The Developmental Role of Intuitive Principles in Choosing Mathematical Strategies.

This study investigated the relation between the development of understanding principles that govern a problem and the development ofmathematical strategies used to solve it. College students and 2nd, 5th, 8th, and I lth graders predicted the resulting temperature when 2 containers of water were combined. Students first estimated answers to the problems and then solved the problems using math. The pattern of estimated answers provided a measure of the intuitive understanding of task principles. Developmental differences in intuitive understanding were related to the type of math strategy students used. Analysis of individual data patterns showed that understanding an intuitive principle was necessary but not sufficient to generate a math strategy consistent with that principle. Implications for the development of problem solving are discussed. Current models of problem solving propose that a person's conceptual or intuitive understanding is an important factor in solving a problem with formal methods such as mathematics. Conceptual or intuitive understanding involves the qualitative representation of the relevant relations among variables in a task. We call this type of understanding intuitive, following Brunswik (1956) and Hammond (1982; Hammond, Harem,

[1]  S. Siegel,et al.  Nonparametric Statistics for the Behavioral Sciences , 2022, The SAGE Encyclopedia of Research Design.

[2]  Basil Yeaxlee,et al.  A child's understanding , 1965 .

[3]  M. Hoffman,et al.  Review of Child Development Research , 1966 .

[4]  D. Jaeger.  Review of Child Development Research , 1976 .

[5]  C. Gallistel,et al.  The Child's Understanding of Number , 1979 .

[6]  Dorothea P. Simon,et al.  Individual Differences in Solving Physics Problems (1978) , 1978 .

[7]  R. Siegler.  Children's Thinking : What Develops? , 1978 .

[8]  Dorothea P. Simon,et al.  Expert and Novice Performance in Solving Physics Problems , 1980, Science.

[9]  Paul J. Feltovich,et al.  Categorization and Representation of Physics Problems by Experts and Novices , 1981, Cogn. Sci..

[10]  Michelene T. H. Chi,et al.  Expertise in Problem Solving. , 1981 .

[11]  R. Sternberg.  Advances in the psychology of human intelligence , 1982 .

[12]  Richard Gunstone,et al.  A perspective on the differences between expert and novice performance in solving physics problems , 1982 .

[13]  W. Dixon,et al.  BMDP statistical software , 1983 .

[14]  Dedre Gentner,et al.  Structure-Mapping: A Theoretical Framework for Analogy , 1983, Cogn. Sci..

[15]  Diane J. Briars,et al.  An integrated model of skill in solving elementary word problems cognition and instruction , 1984 .

[16]  Robert S. Siegler,et al.  A featural analysis of preschoolers' counting knowledge. , 1984 .

[17]  M. Riley,et al.  Conceptual competence and children's counting , 1984, Cognitive Psychology.

[18]  Alexander Pollatsek,et al.  Usefulness of a balance model in understanding the mean. , 1984 .

[19]  W Kintsch,et al.  Understanding and solving word arithmetic problems. , 1985, Psychological review.

[20]  R. Gelman,et al.  Young children's numerical competence ** , 1986 .

[21]  Stephen K. Reed,et al.  Learning functional relations: A theoretical and instructional analysis , 1987 .

[22]  A. Glenberg,et al.  Inexpert calibration of comprehension , 1987, Memory & cognition.

[23]  T. Pearson,et al.  Direct comparison of the efficacy of intuitive and analytical cognition in expert judgment , 1987, IEEE Transactions on Systems, Man, and Cybernetics.

[24]  Stephen K. Reed,et al.  A structure-mapping model for word problems. , 1987 .

[25]  W. Kintsch,et al.  The role of understanding in solving word problems , 1988, Cognitive Psychology.

[26]  Eric A. Jenkins,et al.  How Children Discover New Strategies , 1989 .

[27]  J. Mestre,et al.  The relation between problem categorization and problem solving among experts and novices , 1989, Memory & cognition.

[28]  Leonard A. Marascuilo,et al.  Statistical methods for the social and behavioral sciences , 1990 .

[29]  Beth A. Haines,et al.  Components of Understanding in Proportional Reasoning: A Fuzzy Set Representation of Developmental Progressions , 1991 .

[30]  C. Moore,et al.  Development of intuitive and numerical proportional reasoning , 1992 .

[31]  K. Crowley,et al.  Constraints On Learning in Nonprivileged Domains , 1994, Cognitive Psychology.