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)     

Enhancing third-grade student' mathematical problem solving with self-regulated learning strategies.

The authors assessed the contribution of self-regulated learning strategies (SRL), when combined with problem-solving transfer instruction (L. S. Fuchs et al., 2003), on 3rd-graders' mathematical problem solving. SRL incorporated goal setting and self-evaluation. Problem-solving transfer instruction taught problem-solution methods, the meaning of transfer, and 4 superficial-problem features that change a problem without altering its type or solution; it also prompted metacognitive awareness to transfer. The authors contrasted the effectiveness of transfer plus SRL to the transfer treatment alone and to teacher-designed instruction. Twenty-four 3rd-grade teachers, with 395 students, were assigned randomly to conditions. Treatments were conducted for 16 weeks. Students were pre- and posttested on problem-solving tests and responded to a posttreatment questionnaire tapping self-regulation processes. SRL positively affected performance. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Recent research on human problem solving.

Though the research on human problem solving behavior from 1946 to 1957 has been characterized by a variety of problem tasks, diverse taxonomy of behavioral processes, non-dimensionalized variables, and a relative lack of integration of data and theory, several tentative conclusions are apparent. Among these it is suggested that problem solving performance varies as a function of simple sets and a few kinds of complex sets, of level of problem difficulty, of aids toward solution, and of such S variables as sex, age, and reasoning ability. 114-item bibliog. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Current status of research and theory in human problem solving.

Summarizes problem-solving theories in 3 areas: traditional learning, cognitive-Gestalt approaches, and more recent computer and mathematical models of problem solving. Recent empirical studies are categorized according to the type of behavior elicited by the particular problem-solving task. Anagram, "insight," water-jar, and arithmetic problems are considered to be solved by covert trial-and-error behavior. Switch-light, classification, probability-learning, and numerous "miscellaneous" tasks are approached by overt trial-and-error behavior. (3 p. ref.) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

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)     

Dynamic assessment of algebraic learning in predicting third graders' development of mathematical problem solving.

Dynamic assessment (DA) involves helping students learn a task and indexing responsiveness to that instruction as a measure of learning potential. The purpose of this study was to explore the utility of a DA of algebraic learning in predicting third graders' development of mathematics problem solving. In the fall, 122 third-grade students were assessed on language, nonverbal reasoning, attentive behavior, calculations, word-problem skill, and DA. On the basis of random assignment, students received 16 weeks of validated instruction on word problems or received 16 weeks of conventional instruction on word problems. Then, students were assessed on word-problem measures proximal and distal to instruction. Structural equation measurement models showed that DA measured a distinct dimension of pretreatment ability and that proximal and distal word-problem measures were needed to account for outcome. Structural equation modeling showed that instruction (conventional vs. validated) and pretreatment calculation skills were sufficient to account for math word-problem outcome proximal to instruction; by contrast, language, pretreatment word-problem skill, and DA were needed to forecast learning on word-problem outcomes more distal to instruction. Findings are discussed in terms of responsiveness-to-intervention models for preventing and identifying learning disabilities. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The New York University conference on human problem solving.

"A conference of about 40 psychologists to explore the present status of research in the field of human problem solving was held at New York University… " in April 1954. "The program consisted of general papers and discussions in the mornings and brief reports of current research in the afternoons." Areas of agreement and disagreement and points of view of the conference discussants are cited. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Organizational patterns in problem solving among Mayan fathers and children.

This study examined the social organization of Guatemalan Mayan fathers' engagement with school-age children in a group problem-solving task. Twenty-nine groups of Mayan fathers varying in extent of Western schooling and 3 related school-age children (ages 6-12 years) constructed a puzzle together. Groups with fathers with 0 to 3 grades more often constructed the puzzle through shared multiparty collaboration involving a common agenda, whereas groups with fathers with 12 or more grades more often structured their contributions through a division of labor. Groups involving fathers with 6 to 9 grades demonstrated patterns of coordination that fell between the other two types of schooling groups. Fathers with greater schooling were also found to propose more explicit division-of-labor plans to children than were fathers with no to little schooling. The results indicate that Western schooling may be gradually transforming the collaborative social organization of group problem solving of indigenous Mayan families. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Organization and creative problem solving.

"Groups from four populations differing in their amount of experience and identification with industrial vocation, were compared in their performances on the Change of Work Procedure problem." Arranged from most to least identified, there were 179 groups. "The results are interpreted as providing support for the proposition that the formal authority relations in organizations inhibit creative problem solving. They also suggest that business may be attracting people who can work comfortably, but not creatively, in such formal authority systems." (12 ref.) From Psyc Abstracts 36:04:4LI77M. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Conformity and problem solving.

Tests of problem solving, conformity, and intelligence were given to 77 women and 64 men introductory psychology students to investigate the possibility that conformity, a nonintellectual variable, contributes to the variability in achievement in problem solving. The results show a negative correlation between tendency to conform and achievement in problem solving when the influence of intelligence is statistically removed. 17 references. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Instruction by mothers and fathers during problem solving with their young children.

Mothers and fathers of 163 5-year-olds were observed interacting with their children in dyads on 2 separate occasions on a familiar and unfamiliar cognitive activity. Within- and between-family comparisons were conducted. Few differences in the instruction provided by mothers and fathers appeared, and those that did were on the unfamiliar task. On this task, instruction by mothers, within and across families, was more responsive to children's changing skill than was instruction by fathers. Directive and disapproving comments by parents were related to poorer posttest performance by the child. High level of instruction by both parents was related to better posttest performance than was low level of instruction by parents. Contributions of parents to their children's cognitive development are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Group problem solving under two types of executive structure.

