Connecting the Points: An Investigation into Student Learning about Decimal Numbers

Abstract

The purpose of this research project was to investigate the effects of a short-term teaching experiment on the learning of decimal numbers by primary students. The literature describes this area of mathematics as highly problematic for students. The content first covered student understanding of decimal symbols, and how this impacted upon their ability to order decimal numbers and carry out additive operations. It was then extended to cover the density of number property, and the application of multiplicative operations to situations involving decimals. In doing so, three areas of cognitive conflict were encountered by students, the belief that longer decimal numbers are larger than shorter ones (irrespective of the actual digits), that multiplication always makes numbers bigger, and that division always makes numbers smaller. The use of a microgenetic approach yielded data was able to be presented that provides details of the environment surrounding the moments where new learning was constructed. The characteristics of this environment include the use of physical artifacts and situational contexts involving measurement that precipitate student discussion and reflection. The methodology allowed for the collection of evidence regarding the highly complex nature of the learning, with evidence of 'folding back' to earlier schema and the co-existence of competing schema. The discussion presents reasons as to why the pedagogical approach that was employed facilitated learning. One of the main findings was that the use of challenging problems situated in measurement contexts that involved direct student participation promoted the extension and/or re-organization of student schema with regard to decimal numbers. The study has important implications for teachers at the upper primary level wanting to support student learning about the decimal numbers system.