Enhancing Assignment Perceptions in Students with Mathematics Learning Disabilities by Including More Work: An Extension of Interspersal Research

Transcription

1 School Psychology Quarterly, Vol. 19, No. 2, 2004, pp Enhancing Assignment Perceptions in Students with Mathematics Learning Disabilities by Including More Work: An Extension of Interspersal Research Mark E. Wildmon Center for Behavioral Pediatrics Christopher H. Skinner University of Tennessee, Knoxville T. Steuart Watson Mississippi State University L Shan Garrett Center for Behavioral Pediatrics Active student responding is often required to remedy computation skill deficits in students with learning disabilities. However, these students may find computation assignments unrewarding and frustrating, and be less likely to choose to engage in assigned computation tasks. In the current study, middle school students with learning disabilities worked on control assignments containing 15 four-digit minus four-digit target computation problems and interspersal assignments containing 15 similar problems and five additional one-digit minus one-digit problems. Results showed that interspersing the brief problems did not reduce target problem accuracy levels or opportunities to respond to target problems. Students did complete more total problems (i.e., target and single-digit problems) on the interspersal assignment. Even though the interspersal assignment contained more work, significantly more students rated it as requiring less effort to complete and selected it for homework. Discussion focuses on applied implications, causal mechanisms, and future research related to the interspersal procedure and the discrete task completion hypothesis. While much attention has been paid to skill deficits and learning disabilities in reading, evidence suggests that difficulties with mathematics achievement may Address correspondence to Christopher H. Skinner, The University of Tennessee College of EHHS, Claxton Complex, A-518, Knoxville TN ; cskinnel@utk.edu. 106

2 INTERSPERSAL PROCEDURE 107 be as prevalent (Fleischner & Manheimer, 1997). Students with learning disabilities often have computation skills deficits including inaccurate and dysfluent (i.e., accurate but slow) responding (Erenberg, 1995). Enhancing accuracy and speed of computation skills, often called fluency or automaticity, typically requires students to engage in active academic responding (Erenberg, 1995; Goldman, Pellegrino, & Mertz, 1988; Greenwood, Delquadri, & Hall, 1984; Skinner, Belfiore, Mace, Williams, & Johns, 1997). Within classroom settings, at any given moment students may choose to engage in assigned academic behaviors or an infinite number of alternative behaviors. While educators can develop and assign tasks designed to enhance computation skills, these assignments are of little use unless students choose to engage in assigned work (Cates & Skinner, 2000). Due to their skill deficits, students with learning disabilities in mathematics may be less likely to choose to engage in assigned academic activities. This process can cause a downward spiral where students fall farther behind their peers with respect to skill development as they choose to engage in alternative behaviors, which further decreases the probability of these students choosing to engage in future mathematics assignments (Skinner, 1999). VARIABLES INFLUENCING CHOICE BEHAVIOR Researchers have identified several variables that influence students' choice behavior. Much of this research has been based on the matching law, which states that when given a choice of two behaviors, students will allocate time to those two behaviors based on relative rates of reinforcement for each behavior (Herrnstein, 1961). For example, assume a student is reinforced every 10 minutes for engaging in assigned academic tasks, but every 5 minutes for engaging in other behaviors (e.g., sharpening pencils, talking with peers). If all other variables are equal, in a typical 30-minute class period that student can be expected to engage in academic behaviors one third of the time (5/5 + 10) or for 10 minutes (Myerson&Hale, 1984). Researchers investigating student choice behavior have conducted numerous studies that confirmed the matching law. Several researchers have collected data on student behavior (e.g., on-task and off-task) and teacher behavior (e.g., social reinforcement in the form of attention) in classroom settings and found that the matching law could predict the time students spend engaged in desired behaviors as well as other behaviors (Martens, Halperin, Rummel, & Kilpatrick, 1990; Martens & Houk, 1989; Shriver & Kramer, 1997). Martens, Lochner, and Kelly (1992) extended this research to show how the matching law could be used to enhance students' on-task behavior. Researchers used a bug-in-the-ear device to alter relative rates of reinforcement (i.e., teacher attention) delivered to students for on-task and off-task behavior. Results confirmed the matching law and showed how manipulating relative rates of reinforcement, as opposed to absolute rates of reinforcement, increased on-task behavior. Mace, McCurdy, and

