scholarly journals Problem solving and computational skill: Are they shared or distinct aspects of mathematical cognition?

2008 ◽  
Vol 100 (1) ◽  
pp. 30-47 ◽  
Author(s):  
Lynn S. Fuchs ◽  
Douglas Fuchs ◽  
Karla Stuebing ◽  
Jack M. Fletcher ◽  
Carol L. Hamlett ◽  
...  
1980 ◽  
Vol 11 (5) ◽  
pp. 335-346 ◽  
Author(s):  
Jane O. Swafford

The study investigated sex-related differences among first-year algebra students with respect to achievement, attitude, and consumer problem-solving skills. The subjects were 329 females and 294 males enrolled in first-year algebra courses in 17 schools across the country. In the fall, no sex-related differences were evident in arithmetic computational skill or attitude about the usefulness and enjoyment of mathematics. Males showed a slight advantage on consumer items. In the spring, no sex-related differences in algebra achievement were found; a decline in attitude was observed for both groups; and the differences on consumer exercises became more pronounced.


1979 ◽  
Vol 27 (1) ◽  
pp. 2-3
Author(s):  
Marilyn J. Zweng

Why can't kids solve story problems? The two overly simplistic answers typically given to this question are “they can't read” and “they can't compute.” True, if children can't read or if they can't compute they're not going to be successful in solving verbal problems, but many students can do both and nevertheless perform poorly. Furthermore, there is good evidence that lack of reading ability and computational skill are not the major factors contributing to poor problem-solving performance. Knifong and Holtan (1977) found that the majority of students who solved problems incorrectly could read the problems orally and could retell the story of the problem in their own words; that is, they could comprehend the problem. The authors conclude, “Even assuming a biased interpretation, it is difficult to imagine that poor reading accounts for more than 1O% of these erred problems.” With respect to computation, the results of the 1972 NAEP Mathematics Assessment provide a convincing argument against the “they can't compute” explanation for problem-solving failures.


1989 ◽  
Vol 20 (2) ◽  
pp. 213-218
Author(s):  
Paul Cobb

The notion of intuition frequently crops up in accounts of mathematical experiences (e.g., Davis & Hersh, 1981), and we have an intuitive idea of what is meant. As Fischbein notes, “intuition is generally seen as a primary phenomenon which may be described but which is not reducible to more elementary components” (p. ix). To rectify this situation, Fischbein presents a theory of mathematical and scientific intuition. In doing so, he synthesizes empirical research on problem solving, images and models, beliefs, and developmental stages of intelligence, drawing on examples from the history of science and mathematics. The book is marked by a masterly display of scholarship and makes a fundamental contribution to the analysis of mathematical cognition.


2010 ◽  
Vol 22 (4) ◽  
pp. 790-805 ◽  
Author(s):  
Valorie N. Salimpoor ◽  
Catie Chang ◽  
Vinod Menon

We investigated the neural basis of repetition priming (RP) during mathematical cognition. Previous studies of RP have focused on repetition suppression as the basis of behavioral facilitation, primarily using word and object identification and classification tasks. More recently, researchers have suggested associative stimulus-response learning as an alternate model for behavioral facilitation. We examined the neural basis of RP during mathematical problem solving in the context of these two models of learning. Brain imaging and behavioral data were acquired from 39 adults during novel and repeated presentation of three-operand mathematical equations. Despite wide-spread decreases in activation during repeat, compared with novel trials, there was no direct relation between behavioral facilitation and the degree of repetition suppression in any brain region. Rather, RT improvements were directly correlated with repetition enhancement in the hippocampus and the posteromedial cortex [posterior cingulate cortex, precuneus, and retrosplenial cortex; Brodmann's areas (BAs) 23, 7, and 30, respectively], regions known to support memory formation and retrieval, and in the SMA (BA 6) and the dorsal midcingulate (“motor cingulate”) cortex (BA 24d), regions known to be important for motor learning. Furthermore, improvements in RT were also correlated with increased functional connectivity of the hippocampus with both the SMA and the dorsal midcingulate cortex. Our findings provide novel support for the hypothesis that repetition enhancement and associated stimulus-response learning may facilitate behavioral performance during problem solving.


1991 ◽  
Vol 55 (5) ◽  
pp. 327-331 ◽  
Author(s):  
GT Chiodo ◽  
WW Bullock ◽  
HR Creamer ◽  
DI Rosenstein
Keyword(s):  

1982 ◽  
Vol 13 (2) ◽  
pp. 129-133
Author(s):  
A. D. Pellegrini

The paper explores the processes by which children use private speech to regulate their behaviors. The first part of the paper explores the ontological development of self-regulating private speech. The theories of Vygotsky and Luria are used to explain this development. The second part of the paper applies these theories to pedagogical settings. The process by which children are exposed to dialogue strategies that help them solve problems is outlined. The strategy has children posing and answering four questions: What is the problem? How will I solve it? Am I using the plan? How did it work? It is argued that this model helps children systematically mediate their problem solving processes.


1989 ◽  
Vol 20 (3) ◽  
pp. 320-332 ◽  
Author(s):  
David A. Shapiro ◽  
Nelson Moses

This article presents a practical and collegial model of problem solving that is based upon the literature in supervision and cognitive learning theory. The model and the procedures it generates are applied directly to supervisory interactions in the public school environment. Specific principles of supervision and related recommendations for collaborative problem solving are discussed. Implications for public school supervision are addressed in terms of continued professional growth of both supervisees and supervisors, interdisciplinary team functioning, and renewal and retention of public school personnel.


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