by implementing an intervention with a high likelihood for success. The current article demonstrates the utility of using a brief experimental analysis (BEA) to identify a letter-formation intervention for a second-grade student with handwriting difficulties. The results suggested that the BEA led to differentiated results for letter formation interventions, and the identified intervention was implemented for 8 weeks with moderate effectiveness. Suggestions for future research are included.     

Using Brief Experimental Analysis to Select Oral Reading Interventions: An Investigation of Treatment Utility

This study examined the treatment utility of brief experimental analysis for selecting skill-based oral reading interventions that targeted acquisition and fluency. Two second and one third grade student served as participants. The potentially most and least effective instructional packages identified from the brief experimental analysis for each student were alternated during an extended analysis phase. The instructional components that were compared were based on an ease of implementation hierarchy, with the brief experimental analysis used to select the hypothesized most effective instructional package for oral reading. Visual analysis of extended analysis data revealed that the hypothesized most effective combination of instructional components identified from the brief analysis produced greater initial gains in reading for two children (i.e., over 29 and 21 intervention days) and greater gains in reading throughout the extended analysis phase for the third child. Thus, the investigation provided preliminary evidence for the treatment utility of using brief experimental analysis to select effective and efficient oral reading instructional interventions. Implications, limitations, and future research topics are discussed.     

Brief experimental analysis of early reading interventions

The purpose of this study was to investigate how brief experimental analyses (BEAs) could be used to identify effective interventions for Kindergartners (2 girls and 2 boys, 5 years and 7-10 months old) with low performance and/or growth slope in letter sound fluency (LSF). Interventions were tested within a multielement design with brief mini-reversals until an intervention yielding at least 20% improvement on a specific subskill measure or a curriculum-based measure of LSF was identified. BEA-identified interventions were implemented one-on-one for 5 to 9 weeks. A multiple-baseline design across participants showed large intervention effects (average adjusted d = 2.4) on general outcome measures, supporting treatment validity of BEAs. Findings extend the BEA literature to younger participants, early reading interventions, and early reading measures.     

An Experimental Analysis of Mathematics Instructional Components: Examining the Effects of Student-Selected Versus Empirically-Selected Interventions

Within the context of an experimental analysis, the current study examined the effects of student- and empirically-selected interventions on the mathematics computational fluency of three elementary-aged students. For all of the participants, the empirically-selected intervention resulted in higher levels of computational fluency then the student-selected intervention. These results suggest that empirically-selected interventions may enhance the mathematics computational fluency of students experiencing mathematics problems. However, individual responsiveness to empirically-selected interventions suggests the importance of conducting brief experimental analyses to determine the most efficacious intervention. The implication of these results for intervention selection and incorporating choice-making opportunities into academic interventions are discussed.     

A Comparison of Taped Problems With and Without a Brief Post-Treatment Assessment on Multiplication Fluency

An adapted alternating treatments design was used to compare the effectiveness of a taped-problems (TP) intervention with TP and an additional immediate assessment (TP + AIA) on the multiplication fluency of six fifth-grade students. During TP, the students listened to a tape playing a series of multiplication problems and answers three times. Students were instructed to try to beat the tape by writing each answer before they heard it on the tape. The interval between each problem and answer was varied as the problems were repeated. For the TP + AIA condition, immediately after completing TP, students completed an extra assessment sheet consisting of the same problems heard on the tape. Results showed increases in math-fact fluency across both treatment sets of problems (TP and TP + AIA) and a control set of problems. However, results varied across students and only two of the students showed meaningful gains when the TP was supplemented with the AIA. Implications and directions for future research are discussed.     

Promoting Generalization of Oral Reading Fluency: Providing Drill versus Practice Opportunities

Extensive evidence exists demonstrating the benefits of repeated readings (RR) interventions at increasing students’ fluency on intervention passages. Few studies however have examined the extent to which repeatedly reading one passage improves students’ reading fluency on similar passages. Using an alternating treatment design, we examined the extent to which two interventions resulted in improvements in students’ fluency on generalization passages. While both interventions incorporated RR, one intervention involved students reading one passage four times and the other involved students reading two similar passages each twice. Intervention effects were evaluated by having students read a generalization passage prior to and following intervention implementation. Results indicate that both interventions were effective in increasing students reading fluency on generalization passages. For 3 participants the RR intervention produced greater gains in fluency on the generalization passages, while data for the remaining 3 participants are inconclusive. Implications of these findings for practice and for better understanding application of the instructional hierarchy to the development of reading interventions are discussed.

