Teaching with concrete and abstract visual representations: Effects on students' problem solving, problem representations, and learning perceptions.

In 3 experiments, we examined the effects of using concrete and/or abstract visual problem representations during instruction on students' problem-solving practice, near transfer, problem representations, and learning perceptions. In Experiments 1 and 2, novice students learned about electrical circuit analysis with an instructional program that included worked-out and practice problems represented with abstract (Group A), concrete (Group C), or abstract and concrete diagrams (Group AC), whereby the cover stories were abstract in Group A and concrete in Groups C and AC. Experiment 3 added a 4th condition (C-A) with a concrete cover story and abstract diagrams. Group AC outperformed Groups A and C on problem-solving practice in Experiments 1 and 2 and outperformed Group C on transfer across the 3 experiments; Group AC also outperformed Group C-A in Experiment 3. Further, Group A outperformed Group C on transfer in Experiments 2 and 3 and outperformed Group C-A in Experiment 3. Transfer scores were positively associated with the quality of the diagrams and the number of abstract representations drawn during the transfer test. Data on students' learning perceptions suggest that the advantage of Group AC relies on the combined cognitive support of both representations. Our studies indicate that problem solving is fostered when learners experience concrete visual representations that connect to their prior knowledge and are enabled to use abstract visual representations. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

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)     

A comparison of single and multiple strategy instruction on third-grade students' mathematical problem solving.

The purposes of this study were to assess the differential effects of a single strategy (schema-based instruction; SBI) versus multiple strategies (general strategy instruction, GSI) in promoting mathematical problem solving and mathematics achievement as well as to examine the influence of word problem-solving instruction on the development of computational skills. Eighty-eight 3rd graders and their teachers were assigned randomly to conditions (SBI and GSI). Students were pre- and posttested on mathematical problem-solving and computation tests and were posttested on the Pennsylvania System of School Assessment Mathematics test, a criterion-referenced test that measures student attainment of academic standards. Results revealed SBI to be more effective than GSI in enhancing students' mathematical word problem-solving skills at posttest and maintenance. Further, results indicate that the SBI groups' performance exceeded that of the GSI group on the Pennsylvania System of School Assessment measure. On the computation test, both groups made gains over time. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Effects of small-group tutoring with and without validated classroom instruction on at-risk students' math problem solving: Are two tiers of prevention better than one?

This study assessed the effects of small-group tutoring with and without validated classroom instruction on at-risk students' math problem solving. Stratifying within schools, 119 3rd-grade classes were randomly assigned to conventional or validated problem-solving instruction (Hot Math, schema-broadening instruction). Students identified as at risk (n=243) were randomly assigned, within classroom conditions, to receive or not receive Hot Math tutoring. Students were tested on problem-solving and math applications measures before and after 16 weeks of intervention. Analyses of variance, which accounted for the nested structure of the data, revealed that the tutored students who received validated classroom instruction achieved better than the tutored students who received conventional classroom instruction (effect size=1.34). However, the advantage for tutoring over no tutoring was similar whether students received validated or conventional classroom instruction (effect sizes=1.18 and 1.13). Tutoring, not validated classroom instruction, reduced the prevalence of math difficulty. Implications for responsiveness-to-intervention prevention models and for enhancing math problem-solving instruction are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Effects of solving related proofs on memory and transfer in geometry problem solving.

Three experiments investigate the relationship between memory and problem solving in the domain of geometry theorem proving. In Exp 1, Ss' memories for an original problem-solving episode were interfered with retroactively by solving a 2nd problem that had the same diagram, but no memory effects were observed that depended on the 2nd problem's logical similarity to the original. Results suggest that the diagram is the basis for geometry problem-solving memories. Exps 2 and 3 investigated problem-solving memories in use by examining Ss' transfer to a 3rd (test) problem. As with the memory results, transfer was reduced when the 1st 2 problems had the same diagram relative to when they had 2 different diagrams. Transfer was reduced most in the condition with the greatest proportion of memory-interfering steps. Results suggest that the structure and quality of problem-solving memories affect problem-solving transfer. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Can offline metacognition enhance mathematical problem solving?

