Children's Problem Solving Research Articles

Models of Problem Solving: A Study of Kindergarten Children's Problem-Solving Processes

Seventy kindergarten children who had spent the year solving a variety of basic word problems were individually interviewed as they solved addition, subtraction, multiplication, division, multistep, and nonroutine word problems. Thirty-two children used a valid strategy for all nine problems and 44 correctly answered seven or more problems. Only 5 children were not able to answer any problems correctly. The results suggest that children can solve a wide range of problems, including problems involving multiplication and division situations, much earlier than generally has been presumed. With only a few exceptions, children's strategies could be characterized as representing or modeling the action or relationships described in the problems. The conception of problem solving as modeling could provide a unifying framework for thinking about problem solving in the primary grades. Modeling offers a parsimonious and coherent way of thinking about children's mathematical problem solving that is relatively straightforward and is accessible to teachers and students alike. The construction of a model or representation of a problem situation is one of the most fundamental problem-solving processes. Many problems can be solved by representing directly the critical features of the problem situation with an equation, a computer program, or a physical or pictorial representation. Modeling also turns out to be a relatively natural problemsolving process for young children. There is an extensive body of research documenting that even before they receive formal instruction in arithmetic, young children can solve a variety of different types of addition and subtraction word problems by directly modeling with counters the different action and relationships described in the problems (Carpenter, 1985;

Models of Problem Solving: A Study of Kindergarten Children's Problem-Solving Processes

Seventy kindergarten children who had spent the year solving a variety of basic word problems were individually interviewed as they solved addition, subtraction, multiplication, division, multistep, and nonroutine word problems. Thirty-two children used a valid strategy for all nine problems and 44 correctly answered seven or more problems. Only 5 children were not able to answer any problems correctly. The results suggest that children can solve a wide range of problems, including problems involving multiplication and division situations, much earlier than generally has been presumed. With only a few exceptions, children's strategies could be characterized as representing or modeling the action or relationships described in the problems. The conception of problem solving as modeling could provide a unifying framework for thinking about problem solving in the primary grades. Modeling offers a parsimonious and coherent way of thinking about children's mathematical problem solving that is relatively straightforward and is accessible to teachers and students alike.

An Information Processing Analysis of Learning Disabled Children's Problem Solving

An Information Processing Analysis of Learning Disabled Children's Problem Solving

Social problem solving among popular and unpopular children.

The present study investigated two issues related to children's social status and problem solving: the content of problem-solving measures and judgments of the quality of responses to social problems. Three types of social problem situations were studied: peer entry/initiation, maintaining social interaction, and management of conflict. The quality of children's strategies for solving these problems was rated on two dimensions: effectiveness and social competence. Liked-most children obtained significantly more effective and socially competent ratings than liked-least children for only one of the social problem situations--management of conflict. Significant differences between liked-most and liked-least children were also found between the quality of their best effective and best socially competent solution and their worst socially competent solutions. Results are discussed in terms of the psychometric adequacy of social problem-solving measures and the resultant problems in interpretation.

Parents and Children Learning Together A Study of the Effectiveness of Parental Involvement on Children's Problem Solving Skills

This study developed from the findings of a previous set of studies into parental involvement in pre-school education. Amongst some interesting results, significant were parents concerns, and uncertainties about their roles in facilitating the learning experiences of their children in the home environment. Additionally, the findings revealed that when parents do spend time with their children, reading stories and playing board games were popular past-times. Research elsewhere reveals that the kinds of pre-school activities most effective in the development of thinking skills, involve construction, drawing and board games. Thus, an aim of this study, is to investigate the extent to which parents' understanding of the competencies involved in these activities, affects their involvement in them at home and the progress of their children in school. This paper presents the findings of a pilot study of the role of the tutor in problem solving. It is an attempt to identify the kinds of knowledge and information ...

Degree of Bilingualism and Arithmetic Problem Solving in Hispanic First Graders

This study demonstrated that 45 first-grade Hispanic bilingual children's problem solving was related to the semantic structures of word problems (a) in a similar manner across their 2 languages, and (b) in a manner similar to that of monolingual populations. I also investigated the relationship between proficiency in each language and arithmetic problem solving in that language. When language proficiency was measured via the Preschool Version, Language Assessment Scales story-retelling task, an indicator of surface fluency, no such relationship was found. However, when proficiency was measured via verbal counting up and counting down, these relationships were found across both languages. Finally, I examined the relationship between degree of bilingualism and problem solving in English and in Spanish that goes beyond the connection between a language and problem solving in that language. This last relationship was found only for English as measured by each of the verbal counting tasks. The results suggest (a) that Hispanic bilingual children enter school with greater competence in solving addition and subtraction word problems than they are usually credited with; (b) that the cognitive benefits of being bilingual might appear, at least initially, in academic subjects; and (c) that these benefits depend on the development of decontextualized, academic language proficiency.