Promoting Generalization of Reading: A Comparison of Two Fluency-Based Interventions for Improving General Education Student’s Oral Reading Rate

The generalization effects of empirically-supported fluency-based reading interventions have been largely ignored. The purpose of this study was to evaluate the effects of two fluency-based reading interventions, Repeated Readings and Multiple Exemplars, on elementary-aged children’s immediate and generalized oral reading fluency rate. Using a within-subjects group design, a total of 42 second (n = 25) and fourth (n = 17) grade general education students were administered both interventions and their generalized responding to passages containing high word and medium word overlap was assessed. Results indicated that children’s oral fluency on intervention passages was significantly greater during the Repeated Readings intervention. However, children’s oral reading fluency on generalization passages containing medium word overlap was significantly greater following the Multiple Exemplars intervention. This difference was however possibly due to the Multiple Exemplar medium word overlap passage being easier for students to read. No significant differences between the two interventions were observed in children’s oral reading fluency on generalization passages containing high word overlap. Implications and limitations of the study are discussed in relation to improving students’ reading fluency on generalization passages.     

Evaluating Generalization of Addition-Fact Fluency Using the Taped-Problems Procedure in a Second-Grade Classroom

A multiple-baseline design across math-fact sets was used to evaluate the effects of a taped-problems intervention on students’ performance with addition facts and their inverses in an intact, rural, second-grade classroom. Results suggested that the procedure was effective in improving fluency on math facts as well as their inverses. Across 3 sets of math facts, 15 students increased their fluency (i.e., average increases of 5 digits correct per min or more) on math-problem sets and these improvements were maintained over time. Additionally, results provide evidence that these increases generalized to inverse-problem sets. However, 4 students showed little gains (i.e., average increases of fewer than 5 digits correct per min) on math problems. Discussion focuses on evaluating academic interventions for generalization and directions for future research.     

Imagine Math Facts Improves Multiplication Fact Fluency in Third-Grade Students

Math fact fluency is foundational for later mathematics education. Unfortunately, many students across the nation continue to struggle with these core skills. Computer-assisted instruction may be a potentially valuable tool for improving math fact fluency due to its ability to differentiate instruction at the student level, provide added practice opportunities, and improve student interest and motivation. However, research is currently lacking to demonstrate the effectiveness of many computer-assisted interventions. One such program is Timez Attack by Imagine Math Facts, a multiplication fact fluency training program for elementary-age students. Using a multiple baseline across groups design, we sought to determine the effectiveness of Timez Attack in improving math fact fluency in third-grade students. We randomly assigned 63 students to three study groups and regularly assessed for multiplication fact fluency for 12 weeks. Compared to baseline averages, all three study groups demonstrated improved multiplication fact fluency following the onset of the intervention phase. Further, performance during a follow-up maintenance phase demonstrated persistence of learning. The results of this study suggest that Timez Attack may be an effective computer-assisted instruction option for improving multiplication fact fluency in elementary-age students.     

Evaluating the effect of parent reading interventions on improving reading fluency of students with reading difficulties

The current study examines the effect of parent reading interventions on the reading fluency of students with reading disabilities. The experimental procedure was carried out in two stages. In the first stage, the Brief Experimental Analysis procedure was followed to determine the most effective reading fluency intervention for all participants, and in the next step, the parental delivery of the selected intervention procedure took place. Brief experimental analysis was used to identify appropriate reading fluency intervention for each participant. Parents were trained to use the intervention strategies with their children. They implemented the procedures during parent‐tutoring sessions at home and results were measured continuously to determine whether generalization occurred. Parent and child satisfaction with the interventions was assessed. Results demonstrated generalized increases in reading fluency in both high‐word‐overlap and low‐word‐overlap passages as a function of parent tutoring. Also, acceptability ratings by children and their parents indicated that they viewed the interventions as acceptable and effective.     

