In my humble opinion as a math student and considering that my main area of interest is computer science, I see that one of the most important skills required to solve problems is the mathematic thinking - a skill that involves the ability to look into a problem and extract informations.
With my background from high school, I developed a "mechanical way" to look into solutions for a problem, searching for formulas, techniques and theories that can be applied towards the solution. This can be problematic for many reasons: this "mechanical way" can lead to wrong formulas, bad abstraction of the problem, etc.
As I see, many people share this way of thinking. I'd like to receive a constructive feedback to start building confidence and think as a mathematician.