3 108 WILDMON ET AL Quigley (1990) found similar results. Researchers allowed students to make repeated choices between two academic behaviors (division or multiplication problems). Results showed how time allocated toward one behavior or the other could be predicted based on relative rates of reinforcement for the two behaviors. In addition to relative rates of reinforcement, researchers have found that quality and immediacy of reinforcement also impact student choice behavior (Neef, Mace, & Shade, 1993; Neef, Mace, Shea, & Shade, 1992; Neef, Shade, & Miller, 1994). A final variable that impacts choice behavior is relative effort required to engage in competing behaviors. When reinforcement rates, immediacy, and quality are held constant across two behaviors, students are more likely to choose to engage in the behavior that requires the least amount of effort (Homer & Day, 1991; Meadows & Skinner, 2002). Students with mathematics learning disabilities may need more opportunities to respond to remedy computation skill deficits (Skinner, Belfiore, & Watson, 1995). However, these students may be less likely to choose to engage in assigned tasks than general education peers because assignments require more effort to complete. Additionally, reinforcement quality may be diminished when students with learning disabilities make more errors (e.g., a grade of a B is a lower quality reinforcer than an A). Even when accuracy levels are high, rates of reinforcement are reduced when students with disabilities require much time to complete their mathematics assignments. For example, a general education student may complete a mathematics assignment in 10 minutes, while a student with learning disabilities may require 30 minutes. Assuming both receive teacher praise and a letter grade of B contingent upon their work, the rate of reinforcement for the general education student is one reinforcer for every 10 minutes of mathematics work, while the rate of reinforcement for the student with the learning disabilities is one reinforcer for every 30 minutes of mathematics responding. This lower rate of reinforcement associated with dysfluent or slower work decreases the probability that these students will choose to engage in assigned academic tasks (Skinner, 1999). MANIPULATING VARIABLES THAT INFLUENCE CHOICE When attempting to enhance the probability of students with learning disabilities choosing to engage in assigned tasks, educators could enhance the rate, immediacy, and quality of reinforcement for desired academic behaviors, while decreasing rate, immediacy, and quality of reinforcement for other behaviors. Because it is difficult to identify all competing alternative responses and control reinforcement for those responses (e.g., peers laughing when a student engages in disruptive behavior), educators should consider enhancing rates, quality, and immediacy of reinforcement for engaging in desired academic behaviors (Meadows & Skinner, 2002). Additionally, educators can increase the probability of students choosing to engage in assigned academic work by

4 INTERSPERSAL PROCEDURE 109 decreasing the effort required to complete that work. Rate and immediacy of reinforcement can be increased using computer- (see Neef et al., 1994) or peerdelivered (see Greenwood, Delquadri, & Hall, 1984) immediate feedback and reinforcement. Reinforcer quality often varies across students. For example, for Ralph, teacher attention may be more reinforcing than peer attention, but for John the opposite is true. Additionally, relative reinforcer quality may not be stable. For example, initially gold stars may be higher quality reinforcers than peer attention. However, as the school year progresses, peer attention may become a higher quality reinforcer than gold stars. Procedures designed to address idiosyncratic and unstable characteristics of reinforcer quality include using token economies that allow students to choose reinforcers and using unknown or randomly selected reinforcers (Moore, Waguespack, Wickstrom, Witt, & Gaydos, 1994; Neef et al., 1994; Skinner, Skinner, & Sterling, 2002). While procedures designed to enhance rate, quality, and immediacy of reinforcement have empirical support, such procedures are not typically used in classroom environments. A variety of variables may account for this, including teacher time required to implement such procedures (e.g., managing a token economy), resource requirements (e.g., computers and software), and concerns with negative side effects associated with enhancing reinforcement for assigned academic behavior such as reducing intrinsic motivation, bribing students, and maintenance of academic behaviors when reinforcement procedures are diluted (Elliott, Witt, & Kratochwill, 1991; Hall, 1991; Lepper, Green, & Nisbett, 1973; O'Leary, Poulos, & Devine, 1972). Another strategy is to alter assignments so that students are more likely to choose to engage in academic tasks. Educators can reduce the effort required to complete assignments by making assignments easier or briefer (Dunlap et al., 1994; Homer & Day, 1991; Kern, Childs, Dunlap, Clarke, & Falk, 1994). For example, Cooke, Guzaukas, Pressley, and Kerr, (1993) found that replacing instructional level items with known items enhanced students' preference for assignments. While these assignment alteration procedures may increase the probability of students with disabilities choosing to engage in assigned tasks, several studies have found that altering assignments by removing instructional-level items and replacing them with known or mastered items can decrease students' learning rates (Roberts, Turco, & Shapiro, 1991; Roberts & Shapiro, 1996). Thus, while effort reduction procedures may increase the probability of students with learning disabilities engaging in assigned work, they may also contribute to their learning problems by decreasing skill development. INTERSPERSAL PROCEDURE Recently researchers have developed an assignment alteration procedure that may enhance students' perceptions of assignments and increase the probability of students choosing to engage in assigned work without reducing assignment

