Comprehension of arithmetic word problems: Evidence from students' eye fixations.

Students have difficulty solving arithmetic word problems containing a relational term that is inconsistent with the required arithmetic operation (e.g., containing the term less, yet requiring addition) rather than consistent. To investigate this consistency effect, students' eye fixations were recorded as they read arithmetic word problems on a computer monitor and stated a solution plan for each problem. As predicted, low-accuracy students made more reversal errors on inconsistent than consistent problems, students took more time for inconsistent than consistent problems, this additional time was localized in the integration/planning stages of problem solving rather than in the initial reading of the problem, these response-time patterns were obtained for high-accuracy but not for low-accuracy students, and high-accuracy students required more rereadings of previously fixated words for inconsistent than for consistent problems. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Too upset to think: The interplay of borderline personality features, negative emotions, and social problem solving in the laboratory.

Borderline personality disorder (BPD) is associated with poor social problem solving and problems with emotion regulation. In this study, the social problem-solving performance of undergraduates with high (n = 26), mid (n = 32), or low (n = 29) levels of BPD features was assessed with the Social Problem-Solving Inventory—Revised and using the means-ends problem-solving procedure before and after a social rejection stressor. The high-BP group, but not the low-BP group, showed a significant reduction in relevant solutions to social problems and more inappropriate solutions following the negative emotion induction. Increases in self-reported negative emotions during the emotion induction mediated the relationship between BP features and reductions in social problem-solving performance. In addition, the high-BP group demonstrated trait deficits in social problem solving on the Social Problem-Solving Inventory—Revised. These findings suggest that future research must examine social problem solving under differing emotional conditions, and that clinical interventions to improve social problem solving among persons with BP features should focus on responses to emotional contexts. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Problem solving in video-based microworlds: Collaborative and individual outcomes of high-achieving sixth-grade students.

The effect of collaboration on problem-solving performance and learning was investigated in the context of a complex, video-based mathematics problem. Ninety-six high-achieving 6th-grade students were randomly assigned to collaborative or individual problem-solving conditions. Two hypotheses were tested: (a) that triads would perform better than individuals when first presented with the problems and (b) that students who had first worked in triads would perform better than students who had worked individually when asked to solve the same problem and a near-transfer problem on their own. Three measures of problem solving and planning were used. Students in the collaborative condition outperformed students in the individual condition on their initial attempt at the problem. In addition, students in the collaborative condition performed better on the mastery and near-transfer problems on 2 out of 3 performance measures. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Variability of worked examples and transfer of geometrical problem-solving skills: A cognitive-load approach.

Studied 4 computer-based training strategies for geometrical problem solving in the domain of computer numerically controlled machinery programming with regard to their effects on training performance, transfer performance, and cognitive load. A low- and a high-variability conventional condition, in which conventional practice problems had to be solved (followed by worked examples), were compared with a low- and a high-variability worked condition, in which worked examples had to be studied. Results showed that students who studied worked examples gained most from high-variability examples, invested less time and mental effort in practice, and attained better and less effort-demanding transfer performance than students who first attempted to solve conventional problems and then studied work examples. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The effects of schema-based instruction on the mathematical word-problem-solving performance of students with learning disabilities

This study examined the effects of a schema-based direct instruction strategy on the word-problem-solving performance of three third- and fourth-grade students (2 girls, 1 boy) with learning disabilities. An adapted multiple-probe-across-students design was used. Results indicated that the intervention was successful in increasing the percentage of correct solutions to word problems for all 3 students. In addition, maintenance of word-problem solving was seen 2 to 3 weeks after the study. Student interviews indicated that the strategy was beneficial. Further research with different students and problem types (e.g., multistep) and an investigation of the long-term effects of the strategy and its use in novel settings appear warranted.     

Enhancing Mathematical Problem Solving Among Third-Grade Students With Schema-Based Instruction.

