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Problem-solving in school mathematics has traditionally been considered as belonging only to the concrete symbolic mode of thinking, the mode which is concerned with making logical, analytical deductions. Little attention has been given to the place of the intuitive processes of the ikonic mode. The present study was designed to explore the interface between logical and intuitive processes in the context of mathematical problem solving. Sixteen Year 9 and 10 students from advanced mathematics classes were individually assessed while they solved five mathematics problems. Each student’s problem-solving path, for each problem, was mapped according to the type of strategies used. Strategies were broadly classified into Ikonic (IK) or Concrete Symbolic (CS) categories. Students were given two types of problems to solve: (i) those most likely to attract a concrete symbolic approach; and (ii) problems with a significant imaging or intuitive component. Students were also assessed as to the vividness and controllability of their imaging ability, and their creativity. Results indicated that the nature of the problem is a basic factor in determining the type of strategy used for its solution. Students consistently applied CS strategies to CS problems, and IK strategies to IK problems. In addition, students tended to change modes significantly more often when solving CS-type problems than when solving IK-type problems. A switch to IK functioning appeared to be particularly helpful in breaking an unproductive set when solving a CS-type problem. Individual differences in strategy use were also found, with students high on vividness of imagery using IK strategies more frequently than students who were low on vividness. No relationship was found between IK strategy use and either students’ degree of controllability of imagery or their level of creativity. The instructional implications of the results are discussed.

Item Type:	Refereed Article
Keywords:	cognitive functioning, mathematical problem solving during early adolescence, journal article
Research Division:	Education
Research Group:	Curriculum and pedagogy
Research Field:	Mathematics and numeracy curriculum and pedagogy
Objective Division:	Education and Training
Objective Group:	Learner and learning
Objective Field:	Learner and learning not elsewhere classified
UTAS Author:	Collis, KF (Professor Kevin Collis)
UTAS Author:	Watson, JM (Professor Jane Watson)
ID Code:	137661
Year Published:	1993
Funding Support:	Australian Research Council (AC9031914)
Deposited By:	Office of the Faculty of Education
Deposited On:	2020-02-26
Last Modified:	2020-03-23
Downloads:	18 View Download Statistics