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.     

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.     

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.     

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.     

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.     

Comparison of the Explicit Timing and Interspersal Interventions: Analysis of Problem Completion Rates,Student Preference,and Teacher Acceptability

Explicit timing and interspersal interventions were investigated using a within-subjects design with 45 third-grade students. A control assignment consisted of subtraction of a two digit number from a two digit number (i.e., target problem) and served as a baseline. An explicit timing assignment consisted of similar problems as those for the control assignment. The interspersal assignment consisted of similar problems as those for the control and explicit timing assignments with the addition of subtraction of a one digit number from a one digit number interspersed following every third target problem. Total problem completion rates, target problem completion rates, accuracy on target problems and students' rating regarding difficulty, time, effort, and preference between assignments for class work were collected. Student preference choices were analyzed for fit with the discrete task completion hypothesis. Three trials were administered. Results indicated that: (a) students completed more total problems during interspersal, (b) target problem completion rates were higher during explicit timing, (c) accuracy rates remained constant, (d) students rated the explicit timing assignment as requiring more time and being more difficult for all trials and as requiring more effort for trial 2 and 3, (e) students selected the interspersal assignment to do in class as compared to the explicit timing assignment for all trials, and (f) the data fit the discrete task completion hypothesis relatively well for all trials. Discussion focuses on comparing academic interventions based on problem completion rates, student preference, and acceptability data.     

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.     

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.     

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.     

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.     

Boys Don’t Work? On the Psychological Benefits of Showing Low Effort in High School

Male students show less academic effort and lower academic achievement than do female students. The present study aimed to shed more light on the reasons for why male students show low academic effort despite the finding that this undermines their academic achievement. We explored whether students experience psychological benefits from showing low effort or “effortless” achievement in school and whether these benefits are greater for male than for female students. In two experimental vignette studies with independent samples of German ninth graders (N?=?210) and teachers (N?=?176), we systematically varied student targets’ gender, effort, and achievement and tested for effects on targets’ ascribed intelligence, popularity, likeability, masculinity, femininity, and gender-typicality. The “effortless” achiever was rated as more popular than students showing high effort. Teachers perceived the effortless achiever as the most intelligent target. Academic effort further increased students’ ratings of a low-achieving target’s likeability and students’ and teachers’ ratings of all targets’ femininity as well as decreased students’ ratings of all targets’ masculinity. Students and teachers perceived targets showing low (vs. high) effort as more similar to a typical boy, whereas teachers perceived targets showing high (vs. low) effort as more similar to a typical girl. Results indicate a need to understand the psychological benefits of low academic engagement, especially for male students, and to address the feminine stereotyping of (academic) effort.     

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.     

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.     

Delaying feedback promotes transfer of knowledge despite student preferences to receive feedback immediately

Educators and researchers who study human learning often assume that feedback is most effective when given immediately. However, a growing body of research has challenged this assumption by demonstrating that delaying feedback can facilitate learning. Advocates for immediate feedback have questioned the generalizability of this finding, suggesting that such effects only occur in highly controlled laboratory settings. We report a pair of experiments in which the timing of feedback was manipulated in an upper-level college engineering course. Students practiced applying their knowledge of complex engineering concepts on weekly homework assignments, and then received feedback either immediately after the assignment deadline or 1 week later. When students received delayed feedback, they performed better on subsequent course exams that contained new problems about the same concepts. Although delayed feedback produced superior transfer of knowledge, students reported that they benefited most from immediate feedback, revealing a metacognitive disconnect between actual and perceived effectiveness.     

Culture and importance of backgrounds: a cross-cultural study of photograph taking

To compare the focus on targeted people while taking a photograph, samples of American and Chinese college students were randomly selected and asked to take casual pictures of people around them with digital cameras. About 200 photographs were rated for the focus on the intended target in the picture. American students were more likely to focus on the targeted individual, while the Chinese students were more likely to attend to the background and the environment of the targeted individual. The findings imply that for the Chinese college students, the environment can be equally important as the person. Possibly for Americans the environment is less important due to the more individualistic culture.     

Effort is virtuous,but it's better to have ability: Evaluative responses to perceptions of effort and ability

Evaluative responses to imagined task outcomes were found to depend on the question asked, as well as on perceptions of effort and ability. When university students were asked when they would experience pride or shame, they indicated effort would increase pride over success and reduce shame over failure. On the other hand, when asked what type of person they would like to be they chose high ability regardless of outcome. This modified Weiner's (1972) statement of the relation of causal attributions and affective expression. Individual differences in responses to these questions related to differences in self-concept of ability. This result suggested extensions of the attributional analysis of achievement motivation.     

Toward an Integration of Goal Setting Theory and the Automaticity Model

Two laboratory experiments were conducted to assess the extent to which goal setting theory explains the effects of goals that are primed in the subconscious on task performance. The first experiment examined the effect on performance of three primes that connote the difficulty levels of a goal in the subconscious. Participants (n = 91) were randomly assigned to one of three conditions where they were primed with either a photograph of a person lifting 20 pounds (easy goal), 200 pounds (moderately difficult goal), or 400 pounds (difficult goal). Following a filler task, participants were asked to “press as hard as you can” on a digital weight scale. Participants who were primed with the difficult goal exerted more effort than those who were primed with the moderate or easy goal. The second experiment examined whether choice of goal difficulty level can be primed. Participants (n = 133) were randomly assigned to one of two conditions. Those primed with a difficult goal consciously chose to set a more difficult goal on a brainstorming task than those who were primed with an easier goal. Similarly, their performance was significantly higher. Conscientiousness moderated the subconscious goal–performance relationship while the self‐set conscious goal partially mediated the subconscious goal–performance relationship.     

Academic responses and attitudes engendered by a programmed course in child development

Both a small course section and a large course section were taught with methods that involved breaking material down into weekly units that had to be mastered by students as indicated by weekly tests. Attendance at lectures was voluntary and students were not tested on lecture material. In a system in which a student could receive only an A or an F for a course grade, less than 2% of the students receiving credit failed to master all material and received Fs. Students in the large course performed better on weekly tests and received fewer Fs than their counterparts in the small course, even though they rated their experience less favorably. Within the large course, the methods of tutorial interview, group discussion, and written assignment were compared in terms of their effectiveness in preparing students for weekly tests. Tutorials and written assignments were superior to group discussions in this regard. Students rated the effectiveness and enjoyability of these three methods in the reverse order from their actual effectiveness for test preparation. Some consequences of lack of congruity between attitude measures and performance measures were discussed.