The lived space of mathematics learning

Abstract

Students’ conceptions of mathematics and mathematics learning are important research issues in mathematics education, as they bear significant relationship to student’s mathematics performance. In this paper, as an attempt to reconceptualise students’ conceptions of mathematics, the notion of “the lived space of mathematics learning” is introduced, referring to the space experienced by learners and spanned by all the dimensions in which problems in mathematics vary from each other, and from non-mathematical problems. This “lived space” constrains what the learners will regard as mathematics and as mathematics learning, and constrains therefore their conceptions of mathematics and mathematics learning. Based on this understanding, the present study is aimed at investigating the relationship between students’ conceptions of mathematics and how they actually tackle mathematical problems. By using a variety of open-ended non-routine mathematical problems, the extent of variations in students’ conceptions of mathematics and in their lived space of mathematics learning were explored. Non-routine mathematics problems as tasks could bring about a sharp contrast with the usual problems in their classroom learning. Students were interviewed after they were asked to attempt several mathematical problems, some being routine and some open-ended. Through a detailed analysis of students’ interview protocols, characteristic features of their conceptions of mathematics and mathematics learning have been revealed. These were discussed in terms of the existing classroom teaching and examination culture. It is argued that the present notion of the lived space can also point to ways to broaden students’ current narrow conceptions of mathematics.