Student Preference for Explicit Timing and Interspersal Procedures as a Function of Math Problem Completion Rates: Testing the Discrete Task Completion Hypothesis

A within-subjects design was used to compare explicit timing and interspersal with college students. Students were given 3 minutes to complete problems on the explicit timing assignment (25 problems, 3 digits –3 digits) and the interspersal assignment (25 similar problems and 10 problems, 1 digit –1 digit). Results indicated that: (a) students completed more total problems during interspersal for both trials, (b) students completed more target problems during explicit timing for the second trial, and (c) students only preferred interspersal for the first trial. The data from trial one fit the discrete task completion hypothesis and matching law, yet the data from trial two do not match as closely (Skinner, 2002). Discussion focuses on continued need for more research on academic interventions, comparing academic interventions, the discrete task completion hypothesis, and the matching law.     

Effects of Interspersing Briefer Mathematics Problems on Assignment Choice in Students with Learning Disabilities

Within- and between-series designs were combined and used to evaluate the effects of interspersing briefer math problems (i.e., one-digit by one-digit multiplication, 1 × 1) with more time-consuming problems (i.e., two-digit by one-digit multiplication, 2 × 1) on time allocation to one of two concurrent computer-delivered mathematics computation assignments in four high school students with specific learning disabilities in mathematics. The computer presented students with a choice of 2 × 1 problems with 1 × 1 problems interspersed every third problem (i.e., experimental assignment) or 2 × 1 problems without interspersal (i.e., control assignment). Visual and statistical analysis showed that students allocated a greater percentage of their time to the interspersal assignments. These results support previous research on the matching law and problem completion rates and suggest that students' preference for assignments can be improved through the interspersal technique. Discussion focuses on future research and applied educational implications for curricula construction and task sequencing.     

Effects of Interspersing Rate on Student Preferences for Mathematics Assignments

This study investigated the extent to which interspersing effects are consistent with the effects of reinforcement on predicting students preferences for mathematics assignments. Students were exposed to 4 pairs of assignments. Each assignment pair contained a control assignment with 15 problems requiring multiplication of a three digit number by a two digit number, and an experimental assignment consisting of 15 similar multiplication problems plus additional brief one-digit by one-digit multiplication problems interspersed at four different rates (i.e., no interspersing, every other, every third, or every fifth problem) across assignment pairs. Performance data were collected for accuracy, total problem completion rate and target problem completion rate. In addition to performance data, students were asked to rate each assignment with regard to relative difficulty, time, effort to complete, and preference between assignments for homework. Results suggest that although interspersing rates do not affect accuracy, they do affect problem completion rate, and student preferences for academic assignments. Discussion focuses on interspersing rate and schedules of reinforcement with emphasis on both applied and theoretical implications.     

An Empirical Analysis of Interspersal Research: Evidence, Implications, and Applications of the Discrete Task Completion Hypothesis

Because assignment completion is often reinforced, researchers have posited that when students work on assignments with many discrete tasks (e.g., 20 mathematics problems), that each completed discrete task may be a conditioned reinforcer (e.g., Skinner et al., 1999). If the discrete task completion hypothesis is accurate, then relative task completion rates should influence choice behavior in the same manner as relative rates of reinforcement. In the current study, previous interspersal research was combined across experiments and regression analysis revealed a linear relationship between relative problem completion rates (RPCR) and choice in accordance with the matching law (Herrnstein, 1961, 1970). These results support the discrete task completion hypothesis and suggest that interspersing additional brief tasks enhances interval schedules of reinforcement. Theoretical and applied implications of the current study and the discrete problem completion hypothesis are discussed and directions for future research are provided.     

Getting Students to Choose to Do More Work: Evidence of the Effectiveness of the Interspersal Procedure

College students were exposed to two sets of mathematics assignments. For each set students were given an experimental and a control assignment. The control assignments contained 15 three-digit by two-digit target problems. The experimental assignments contained 18 similar target problems as well as six one-digit by one-digit multiplication problems interspersed after every third target problem. In the first assignment set, students were asked to work each assignment for 5 minutes. Although the experimental assignments contained more target problems, results showed that significantly more students chose the experimental assignment and rated it as less difficult and as requiring less effort to complete. In the second assignment set, students were asked to complete both assignments. Again significantly more students rated the experimental assignment as being less difficult and as requiring less effort to complete. Although more students chose the experimental assignment for homework, this difference was not significant. Discussion focuses on using the interspersal procedure to enhance students' perceptions of assignments and alter their choice behavior.     

