Cover-Copy-Compare for Multiplication With Students With Emotional and Behavioral Disorders: A Brief Report

Abstract

A multiple-baseline across participants design was used to investigate the effect of the Cover-Copy-Compare (CCC) intervention on multiplication-fact fluency for students with emotional and behavioral disorders (EBD). Although CCC is a well-researched intervention for mathematics, limited research has been conducted with students with EBD even though these students often struggle academically. Results indicate that a functional relation was established between CCC and an improved number of digits correct per minute for multiplication problems for only one of three elementary-age boys with EBD. Tau-U effect sizes ranged from no effect for one participant to a large effect for another participant. The length of the intervention and the initial level of a student’s skills may be related to the effectiveness of CCC for students with EBD and should be explored in future studies.

Keywords

emotional disturbance disorders/disabilities academic interventions elementary age group

The number of students struggling with mathematics in the United States is alarming. According to the latest Nation’s Report Card statistics, only 40% of fourth-grade students are at or above a proficient level in mathematics (National Center for Education Statistics, 2017). These data also illustrate the gap between the performance of students with and without disabilities; only 16% of students with disabilities (compared with 44% of students without disabilities) performed at or above the proficient level in fourth-grade mathematics. These statistics confirm the need for schools to prioritize effective mathematics instruction and intervention for students with disabilities. Students with emotional and behavioral disorders (EBD) appear to be at particular risk for low performance in mathematics.

Although students with EBD are primarily characterized by emotional and behavioral issues, they also struggle academically. Research has indicated that students with EBD perform significantly below their peers in all academic areas. For example, Lane, Barton-Arwood, Nelson, and Wehby (2008) found that students with EBD in a self-contained school performed well below the 25th percentile on reading, mathematics, and writing measures. In their meta-analysis, Reid, Gonzalez, Nordness, Trout, and Epstein (2004) documented similar difficulties, noting the overall achievement level of students with EBD was at the 25^th percentile, with moderate to large overall differences between their performance and their peers without disabilities.

Some evidence suggests students with EBD perform just as poorly as their peers with learning disabilities (LD) in mathematics (Reid et al., 2004). Multiple studies note the importance of addressing these difficulties early, as deficits in mathematics worsen as students with EBD get older (Lane et al., 2008). In addition, although behavioral variables (i.e., school adjustment, externalizing and internalizing behavior patterns) predicted broad reading and writing performance, they did not predict mathematics performance (Lane et al., 2008), suggesting that behavioral interventions alone are not sufficient to address the mathematics difficulties of students with EBD. Unfortunately, there remains a limited amount of scientific research on academic interventions for this population (Lane, Jolivette, Conroy, & Nelson, 2011), including those that target mathematics (Templeton, Neel, & Blood, 2008).

Research indicates being able to respond fluently to basic mathematics problems predicts success in higher level mathematics (Stading, Williams, & McLaughlin, 1996). Students who do not master mathematical facts can end up more frustrated with complex mathematics, have less cognitive attention and energy for more complicated procedures, and fall further behind their peers as they advance (Poncy, Skinner, & Axtell, 2010). A variety of interventions have explored how to improve students’ fact fluency, including flashcard drills, mnemonic strategies, peer tutoring, taped problems, and computer-delivered practice sessions (Burns, Codding, Boice, & Lukito, 2010; Nelson, Burns, Kanive, & Ysseldyke, 2013). Although some have produced large changes in student performance, not all interventions help students master fact fluency and catch up to their peers (Nelson et al., 2013). There is also a need to identify interventions that are effective for particular subgroups of students. For example, a meta-analysis by Burns and colleagues (2010) highlighted that interventions that focus on the acquisition of missing mathematical skills produced the largest effects on the performance for students whose skills are in the frustrational range.

Cover-Copy-Compare Intervention

Given the importance of mathematical fact acquisition, schools need to provide struggling students, such as those with EBD, with intervention targeting this subskill. One acquisition intervention that serves this purpose is the cover-copy-compare (CCC) procedure. The technique was originally developed by McGuigan (1975) to improve students’ spelling performance, but was later adapted for use with mathematics facts (i.e., addition, subtraction, multiplication, and division). The traditional CCC procedure involves the following steps: (a) look at and study a completed problem; (b) cover the problem; (c) write the problem and answer from memory; (d) uncover the sample problem; (e) compare own answer with the sample; and (f) move on to the next problem if correct, start over with the first step if incorrect. These steps have shown to be an effective and efficient intervention for mathematical fact acquisition and fluency (Becker, McLaughlin, Weber, & Gower, 2009; Cieslar, McLaughlin, & Derby, 2008; Hayden & McLaughlin, 2004). The intervention utilizes a behavioral approach with explicit instruction and guided practice (Poncy, McCallum, & Schmitt, 2010). It also could uniquely benefit students with EBD because although student behavior is guided, students are required to self-regulate their own learning through checking their own work.

