Student's Mathematical Knowledge Construction Patterns in Problem Solving Context

Abstract

The study investigated the nature of knowledge construction patterns (or thinking schemata) students manifested in solving a non-routine problem, distribution of students according to knowledge construction patterns and their success rates when grouped according to relatedness of course to mathematics and degree of exposure to mathematics. There were 217 respondents from different degree programs and year levels who were given carefully selected non-routine problem which they solved in one hour.

Results showed there exist seven different knowledge construction patterns with varying degrees of success. The proportion of respondents exhibiting successful knowledge construction patterns accounts for 12.9%, partially successful, 48.93% and not successful, 39.17%, thus indicating that large proportion of students need appropriate training in solving non-routine problems to improve their solving abilities. The proportions of respondents manifesting similar knowledge construction patterns across groups, as well as their success rates, are not significantly different. The results indicate that motivation and exposure to routine mathematics are not factors that differentiate between those with successful knowledge construction patterns and those with less successful ones and that students’ mathematics learnings are independent of the development of productive thinking schemata and solving abilities.