5 110 WILDMON ET AL demands. The interspersal procedure developed by C. H. Skinner and colleagues (see Skinner, 2002 for a comprehensive review) is similar to the substitution procedures used by other researchers (e.g., Cooke et al., 1993). However, rather than replacing difficult items with easy items, researchers merely added and interspersed briefer, and in many studies, easier items. In their first experiment, Skinner, Robinson, Johns, Logan, and Belfiore (1996) had college students work on two different mathematics computation assignments. The control assignment contained 16 target, three-digit by two-digit problems (3 x 2) and the interspersal assignment contained 16 equivalent target problems plus six additional one-digit by one-digit problems (1 x 1) interspersed after every third 3><2 problem. After working on each assignment for 305 seconds, students rated the assignments and chose a new assignment for homework. Results showed no difference in performance on target problems (rate or accuracy), but total problem completion rates were significantly higher on the interspersal assignment. Even though it required more work, due to the additional brief problems, significantly more students rated the interspersal assignment as requiring less time and effort to complete and chose a new interspersal assignment for homework. Subsequent studies showed that the additive interspersal procedure had a similar effect across students (e.g., sixth-grade students and high school students) and tasks including word problems and grammar assignments (Logan & Skinner, 1998; Meadows & Skinner, 2002; Wildmon, Skinner, McCurdy, & Sims, 1999; Wildmon, Skinner, & McDade, 1998). In other studies, researchers tested the strength of the interspersal procedure by giving students the choice between control assignments containing only longer target tasks and interspersal assignments that contained both the additional brief tasks and more longer target tasks than the control assignment. Results showed how educators could cause students to choose to engage in assignments that contained 20% and even 40% more high-effort target tasks by assigning even more tasks, the brief problems (Cates & Skinner, 2000; Cates et al., 2001; Meadows & Skinner, 2002). Finally, researchers showed how interspersing additional briefer tasks increased on-task levels in a general education elementary school student (McCurdy, Skinner, Grantham, Watson, & Hindman, 2001) and middle school students with behavior disorders (Skinner, Hurst, Teeple, & Meadows, 2002). Experiments were conducted to attempt to determine the causal mechanism responsible for interspersal effects. Results suggested that problem ease and novelty effects were not responsible for interspersal effects (Martin, Skinner, & Neddenriep, 2001; Skinner, Robinson et al., 1996, Experiment II; Skinner, Fletcher, Wildmon, & Belifore, 1996). Other studies suggested that a completed discrete task might be a conditioned reinforcer (Skinner et al., 1999). By increasing discrete task completion rates, interspersing additional brief problems also enhances rates of reinforcement. This increase in reinforcement rates may cause students to prefer and choose interspersal assignments (see Skinner, 2002, for a comprehensive description of the discrete task completion hypothesis).