The research on CCC has documented its effectiveness for a variety of mathematical skills including the fluency of multiplication and division facts (Becker et al., 2009; Cieslar et al., 2008; Hayden & McLaughlin, 2004). In reviewing the literature, we identified only two studies published in the past 30 years on using CCC with students with EBD. Skinner, Turco, Beatty, and Rasavage (1989) utilized a multiple-baseline design with two fourth graders and two 10th graders working on multiplication facts at a university-affiliated school. Although one fourth-grade student refused to follow the procedures, the CCC intervention improved the rate of correct responses and accuracy of the three remaining participants. Then Skinner, Ford, and Yunker (1991) conducted an alternating treatment design with two elementary students with EBD at a university-affiliated residential school. Students alternated between CCC problem responses produced verbally and in writing. Only one participant showed improvement in his multiplication fluency (digits correct per minute) and accuracy when required to produce written repsonses, but both participants made improvements when required to provide verbal responses.

Purpose

There is limited research on mathematics interventions for students with EBD (Templeton et al., 2008). Research examining the effects of CCC for improving fact fluency for students with EBD is scarce, particularly in recent years. In addition, the two extant studies (Skinner et al., 1991; Skinner et al., 1989) are dated and were both conducted in university-affiliated schools. The purpose of the present study was to expand the literature on using CCC to improve the multiplication skills of students with EBD. Specifically, the study addressed the following research question:

Research Question 1: What is the effect of CCC multiplication fact fluency for three elementary students with EBD in a public school?

Method

Design

This project utilized a multiple-baseline across participants design to evaluate the effectiveness of CCC for multiplication fact fluency. The treatment variable, CCC, was introduced to each of the three students based on staggered start dates and stability of the baseline data. Stability was defined as baseline data without an ascending trend (i.e., last three successive data points not in an ascending trend) and data with little variability (i.e., data points fall within M +/- 1/3M).

Participants

The three male participants all attended a public regional school for students with EBD in the Midwest. The participants all attended this alternative placement because they were identified as students with EBD per state special education guidelines and had behavioral issues that hindered their academic progress. Their classroom teacher reported that they had emotion regulation and executive functioning deficits. Specific information on the students’ clinical diagnoses, overall mathematics performance, and writing fluency was unavailable, but no fine motor-skill problems were reported. The students, all from the same class of nine students, were selected by their teacher based on their slow rates of multiplication fact fluency in the classroom. Multiplication fact fluency was selected for these students based on the teacher’s identified target skills for his existing intervention groups. In addition, all the students had mathematics goals on their Individualized Education Programs. Demographic information is in Table 1.

Table 1.

Student Demographics.

Student^a	Grade	Age	Race/ethnicity
Jaden	4	10 years	African American
Shawn	3	9 years	Caucasian
Collin	4	10 years	African American

Actual student names were replaced with pseudonyms to protect anonymity.

Measures

Multiplication computation fluency curriculum-based measures (CBM-Computation Fluency) were created using Intervention Central (https://www.interventioncentral.org/curriculum-based-measurement-reading-math-assesment-tests) to assess students’ skills throughout baseline and intervention phases. The problems on all probes were randomized and contained 24 single-digit (0–9) multiplication problems. The range of problems was selected based on the teacher’s regular classroom instruction. Students were given 1 min to complete as many problems as they could. Each CBM-Computation Fluency probe was scored based on the number of correctly written digits in the answers. For example, if a student correctly answered 5 × 4 = 20, it would count as two digits correct and a partially correct answer of 24 would count as one digit correct. The total number of correct digits on a probe was calculated and used as a digits correct per minute (DCPM) score. This type of mathematical fluency assessment has been found useful in screening or instructional planning based on its alternate-form reliability (r = .42–.88) and criterion-related validity (r = .29–.61 with the Stanford Achievement Test, Ninth Edition; Burns, VanDerHeyden, & Jiban, 2006). Accuracy data (i.e., percentage correct) were not collected and analyzed as part of the present study. In general, participants had high levels of accuracy on the assessment probes, and normative performance levels (mastery, instructional, and frustrational; Burns et al., 2006) are reliably based on DCPM scores rather than accuracy.

