Mathematical Modelling: A ‘Growing Tree’ for Creative and Flexible Thinking in Pre-service Mathematics Teachers

This qualitative case study was guided by the research question: To what extent are pre-service mathematics teachers competent in invoking and using modelling processes to solve a real practical problem? They were required to determine the height of a tree. In-depth analysis of the written reports and presentations of two groups showed they were not only able to experience the modelling process but also able to creatively invoke and apply necessary skills and abilities to enable them to move from one step to the next. They were able to make assumptions, set up a mathematical model through mathematizing, use their mathematical knowledge to solve the model and interpret and critically reflect on their solutions to see they made sense. The kinds of novel models built and used in creating unexpected solutions suggest the tree modelling task stimulated creative and flexible thinking.