Children's Problem-Solving Performance: The Effects of Compliance and Cognitive Factors

Abstract This study was designed to examine the robustness of Crombie and Gold's finding (1989) that a high degree of compliance is negatively related to children's problem-solving performance. The effect of compliance on children's problem-solving performance was examined by extending Crombie and Gold's investigation to a different task, assessing the effects of a training session in which children's nonreliance on an adult model was reinforced, and measuring the contribution of relevant cognitive factors. Children's problem-solving competence was examined with a standardized measure of general problem-solving performance and a task-specific measure. Age, verbal intelligence, and task-oriented memory were entered as covariates. High-compliant children did not perform as well as their low-compliant peers on the general problem-solving measure, and this group difference remained significant after the effects of the covariates were taken into consideration. On the task-specific measure, which requires respo...

Children's Problem Solving Series (Book)

Children's Problem Solving Series (Book)

Maternal Regulation of Children's Problem-Solving Behavior and Its Impact on Children's Performance

Maternal Regulation of Children's Problem-Solving Behavior and Its Impact on Children's Performance

Book Reviews Miscellaneous Reviews David Crookall : Prutzman, P., Stern, L., Burger, M. L., and Bodenhamer, G. 1987. The Friendly Classroom for a Small Planet: A Handbook on Creative Approaches to Living and Problem Solving for Children. Nyack, NY: CCRC (Children's Creative Response to Conflict Program, Fellowship of Reconciliation, Box 271, Nyack, NY 10960-0271, USA

Book Reviews Miscellaneous Reviews David Crookall : Prutzman, P., Stern, L., Burger, M. L., and Bodenhamer, G. 1987. The Friendly Classroom for a Small Planet: A Handbook on Creative Approaches to Living and Problem Solving for Children. Nyack, NY: CCRC (Children's Creative Response to Conflict Program, Fellowship of Reconciliation, Box 271, Nyack, NY 10960-0271, USA

Social influences on children's problem solving.

Three studies examined the nature and limiting conditions of effects of peer interaction on children's problem solving. 150 children (4 to 11 years old) worked alone or with a same-age peer at a computer

Social influences on children's problem solving.

Social influences on children's problem solving.

Influence of Positive Affect upon Creative Thinking and Problem Solving in Children

A study was designed to assess whether positive affect may promote creativity and facilitate problem solving of children. The task used to measure creativity involved word generation. Subjects were presented a category name and asked to generate as many exemplars as possible. Duncker's (1945) candle task was used to assess problem-solving skills. Eighth grade students were randomly assigned to the Positive Affect or Neutral condition. A positive mood was induced in subjects in the Positive Affect condition by presenting compliments and gifts before the experimental session began. Subjects in the Neutral condition began the experiment without compliments or gifts. Subjects in the Positive Affect condition generated more exemplars for the categories and more unusual exemplars than did subjects in the Neutral condition. More subjects in the Positive Affect condition correctly solved the candle problem than did those in the Neutral condition. These results suggest that positive affect may promote creativity and facilitate problem solving by young adolescents.

Linguistic processes in disagreements occurring in young children's dyadic problem solving

Conflict and collaboration between children have been postulated as causal mechanisms in cognitive development, but the constitutive processes of such interaction patterns remain largely unstudied and unspecified. This study examined dyads of young children as they worked together on a goal‐directed problem‐solving task. Pairs of 7‐ and 9‐year‐old children were classified as joint or disjoint collaborators on the basis of their early interaction, enabling predictions to be made regarding the linguistic processes during disagreements. Dividing disagreements into antecedent, opposition and resolution events enabled comparisons to be made between dyads regarding the specific linguistic processes of disagreements. While the dyadic types were more similar than different, it was found that disjoint dyads required more language to solve their disputes and joint dyads marked disagreements in ways that promoted social monitoring or identified the specific cause of the disagreement. Older children disagreed more but acknowledged the social nature of the problem‐solving task and the need to communicate. Such verbal use of problem‐solving strategies may allow young children to benefit cognitively from working together.