Procedures

The baseline and intervention sessions were conducted one-on-one with the interventionist, a second-year school psychology graduate student. The sessions were conducted two or three times per week in a private office at the school and each session occurred when the students would normally have unstructured free time in the classroom. Throughout the baseline and intervention phases, the students received the standard mathematics instruction in their classroom. This consisted of approximately 1 hr of whole group instruction per school day including some time dedicated to mathematical fact fluency (e.g., flashcard drills, repeated timed assessments). Each student participated in a total of 29 sessions, although the number of intervention sessions varied by student due to the multiple-baseline design. Each baseline session only involved completing the 1-min CBM-Computation Fluency assessment. Each intervention session lasted 10 to 15 min. Although most sessions were 15-min long, some sessions were cut short at the teacher’s request.

On the first day of the CCC intervention phase, each student was taught how to follow the CCC procedures. Specifically, students were taught to complete six steps: (a) look at and study a completed problem; (b) cover the problem; (c) write the problem and answer from memory; (d) uncover the sample problem; (e) compare own answer with the sample; and (f) move on to the next problem if correct, start over with first step if incorrect. The researcher modeled the steps, completed the steps jointly with the student, and then let the student work through the steps independently using the premade CCC worksheets. Each subsequent intervention session began with the interventionist modeling the steps as a reminder of the expectations. In addition, the interventionist was present each session to observe. In each session, a student completed two to three CCC worksheets with 10 problems per worksheet. The problems on the worksheets were selected by the students’ classroom teacher because they were unknown facts from classroom assessments. These target facts were repeated on the worksheets throughout the intervention. Every intervention session ended with the 1-min CBM-Computation Fluency assessment.

Interscorer Agreement and Intervention Fidelity

Twenty-five percent of the administered CBM-Computation Fluency probes were randomly selected and scored by another individual to calculate interscorer agreement. Interscorer agreement ranged from 92% to 98% with an average agreement of 95%. Discrepancies in scoring were primarily because of students’ handwriting and were discussed among the two scorers before determining a final score.

An intervention checklist covering the previously described six steps was developed by the interventionist to assess implementation fidelity. This fidelity checklist was used four times per student. First, it was used during the first three intervention sessions to establish students’ mastery of the CCC procedure, and then during one other randomly selected intervention session. Each student quickly displayed an understanding of the CCC procedure as evidenced by the intervention fidelity average score of 95%. In addition, the interventionist was always present during sessions to observe students and provide feedback if students deviated from the required CCC steps. Each student generally needed minor feedback once every other session.

Data Analysis

Visual analysis was used to examine the existence of a functional relation between CCC and students’ DCPM. We examined data for patterns regarding the level, trends, and variability. Slopes for visual analysis were calculated using a statistical software program as the slope of a linear regression line through the data points. We calculated Tau-U (Vannest, Parker, Gonen, & Adiguzel, 2016) using an online calculator (http://www.singlecaseresearch.org/calculators/tau-u) to supplement visual inspection when examining the effect of CCC, using interpretation guidelines outlined by Vannest and Ninci (2015).

Results

Baseline and intervention phase Ms, SDs, slopes, and ranges for all three participants are provided in Table 2. Figure 1 illustrates students’ DCPM across baseline and CCC intervention phases. Although there was no immediate change in Jaden’s level of DCPM after intervention began, his scores illustrated an increasing trend with limited variability in the intervention phase. Jaden’s data provide evidence of a functional relation between the CCC intervention and improved DCPM scores. Jaden’s Tau-U score showed a large intervention effect (Tau-U = .85, p < .001). Shawn showed a small change in level after the CCC intervention began but his performance in the intervention phase was variable. Although his baseline data met the criteria for stability, he did have an overall increasing trend during the baseline phase and a similar trend during the intervention. His data do not provide clear evidence of a functional relation, although a Tau-U of .54 (p = .01) indicate a moderate intervention effect. Finally, Collin showed some variability during baseline, but a stable, flat trend was established. Though he initially performed poorly after intervention began, his scores began to improve during the last two sessions, showing an increasing trend. However, a functional relation could not be established for Collin, and a Tau-U of .25 (p = .28) indicates little to no change.

Table 2.

Multiplication Fact Fluency (Digits Correct Per Minute).

Student	Baseline					CCC
Student	M	SD	Slope	Minimum	Maximum	M	SD	Slope	Minimum	Maximum
Jaden	13.57	1.51	0	11	15	16.50	1.50	2.41	13	19
Shawn	9.57	1.16	1.38	8	11	11.33	1.35	1.70	9	13
Collin	8.95	1.31	−0.10	7	11	9.90	1.85	1.21	8	13

Note. CCC = Cover-Copy-Compare.

Figure 1.

Visual display of digits correct per minute across students.

Discussion

The ability to correctly answer basic mathematical problems is critical to further success in math (Stading et al., 1996), highlighting the importance of effective interventions that target mathematical fact acquisition, such as CCC. These interventions should be considered for students with EBD, who often struggle with mathematics (Lane et al., 2008). CCC has been used effectively with a variety of students to improve basic mathematics skills (Becker et al., 2009; Hayden & McLaughlin, 2004; Poncy, Skinner, & Jaspers, 2006) and can help students with EBD self-regulate their own learning. The current study expanded upon the limited research on CCC with students with EBD.