The effectiveness of a short metacognitive intervention combined with algorithmic cognitive instruction was assessed in an elementary school setting. Two hundred thirty-seven 3rd-grade children were randomly assigned to a 5-session metacognitive strategy instruction, an algorithmic direct cognitive instruction, a motivational program, a quantitative-relational condition, or a spelling condition. Children in the metacognitive program achieved significant gains in trained metacognitive skills compared with the 4 other conditions. Moreover, the children in the metacognitive program performed better on trained cognitive skills than children in the algorithmic condition, with a follow-up effect on domain-specific mathematics problem-solving knowledge. Despite the consistency of findings, no generalization effects were found on transfer of cognitive learning. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Problem-solving instruction and problem-solving transfer: The correspondence issue.

R. E. Mayer and A C. Wittrock (1996) have raised the specificity-generality issue as it applies to the teachable aspects of problem-solving transfer. Simply put, do the instructional practices that foster more efficient acquisition-learning of problem-solving strategies automatically foster more efficient problem-solving transfer? On the basis of the present findings the answer is "no." Four instructional conditions differing in levels of specificity produced different levels of acquisition. However, when the same students engaged in a delayed problem-solving task, comparable levels of problem-solving transfer performance were observed. In this case, a general approach to problem-solving instruction produced significantly poorer acquisition-learning performance but equally good problem-solving transfer performance. Results are discussed within the context of investigating prior knowledge (F Dochy, M. Segers, & A M. Buehl, 1999) and the identification of source memory (A. Koriat, M. Goldsmith, & A. Pansky, 2000) as a viable tool in this effort. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Investigating preservice teachers' professional growth in self-regulated learning environments.

Educational reforms have suggested that the ability to self-regulate learning is essential for teachers' professional growth during their entire career as well as for their ability to promote these processes among students. This study observed teachers' professional growth along 3 dimensions: self-regulated learning (SRL) in pedagogical context, pedagogical knowledge, and perceptions of teaching and learning. The authors examined 194 preservice teachers' professional growth in 4 learning environments: e-learning (EL) and face-to-face (F2F) learning, either supported by SRL (EL + SRL; F2F + SRL) or unsupported by SRL (EL; F2F). SRL support was based on the IMPROVE metacognitive self-questioning method (B. Kramarski & Z. R. Mevarech, 2003). Mixed quantitative and qualitative analyses showed that preservice teachers in both supported SRL conditions outperformed their unsupported peers on all professional growth measures. Moreover, EL + SRL teachers exhibited the highest SRL ability (cognition, metacognition, motivation), pedagogical knowledge (designing a learning unit), and student-centered learning perceptions (self-construction of knowledge). (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Lasting Reductions in Illegal Moves Following an Increase in Their Cost: Evidence From River-Crossing Problems.

The authors present 3 experiments demonstrating ways to reduce illegal moves in problem-solving tasks. They propose a 3-stage framework for the rejection of illegal moves. An illegal move must come to mind and be selected, checked for legality, and correctly rejected. Illegal move reduction can occur at any stage. Control group participants benefited from solving the same problem twice but failed to show transfer to an isomorph, replicating results from S. K. Reed, G. W. Ernst, and R. Banerji (1974). Participants who were penalized for making illegal moves showed reductions in illegal moves even when solving a novel isomorph without penalty. The authors propose that illegal move reduction occurs when solvers are cautious and check moves for legality frequently. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Skill acquisition: Compilation of weak-method problem situations.

Cognitive skills are encoded by a set of productions, which is organized according to a hierarchical goal structure. People solve problems in new domains by applying weak problem-solving procedures to declarative knowledge they have about this domain. From these initial problem solutions, production rules are compiled that are specific to that domain and that use of the knowledge. Numerous experimental results may be predicted from this conception of skill organization and skill acquisition. These include predictions about transfer among skills, differential improvement on problem types, effects of working memory limitations, and applications to instruction. The theory implies that all varieties of skill acquisition, including those typically regarded as inductive, conform to this characterization. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Enhancing students' comprehension of the conceptual structure of algebra word problems.

