Mathematics Assignments Research Articles

Increasing Math Assignment Completion Using Solution-Focused Brief Counseling

Solution-focused brief counseling (SFBC) is an efficient and direct approach to therapy that emphasizes problem identification and solutions. A multiple-baseline-across-participants design was used to evaluate the effects of a SFBC intervention on mathematics assignment completion and accuracy across six fifth-grade students who were failing math. The majority of the participants showed an immediate improvement in assignments completed and these improvements were generally maintained. Although intervention accuracy rates were higher than baseline accuracy rates, they continued to remain fairly low across phases. Discussion focuses on the utility of SFBC as an academic intervention in school settings. Strengths and limitations of the current study are addressed along with implications for practice and future research.

OptAssign—A web-based tool for assigning students to groups

A frequent task in educational settings is to assign students to groups based on stated preferences for some projects or topics. This paper introduces a web-based tool supporting both the work flow of collecting student data and the group formation. The latter is based on finding optimal solutions to suitable mathematical assignment problems, allowing for a number of constraints regarding size and structure of the groups. Evaluation results show advantages compared to manual procedures in terms of time savings for lecturers, and higher fairness and correctness as perceived by students.

Effects of interspersing rates on students performance on and preferences for mathematics assignments: Testing the discrete task completion hypothesis

AbstractThe current study investigated the discreet task completion hypothesis presented by C. H. Skinner (2002) by investigating how the rate of interspersing affects performance on and preferences for academic assignments. Specifically, 70 sixth‐, seventh‐, and eighth‐grade students were presented with four assignment pairs of multiplication problems. Each pair consisted of a control assignment (i.e., no interspersing) and an experimental assignment (i.e., interspersing) that interspersed at one of four rates (i.e., no interspersing, every other problem, every third problem, or every fifth problem). After working on each assignment pair, assignment acceptability was measured. Results indicated that although students completed the same number of target problems with the same level of accuracy within assignment pairs, total problem completion rates were affected by the rate of interspersing. In addition, students' acceptability of the assignments was strongly related to the discrepancy in total problems completed across assignment types within assignment pairs. Discussion focuses on predicting students' preferences for academic assignments, implications for practitioners, and directions for future research. © 2007 Wiley Periodicals, Inc.

Effects of problem order on accuracy, preference, and choice of multiplication assignments.

College students (N = 151) completed three in-class mathematics assignments that varied with respect to the order of short, medium, and long multiplication problems, including a short-to-long order, a long-to-short order, and a random order. Problem order within assignments did not significantly affect work accuracy, completion time, or assignment preference. However, participants rated (1) the assignment with random order as less difficult than the other two assignments and (2) the assignment with long-to-short order as requiring less time than the other two assignments. Participants were likely to choose a related homework assignment viewed as less effortful, less difficult, or less time consuming. Several concepts (e.g., matching law, behavioral momentum, and Premack reinforcement principle) were used in interpreting the results. Keywords: problem order, mathematics, homework, matching law, behavioral momentum, Premack reinforcement principle. ********** Academic assignments and tests often involve a series of tasks or problems that can be ordered in a variety of ways. A typical pattern is to begin the assignment with the less demanding tasks (briefer, easier) and proceed to the more demanding. A less common order is to begin with the more demanding tasks and proceed to the less demanding. A third order is to randomize task order with respect to difficulty. Because order of tasks within an assignment could affect performance on the assignment, time to complete the assignment, and favorability rating of the assignment, one would expect a plethora of research dealing with the effect of task order on student performance and preference of task order. However, an examination of research on assignment performance and assignment preference reveals few studies that deal specifically with the effects of task order within assignments. Research in this area has focused mainly on exams rather than assignments. Studies of multiple-choice exams have demonstrated mixed effects of item order on performance accuracy. Balch (1989) found that sequential exams (in which the test material was presented in the same order that material was presented in texts or lectures) produced higher scores than randomized or chapter-sequenced exams. In contrast, Neely, Springston, and McCann (1994) reported no differences in accuracy between sequential and randomized questions on undergraduate psychology exams. Similarly, Perlini, Lind, and Zumbo (1998) found no influence of easy-to-hard, hard-to-easy, or random item order on psychology exam performance. Studies of difficulty ratings of exams with different task orders have also produced mixed results. Laffitte (1984) found no differences in perceived difficulty of exams organized as easy-to-hard by chapter, easy-to-hard across chapters, randomly within chapters, and randomly across chapters. In contrast, Olson and Barickowski (1976) reported that hard-to-easy tests were viewed as easier than easy-to-hard, with no differences in accuracy of answers. Whether these research findings on item order with psychology exams can be generalized to assignments that involve skill building in a variety of academic domains remains an issue for further investigation. Research regarding the effects of choosing assignment sequence has been done mainly with children and adults with special needs (e.g., autism, mental retardation) and has typically dealt with the scheduling of assignments rather that the order of tasks within assignments. For example, Kern, Mantegna, Vorndran, Bailin, and Hilt (2001) found that students having intellectual and behavioral problems improved both in task engagement and appropriate conduct when allowed to schedule the sequence of required tasks. Similarly, Seybert, Dunlap, and Ferro (1996) reported that giving high school students with severe mental retardation the opportunity to schedule their tasks increased task engagement and task productivity. …

