This is how mathematicians behave. In the past decade, there has been a lot of research studying mathematicians, finding out how they go about solving problems. This has led to strands such as 'Working Mathematically' or "Working Like a Mathematician" being the focal point for all mathematics curricula.
A student must have the right mindset to master mathematics. They have to move past 'when will I need this in real life!' A negative mindset will shut down a student's creativity.
Secondly, there are certain traits that are essential such as: curiosity, patience, courage, perseverance and versatility.
Thirdly, a mathematician has certain habits which help with their mathematical inquiry, modelling or problem solving: self management, personal engagement, estimation, reflection and metacognition.
There are three main areas: