Variation, technology and Newton Raphson

Ideas of variation in mathematics are not new, as is shown In the ATM publication Variation in mathematics teaching and learning (Watson, 2018), which showcases a number of MT articles grouped around this theme. Digital technology can have a special affinity with variation, because of the simplicity of changing something in a mathematical object and observing the effect. During this period, I was teaching a number of advanced content areas but decided that the Newton Raphson method of approximating roots of functions was a useful one to explore by using digital technology. [...]by creating a draggable point (Figure 2), the learners could explore that, within certain conditions, different starting points always tended towards a particular root of the function.