Learning disabled children's problem solving: Identifying mental processes underlying intelligent performance

Learning disabled and nondisabled children's “thinking aloud” protocols were analyzed from a picture arrangement task. Protocols were analyzed at three levels: (a) global mental processing and task performance, (b) groupings of subroutines that function as heuristic processes, and (c) groupings of subroutines that function as strategies. Although learning disabled and nondisabled children were comparable in global mental processing and task performance, learning disabled children had difficulty in the heuristic subroutine of problem representation and deleting irrelevant information. In addition, nondisabled children were superior to learning disabled children in using strategy subroutines that relate to evaluation, systematic problem solving, feedback, and pattern extraction. A stepwise regression analysis suggested that learning disabled children's overall mental processing was best predicted by a heuristic, whereas nondisabled children's overall mental processing was best predicted by specific strategy subroutines. Theoretical and educational implications of the results were discussed.

Learning Through Instruction: The Study of Students' Thinking During Instruction in Mathematics

Researchers studying teaching generally have not focused on the subject matter to be taught or how students learn. In contrast, cognitive science researchers have been concerned with what is learned, but they generally have not addressed the question of how learning occurs. The articles in this issue integrate the perspectives of research on teaching and research on children's thinking and problem solving to study how children learn mathematics from instruction. The articles illustrate alternative paradigms for studying instruction that are consistent with constructivist conceptions of learning and that focus on the subject matter being taught and the goals of instruction.

A comparison of parent-child perceptions of student learning disabilities.

The perceptions of 80 learning disabled(LD) adolescents and their parents were compared in regard to the extent of their learning disablities, current levels of performance in academic and social areas, occupational status, social relationships, and problem academic cognitive, and social aspects of learning disablities persisted into adolescence with parents expressing much more concern about this negative impact. While the LD adolescents saw their skills as generally similar to those of other, parent ratings were significantly. According to the parents, their children were not likely to gradute from lower estimation of their children's social and problem solving skills. Reasons for these difference of opinion are discussed, and implications for improved parent-child communication, parent training, and family counseling are identified.

Nonverbal Assessment of Piagetian Development: An Analysis of Lancy and Goldstein's Procedures

Thirty-four kindergarten through second-grade children were administered classification, conservation of number, and seriation tasks. The tasks assessing these areas were administered in counterbalanced order using the nonverbal procedures developed by Lancy and Goldstein and procedures outlined by Piaget. The purpose of the investigation was to ascertain whether the Lancy and Goldstein approach and materials are veridical measures of Piagetian cognitive development. The areas selected for comparison were those that Piaget and his colleagues have thoroughly analyzed and to which strict Piagetian criteria could be applied. The results indicate that the nonverbal tasks do not effectively measure concrete operational thought as described by Piaget. They do, however, provide an approach for analysis of children's problem-solving strategy and hypothesis development that can be useful in studies of cognitive processes.

The Development of Children's Problem Solving in a Gears Task: A Problem Space Perspective

I examined two contexts of development in children's problem solving: (1) the macro‐context of different age cohorts (8–9 vs 11–12 years of age); and (2) the micro‐context of an approximately one‐hour experimental session. Twenty subjects (even divided across sexes and these two age groups) were individually presented a collection of variously sized gears, a board onto which these gears could be easily attached and rotated, and a knob. Each subject was asked to find all solutions, in which two marked gears were turning the same way, and to represent these solutions graphically. Subjects applied four different problem spaces to the task: the Euclidean, the Kinematic, the Dynamic, and the Topological. The Arithmetic Modifier could be applied to any of these problem spaces, resulting in a numerical characterization of the gear constructions and/or production strategies. The 11–12's tended to shift problem spaces adaptively; the 8–9's seldom did so. Analysis of the pathways of transition between the problem spaces revealed a complex picture of partial or complete incorporation, and substitution.

Two children's anticipations, beliefs, and motivations

This paper discusses the roles played by anticipation, belief, and motivation in two young children's problem solving activity. It is argued that a solver's beliefs and motivations are intimately related. The analysis also identifies an increasingly global hierarchy of anticipations corresponding to specific conceptual structures or problem representations, heuristics, and beliefs. Analogies drawn from the philosophy of science and from the field of artificial intelligence are used to illustrate that the discussion of the two children's behaviors may have some generality.