6 INTERSPERSAL PROCEDURE 111 PURPOSE Interspersing additional brief tasks would appear to be a resource-efficient procedure for enhancing rates of reinforcement for working on computation assignments that may enhance assignment perceptions and the probability of students choosing to engage in assigned tasks (Logan & Skinner, 1998). However, researchers have not investigated the effects of interspersing additional brief items on choice and assignment perceptions in students with learning disabilities. The purpose of the current study was to extend research on the interspersal procedure to middle school students with learning disabilities in mathematics. Participants and Setting METHOD Permission to participate in this study was solicited from the parents of all 101 seventh-grade and eighth-grade students diagnosed with a learning disability from a southeastern middle school. Each student was identified as having a mathematics learning disability as determined by a significant discrepancy between level of intelligence and standardized achievement scores. From this initial group, 39 students (24 males and 15 females; 22 seventh-grade and 17 eighth-grade students; and 18 African American students, 20 Caucasian students, and one student who did not respond to the race item) returned permission slips and assented to participate. Participants were consolidated into a single special education mathematics classroom where the current experiment was conducted. The primary researcher conducted the study with the assistance of two special education teachers who remained in the classroom throughout the experiment. Materials During the experiment each participant was given a four-page (8.5 x 11-inch paper) packet. Each packet contained an experimental (i.e., interspersal) and control assignment. To assist the students in discriminating between assignments, each assignment was labeled with either a "plus" or "star" symbol in the top right corner of the paper. These two assignments were separated with an additional sheet of paper that was labeled "STOP. THIS ASSIGNMENT IS COM- PLETE." The final sheet of paper contained a student questionnaire used to collect demographic data (i.e., sex and grade) and four items related to the two assignments: (a) which assignment took the most time, (b) which assignment was the most difficult, (c) which assignment required the most amount of effort, and (d) which assignment would the student prefer to complete for homework. The students' special education teachers (three different teachers) and the primary experimenter met in order to identify computation problems that would serve as target problems for the current study. Each teacher provided samples of computation problems that were included in most of their students' current curriculum.

7 112 WILDMON ET AL After reviewing this sample, each teacher reported that four-digit minus four-digit (4-4) problems were instructional-level problems and that all their students had similar problems as part of the mathematics Individual Education Plan (IEP) objectives. The three teachers reported that all or almost all of their students could perform the steps, but their speed and accuracy on these problems suggested they needed more opportunities to respond to enhance their fluency with these problems. These teachers also reported that their students' speed and accuracy levels were much higher on one-digit minus one-digit (1-1) computation problems. Initially researchers constructed two matched control assignments (Control A and Control B). The first assignment, Control A, contained target problems. The Control B assignment was constructed by altering the sequence of digits within each problem. For example, the first target problem on Control A was 4,753-3,362 and the first target problem on Control B was 3,574-2,633. Each target problem required the student to borrow once. Each of these control assignments was used to construct two experimental (i.e., interspersal) assignments (A and B). Experimental assignments contained the same 15 problems, in the same sequence, with five additional 1-1 problems interspersed following every third 4-4 target problem. The first problem on each interspersal assignment was a 1 1 problem across all four assignments; the problems were not numbered and were distributed unequally throughout the assignment (i.e., an unequal number of problems per row). Experimental Procedures The students were presented with a four-page packet placed face down on each desk. Each packet contained an experimental and a control assignment. Counterbalancing across packets was used, so that approximately half of the students had the Control A assignment and the Experimental B assignment, and half had the Control B assignment and the Experimental A assignment. Control and Experimental were presented in a counterbalanced order across students to control for sequence effects (e.g., fatigue, practice). Finally, the "plus" and "star" were assigned to control and experimental assignments in a counterbalanced fashion. After being seated at their desks, students were told they would be given a limited amount of time to complete as many problems as they could on the first assignment. The students were instructed to work from the left to the right without skipping any problems, raise their hands if they finished before being told to stop, and work as quickly as possible without making errors. The students were instructed to turn their packets over and begin working on the first assignment as a stopwatch was started. After six minutes, the students were asked to stop writing and to wait for instructions. No students completed the assignment before the allotted time expired. Next, students were asked to turn to the next page that separated the assignments and wait for instructions. After all participants complied, they were instructed to turn to the next assignment and the procedures were repeated.

