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)     

Cognitive technology: Some procedures for facilitating learning and problem solving in mathematics and science.

An argument is detailed for modifications to some traditional procedures of mathematics and science instruction. It is suggested that cognitive research findings, in revealing the essential domain specificity of problem-solving skills, have pointed to negative aspects of some traditional emphases. As a major example, conventional problem solving frequently can interfere with the acquisition of knowledge. Alternatives to problem solving such as studying worked examples can be equally ineffective unless they are designed in accordance with current findings. It is concluded that if material is structured with learning rather than goal attainment in mind, problem-solving skills can be enhanced substantially. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Guidance during mathematical problem solving.

Researchers have suggested that often, having students study worked examples may be superior to active problem solving. The guidance provided by such examples reduces cognitive load compared with that imposed by the means–ends strategy used by most novice problem-solvers. This may facilitate schema acquisition. The guidance provided by worked examples or other sources of information, such as subgoals, must not themselves require significant cognitive resources for effective processing. In many areas of mathematics, conventional methods of presentation may result in a splitting of attention between multiple sources of information that must be mentally integrated. The cognitive load imposed may eliminate any benefit of a worked example or other form of guidance. A series of 5 geometry experiments provided evidence for this hypothesis. When guidance in the form of subgoals or worked examples was provided using a conventional format requiring attention to 2 sources of information, Ss' performance was no better and possibly worse than when solving conventional problems. Presenting information using a format that did not split attention resulted in a superiority of worked examples over conventional problems. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The subgoal learning model: Creating better examples so that students can solve novel problems.

Learners have great difficulty solving problems requiring changes to solutions demonstrated in examples. However, if the solution procedures learners form are organized by subgoals, then they are more successful. Subgoal learning is hypothesized to be aided by cues in example solutions that indicate that certain steps go together. These cues may induce a learner to attempt to self-explain the purpose of the steps, resulting in the formation of a subgoal. Across 4 experiments it was found that a label for a group of steps in examples helped participants form subgoals as assessed by measures such as problem-solving performance and talk aloud protocols. Abstract labels were more likely than superficial labels to lead participants to form subgoals with fewer ties to surface features. Subgoals guide problem solving by helping learners focus on the steps to modify in novel problems that involve the same subgoals but require new steps to achieve them. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Dimensions of perceived competence in professional psychology.

Appraised levels of general professional competence for 126 trainees in professional psychology by supervisors who had worked closely with the students. After rating the students, supervisors were asked to describe the dominant characteristics of "outstanding" and "incompetent" trainees. The most commonly mentioned quality of outstanding practitioner-trainees was high intelligence. The most commonly mentioned characteristic of incompetent trainees was lack of knowledge. A rating schedule composed of the 28 most commonly used terms was then employed by supervisors in rating students the following year. Four factors—Professional Responsibility, Interpersonal Warmth, Intelligence, and Experience—emerged from analysis of intercorrelations among variables. Intercorrelations of factor scores with ratings of overall competence showed that behaviorally oriented supervisors gave less weight to warmth in evaluating general competence than did supervisors with psychodynamic or eclectic viewpoints. (14 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Schema induction in children's analogical problem solving.

Three experiments were conducted to explore the ability of school-age children to transfer solutions to analogous problems. This research addressed the issue of how the variability of procedural features in source examples facilitates the induction of a general problem schema and, thus, promotes subsequent transfer. Children were asked to solve a series of problems analogous to A. S. Luchins's (1942) classic waterjar problems. All the problems shared a common isomorphic structure and a general solution but required either similar or different specific procedures. Children who experienced problems with variant procedural features were more likely than those who experienced problems with invariant procedural features to construct a general problem schema and to solve novel problems requiring unfamiliar procedures. This research sheds light on the cognitive mechanisms involved in strategy generalization and analogical problem solving. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Teaching thinking and problem solving: Research foundations.

Reviews 2 general research approaches to the development and effective teaching of reasoning, thinking, and problem solving. The first derives from studies of individuals who are experts in particular domains and emphasizes the role of domain-specific knowledge. The second emphasizes general strategic and metacognitive knowledge; ideally, people who develop the ability to learn new information and to monitor their current levels of proficiency will be able to function more effectively in a variety of contexts. Issues discussed include developmental and intraindividual differences, the representation of knowledge, means of facilitating memory access, and the concept of metacognition. It is concluded that many existing programs designed to teach thinking and problem solving could be strengthened by focusing more explicitly on domain knowledge, especially when students are helped to understand how different ways of learning new knowledge can affect their abilities to solve relevant problems. (3? p ref) (PsycINFO Database Record (c) 2010 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)     

Generalizing from the use of earlier examples in problem solving.