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.

The Effects of Task Demands and Additive Interspersal Ratios on Fifth-Grade Students’ Mathematics Accuracy

.Assignments were altered to determine if interspersing additional briefer and easier mathematics problems enhanced students’ accuracy on longer, more difficult target problems across two types of mathematics assignments. Students (N = 52) from three fifth-grade classes completed six math assignments incorporating two task demands and three interspersal ratios. The interspersal ratios were no interspersal, one interspersed problem per three target problems (1:3), and one interspersal problem per one target problem (1:1). For the written (low-attention) assignments, students completed problems via paper and pencil. For the cognitive (high-attention) assignments, the experimenter read problems aloud and students had to compute mathematics problems in their heads, using paper and pencil only to record answers. Results showed that for the cognitive assignments, target problem accuracy was significantly higher for the 1:3 ratio relative to the other two ratios. On the written assignments, target problem accuracy levels were significantly higher on the 1:1 ratio assignments relative to the no interspersal assignments. Discussion focuses on applied and theoretical implications of the current results.

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.

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.

Conservative Approach to Computerised Marking of Mathematics Assignments

Conservative Approach to Computerised Marking of Mathematics Assignments

FOCUS ON INCLUSION RECIPROCAL TEACHING AS A COMPREHENSION STRATEGY FOR UNDERSTANDING MATHEMATICAL WORD PROBLEMS

Ms. Johnson was concerned about the inconsistent performance of several of her students in solving mathematical word problems. A number of her students were one to two grade levels below their grade placement in reading, spoke English as a second language, and had identified reading disabilities. On mathematics assignments that required minimal reading, all the students in Ms Johnson's class performed adequately. The major state assessment in mathematics was in four months time but Ms Johnson was worried that these students might fail because the state assessment invariably contained a significant number of mathematical word problems. Ms. Johnson felt frustrated by her inability to help her students read and comprehend mathematical word problems.

Increasing on‐task behavior during mathematics independent seat‐work in students with emotional disturbance by interspersing additional brief problems

AbstractAlternating treatments designs were used to compare on‐task levels in 4 students diagnosed as emotionally disturbed while working on control and experimental independent seat‐work mathematics assignments. Control and experimental assignments were similar except experimental assignments contained additional briefer mathematics problems interspersed following every third problem. Results showed greater on‐task levels while working on experimental assignments across 3 of the 4 students. Discussion focuses on problem completion being a conditioned reinforcer and applying this theory to prevent and remedy academic and social‐behavior problems in students with behavior disorders. © 2002 John Wiley & Sons, Inc.

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.