8 INTERSPERSAL PROCEDURE 113 Students were then asked to turn to the fourth page of the packet. The experimenter read each question aloud and provided the participants with time to respond before reading additional questions. The students were instructed to refer to the symbols (i.e., star or plus) in the top right corner of the assignments while responding. The students were told to record which assignment required the most time to complete from start to finish, which assignment was the most difficult, and which assignment would require the most effort to complete by circling either the star or plus symbol following each item. Next, students were told that they had to complete an additional assignment for homework, and that they could select either a new star or new plus assignment. Each question required a forced choice response and the students were told that they could look back over the assignments before responding. After all students made their choices, packets were collected and the students were informed that because they cooperated so well, they would not have to complete their chosen assignments for homework. Experimental Design A within-subjects design was used to compare each student's mathematics performance across assignments as well as analyze his/her choice and ranking data following exposure to assignments. Within-subjects designs are susceptible to sequence effects (e.g., fatigue) and multiple-treatment interference. To enhance assignment discrimination and reduce multiple-treatment interference, the different assignments were labeled as either a star or a plus symbol. Counterbalancing was used to control sequence effects, symbol preference effects (i.e., preference for star or plus symbol), and assignment difficulty levels. Dependent Variables and Data Analysis Procedures The data collected from the assignment sheets and the questionnaires were used as the dependent measure. The assignments were used to collect data on: (a) the total number of problems completed (i.e., 4-4 problems on control assignments, 4-4 and 1-1 problems on experimental assignments), (b) the number of target 4-4 problems completed, and (c) the percentage of 4-4 problems accurately completed. The questionnaires were used to collect data on each student's perception of time, effort, difficulty, and homework assignment selection. Chi-square Goodness of Fit tests were used to analyze student choice data across assignments as well as assignment difficulty, time, and effort rankings. Within-subjects, dependent t-tests were used to test for statistically significant differences across assignments on each mathematics performance variable. An alpha level of/? <.05 was used for all statistical tests. Interscorer Agreement One experimenter scored all the assignment sheets, and a second experimenter independently scored 30% of the data for each dependent variable. Interscorer

9 114 WILDMONETAL agreement was calculated by dividing the number of agreements by the number of agreements plus disagreements and multiplying by 100%. Interscorer agreement was 100% for problems completed, 100% for problems correct, and 100% for choice and rank data. RESULTS Table 1 displays the descriptive statistics for the total number of problems completed (4-4 and 1-1 problems), the number of 4-4 problems completed, and the percentage of completed 4-4 problems that were accurate across assignments. Dependent t-tests showed that students completed significantly more total problems on the experimental assignment,?(38) = 8.29, SE =.435, p <.001. The effect size was.97. No significant differences were found for the number of target problems completed, f(38) =.521, SE =.344, p =.605, or the percentage of target problems completed accurately,?(38) =.321, SE = 2.79, p =.750. Students' rankings of difficulty, time, and effort across both assignments are provided in Table 2. This table shows that 72% of the students reported that the experimental assignment was less difficult, 62% reported that the experimental assignment required less effort, and 72% reported that the experimental assignment required less time than the control assignment. Chi-square Goodness-of-Fit analysis indicated significant differences for difficulty, x2(38, 2) = 7.41,/? <.01, and time x2(38, 2) = 7.41,/? <.01. No significant differences were found for effort, x2(38, 2) = 3.02,/? =.150. Homework choice data showed that 87% of the students chose the experimental assignment. Chi-square Goodness-of-Fit analysis showed that this difference was statistically significant, x2(38, 2) = 21.56,/? <.005. DISCUSSION The purpose of the current study was to extend research on the interspersal procedure by investigating the effects of adding and interspersing additional brief computation problems on academic performance, assignment perceptions, and homework choice in students with mathematics learning disabilities. Results TABLE 1. Problem Completion Rates and Accuracy Levels for the Control and Experimental Assignments with Middle School Special Education Students Total Problems Completed Target Problems Completed Percent Target Problems Accurate Mean Control SD Experimental Mean SD 4.04* Effect Size d *Significant at the/; <.05 level.