Novices often are reminded of earlier examples during problem solving. Four experiments examine the hypothesis that the use of earlier examples promotes generalizations about problem types, thereby influencing what is learned about the domain. Subjects studied four probability principles with word problems and then tried to solve two test problems for each principle. For half of the first tests, cues indicated which study problem might be used. All second tests were uncued. Experiments 1 and 2 showed that the first-test cuing led to an advantage on second-test performance for both the access and the use of relevant information. Experiments 3 and 4 demonstrated that this cuing benefit is due to some generalization induced from using the study problem to solve the first-test problem. Discussion focuses on the distinctions about how problem comparisons are used in learning and the implications of the view that remindings lead to generalizations. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Using worked examples as an instructional support in the algebra classroom.

In 2 experiments, high school students studied worked examples while learning how to translate English expressions into algebraic equations. In Exp 1, worked examples were used as part of the regular classroom instruction and as a support for homework. In Exp 2, students in a remedial mathematics class received individual instruction. Students using worked examples outperformed the control group on posttests after completing fewer practice problems; they also made fewer errors per problem and fewer types of errors during acquisition time, completed the work more rapidly, and required less assistance from the teacher. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Perceived self-efficacy and everyday problem solving among young and older adults.

This research tested the hypothesis that age differences in both self-efficacy perceptions and problem-solving performance would vary as a function of the ecological relevance of problems to young and older adults. The authors developed novel everyday problem-solving stimuli that were ecologically representative of problems commonly confronted by young adults (young-adult problems), older adults (older adult problems), or both (common problems). Performance on an abstract problem solving task lacking in ecological representativeness (the Tower of Hanoi problem) also was examined. Although young persons had higher self-efficacy beliefs and performance levels on the Tower of Hanoi task problem and the young-adult problems, this pattern reversed in the domain of older adult problems, where the self-efficacy beliefs and performance of older persons exceeded those of the young. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Metareasoning and meta-level learning in a hybrid knowledge-based architecture

Ahybrid knowledge-based architecture integrates different problem solvers for the same (sub)task through a control unit operating at a meta-level, the metareasoner, which coordinates the use of, and the communication between, the different problem solvers. A problem solver is defined to be an association between a knowledge intensive (sub)task, an inference mechanism and a knowledge domain view operated by the inference mechanism in order to perform the (sub)task. Important issues in a hybrid system are the metareasoning and learning aspects. Metareasoning encompasses the functions performed by the metareasoner, while learning reflects the ability of the system to evolve on the basis of its experiences in problem solving. Learning occurs at different levels, learning at the meta-level and learning at the level of the specific problem solvers. Meta-level learning reflects the ability of the metareasoner to improve the overall performance of the hybrid system by improving the efficiency of meta-level tasks. Meta-level tasks include the initial planning of problem solving strategies and the dynamic adaptation of chosen strategies depending on new events occurring dynamically during problem solving. In this paper we concentrate on metareasoning and meta-level learning in the context of a hybrid architecture. The theoretical arguments presented in the paper are demonstrated in practice through a hybrid knowledge-based prototype system for the domain of breast cancer histopathology.     

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 effects of operator implementation cost on planfulness of problem solving and learning

This paper explores the idea that problem solving search strategies are chosen so as to optimize performance within the constraints of a particular situation. Four experiments are reported that examine the hypothesis that the cost of performing an operation affects "planfulness"--the level of planning during problem solving. The first experiment investigated problem solving with the 8-puzzle and compared strategies adopted when there was a high versus a low cost of making a move, manipulating cost in terms of command length. The second experiment used protocol analysis to provide more direct evidence for increased planning. The third and fourth experiments looked at the effects of these different strategies on learning: the third examined how problem solving performance on a direct manipulation interface is affected by prior problem solving experience in the same domain with either a high cost or low cost command-driven interface, demonstrating improved performance as a result of training on an interface with high cost operations; the fourth experiment, like the third, examined the effects of prior problem solving experience with either a high cost or low cost interface on subsequent problem solving performance in a different domain using a direct manipulation interface showing no effect to training interface on subsequent performance.     

Evaluating a training-for-action job health and safety program

This paper describes an action research evaluation method developed to assess a worker training program which encourages trainees to use knowledge acquired to correct health and safety problems in their workplaces. The project teaches trainees from the same workplace to identify problem areas collectively using a tool called a Risk Chart and then to prioritize problems to work on with the aid of an Action Plan. Follow-up trainee interviews are conducted to determine what impact the training has on trainees. The methodology is presented and preliminary results are discussed, with particular emphasis on the advantages and limitations of this method.     

