Simple ideas like recording results, keeping all but one variable fixed, trying very small or very large numbers, and varying parameters in regular ways are missing from the backgrounds of many high school students. When faced with a mathematical problem, a student should immediately start playing with it, using strategies that have proved successful in the past. Students should also develop a healthy skepticism for experimental results. Results from empirical research can often suggest conjectures, and occasionally they can point to theoretical justifications. But mathematics is more than data-driven discovery, and students need to realize the limitations of the experimental method.
Many people claim that mathematics is a language.
If so, it is a superset of ordinary language that contains extra constructs and symbols, and it allows you to create, on the fly, new and expressive words and descriptions. Students should develop some expertise in playing the mathematics language game. Describing what you do is an important step in understanding it. Students should develop the habit of writing down their thoughts, results, conjectures, arguments, proofs, questions, and opinions about the mathematics they do, and they should be accustomed to polishing up these notes every now and then for presentation to others. Formulating written and oral descriptions of your work is useful when you are part of a group of people with whom you can trade ideas.