The purposes of this study were to assess the effects of schema-based instruction (SBI) in promoting mathematical problem solving and to investigate schema induction as a mechanism in the development of mathematical problem solving. Twenty-four 3rd-grade teachers, with 366 students, were assigned randomly to conditions that provided instruction on 4 types of word problems. The 3 16-week conditions were contrast, SBI, and SBI with practice in sorting word problems into schemas. Students were pre- and posttested on mathematical problem-solving tests and were posttested on schema development. Students receiving SBI, with and without sorting practice, improved more than the contrast group on problem-solving measures. Concurrently, the SBI groups' schema development exceeded that of the contrast group, and schema development explained a substantial portion of unique variance in students' posttreatment problem-solving performance. Results also suggested the need for additional research testing the contribution of practice in sorting word problems. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Cognitive benefits and costs of bilingualism in elementary school students: The case of mathematical word problems.

Previous research has emphasized the importance of language for learning mathematics. This is especially true when mathematical problems have to be extracted from a meaningful context, as in arithmetic word problems. Bilingual learners with a low command of the instructional language thus may face challenges when dealing with mathematical concepts. At the same time, speaking two languages can be associated with cognitive benefits with regard to attentional control processes, although such benefits have only been found in highly proficient bilinguals. In the present study, we attempted to disentangle the effects of bilingual proficiency on mathematical problem solving in Turkish–German bilingual elementary school students. We examined whether the positive cognitive effects of bilingualism could be found not only in highly proficient bilinguals but also in students with an immigrant background and a low command of the instructional or native language. Our findings emphasize the importance of language proficiency for mathematics problem solving, as shown by the predictive value of students' proficiency in the language of testing (German/Turkish) for their performance on mathematical word problems. No additional effect of the language of instruction (German) was found for problem solving in the bilingual students' native language (Turkish). Furthermore, bilinguals gained scores comparable to those of their monolingual peers on word problems that required attentional control skills although performing significantly below their monolingual classmates on ordinary word problems, suggesting that bilinguals have an advantage when it comes to attentional control. Finally, bilingual students with a relatively high command of the instructional language performed better on word problems presented in German than on those presented in Turkish, thus facing cognitive costs when transferring knowledge from one language to the other. Implications of our findings for bilingual education are discussed. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Global Optimization of Combined Region Aggregation and Leveling Model

The advent and widespread use of innovative spatial analysis technologies, such as geographic information systems (GIS), computer aided design (CAD) systems, and global positioning systems (GPS), have prompted great interest in spatial optimization. The tasks of selecting an optimal subregion from a larger region—region aggregation—and determining an optimal strategy for cutting and filling that subregion to a uniform elevation—land leveling—are examples of spatial analyses that can benefit from these powerful computer technologies. The combined region aggregation and leveling problem is a complex spatial problem that often involves the comprehensive consideration of multiple, incommensurate, and often conflicting objectives, while at the same time satisfying a set of prespecified physical and logical constraints. Traditionally, these two problems are solved separately, often precluding the identification of global optima. Through this research, a multiobjective integer programming model that considers these problems simultaneously is formulated, a computational algorithm for solving the model is presented, and numerical results that demonstrate the efficiency and effectiveness of this procedure are discussed. Computational experiments report polynomial complexity of the heuristic procedure against exponential worst-case complexity of traditional enumerative methods.     

Practice schedules and the use of component skills in problem solving.

In motor and verbal learning, random practice schedules produce poorer acquisition performance but superior retention relative to blocked practice. We extend this contextual interference effect to the case of learning cognitive procedural skills to be used in problem solving. Subjects in three experiments practiced calculation with Boolean functions. After this acquisition phase, subjects solved problems requiring these procedures. Experiments 1 and 2 demonstrated superior transfer to problem solving for skills acquired under random schedules. In Experiment 3, subjects practiced component skills in a blocked schedule, with one of four tasks—same–different judgment, mental arithmetic, short-term memory, or long-term memory—intervening between trials. For same–different judgments and mental arithmetic, transfer performance was comparable to that found for random schedules in Experiments 1 and 2. This result suggests that the differences depend on processing rather than storage demands of intertrial activity. Implications for theories of problem solving and part–whole transfer are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Comparison of three counseling center referral sources in terms of their rating of the appropriateness of potential helpers.

Random samples of residence hall personnel, faculty, and students were compared on their ratings of 7 potential campus helpers on 7 typical student problems. Properly completed questionnaires were returned from 68 students, 43 faculty, and 36 student residence hall personnel. Discriminant analyses and within-group orthogonal t tests for the student sample indicated that (a) these 3 groups differentiate potential helpers in terms of the problem presented, (b) these groups have significantly different opinions as to the appropriateness of various helpers for a problem or groups of problems, and (c) the student does not see a "friend" as the best helper for all problem situations. Further research was suggested to determine the basis these groups have for evaluating the appropriateness of various helpers. (8 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Where should "you" go in a math compare problem?

