Developing understanding of number system structure from the history of mathematics

Abstract

The use of the historical development of mathematical concepts to inform current teaching and learning has been a debatable process. Historically, in Indian mathematics (and Mayan), a study of large numbers seems to have provided the impetus for the development of a place value number system. Present day students do not have to create a number system, but they do need to understand its structure in order to develop number sense and operations. In order to investigate the value of this approach we considered the use of a combination of historical development of large numbers, number systems and modeling with concrete materials as a way of enhancing students’ knowledge and understanding of place value structure. Additionally, we also looked at place value in different number bases and linked multiple representations in an attempt to strengthen understanding of the structure of the number system. The results suggest that this historical and concrete approach helped students to gain competence in naming and using large numbers, and in understanding positional notation through exponentiation, to the extent of generalizing it to other bases.