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.     

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.     

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.     

The importance of home practice for progressive relaxation training

The efficacy of home practice assignments was evaluated as a component of standardized progressive relaxation training. Subjects reporting general anxiety and tension problems were assigned to either a home practice relaxation, no home practice relaxation or wait-list control condition. Treatment was conducted for 10 sessions over a 5-week period. In addition, subjects in both conditions engaged in in-vivo application of their relaxation skills during a final 2-week application period. Group comparisons showed that both progressive relaxation conditions significantly improved on daily self-monitored general anxiety and tension levels relative to the wait-list control condition. Group analyses of percent subject improvements supported the effectiveness of home practice assignments, especially during the application period. No systematic differences between groups, on physiological and self-report variables, were found during several laboratory relaxation evaluation sessions. This study supports the contribution of home practice assignments to progressive relaxation training.     

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.     

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.     

Homework assignments, consequences, and classroom performance in social studies and mathematics

Elementary school students who frequently answered questions incorrectly in class were given daily homework assignments in social studies and math, but they rarely completed the assignments accurately and their classroom performance in social studies and math was only slightly better than when they did not have homework assignments. However, consequences provided for accurate completion of homework assignments increased the number of students completing homework and the accuracy with which homework assignments were completed. Further, assignments of homework with consequences for accuracy were associated with more accurate classroom performance.     

Empiricism,probability, and knowledge of arithmetic: A preliminary defense

The topic of this paper is our knowledge of the natural numbers, and in particular, our knowledge of the basic axioms for the natural numbers, namely the Peano axioms. The thesis defended in this paper is that knowledge of these axioms may be gained by recourse to judgments of probability. While considerations of probability have come to the forefront in recent epistemology, it seems safe to say that the thesis defended here is heterodox from the vantage point of traditional philosophy of mathematics. So this paper focuses on providing a preliminary defense of this thesis, in that it focuses on responding to several objections. Some of these objections are from the classical literature, such as Frege's concern about indiscernibility and circularity (Section 2.1), while other are more recent, such as Baker's concern about the unreliability of small samplings in the setting of arithmetic (Section 2.2). Another family of objections suggests that we simply do not have access to probability assignments in the setting of arithmetic, either due to issues related to the ω-rule (Section 3.1) or to the non-computability and non-continuity of probability assignments (Section 3.2). Articulating these objections and the responses to them involves developing some non-trivial results on probability assignments (Appendix A–Appendix C), such as a forcing argument to establish the existence of continuous probability assignments that may be computably approximated (Theorem 4 Appendix B). In the concluding section, two problems for future work are discussed: developing the source of arithmetical confirmation and responding to the probabilistic liar.     

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.     

Writing to Learn the Reformation: Or,Who Was Ulrich Zwingli And Why Should I Care?

This article describes the use of “Writing to Learn” assignments in a course on the Theology of the Protestant and Catholic Reformations. These short, informal assignments promote active learning by focusing on writing as a process for critical thinking and as a way to learn the content of the course. They help students creatively engage with the texts, thoughtfully reflect on them, and critically assess their significance. This article describes the theory behind these assignments, provides examples of different types of assignments as well as excerpts from student papers, and concludes with an evaluation of their effectiveness. The students in the course found the assignments helpful in learning the content of the course and their attitude toward writing in this course significantly improved.     

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.     

Assigning Homework to Couples and Families

Homework assignments, or “out-of-session assignments,” have gained popularity among couple and family therapists due to their potential to solidify the work achieved during the course of therapy and to help clients take responsibility for their own change. Homework assignments also serve as a testing ground in therapy to determine what works and what does not. This article provides an update on some of the empirical literature on homework assignments and its reported effectiveness in the domain of couples and family therapy. It also highlights the need for and the effectiveness of out-of-session assignments during the course of treatment.     