This study examined the cognitive effects of self-referencing in math word problems in 100 3rd, 4th, and 5th graders. Two types of compare problems were used: compare unknown (CU) and referent unknown (RU). The word you was placed in the problems either as the known or the unknown term. For the CU problems, self-referencing facilitated students' performance regardless of the position of the you term. When self-referencing was applied, students asked for fewer repeats and solved these CU problems faster and with greater accuracy. For the RU problems, however, students benefited from self-referencing only when the self term was placed as the compare (known) term. When the you term was placed as the referent term, the facilitative effect of self-referencing disappeared. The position of the you term in a RU problem apparently has an impact on the translation procedure required in solving the problem. Further research on the cognitive processing issues raised by these data is suggested and the educational implications of the findings are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The role of learning from examples in the acquisition of recursive programming skills.

Presents an analysis and simulation model of the verbal protocols of 2 college students and 1 8-yr-old S learning to program recursive functions. The model is formalized as a production system capable of acquiring new production rules based on problem-solving experience. The model and protocols suggest that (a) problem solving by analogy to worked-out examples is frequent in initial attempts by novices to write recursive functions; (b) different representations of examples are used to guide problem solving by analogy; and (c) performance on later problems reflects the particular representations used in problem solving by analogy on earlier problems. The protocols and simulations also suggest that learning is facilitated by using abstract representations of the structure of recursion examples to guide initial coding attempts. (French abstract) (25 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The shame of American education.

Recent analyses of American schools and proposals for school reform have missed an essential point: Most current problems could be solved if students learned twice as much in the same time and with the same effort. It has been shown that they can do so (a) when the goals of education are clarified; (b) when each student is permitted to advance at his or her own pace; and (c) when the problem of motivation is solved with programmed instructional materials, so designed that students are very often right and learn at once that they are. The theories of human behavior most often taught in schools of education—particularly cognitive psychology—stand in the way of this solution to the problem of American education, but the proposal that schools of education simply be disbanded is a step in the wrong direction. Teachers need to be taught how to teach, and a technology is now available that will permit them to teach much more effectively. (17 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

An aptitude?×?strategy interaction in linear syllogistic reasoning.

Results of a study with 144 graduate and undergraduate students support the hypothesis that the efficiency of each of 4 alternative strategies for solving linear syllogisms—problems such as "John is taller than Bill; Bill is taller than Pete; who is tallest?"—would depend on Ss' patterns of verbal and spatial abilities. The research also had 3 subsidiary goals. The 1st was to determine whether it is possible to train Ss to use various classes of strategies for solving linear syllogisms; it was found that such training is possible. The 2nd goal was to compare the average efficiencies of 4 alternative strategies adopted spontaneously by Ss. It was found that one strategy (used spontaneously by only a small number of Ss but easily trainable) is more efficient than the alternative strategies that Ss seem to use spontaneously. The 3rd was to provide a series of converging operations for testing the validity of one particular account of linear syllogistic reasoning—a spatial–linguistic mixture model—for Ss receiving no explicit instruction in the solution of linear syllogisms. The validity of this model for the untrained Ss was supported. It is concluded that componential analysis (a series of conceptual and methodological techniques for investigating intelligent performance) can provide a useful means for studying interactions between aptitudes and experimental treatments. (30 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Students' help seeking during problem solving: Influences of personal and contextual achievement goals.

The author investigated how different types of achievement goals influence elementary school students' help seeking. Fourth and 5th graders were asked to solve math problems and were given the opportunity to request help from an adult. Goals were conceptualized on 2 nested dimensions: (a) locus of the goal (i.e., personal goals that students held at the beginning of the study vs. contextual goals that characterized the task situation) and (b) emphasis of the goal (i.e., the relative importance of learning vs. performance). Personal learning goals had a positive influence and personal performance goals had a negative influence on the frequency of confirmation requests and on actual problem solving. For students who had strong personal performance goals, a contextual learning goal resulted in more process-related help seeking than did a contextual performance goal. Both types of help seeking (i.e., confirmation and process-related requests) had a positive influence on problem solving. Interactions among goals are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Understanding multiplicative contexts involving fractions.