Stable Boundary Element Method/Finite Element Method Procedure for Dynamic Fluid–Structure Interactions

The stability problem has prevented the application of the boundary element method/finite element method (BEM/FEM) coupling procedure in dynamic fluid–structure interaction problems for the last 2 decades. It has been proved that the linear θ method can make a significant stability improvement for the time domain BEM scheme. With the use of the linear θ method, the BEM/FEM coupling procedure is applied to two-dimensional time domain fluid–structure interaction problems. The fluid domain is acoustic and modeled by taking advantage of the BEM scheme that is suitable to either finite or infinite domains. An internal source has been considered in BEM formulations, and no artificial boundary needs to be introduced for the infinite domain. The structure is modeled by finite elements that can be either linear or nonlinear. Two classical examples are given to show the validity of the coupling procedure in fluid–structure interaction problems and the significant stability improvement given by the linear θ method to the BEM/FEM coupling procedure.     

Management and prevention of personal problems in older adolescents via schematic maps and peer feedback

The purpose of the present study was to provide a basis for enhancing personal development in older adolescents by examining the usefulness of two information-processing tools in solving personal problems: schematic maps and peer feedback. Ninety-five college students were assigned to either a schematic map group or an essay group, and further subdivided into groups that worked alone or with a vicarious partner. Assessment consisted of analyzing and generating alternatives to a scenario involving a college student with a drinking problem. Results indicated that alternative generation, an important step in the problem-solving process, is susceptible to experimental manipulation. Schematic maps facilitate the generation of wider-ranging, viable, synergistic alternatives to an uncomfortable situation. Maps help illustrate the complex systems within which problems occur and how patterns of behavior are maintained through reinforcement. Peer feedback may provide information about strategies for the development of additional options.     

The importance of prior knowledge when comparing examples: Influences on conceptual and procedural knowledge of equation solving.

Comparing multiple examples typically supports learning and transfer in laboratory studies and is considered a key feature of high-quality mathematics instruction. This experimental study investigated the importance of prior knowledge in learning from comparison. Seventh- and 8th-grade students (N = 236) learned to solve equations by comparing different solution methods to the same problem, comparing different problem types solved with the same solution method, or studying the examples sequentially. Unlike in past studies, many students did not begin the study with equation-solving skills, and prior knowledge of algebraic methods was an important predictor of learning. Students who did not attempt algebraic methods at pretest benefited most from studying examples sequentially or comparing problem types, rather than from comparing solution methods. Students who attempted algebraic methods at pretest learned more from comparing solution methods. Students may need sufficient prior knowledge in a domain before they benefit from comparing alternative solution methods. These findings are in line with findings on the expertise-reversal effect. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Effects of overt controlled verbalization and goal-specific search on acquisition of procedural knowledge in problem solving.

The effects of verbalization (overt or covert) and goal specificity (specific goal or nonspecific goal) were investigated in a two-factor design. 64 university students individually solved 6 acquisition problems requiring numeral conversions between different base systems and returned 2 days later for a test measuring both near and far transfer. Analysis of acquisition measures indicated that overt verbalizers (a) made fewer excess moves, (b) worked forward on more problems, and (c) required more time than covert verbalizers. Problem solvers working under specific goal conditions made fewer excess moves than those working under nonspecific goal conditions. The treatment factors did not influence transfer performance. However, correlational data obtained between working forward and levels of transfer yielded significant positive relations for overt verbalizers only. The results suggest that the goal-directed search of novices does not necessarily interfere with learning during problem solving and that task demands may influence the relative effectiveness of overt verbalization and reduced goal specificity. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Effects of mother and older sibling on the problem-solving behavior of the younger child.

Determined the effects of aid from mother or older sibling on the child's problem-solving behavior in relation to the sex of the 2 siblings and family size. Ss were 120 1st-grade children with a 3rd- or 4th-grade sibling, half from 2-child families and half from larger families; the 4 possible sex combinations were equally represented. Ss worked on practice problems alone or were aided by sibling or mother prior to testing. Ss with older brothers performed as well alone as after aid by sibling or mother, whereas Ss with older sisters showed more advanced problem solving after aid by sibling or mother. Ss with same-sex siblings solved the problems more rapidly; family size had no effect. Results are interpreted in terms of family interaction patterns. (39 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)