Interspersing Additional Brief, Easy Problems to Increase Assignment Preference on Mathematics Reading Problems

We extended previous research on student preference for academic assignments by presenting college students with a control assignment containing eight, two-digit × two-digit + two-digit × two-digit (2 × 2 + 2 × 2) mathematics reading problems and an experimental assignment that contained eight equivalent, 2 × 2 + 2 × 2 problems plus three additional interspersed four-digit + four-digit mathematics reading problems. After spending 9 min 15 s working on each assignment, significantly more students ranked the experimental assignment as being less difficult and requiring less effort to complete. When given a choice between the two assignments for homework, significantly more students chose the experimental assignment. No differences between assignments were found on target problem (i.e., 2 × 2 + 2 × 2) accuracy levels. Results support earlier research that showed how students' preference for assignments could be improved by interspersing additional brief tasks among more time consuming target tasks. In addition to applied implications, theoretical implications related to task completion as a reinforcing event, choice, and relative rates of reinforcement are discussed.     

Causing Students to Choose More Language Arts Work: Enhancing the Validity of the Additive Interspersal Procedure

Research on the additive interspersal procedure was extended by exposing seventh-grade students to curricula-based (e.g., educationally valid) language arts assignments. In Experiment I, each student was given a control language arts assignment containing 20 discrete target items and an experimental assignment containing 24 equivalent target items, plus eight interspersed briefer items. After working on both assignments for 10 minutes, significantly more students chose a new experimental assignment for homework. Individual analysis showed that 85% of the students preferred or chose the assignment associated with higher discrete task completion rates. In Experiment II, students completed both assignments. Results extended previous research by showing that even after expending more effort to complete the 20% more target items plus the additional interspersed items on the experimental assignments, significantly more students chose an experimental assignment for homework. Applied and theoretical implications are discussed along with limitations of the current study and directions for future research.     

Reducing Perceptions of Time Required to Complete Math Assignments by Adding Problems to Assignments: A Synthesis of the Additive Interspersal Research

Results from nine experiments were analyzed to evaluate the relationship between relative problem completion rates (RPCR) and judgments of time involving mathematics assignments. For each experiment, control assignments contained only target mathematics computation or word problems. Matched experimental assignments contained similar target problems with additional, briefer problems interspersed after every third target problem. After working on each assignment for the same amount of time, students selected the assignment that they judged would require the least or most amount of time to complete. Regression analysis revealed a significant linear relationship between RPCR (i.e., PCR on experimental assignments/PCR on control assignments) and time perceptions (r=.97). As RPCR increased, the percentage of students judging the experimental assignments as being less time consuming increased proportionally. Discussion focuses on application of time perception theories to educational settings.     

Improving assignment preference through interspersing additional problems: Brief versus easy problems

College students were exposed to a control mathematics assignment containing 16 three-digit by two-digit multiplication (3×2) problems and two experimental assignments that contained 16 equivalent 3×2 problems and six additional interspersed problems. On one experimental assignment, 4-digit plus 4-digit problems (4+4) were interspersed. On the other experimental assignment, 2-digit divided by 1-digit with whole number answers problems (2/1) were interspersed. When given a choice, significantly more students choose the 2/1 assignment over the control and 1+4 assignment. Students also ranked the 2/1 sheet as requiring less time to complete than the control or 4+4 assignment but no differences were found on assignment difficulty rankings between the 4+4 and 2/1 assignments. No differences were found on accuracy levels or rates of responding on the target 3×2 problems across assignments. Results showed that interspersing additional problems that take relatively less time to complete may be more important for altering student preference for assignments than interspersing easier problems. Discussion focuses on schedules of reinforcement and resource efficient procedures for increasing student preference for assignment without compromising curricula integrity.     

EFFECTS OF EXPLICIT TIMING ON MATHEMATICS PROBLEM COMPLETION RATES IN AFRICAN-AMERICAN THIRD-GRADE ELEMENTARY STUDENTS

A multiple baseline design was used to evaluate the effects of Van Houten and Thompson's (1976) explicit timing procedure on problem completion rates and accuracy levels in African-American third-grade students. During the explicit timing phase, students were told that they were being timed and were instructed to circle the last problem completed at each 1-min interval. Results showed that the explicit timing procedure increased problem completion rates. A decreasing trend in percentage of problems correct also occurred. Exploratory data analysis suggested that decreases in accuracy were not caused by the explicit timing procedure and did not occur in students who had attained high levels of preintervention accuracy. Discussion focuses on recommendations for educators who wish to use timing procedures to increase students' rates of accurate responding.     