Numerous studies indicate that performance in solving single-step multiplicative word problems is influenced by both problem structure and the types of numbers involved in the problem. For example, including numbers less than 1 often increases the difficulty of a problem. What remains unclear is how problem structure and number type interact in influencing difficulty. This study systematically investigates these 2 factors with math-proficient and remedial college students. Findings indicate that it is the role played by fractions in word problems that influences difficulty rather than simply the number of fractions in the problem. Pedagogical strategies for improving students' ability to perceive and represent multiplicative word problems are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

How tree shrews (Tupaia belangeri) perform in a searching task: Evidence for strategy use.

This study investigated how male tree shrews (Tupaia balngeri) performed in a searching task while in their home cages and assessed whether different food distributions affected their performance. The animals were faced with a holeboard containing 9 food sources arranged in a 3 X 3 matrix or in 3 clusters, each containing 3 sources. Animals tended to start and end the trials from preferred locations, thereafter solving the task by strategically organizing the reward collection according to a minimum-distance principle. In the cluster configuration, they visited the sources hierarchically. Food distribution did not affect the performance. Comparison with data from mice and capuchin monkeys revealed that tree shrews and capuchins solved the task in a similar strategic way, whereas mice did not. These findings attract particular attention because of the phylogenetic position of tree shrews, which are regarded as closely related to primates. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Teachers as leaders: A moderator variable approach.

A review of research on teachers as leaders shows that current approaches have produced unclear and inconsistent results. A new approach—viewing teachers in a situational context—is suggested. 155 students filled out 2 questionnaires; the 1st (administered during the 5th wk of class) contained measures of teacher leadership behavior and student role clarity, and the 2nd (administered during the 10th wk) measured overall student satisfaction with the class. Student performance was also assessed at the 10th wk. It was found that (a) student performance significantly correlated with teacher supportiveness and directiveness under low role clarity but not high role clarity, and (b) the differences in these correlations were statistically significant. (23 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Grid-Enabled Simulation-Optimization Framework for Environmental Characterization

Many engineering and environmental problems that involve the determination of unknown system characteristics from observation data can be categorized as inverse problems. A common approach undertaken to solve such problems is the simulation-optimization approach where simulation models are coupled with optimization or search methods. Simulation-optimization approaches, particularly in environmental characterization involving natural systems, are computationally expensive due to the complex three-dimensional simulation models required to represent these systems and the large number of such simulations involved. Emerging grid computing environments (e.g., TeraGrid) show promise for improving the computational tractability of these approaches. However, harnessing grid resources for most computational applications is a nontrivial problem due to the complex hierarchy of heterogeneous and geographically distributed resources involved in a grid. This paper reports and discusses the development and evaluation of a grid-enabled simulation-optimization framework for solving environmental characterization problems. The framework is designed in a modular fashion that simplifies coupling with simulation model executables, allowing application of simulation-optimization approaches across problem domains. The framework architecture utilizes standard communications protocols and the message passing interface with an application programming interface to establish a connection between a centralized search application and simulation models running on TeraGrid resources. Sets of performance and scalability results for solving a groundwater source history reconstruction (SHR) problem are presented. The results show that for a given set of resources, parameters controlling the granularity at various levels of parallelism play an important role in the overall parallel performance. A production run for solving the SHR problem using three geographically distributed grid resources indicates that even in a cross-site grid environment a factor of 90 speedup is possible using 140 computer processors.     

Social technology.

Discusses problems that relate to the differences between research and application and presents a systems approach to solving problems in the social area—that is, social technology. In the systems approach, solutions are generated by combining findings from widely different specializations in basic research in the social sciences. Three cases of such applications are described in which students, after receiving adequate training in this social technology, were able to solve problems. Other areas in which social technology has proved useful are mentioned, among which are the problems found in organizations, such as eliminating or reducing the aftermath of discontent following a promotion on the part of those not promoted, friction between computer programers and other members of the team, and sales. The need is stressed for social science to move out from the area of pure research and into the practical application of the findings already discovered. (28 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)