Extending research on the interspersal procedure to perceptions of continuous reading assignments: Applied and theoretical implications of a failure to replicate

AbstractResearchers have shown that students' perceptions of mathematics assignments could be improved by interspersing additional briefer, easier problems (e.g., Logan and Skinner, 1998). The current study was designed to extend this research to reading tasks. Seventh‐grade students read out loud both a control passage and a similar experimental passage that contained additional interspersed brief (i.e., 16 words), easy (i.e., first‐grade reading level) paragraphs. Students then selected the passage that would require the least effort to read and the least time to read. Students also indicated the passage they liked most (preference) and the passage that they would like to read again (choice). Significantly more students selected the control passage as requiring less time to read, but no differences were found for preference, choice, or effort selections. The results failed to confirm earlier research on the interspersal procedure, thus our findings have applied and theoretical implications regarding causal variables that may account for the effectiveness of the interspersal procedure. Specifically, the current study suggests that the interspersal procedure may improve assignment perception only when the procedure increases discrete task‐completion rates. © 2001 John Wiley & Sons, Inc.

Increasing On-Task Behavior in an Elementary Student During Mathematics Seatwork by Interspersing Additional Brief Problems

Using analogue conditions, previous researchers improved students' perceptions of mathematics assignments by adding and interspersing brief problems to mathematics worksheets (e.g., Logan & Skinner, 1998). In the current study, an alternating treatments design was used to evaluate the effects of the interspersal procedure on an elementary student who was referred to a school psychologist for high rates of off-task behavior during independent seatwork. Results showed that the procedure increased the student's on-task levels during classroom mathematics assignments. Discussion focuses on implications for practitioners and on future research designed to improve students' (a) academic behaviors, (b) academic performance, and (c) perceptions of assignments.

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.

Enhancing Perceptions of Mathematics Assignments by Increasing Relative Problem Completion Rates Through the Interspersal Technique

Students solved mathematics problems from 4 assignment pairs. Each control assignment contained 18 target multiplication problems that were 4 × 1-digit (4 × 1), 4 × 2, 4 × 3, or 4 × 4. Each paired experimental assignment contained 18 similar problems plus 6 interspersed 1 × 1-digit problems. After computing problems from each pair of assignments, the students rated them and chose 1 for homework. Across all assignment pairs, problem completion rates were greater on the experimental assignments, and significantly more students chose a new experimental, rather than control, assignment for homework. Furthermore, as the discrepancy between problem completion rates increased across assignment pairs, the probability of students' choosing the experimental assignment for homework and rating the experimental assignment more favorably with respect to difficulty, effort, and time also increased. The relationship between student choice behaviors and relative problem completion rates has theoretical and applied implications for choice research and the design of activities composed of discrete tasks.

Great Expectations: The Negative Consequences of Falling Short1

The present study shows conditions under which a positive stereotypic belief–Asians are good in mathematics–can have negative consequences. Participants graded a poorly performed mathematical assignment that they believed was the work of an Asian or a White target person. Under no accuracy instructions, participants who spent less time grading (unmotivated participants) assigned fewer points to the Asian than the White target. There was no difference in assignment of points to the Asian or the White target when participants were given accuracy instructions or spent more time grading (motivated participants). The findings suggest that group members may experience negative consequences when they fall short of “great expectations” stemming from a positive stereotypic belief about their group.

Linguistic and cultural factors in the readability of mathematics texts: the Whorfian hypothesis revisited with evidence from the South African context

South Africa is a country of many languages and cultures. Education is mostly in English which implies that about 80% of all secondary school students are second language learners. Currently many mathematical problems are posed in real‐life contexts. This not only introduces more language in mathematics texts, but also more issues related to culture. When considering the influence on readability, it is difficult to disentangle the role of linguistic and cultural factors and this in turn seems to be a manifestation of the Sapir‐Whorf hypothesis. The study was therefore guided by research questions such as: what linguistic and cultural factors in the ordinary language of mathematics texts influence readability? Protocol analysis was used with students aged 17–18 years to establish readability problems. Linguistic as well as cultural factors were identified and the hypothesis that improved readability of mathematics assignments improves achievement was confirmed in a number of cases. Writers of mathematics texts should therefore consider linguistic as well as cultural factors when writing for different reading audiences. Other conclusions address teaching and examination practice.

Improving students' perceptions of a mathematics assignment by increasing problem completion rates: Is problem completion a reinforcing event?

Improving students' perceptions of a mathematics assignment by increasing problem completion rates: Is problem completion a reinforcing event?