Effects of Interspersed Brief Problems on Students' Endurance at Completing Math Work

An alternating treatments design was used to compare the effects of baseline, interspersed brief problems, and interspersed brief problems plus token reinforcement on students' endurance while completing math worksheets. By pairing the completion of brief problems with token reinforcement, the role of problem completion as a conditioned reinforcer was examined consistent with the discrete task completion hypothesis. Four 5th grade students who were low achieving in math participated. Each day the students completed a stack of math worksheets containing 3-digit by 3-digit addition problems with or without interspersed single-digit problems for 10 min. Dependent measures included total digits correct per session and during each min of the 10 min work period (i.e., a measure of endurance). Results indicated that total digits correct per session was highest during the interspersal plus reinforcement condition followed by interspersal and then baseline for three of the four students. In addition, both interspersal conditions resulted in greater endurance than baseline. Limitations of the current study and implications for increasing students' persistence on classroom tasks are discussed.     

Moderating Effects of Mathematics Anxiety on the Effectiveness of Explicit Timing

Explicit timing is an empirically validated intervention to increase problem completion rates by exposing individuals to a stopwatch and explicitly telling them of the time limit for the assignment. Though explicit timing has proven to be effective for groups of students, some students may not respond well to explicit timing based on factors such as mathematics anxiety. The present study examined the effects of explicit timing on mathematics performance for 81 fourth and fifth graders with differing levels of mathematics anxiety. Students completed more digits correct during explicit timing as compared to baseline and control. Additionally, results indicated there was a significant linear relationship between mathematics anxiety and mathematics performance. Students with low and medium mathematics anxiety completed more digits correct with higher accuracy than students with high mathematics anxiety. Lastly, digits correct and accuracy remained consistent during baseline, control, and explicit timing when condition and anxiety level were both considered. Educational professionals must be cognizant not only of academic variables impacting students learning, but also mental health variables, such as mathematics anxiety, in order to provide a comprehensive treatment package capable of ameliorating academic difficulties.     

Effects of Interspersing Additional Brief Math Problems on Student Performance and Perception of Math Assignments: Getting Students to Prefer to Do More Work

Three experiments were conducted to assess the effects of the interspersing procedure on students' mathematics performance, perceptions of mathematics assignments, and preference for mathematics assignments when more work was added. In Experiment I, college students worked computation problems from two assignments. The control assignment contained 15 three-digit by two-digit problems (3 × 2) and the experimental assignments contained 18 3 × 2 problems and 6 additional interspersed one-digit by one-digit problems (1 × 1). Students then rated the assignments and chose one for homework. Results showed significantly more students preferred (i.e., chose it for homework) the experimental assignment with the additional target (i.e., 3 × 2) and interspersed problems. Furthermore, significantly more students rated this experiment as requiring less effort and being less difficult. Moreover, students' mathematics performance was not affected by the procedure. Experiment II strengthened the internal validity by showing that students did not prefer the experimental assignment because it contained more target problems. Experiment III showed that the interspersing procedure was not powerful enough to extend findings beyond the 20% level (i.e., 40 and 60% more conditions). Results showed how the interspersing procedure could be used to encourage students to choose to do more target computation tasks. Discussion focuses on the applied value of the interspersing procedure and plausible causal mechanisms that may account for current and past findings related to student choice and interspersing brief tasks.     

Interspersing easy math problems among challenging problems: detection of interspersal effects in whole-class applications

Interspersing easy problems among challenging problems has been shown to both increase students’ preference for completing math worksheets and the fluency with which they complete challenging problems. Although early research examining the interspersal procedure in mathematics was conducted with college-age students, there are a growing number of studies utilizing the interspersal procedure in elementary and secondary school settings. A particular concern with existing research however is whether the beneficial effects are maintained across multiple sessions and whether effects generalize when implemented with large groups of students. The current study addressed this concern by administering both control and interspersal math worksheets consisting of instructionally relevant problems to 75 fourth grade students across four sessions. Because students’ instructional levels differed, analyses were conducted separately for students identified as fluent and less fluent based upon student performance on the control worksheet administered during session 1. Dependent measures included digits correct and problems correct as well as students’ responses to four preference questions following each session. Although results differ from previous research in that students completed significantly more digits correct on control worksheets, explanations of these differences are examined and implications are discussed.     

Longitudinal evaluation of the importance of homework assignment completion for the academic performance of middle school students with ADHD

The primary goal of this study was to longitudinally evaluate the homework assignment completion patterns of middle school age adolescents with ADHD, their associations with academic performance, and malleable predictors of homework assignment completion. Analyses were conducted on a sample of 104 middle school students comprehensively diagnosed with ADHD and followed for 18 months. Multiple teachers for each student provided information about the percentage of homework assignments turned in at five separate time points and school grades were collected quarterly. Results showed that agreement between teachers with respect to students assignment completion was high, with an intraclass correlation of .879 at baseline. Students with ADHD were turning in an average of 12% fewer assignments each academic quarter in comparison to teacher-reported classroom averages. Regression analyses revealed a robust association between the percentage of assignments turned in at baseline and school grades 18 months later, even after controlling for baseline grades, achievement (reading and math), intelligence, family income, and race. Cross-lag analyses demonstrated that the association between assignment completion and grades was reciprocal, with assignment completion negatively impacting grades and low grades in turn being associated with decreased future homework completion. Parent ratings of homework materials management abilities at baseline significantly predicted the percentage of assignments turned in as reported by teachers 18 months later. These findings demonstrate that homework assignment completion problems are persistent across time and an important intervention target for adolescents with ADHD.     