10 INTERSPERSAL PROCEDURE 115 TABLE 2. Time and Difficulty Rankings for Control and Experimental Assignments with High School Students Least Difficult Least Effort Least Time to Finish Homework Choice *Significant at thep <.05 level. N Control % Experimental N % 72* 62 72* 87* Effect Size Phi showed that target problem (i.e., 4-4) completion rates and accuracy levels did not differ across control and interspersal assignments. However, students completed significantly more total problems on the interspersal assignment. These results confirmed earlier studies conducted with general education and college students, which showed that interspersing brief computation problems increased problem completion rates, without reducing opportunities to respond to target problems or accuracy on target problems (e.g., Logan & Skinner, 1998; Skinner, Robinson et al., 1996). Analysis of choice and ranking data showed students preferred the interspersal assignment. Perhaps the best indication of preference comes from the homework choice data, which showed that significantly more students (87%) chose a new interspersal assignment for homework. Significantly more students rated the interspersal assignment as less difficult, which is not unexpected given that the interspersed problems were easier. Although the interspersal assignments contained five additional brief problems, significantly more students reported that this assignment would require less time to complete and no significant difference was found for students' rankings of assignments with respect to effort required to complete each assignment. Although these results appear to be counterintuitive, they support earlier studies conducted with general education and college students (e.g., Logan & Skinner, 1998; Skinner et al., 1999). The current results have implications for both practitioners and researchers. Students with learning disabilities in mathematics often have computation skill deficits, including dysfluent responding (Erenberg, 1995; Fleischner & Manheimer, 1997). Because of these deficits, these students are more likely to find mathematics assignments difficult and frustrating. One way to enhance student perceptions of mathematics assignments is to make them brief or easier. However, such procedures fail to remedy skill deficits because they reduce students' opportunities to respond and learning rates (Erenberg, 1995; Roberts & Shapiro, 1996; Roberts et al., 1991). The current study shows how increasing assignment demands by adding and interspersing brief problems can enhance students' perceptions of assignments without reducing responding rates to target problems.

11 116 WILDMONETAL Additionally, adding and interspersing the briefer problems is likely to enhance maintenance of skills associated with the brief problems (Underwood, Kapelak, & Malmi, 1976). Future researchers should conduct studies designed to address limitations of the current study and extend research on the interspersal procedure. In the current study, students with mathematics learning disabilities were exposed to the two types of assignments briefly and only given one opportunity to choose between the two assignments. Future researchers should conduct longitudinal studies to determine if interspersing additional brief problems enhances assignment perceptions after being given many opportunities to choose. Longitudinal studies are also needed to determine if interspersing brief problems enhances students' overall perceptions of mathematics and their feelings about their mathematics abilities (e.g., mathematics esteem). Finally, researchers should determine if such procedures increase computation responding and enhance learning rates in students with mathematics disabilities. In the current study, parental consent for participation was obtained from less than 40% of the participant pool. Thus, internal validity may have been affected by interactions between selection and treatment, and the current results may not generalize to other groups of students with learning disabilities. The limitations associated with the current study are mitigated by previous studies where similar results were obtained with college, general education secondary, and elementary students (see Skinner, 2002). Previous researchers have found evidence to suggest that a completed discrete task, in the current study a completed mathematics problem, is a reinforcing stimulus (Skinner, 2002). Research on the matching law has shown that students will choose to engage in behaviors associated with higher rates of reinforcement (e.g., Mace et al., 1990). The current study supports the discrete task completion hypothesis as problem completion rates were higher on the interspersal assignments and significantly more students chose the interspersal assignment for homework. However, more research is needed to directly demonstrate that a completed discrete task is a reinforcing event and delineate the process of how completed discrete tasks become reinforcers. A more thorough understanding of the process whereby completed discrete tasks become conditioned reinforcing stimuli may allow educators to strengthen the quality of these conditioned reinforcers, thereby enhancing the effectiveness of the interspersal procedure (Skinner etal., 1999). Researchers also should determine if other procedures that enhance discrete task completion rates (e.g., explicit timing, rapid pacing) enhance students' assignment perceptions and the probability of their choosing to engage in assigned work (Logan & Skinner, 1998). Future researchers should determine if interspersal procedures used in the current study alter other behavior. For example, researchers should determine if the additive interspersal procedure could be used to increase homework completion rates and decrease procrastination in students with learning disabilities (Skinner, 2002).

