The Value of Historical Knowledge Through Challenging Mathematical Tasks

Abstract

Learning mathematics does not simply mean acquiring/developing a set of content knowledge. It also means being able to solve problems, think mathematically and communicate ideas with others. If we think about the mathematics taught to prospective mathematics teachers, the study of the nature of mathematical knowledge, mathematical processes and their historical development is fundamental to their future teaching practice. To achieve this goal, we designed a formative experience in which were proposed challenging, historically framed mathematical tasks to prospective mathematics teachers who teach in the early years (Kindergarten and Primary). In this setting, the study aims to understand how challenging mathematical tasks, which bear upon historical context, contributed to student learning in terms of understanding: the nature of mathematics; the historical development of mathematical knowledge and the processes by which it is developed; mathematical concepts and their modes of representation. The study applies a qualitative and interpretive methodology with the participation of 45 prospective teachers who recently enrolled in the undergraduate programme. The data comes from student resolutions, individual reflections, observations and field notes. The results reveal that as a corollary to working with challenging mathematical tasks framed historically, students have developed their knowledge of mathematics and the nature of mathematical knowledge. They understand the value of problem solving towards an improvement of their historical knowledge and in the development of some fundamental mathematical concepts taught in the initial school years, such as number, operation, regularity, geometric objects.