From Civic Engagement to Circles of Grace: Mid‐Range Reflection on Teaching for Global Citizenship

The course “Empowering Youth for Global Citizenship” seeks to equip students to teach global citizenship by engaging them in practices of ascetic withdrawal from consumer habits and active engagement in the public sphere. These goals underlie the design of the assignments, but should have also shaped the relationship between the assignments themselves. This article addresses the issue of course design in the service of empowering students for engagement in the public sphere by reflecting upon the course assignments, with emphasis on a project that worked well, and the implications this has for its relationship to the other course assignments, including one that missed the mark. The exploration of this misalignment between the learning goals and actual outcomes of the different assignments brings to light the unique role of learning communities of accountability and acceptance in deepening the impact of assignments aimed at personal transformation, as well as the rich dynamic that can come from coordinating course assignments to bring “head, heart, and hands” together.     

TEACHING ELEMENTARY STUDENTS WITH DEVELOPMENTAL DISABILITIES TO RECRUIT TEACHER ATTENTION IN A GENERAL EDUCATION CLASSROOM: EFFECTS ON TEACHER PRAISE AND ACADEMIC PRODUCTIVITY

Four fourth graders with developmental disabilities were trained to recruit teacher attention while they worked on spelling assignments in a general education classroom. The students were taught to show their work to the teacher two to three times per session and to make statements such as, “How am I doing?” or “Look, I'm all finished!” Training was conducted in the special education classroom and consisted of modeling, role playing, error correction, and praise. A multiple baseline across students design showed that recruitment training increased (a) the frequency of students' recruiting, (b) the frequency of teacher praise received by the students, (c) the percentage of worksheet items completed, and (d) the accuracy with which the students completed the spelling assignments.     

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.     

Climbing the corporate ladder: do female and male executives follow the same route?

This study compares the careers of matched samples of 69 female executives and 69 male executives by examining perceived barriers and facilitators of advancement, self-reported developmental experiences, and career histories. Consistent with tokenism theory, women reported greater barriers, such as lack of culture fit and being excluded from informal networks, and greater importance of having a good track record and developing relationships to facilitate advancement than did men. Career success, measured by organizational level and compensation, was positively related to breadth of experience and developmental assignments for both genders, but successful women were less likely than successful men to report that mentoring facilitated their advancement. Developmental experiences and career histories were similar for female and male executives, but men had more overseas assignments and women had more assignments with nonauthority relationships.     

The effects of access to a playroom on the rate and quality of printing and writing of first and second-grade students

The major dependent variable was the rate at which first and second-grade students printed or wrote daily copying assignments. Data were also taken on the percentage of letters scored as errors according to a set of scoring criteria. Initially, these data were collected during a baseline condition in which each child returned to his seat as soon as his completed work had been scored, to wait for the rest of the class to finish their assignments. When the children were allowed to go to a playroom after their papers had been scored, there was a reliable increase in the mean printing or writing rates. Subsequent introductions of the baseline and playroom conditions replicated the relative effectiveness of access to the playroom to produce higher work rates. Finally, the total amount of time allowed for children to complete their assignments and then play was progressively reduced from 50 to 35 minutes. A progressive increase in work rates was correlated with these changes. Throughout the experiment, there was considerable variability in the mean number of letters scored as errors but there was a clear trend towards fewer errors.     

Effects of the contingency for homework submission on homework submission and quiz performance in a college course

Effects of the contingency for submission of homework assignments on the probability of assignment submission and on quiz grades were assessed in an undergraduate psychology course. Under an alternating treatments design, each student was assigned to a points condition for 5 of 10 quiz-related homework assignments corresponding to textbook chapters. Points were available for homework submission under this condition; points were not available under the no-points condition. The group-mean percentage of homework assignments submitted and quiz grades were higher for all chapters under the points condition than in the no-points condition. These findings, which were replicated in Experiment 2, demonstrate that homework submission was not maintained when the only consequences were instructor-provided feedback and expectation of improved quiz performance.     

EFFECTS OF CHOOSING ACADEMIC ASSIGNMENTS ON A STUDENT WITH ATTENTION DEFICIT HYPERACTIVITY DISORDER

The effects of choosing academic assignments on the undesirable behaviors manifested by a second-grade student with attention deficit hyperactivity disorder were analyzed. This study extended Dunlap et al.'s (1994) research on choice making as a form of antecedent control. A reversal design showed that undesirable behaviors decreased when the student was given a choice of academic assignments.