12 INTERSPERSAL PROCEDURE 117 Previous research indicates that one limitation associated with the interspersal procedure is that it may not be effective with assignments that require students to engage in more continuous responding (Martin et al., 2001). Future researchers should determine if altering continuous tasks by breaking them into smaller discrete tasks (e.g., breaking a long passage into several small passages) would enhance student perceptions of assignments and/or allow researchers to apply interspersal procedure to these tasks. Basic research on choice behavior suggests that educators attempting to remedy computation skill deficits in students with mathematics disabilities are faced with serious challenges. While these students need to engage in more computation responding, they are also likely to find such work frustrating and unrewarding. The additive interspersal procedure may prove to be an efficient procedure that enhances students' perceptions of assignments and the probability of their choosing to engage in computation assignments without watering down the curriculum. Additionally, this procedure may enhance rates of reinforcement for engaging in assigned work in a manner that does not require teachers to deliver higher-quality reinforcers more often or more immediately. Future research is needed to determine if this simple assignment alteration procedure can be used to remedy skill deficits and improve perceptions of mathematics assignments. Additionally, research should determine if this procedure could help prevent the development of skill deficits and negative student perceptions. REFERENCES Cates, G. L., & Skinner, C. H. (2000). Getting remedial mathematics students to prefer homework with 20% and 40% more problems: An investigation of the strength of the interspersing procedure. Psychology in the Schools, 37, 1-9. Cates, G. L., Skinner, C. H., Watkins, C. E., Rhymer, K. N., McNeill, B. S., & McCurdy, M. (2001). Effects of interspersing additional brief math problems on student performance and perception of math assignments: Getting students to prefer to do more work. Journal of Behavioral Education, 9, Cooke, N. L., Guzaukas, R., Pressley, J. S., & Kerr, K. (1993). Effects of using a ratio of new items to review items during drill and practice: Three experiments. Education and Treatment of Children, 16, Dunlap, G., DePerzcel, M., Clark, S., Wilson, D., Wright, S., & Gomez, A. (1994). Choice making to promote adaptive behavior for students with emotional and behavioral challenges. Journal of Applied Behavior Analysis, 27, Elliott, S. N., Witt, J. C, & Kratochwill, T. R. (1991). Selecting, implementing, and evaluating classroom interventions. In G. Stoner, M. R. Shinn, & H. M. Walker (Eds.), Interventions for achievement and behavior problems (pp ). Silver Spring, MD: National Association of School Psychologists. Erenberg, S. R. (1995). An investigation of the heuristic strategies used by students with and without learning disabilities in their acquisition of the basic facts of multiplication. Learning Disabilities: A Multi-disciplinary Journal, 6(1), Fleischner, J. E., & Manheimer, M. A. (1997). Math interventions for students with learning disabilities: Myths and realities. School Psychology Review, 26, Goldman, S. R., Pellegrino, J. W., & Mertz, D. L. (1988). Extended practice of basic addition facts: Strategy changes in learning disabled students. Cognition and Instruction, 5,

