Creative Thinking in Mathematics: Proportional Reasoning
Klazalwr, A. K. ; Tiwari, P. (Pankaj) ; Tripathi, A. K. (Arun Kumari) (2016)
Life without a sense of proportion is difficult to imagine – it is present in all actions of enlargement and reduction. It is used in the home when thinking about the ingredients for cooking for ten people instead of six. It is used in urban planning when thinking about building plans. It is used by policymakers when considering issues of taxation. It is even used by young children, perhaps implicitly, in working out how many sweets to get for several people or how to share a bag of marbles amongst friends. Students therefore come to school with some intuitive understanding and knowledge of proportional reasoning, but they also come with misunderstandings and different levels of understanding. This unit will explore ways to teach proportional reasoning, including inverse and direct proportion in a playful and creative way. In this unit you will learn how to help your students understand that proportional reasoning describes the multiplicative relationship between quantities, ideas to support your students to become more creative in their thinking about mathematics, and suggestions on how to design activities that allow for possibility thinking. This unit links to the teaching requirements of the NCF (2005) and NCFTE (2009) outlined in Resource 1.