Effects of the CCC intervention on fluency with multiplication facts varied across the three participants in this study. Although all three students demonstrated a higher number of correct digits per minute after the intervention and also made higher rates of growth during the intervention phase, these gains were often small. A functional relation was established for only one participant based on visual analysis, and the Tau-U effect size was large only for this student. None of the students moved beyond the frustrational level of DCPM established for their grade level (> 14 DCPM for third grade and > 24 for fourth grade; Burns et al., 2006), even on their highest performing days. Although Burns and colleagues (2010) established that acquisition interventions like CCC have large effects on mathematics performance for students with frustrational-level skills, it is unclear whether the same interventions will be effective for students with EBD. An intervention that provided more teacher guidance or positive reinforcement may have benefited the students more.

The amount of improvement clearly varied based on the number of intervention sessions conducted with each student. In comparing the average DCPM scores of baseline and intervention phases, Jaden, who received the most intervention sessions, made the most improvement, followed by Shawn with the second highest number of intervention sessions, and then Collin. Jaden also had the highest levels of growth during the intervention phase and the largest effect size. These results may indicate that the dosage of the intervention is a key to its effectiveness. Students who received the intervention longer may have had access to larger number of multiplication facts, improving their scores on the CBM probes. Continuing the CCC intervention with the students who started later may have established a functional relation. For example, the student with the lowest number of intervention sessions (Collin) showed a jump in his DCPM score during his last two sessions and may have continued developing his multiplication skills if the intervention continued. Given that the graduate student interventionist’s involvement with the participating school ended, we did not examine this hypothesis in this study. Examining the number of times a multiplication fact needs to be practiced using CCC before it is mastered and maintained could further explore how much dosage plays a role in the intervention’s effectiveness.

It should be noted that the student who made the most progress (Jaden) also had the highest baseline scores of all three participants. Thus, CCC might work best with students with EBD who have initially higher scores. Indeed, all participants with EBD in previously successful CCC studies (Skinner et al., 1991; Skinner et al., 1989) had higher baseline scores than Collin and Shawn. Further research can explore if a certain level of fact fluency predicts the effectiveness of CCC for students including those with EBD.

The current study was not without its limitations. This study solely focused on students’ fluency rates and did not collect information on errors or accuracy rate. Given the behavioral challenges of students with EBD, ensuring students are answering quickly and accurately may be key to establishing CCC as an effective mathematics acquisition intervention for this population. In addition, although the CBM probes included a range of single-digit multiplication problems, the exact proportion of these problems that were facts targeted in the CCC intervention is unknown. If the probes only included problems practiced in the intervention, more improvement may have been observed. No data were collected to ensure students generalized the skills to other measures of mathematics. Although CBM measures are technically adequate, more distal measures of performance could also be useful in establishing intervention effectiveness. The intervention fidelity data in the current study are also limited. The checklist was only used by the interventionist for four sessions per participant and, even though these data showed that students could accurately follow CCC procedures, it is possible that the procedure was not followed consistently across the study.

Although student participants informally reported that they enjoyed working with the interventionist, we did not collect formal social validity data from the student participants. Future research should examine the social validity of the intervention for students with EBD, ideally when it is implemented by regular school staff. A brief Likert-type scale survey was given to the participants’ classroom teacher to assess the social validity of the intervention. The teacher strongly agreed that the CCC intervention focused on an important skill that was also of sufficient concern for these students, that he could easily incorporate the intervention in his classroom, and that he had access to the necessary materials and time for implementation. He also agreed that he could accurately implement the intervention in his classroom. These survey results were not included as outcomes in the current study given that the teacher never implemented the intervention, thereby limiting the validity of his responses.

Further research on CCC with this population is needed, especially to examine the effectiveness with different grade levels, skills, and methods. As the one-on-one intervention sessions provided as part of the current study may not work well in other school contexts, future research should examine its application on a classroom level. Other areas for future research include use of CCC with higher-level mathematical procedures, direct comparisons of CCC effectiveness to other interventions, and investigations of CCC effectiveness as part of a regular curriculum or comprehensive intervention package.

Overall, findings suggest the CCC intervention had mixed effects on the multiplication fact fluency for three students with EBD. CCC is a quick and efficient intervention due to the opportunities to answer problems with guided practice and has the added benefit of teaching students to regulate their own learning. Given the limited effectiveness in the current study, professionals should carefully evaluate whether the CCC intervention is appropriate for students with EBD with difficulties in mathematics and monitor its effectiveness closely.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

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