Association of domain-specific knowledge and analytical ability with insight problem solving in mathematics

Cumali Oksuz
Faculty of Education, Adnan Menderes University, Turkey

PP: 138 - 153

Abstract

In this study, the author investigated how analytical mathematical ability and domain-specific mathematical knowledge were associated with insight problem solving in mathematics. Knowledge and analytical subtests of the Test of Three-Mathematical Minds and nine insight problems were used to measure participants' mathematical knowledge, analytical mathematical ability and insight ability.

Participants included 56 undergraduate students in mathematics and mathematics education departments and 190 undergraduate students in other fields of education.

The results show that domain-specific knowledge significantly contributed to performance in solving insight problems (Beta = .69, p < .001). However, analytical mathematical ability did not have any significant contribution to performance in solving insight problems. One standard deviation above the mean of domain-specific knowledge was found to be a threshold for creativity related to solving insight problems.

Keywords

insight problem solving in mathematics, analytical mathematical ability, domain-specific mathematical knowledge

Article Text

Mathematical creativity sometimes can be observed in solutions of non-routine mathematical problems. Solutions of many non-routine problems involve cognitive flexibility, a switch from one mode of thinking to another, as well as mathematical knowledge and mathematical analysis. Insight problems are prototypes of non-routine problems.

People differ in their performance in solving insight problems as a function of their present repertoire of domain-specific knowledge about insight problems, as well as their level of mathematical ability. A common hypothesis is that the activation of problem-relevant knowledge in memory might inhibit the solution of an insight problem if this knowledge is not required or to be used in an unusual way (Duncker 1945; Gick & Lockhart 1995; Isaak & Just 1995; Mayer 1995; Smith 1995; Wertheimer 1959). Likewise, a tendency to use analytical processes during the solution of an insight problem can hinder the solution process, as the use of analytical processes require focused attention, and the use of insight processes require defocused attention or flexible thinking.

Because solutions of insight problems are assumed to require no or little domain-specific knowledge and defocused attention, people who apply domain-specific knowledge and analytical ability as default tendencies to understand and to solve insight problems might fail in producing leaps of insight.

In this study, the author was interested in how domain-specific knowledge and analytical ability contribute to performance in solving insight problems, and in finding out if there are critical levels of analytical ability and domain-specific knowledge that are optimum in solving insight problems in mathematics.

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