Speed of problem solving by 4-man teams of airmen was measured for 2 conditions of group organization: (a) with responsibility centered in 1 team member, and (b) with responsibility shared equally by all members. Problems in algebraic form required Ss to acquire environmental state information and to adjust the settings of certain response switches. The 2 conditions of group structure and 2 types of problems were varied factorially. Analysis of variance indicates (a) that problems requiring reaction to environmental changes are more quickly solved under the shared responsibility condition, and (b) that problems involving coordination of action among operators are more efficiently solved with a competent centralized authority. Designation of a low aptitude group member as leader produced inferior performance on both problem types. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Evaluation of training in creative problem solving.

"The experiment was designed to evaluate the effects of a creative problem-solving course on creative abilities and selected personality variables." There were 3 matched groups of 54 Ss each. 1 group was enrolled in courses in creative problem solving; the other 2 were enrolled in other courses. 11 prepost test measures were used. "Results are interpreted to indicate that the creative problem-solving course produces a significant increment on certain ability measures associated with practical creativity and on the personality variable dominance." (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Dynamics and constraints in insight problem solving.

This article reports 2 experiments that investigated performance on a novel insight problem, the 8-coin problem. The authors hypothesized that participants would make certain initial moves (strategic moves) that seemed to make progress according to the problem instructions but that nonetheless would guarantee failure to solve the problem. Experiment 1 manipulated the starting state of the problem and showed that overall solution rates were lower when such strategic moves were available. Experiment 2 showed that failure to capitalize on visual hints about the correct first move was also associated with the availability of strategic moves. The results are interpreted in terms of an information-processing framework previously applied to the 9-dot problem. The authors argue that in addition to the operation of inappropriate constraints, a full account of insight problem solving must incorporate a dynamic that steers solution-seeking activity toward the constraints, (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The analysis of problems and prediction of group problem solving.

The time to solve a multiple-stage problem is the sum of the times consumed by separate stages. If each stage is a random all-or-none process, then time to complete a stage is an exponentially distributed random variable, and time to complete the problem will have a gamma distribution (under suitable simplifying assumptions). From this theory, the number of stages in a problem can be estimated and goodness-of-fit tested. Results on 3 word puzzles, administered to 178 individual college students, agreed with theory, and the estimates of number of stages in each problem agreed well with independent judgments of number of stages. The same problems also were administered to groups of 4 Ss. The data suggest that all Ss progress at their usual pace toward solution, except that an S who made a mistake in interpreting the problem consumes and wastes his share of the group's time. This result agrees with the additional observation that the apparent social structure of the groups, as determined from analysis of sociometric choices, was equalitarian. (18 ref.) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Distributing working memory resources during problem solving.

This study examines how problem solvers distribute working memory demands over internal and external resources. Participants recorded notes while performing an arithmetic task. They recorded a majority of intermediate results and labeled many of those results (e.g., "C?=?10"). When more effort was required to take notes, participants recorded fewer results. Participants with a consistent goal structure recorded fewer results and with practice labeled fewer recorded results than those with varied goal structures. When notes were displayed in a consistent spatial arrangement participants labeled fewer recorded results than when notes appeared in varied locations. These findings indicate that individuals use explicit and implicit strategies for indexing intermediate results. The data support the view that individuals flexibly distribute working memory over internal and external resources in response to situational cost-benefit considerations. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Influence of brainstorming instructions and problem sequence on a creative problem solving test.

"The experiment was designed to study the effects on creative problem solving of instructions to express solutions without evaluation (brainstorming) and instructions which required only solutions of good quality and which involved a penalty for solutions of bad quality (nonbrainstorming). Each S [32 college students] was given two problems which required creative ability, in two testing periods." One was with and one without brainstorming. "Significantly more good solutions were produced under brainstorming… . There was no significant difference in the nonbrainstorming performance in the two test periods." (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Quality of first and second solutions in group problem solving.

What effect does having a group solve a problem the second time have on the quality of group solutions? 100 students were divided into 25 groups of 4 each to "role play the case of the Change of Work Procedures. The roles of the foreman and three workers were assigned randomly to the members of each group." When they finished, "they were asked to arrive at a second solution to the problem." Although the double-solution method seemed to require little more time, the "solution quality was generally increased without a loss of acceptance." (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Variable attention facilitates creative problem solving.

Traditionally, researchers have associated creativity with defocused attention. Recent experimental evidence contradicts this notion by demonstrating that in creative people, defocused attention is a variable state rather than a stable trait. Specifically, creative people are better at adjusting their focus of attention as a function of task demands. When the task is ill defined and ambiguity is high, attention is defocused, resulting in slower processing on the task. In contrast, when the task is well defined and ambiguity is low, attention is focused, resulting in faster processing on the task. This flexibility can confer distinct advantages to creative people in the course of problem solving as changes in the structure of the problem necessitate corresponding adjustments in solution strategy. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Personality, problem solving, and the Einstellung effect.

2 hypotheses were raised in this experiment: (a) Ss who show antiscientific or nondynamic tendencies in their perceptions of behavior are more subject to the Einstellung effect; and (b) when achievement anxiety is aroused this relationship is more pronounced. 2 groups of 31 Ss each were given 2 Einstellung-test problem series. For one group standard testing conditions were employed; for the other, achievement anxiety was aroused. Ss were evaluated for dynamic-nondynamic perceptions of others, a measure derived from a modification of Kelly's Role Construct Repertory Test. This measure was not found to be related to Einstellung-test scores, but a significant relationship to achievement anxiety was obtained. (PsycINFO Database Record (c) 2010 APA, all rights reserved)