- Changing Students' Conceptions of Mathematics through the Introduction of Variation
- Wong, Ngai-Ying ; Kong, Chit-Kwong ; Lam, Chi-Chung ; Wong, Ka-Ming Patrick ;
- Research in Mathematical Education, volume 14, issue 4, 2010, Pages 361~380
Abstract
Some 400 Secondary One (i.e. seventh-grade) students from 10 schools were provided with non-routine mathematical problems in their normal mathematics classes as exercises for one academic year. Their attitudes toward mathematics, their conceptions of mathematics and their problem-solving performance were measured both in the beginning and at the end of the year. Hierarchical regression analyses revealed that the introduction of an appropriate dose of non-routine problems would generate some effects on the students' conceptions of mathematics. A medium dose of non-routine problems (as reported by the teachers) would result in a change of the students' conception of mathematics to perceiving mathematics as less of "a subject of calculables." On the other hand, a high dose would lead students to perceive mathematics as more useful and more as a discipline involving thinking. However, with a low dose of non-routine problems, students found mathematics more "friendly" (free from fear). It is therefore proposed that the use of non-routine mathematical problems to an appropriate extent can induce changes in students' "lived space" of mathematics learning and broaden their conceptions of mathematics and mathematics learning.