Splitting, Similarity and Rate of Change: New Approaches to Multiplication and Exponential Functions

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This project examines the development of students' schemes for multiplication and multiplicative rate of change that will enable students to understand the crucial societal and environmental issues of exponential growth. Through the use of teaching experiments, historical analysis and the design of software incorporating new representational and visual forms, the research team seeks to investigate how to improve students' insight in issues of scale, functions, multiplicative rate of change and biological forms of growth. To facilitate the research on secondary students, preliminary work will be undertaken into young children's concepts of multiplication, similarity and growth in relation to a primitive construct labelled "splitting" which is conjectured to be the basis of an approach to multiplication independent of counting. Initial studies will also include an ethnomathematical investigation of scientists' and social scientists' use of exponential functions. Informed by the interview studies, research on whole classroom implementation will be undertaken towards the preparation of applied research products including curricula, case studies of teacher development and software products.