Incorporating Ideas from Indian History in the Teaching and Learning of a General Place Value System

Abstract

The current decimal place value system is foundational to progress in mathematics and yet research shows that many students, including high school students, experience considerable difficulties with the place value concept. Hence this study, adopting a holistic and multi-pronged approach that included a historical-critical methodology, investigated how the history of mathematics could be used to enhance junior secondary school students' conceptual understanding of a general positional notation. Situated in mathematics education research, the first part of this study analysed the history of mathematics, in particular the development of the decimal place value system and algebraic symbolism in Indian history, for ideas relevant to understanding the place value construct, and these ideas were then incorporated into a teaching/learning framework. The second part of the research, a case study, investigated the effectiveness of the framework developed, on junior secondary school students' understanding of a general place value system. The participants were twenty-nine Year 9 (13 year-old) students from a secondary school in Auckland, New Zealand, who worked cooperatively with the researcher, who was also their classroom teacher, for a full term of the academic year. The teaching intervention, employing multiple (including concrete) representations, took place in a classroom environment that is largely compatible with a socio-cultural view of learning. The Indian historical analysis revealed key stages in the evolution of the decimal place value system. Beginning around the Vedic period, there was consistent naming of large numbers including powers of ten, which eventually led to the development of the current Hindu-Arabic place value system with zero. The written numeral system appears to have traversed four main stages; that of additive, multiplicative, 'places' and finally abstract before its final construction. Consequently, rapid progress was made in algebra paralleling the development of algebraic symbolism, a key feature of which was different names (colours) for different unknowns/variables. The empirical data was positive, providing evidence indicating that students were successful to a degree, in understanding place value structure. The research suggests that implementing teaching sequences based on the framework produced could have a positive effect on student understanding of a general place value system.