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14 INTERSPERSAL PROCEDURE 119 Roberts, M. L., & Shapiro, E. S. (1996). Effects of instructional ratios on students' reading performance in a regular education program. Journal of School Psychology, 34, Roberts, M. L., Turco, T. L., & Shapiro, E. S. (1991). Differential effects of fixed instructional ratios on students' progress in reading. Journal of Psychoeducational Assessment, 9, Shriver, M. D., & Kramer, J. J. (1997). Application of the generalized matching law for description of student behavior in the classroom. Journal of Behavioral Education, 7, Skinner, C. H. (1999). Preventing academic skills deficits. In T. S. Watson & F. M. Gresham (Eds.), Handbook of child behavior therapy (pp ). New York: Plenum Press. Skinner, C. H. (2002). An empirical analysis of interspersal research: Evidence, implications and applications of the discrete task completion hypothesis. Journal of School Psychology, 40, Skinner, C. H., Belfiore, P. J., Mace, H. W., Williams, S., & Johns, G. A. (1997). Altering response topography to increase response efficiency and learning rates. School Psychology Quarterly, 12, Skinner, C. H., Belfiore, P. B., & Watson, T. S. (1995). Assessing the relative effects of interventions in students with mild disabilities: Assessing instructional time. Assessment in Rehabilitation and Exceptionality, 2, Skinner, C. H., Fletcher, P. A., Wildmon, M. E., & Belfiore, P. J. (1996). Improving assignment preference through interspersing additional problems: Brief versus easy problems. Journal of Behavioral Education, 6, Skinner, C. H., Hall-Johnson, K., Skinner, A. L., Cates, G., Weber, J., & Johns, G. (1999). Enhancing perceptions of mathematics assignments by increasing relative problem completion rates through the interspersal technique. The Journal of Experimental Education, 68(\), Skinner, C. H., Hurst, K. L., Teeple, D. F., & Meadows, S. O. (2002). Increasing on-task behavior during mathematics independent seatwork in students with emotional disorders by interspersing additional brief problems. Psychology in the Schools, 39, Skinner, C. H., Robinson, S. L., Johns, G. A., Logan, P., & Belfiore, P. J. (1996). Interspersing time efficient, easy, academic tasks to influence students' choice to complete more difficult problems: More is less. Journal of Experimental Education, 65, Skinner, C. H., Skinner, A. L., & Sterling, H. E. (2002). Best practices in contingency management: Application of individual and group contingencies in educational settings. In A. Thomas & J. Grimes (Eds.), Best practices in school psychology /K(pp ). Washington, DC: National Association of School Psychologists. Underwood, B., Kapelak, S., & Malmi, R. (1976). The spacing effect: Additions to the theoretical and empirical puzzles. Memory and Cognition, 4, Wildmon, M. E., Skinner, C. H., McCurdy, M., & Sims, S. (1999). Improving secondary students' perception of the "dreaded mathematics word problem assignment" by giving them more word problems. Psychology in the Schools, 36, Wildmon, M. E., Skinner, C. H., & McDade, A. (1998). Interspersing additional brief, easy problems to increase assignment preference on mathematics reading problems. Journal of Behavioral Education, 8, Action Editor: Cecil R. Reynolds Mark E. Wildmon, Ph.D., is the director of the Center for Behavioral Pediatrics in Jackson, Mississippi. His research interests include academic remediation, the evaluation of idiosyncratic variables that affect treatment outcome, and functional assessment and analysis of challenging behaviors in institution, home, and school settings. Christopher H. Skinner, Ph.D, is Professor and Coordinator of School Psychology Programs at the University of Tennessee. His research interests include prevention and reme-

15 120 WILDMON ET AL diation of academic and social problems within educational settings, single-subject design research, behavioral assessment, and applied behavioral analysis. He received his Ph.D. from Lehigh University in 1989 and is currently serving as co-editor of the Journal of Behavioral Education. The School Psychology Program at the University of Tennessee is accredited by the APA. T. Steuart Watson, Ph.D., is Professor in the School Psychology Program at the Mississippi State University. His research interests include evaluating the effects of direct behavioral consultation as a service delivery model, treatment integrity, and examining the effects of olfactory stimuli on learning. He received his Ph.D. from the University of Nebraska in 1991 and is currently the co-editor of Proven Practice: Prevention and Remediation Solutions for Schools. The School Psychology Program at the Mississippi State University is accredited by the APA. L. Shan Garrett, is a Clinical Assistant at the Center for Behavioral Pediatrics in Jackson, Mississippi. She received her bachelor's degree in Psychology from Mississippi State University in Her research interests include school-based interventions, social and language development in autism, early childhood intervention, and competencybased parent training.