Performance Indicators in Math: Implications for Brief Experimental Analysis of Academic Performance

Brief experimental analysis (BEA) can be used to specify intervention characteristics that produce positive learning gains for individual students. A key challenge to the use of BEA for intervention planning is the identification of performance indicators (including topography of the skill, measurement characteristics, and decision criteria) that meaningfully relate to longer term success in the learning environment. This study investigates the utility of various curriculum-based assessment and measurement estimates of mathematics performance for predicting functional outcomes (i.e., retention of learned skills over time and faster learning of related content in the future). All children in grades 2–5 at the participating school participated in protocol-based computational fluency-building intervention 4 days per week for an entire school year. Specific criteria were applied each week to systematically increase intervention difficulty classwide according to a pre-established sequence of computational skill objectives. Three measurements were routinely obtained. Each week children completed a timed probe of the skill for which intervention was currently occurring and a timed probe of previously mastered skills from the sequence of computational skill objectives. Each month, all children completed a timed probe of mathematics skills representing computational skills that students were expected to master by year’s end at each grade level. At all grade levels, learning a skill that appeared early in the hierarchy or sequence of skills related positively to learning of future related and more complex computational skills. Fluency criteria were specified that predicted retention of the skill over several months.     

Intervening with Multiplication Fact Difficulties: Examining the Utility of the Instructional Hierarchy to Target Interventions

Examining the use of conceptual frameworks such as the instructional hierarchy (IH) to drive academic interventions represents an important area of inquiry in order to understand why an intervention was effective. However, to date, the IH has only been examined retroactively to explain the effectiveness of math interventions and has not been used to drive intervention implementation based on students’ needs. Therefore, the current study used a multiple baseline single-case design to examine the utility of the IH to determine an appropriately targeted acquisition (incremental rehearsal) or proficiency (timed drill) intervention for difficulties with multiplication facts. Students first received the contraindicated intervention (i.e., non-targeted) and then their correctly targeted intervention. Results showed that all students demonstrated greater fluency growth during their targeted intervention and that students in need of an acquisition intervention also demonstrated greater multiplication fact retention and growth rate during their targeted intervention. The utility of the IH as a heuristic to correctly target interventions based on students’ baseline skill levels is discussed.

     

Brief Experimental Analysis of Spanish Reading Fluency: An Exploratory Evaluation

Brief experimental analyses of reading fluency are useful for identifying effective interventions for improving reading fluency. The current study extends previous research by conducting an exploratory evaluation of brief experimental analyses of reading fluency for Spanish reading. A 10-year old Hispanic male presented with reading fluency deficits for English and Spanish reading. Brief experimental analyses of English and Spanish reading identified distinct interventions for each which increased oral reading fluency. Intervention procedures evaluated during brief experimental analyses included listening passage preview, repeated readings, and reward. Replication of analyses was conducted to examine changes in instructional need over time. For English reading, the intervention identified during the initial analysis (i.e., listening passage preview with repeated readings) was identified as the most effective when the analysis was replicated. For Spanish reading, listening passage preview was identified as the most effective intervention during the initial analysis, while repeated readings was identified as most effective when the analysis was replicated. Results are discussed in terms of future research given the exploratory nature of the current study.     

Using Small-Group Instruction to Improve Students' Reading Fluency: An Evaluation of the Existing Research

Reading fluency is necessary for reading comprehension, but approximately 40% of U.S. fourth-grade students have inadequate reading fluency skills. Because small-group (SG) instruction is often used as a first line of intervention for struggling readers, SG instruction targeting deficiencies in text reading fluency ought to be part of every school's intervention toolbox. The authors summarize the existing research on instruction and interventions that specifically targets reading fluency and is implemented by an adult with 3 or more students at once. Key findings revealed that most studies used a single-case design, nearly all studies were rated positively in terms of methodological quality, and the majority of participants significantly improved as a result of receiving SG intervention. Furthermore, of the five studies examining comparable SG and 1-on-1 interventions, 79% of the students performed equally well from both interventions. Implications and several recommendations for future research are discussed.     

Examining Immediate and Maintenance Effects of a Reading Intervention Package on Generalization Materials: Individual Verses Group Implementation

Fluency has been identified as an important outcome of effective reading instruction, and intervention packages utilizing the method of repeated readings have been shown to improve oral reading fluency. In order to improve the efficiency of these intervention packages, more research is needed on the effectiveness of small group reading interventions. An alternating treatments design was used to compare the effects of two versions of an intervention package that included repeated readings on generalization and maintenance of oral reading rate for 6 second grade students. Both intervention packages included listening passage preview, repeated readings, error correction, and contingent reward. The intervention packages differed only in whether intervention components were provided to students individually or in groups of three. Gains in oral reading rate were observed across conditions, with individual and small group interventions resulting in comparable gains for most participants. Individual differences in performance and implications for reading instruction are discussed.