Mathematicians undertake certain processes when they solve a problem. There are two main processes:
Mathematical inquiry allows students to pose their own question (or receive a prompt) and regulate their own learning and activities in order to answer the question.
Mathematical modelling is the process used by mathematicians to help them explain and predict real life phenomena.
Mathematical inquiry is a holistic approach to learning and mastering mathematics. Having students pursue their own interests leads to greater engagement, which in turn increases retention.
Mathematical modelling is vital for understanding our world. Whenever something new is discovered or invented, mathematicians play a vital role in understanding how it works.
In addition to inquiry and modelling, there are four other processes that are important: collaboration, reasoning, proof and communication.