Students’ conceptions of mathematics, and their conceptions of learning, knowing, and self in mathematics

This study examined the conceptions of mathematics, and conceptions of learning, knowing, and self in mathematics held by two typical students in an intact Algebra 12 class. Their learning of logarithms served as the context for this study. The students' various conceptions were largely integrated, and while there were some differences in the views which made up their conceptions, there were many similarities. These included their views that: mathematics was a set of truths, handed down to them by their teachers, in the form of rules and procedures to get answers for the questions encountered in class; knowing and learning in mathematics were undifferentiated from that in other subjects at school, the memorization of unrelated facts; it was the teacher's job to make learning easy for students by presenting new material slowly and in a step-by-step manner; students played a passive role in the learning process; and they "understood" mathematics when they got the right answers for the questions encountered in class. Furthermore, the students lacked confidence in themselves in mathematics and believed that their learning and success depended upon factors which were largely beyond their control. The following conclusions were drawn from this analysis: students' views on the nature of mathematics and on learning and knowing mathematics influence the kind of mathematics knowledge that they construct by shaping the goals that they set for themselves in the process of learning mathematics, profound but subtle failures in communication which hamper students' learning can occur between teachers and students in the mathematics classroom, students' views can play a major role in limiting or enhancing students' participation within the mathematics classroom and therefore their opportunities for learning and success, students may have unresolved conflicts amongst their views which may be a detriment to their learning, and students may hold views about knowing and learning which they constructed in contexts outside of the mathematics classroom and which are inappropriate for learning mathematics. Fundamental changes are needed in mathematics programming and teaching to address students' conceptions relating to mathematics, and mathematics learning and knowing so that their command of mathematics can be improved.Education, Faculty ofGraduat