Three experiments investigated Ss' ability to classify and solve similar algebra word problems. Four groups of problems were used, varying along 2 dimensions: problem equation type (2 types) and problem structure type (2 types). Ss were presented problem pairs and asked to rate the potential usefulness of Problem 1 in solving Problem 2. With no instruction, Ss rated problems sharing conceptual structure as being more helpful, regardless of equation type. Pairs with similar equations did not show this effect (Exp 1). This effect was enhanced by brief instruction, which illustrated structural similarities (Exp 2). Finally, a brief tutorial improved problem-solving performance (Exp 3). The improvement was particularly evident when target problems shared structural components but had different equations. The results are interpreted within S. K. Reed's (1987) structure-mapping model. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Does Training on Self-Regulated Learning Facilitate Students' Learning With Hypermedia?

The authors examined the effectiveness of self-regulated learning (SRL) training in facilitating college students' learning with hypermedia. Undergraduate students (N = 131) were randomly assigned to either a training condition or a control condition and used a hypermedia environment to learn about the circulatory system. Students in the SRL group were given a 30-min training session on the use of specific, empirically based SRL variables designed to foster their conceptual understanding; control students received no training. Pretest, posttest, and verbal protocol data were collected from both groups. The SRL condition facilitated the shift in learners' mental models significantly more than did the control condition; verbal protocol data indicated that this was associated with the use of the SRL variables taught during training. (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)     

Instruction begins in the home: Relations between parental instruction and children's self-regulation in the classroom.

The study examined the effectiveness of 3 aspects of parental instruction for predicting children's self-regulation in school. Fathers, mothers, and their children (52 families) were visited in their homes the summer before the child entered 3rd grade. Metacognitive content (task and strategy information), manner of instruction (small steps at an appropriate pace), and emotional support were coded from parents' instructions to their children for a problem-solving task. Children's self-regulatory behaviors in the classroom were assessed the following school year. Two patterns of relations were observed. Manner of instruction predicted children's attention to instructions and help-seeking in the classroom. Metacognitive content of instructions did not predict these aspects of self-regulation. In contrast, metacognitive content of instructions presented in an understandable manner with emotional support predicted children's monitoring and metacognitive talk. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Role of Guidance, Reflection, and Interactivity in an Agent-Based Multimedia Game.

The authors investigated whether guidance and reflection would facilitate science learning in an interactive multimedia game. College students learned how to design plants to survive in different weather conditions. In Experiment 1, they learned with an agent that either guided them with corrective and explanatory feedback or corrective feedback alone. Some students were asked to reflect by giving explanations about their problem-solving answers. Guidance in the form of explanatory feedback produced higher transfer scores, fewer incorrect answers, and greater reduction of misconceptions during problem solving. Reflection in the form of having students give explanations for their answers did not affect learning. Experiments 2 and 3 showed that reflection promotes retention and far transfer in noninteractive environments but not in interactive ones unless students are asked to reflect on correct program solutions rather than on their own solutions. Results support the appropriate use of guidance and reflection for interactive multimedia games. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Problem solving and learning.

A. Newell and H. A. Simon (1972) provided a framework for understanding problem solving that can provide the needed bridge between learning and performance. Their analysis of means–ends problem solving can be viewed as a general characterization of the structure of human cognition. However, this framework needs to be elaborated with a strength concept to account for variability in problem solving behavior and improvement in problem-solving skill with practice. The ACT* theory (J. R. Anderson, 1983) is such an elaborated theory that can account for many of the results about the acquisition of problem-solving skills. Its central concept is the production rule, which plays an analogous role to the stimulus–response bond in earlier learning theories. The theory has provided a basis for constructing intelligent computer-based tutoring systems for the instruction of academic problem-solving skills. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Goals and everyday problem solving: Manipulating goal preferences in young and older adults.

