Promoting The Foundation Concepts of Proportional Reasoning: A Case Study of P-3 Teachers

Abstract

Proportional reasoning is a sophisticated way of thinking which is used in everyday living, including workplace and educational contexts. Its application is central to many domains throughout mathematics curriculum, as it encompasses many interconnected concepts (e.g. ratio, decimals, and fractions). The foundations of proportional reasoning are established in the early years of school. However, the link between foundational concepts and proportional reasoning is not overtly stated in mathematics curriculum documents.This research aimed to investigate the foundation concepts of proportional reasoning and the promotion of these concepts in the early years of school. The research questions guiding this investigation were:1. What do Preparatory to Year 3 teachers recognise as foundational concepts of proportional reasoning? How do Preparatory to Year 3 teachers promote foundational concepts of proportional reasoning?An exploratory case study design was adopted for this study (as per Yin, 2009).Multiple sources were used for data collection, including focus groups, discussions, concept mapping and interviews. The case study took place in one south east Queensland primary school and the participant group consisted of five teachers -one teacher from each Year level from Preparatory to Year 3 and the participant researcher.The data were analysed using template analysis, which began with pre-determined codes relevant to each research question (King, 2012). As required throughout the analysis, the templates were adapted to represent the collected data.The findings highlighted that the foundational concepts of proportional reasoning evolve from three stages of development, which included additive thinking, transition to multiplicative thinking, and multiplicative thinking. The promotion of these concepts was found to take place through the provision of environmental resources, problem solving, and language. Throughout the data collection the teachers reported that their own knowledge grew and this was reflected in discussions which highlighted a synthesis of the foundational concepts and the promotion of proportional reasoning.iii Implications of this research highlight the significance of teacher knowledge. A teacher needs a deep knowledge of the foundational concepts which underpin a student's development of higher level concepts (additive thinking, transition to multiplicative thinking and multiplicative thinking). The Australian Curriculum:Mathematics requires interpretation for planning and teaching and a deep curriculum knowledge of how foundational concepts, that is lower level concepts relate to higher level concepts. Teacher knowledge has the potential to grow when a teacher is involved in teacher research within the context of a teachers' own school setting.iv