An Investigation of Incremental Effects of Interspersing Math Items on Task-Related Behavior

The purpose of this study was to replicate and extend research on task interspersal. The authors investigated whether changes in on-task behavior of two middle school students were functionally related to changes in the relative percentages of easy and difficult items on math worksheets. They found that the participants remained on task longer while completing worksheets with 33 and 67% interspersed easy problems than while completing worksheets without the interspersed easy problems. Participants’ accuracy in answering the target problems was not affected, however, by the interspersal procedure. The authors concluded that interspersing easy items on independent math seatwork assignments can increase on-task behavior.     

Improving sixth-grade students perceptions of high-effort assignments by assigning more work: Interaction of additive interspersal and assignment effort on assignment choice

Sixth-grade students were exposed to two pairs of mathematics assignments. Assignment Pair A included a high-effort and a moderate-effort assignment, each containing 18 three-digit by two-digit (3×2) problems. Assignment Pair B was similar except the high-effort assignment contained six additional one-digit by one-digit (1×1) problems interspersed following every third 3×2 problem. After exposure to each pair of assignments, students ranked assignments and chose a new assignment for homework. Analysis of Assignment Pair A data showed students preferred the moderate-effort assignment. Analysis of interactions showed that interspersing the additional brief problems to the high-effort assignment caused significantly more students to choose the high-effort assignment for homework and rank it as requiring less effort and time to complete and as being less difficult than the moderate-effort assignment. Results support the hypothesis that a discrete task is a reinforcer and suggest that educators can increase the probability of students engaging in more challenging assignments that require more effort to complete by interspersing additional brief tasks. Applied and theoretical implications are discussed along with future research.     

Improving sixth-grade students perceptions of high-effort assignments by assigning more work: Interaction of additive interspersal and assignment effort on assignment choice

Sixth-grade students were exposed to two pairs of mathematics assignments. Assignment Pair A included a high-effort and a moderate-effort assignment, each containing 18 three-digit by two-digit (3×2) problems. Assignment Pair B was similar except the high-effort assignment contained six additional one-digit by one-digit (1×1) problems interspersed following every third 3×2 problem. After exposure to each pair of assignments, students ranked assignments and chose a new assignment for homework. Analysis of Assignment Pair A data showed students preferred the moderate-effort assignment. Analysis of interactions showed that interspersing the additional brief problems to the high-effort assignment caused significantly more students to choose the high-effort assignment for homework and rank it as requiring less effort and time to complete and as being less difficult than the moderate-effort assignment. Results support the hypothesis that a discrete task is a reinforcer and suggest that educators can increase the probability of students engaging in more challenging assignments that require more effort to complete by interspersing additional brief tasks. Applied and theoretical implications are discussed along with future research.     

Varying Problem Effort and Choice: Using the Interspersal Technique to Influence Choice Towards More Effortful Assignments

College students were exposed to two pairs of mathematics assignments. Assignment Pair A included a high-effort assignment containing 18 long three-digit × two-digit (3×2) multiplication problems with all numerals in each problem being equal to or greater than four and a moderate-effort assignment that contained nine long problems and nine interspersed moderate 3×2 problems with numerals less than four. Assignment Pair B contained similar assignment sheets, the exception being that the high-effort assignment contained six additional one-digit × one-digit (1×1) problems interspersed following every third 3×2 problem. After working on each assignment pair, students ranked assignments and chose a new assignment for homework. Analysis of Assignment Pair A revealed that students overwhelmingly preferred the moderate-effort assignment. Analysis of interaction effects showed that when additional brief problems were added to the high-effort assignments, the proportion of students who chose the high-effort assignment for homework and ranked it as being less difficult, time consuming, and effortful increased significantly. Results support previous research on effort and choice and the hypothesis that a completed discrete problem may serve a reinforcing stimulus.     

An investigation of the partial-assignment completion effect on students' assignment choice behavior

This study was designed to investigate the partial assignment completion effect. Seventh-grade students were given a math assignment. After working for 5 min, they were interrupted and their partially completed assignments were collected. About 20 min later, students were given their partially completed assignment and a new, control assignment that contained the same number of equivalent problems that were incomplete on their partially completed assignment. Students were told that they would have to complete an assignment but could choose which assignment they completed. Significantly more students chose their partially completed assignment. Theoretical and applied implications and directions for future research are discussed.