In the present study, we examined the link between goal and problem-solving strategy preferences in 130 young and older adults using hypothetical family problem vignettes. At baseline, young adults preferred autonomy goals, whereas older adults preferred generative goals. Imagining an expanded future time perspective led older adults to show preferences for autonomy goals similar to those observed in young adults but did not eliminate age differences in generative goals. Autonomy goals were associated with more self-focused instrumental problem solving, whereas generative goals were related to more other-focused instrumental problem solving in the no-instruction and instruction conditions. Older adults were better at matching their strategies to their goals than young adults were. This suggests that older adults may become better at selecting their strategies in accordance with their goals. Our findings speak to a contextual approach to everyday problem solving by showing that goals are associated with the selection of problem-solving strategies. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A role for natural killer cells in the immunopathogenesis of multiple sclerosis

The authors sought to determine the effect of concomitant peroral (PO) administration of cyclosporine (CsA) and sirolimus (SRL, rapamycin) on the tissue distributions of CsA and SRL in the rat. Groups of four adult male Wistar-Furth rats were treated for 14 days with 2.5, 5.0, or 10.0 mg CsA/kg x day. Other groups of four adult male Wistar-Furth rats were treated for 14 days with a 1-to-6.25 weight-to-weight ratio of SRL to CsA at SRL doses of 0.4, 0.8, or 1.6 mg/kg x day. Concentrations of CsA and SRL in homogenates of heart, intestinal, kidney, liver, lung, muscle, spleen, and testes were compared to those in whole blood (WB). There was a large, dose-dependent, distinctive distribution of CsA among rat tissues, as has previously been well documented. At a constant molar dose ratio, concomitant oral administration of SRL produced an approximately two-fold increase in the concentrations of CsA in rat tissues, although SRL did not change the CsA tissue-to-WB partition coefficients. Concomitant oral CsA administration produced dose-dependent increases in SRL tissue concentrations and decreases in the SRL tissue-to-WB partition coefficients. The increases in tissue and WB concentrations on coadministration of both agents may be explained either by an increase in absorption caused by competition between the two agents for binding sites on P-glycoprotein in the gut, a reduced rate of metabolism, or to an as yet unidentified elimination mechanism. The dose-independent and unchanged CsA tissue-to-WB partition coefficients suggest that SRL does not affect the equilibrium of CsA between the central and tissue compartments, namely the tissue uptake or intracellular binding. Altered values of the SRL tissue-to-WB partition coefficients suggest that, under the conditions studied, CsA disturbs the equilibrium of SRL between the central and tissue compartments.     

Mothers' scaffolding of children's problem solving: Establishing a foundation of academic self-regulatory competence.

The study examined relations between dimensions of mothers' scaffolding and children's academic self-regulatory behaviors in school. Mothers and their preschool children (68 dyads) were visited in their homes the summer before the child entered kindergarten. Mothers' metacognitive content and manner of instruction, emotional support, and transfer of responsibility were coded as mothers provided assistance to their children during 4 problem-solving tasks. Children's self-regulatory behaviors were assessed the following school year. Metacognitive content and manner of instruction were predictors of child behaviors related to cognitive awareness and management: metacognitive talk, monitoring, and help seeking. Emotional support and transfer of responsibility were related to children's task persistence and behavior control in school. Mothers' scaffolding appears to lay the foundation for children's subsequent academic self-regulatory competence. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Teachers' knowledge of students' knowledge in mathematics problem solving: Correlational and case analyses.

This study examined the relationship of teachers' knowledge of students' knowledge to teachers' mathematics instruction and to students' mathematics problem solving. First-grade teachers (N?=?20) participated in a 4-week workshop in which they were given access to research-based knowledge on children's mathematics learning. Teachers were observed for 16 days throughout the school year. In May, teachers completed interviews and questionnaires about their knowledge and beliefs; their students completed achievement tests. Correlational analyses showed significant positive relationships between teachers' knowledge of students' knowledge and students' mathematics problem-solving achievement. Teachers with more knowledge of their students questioned students about problem-solving processes and listened to their responses. Teachers with less knowledge of their students explained problem-solving processes to students or observed students' solutions. Case analyses of knowledge and behavior of the most effective teacher and the least effective teacher supported these conclusions and showed important differences in how these teachers thought about and used students' knowledge. (PsycINFO Database Record (c) 2010 APA, all rights reserved)