You can get better and better at solving problems, both by building up your background knowledge and by simply practicing. at the University of Budapest, and was a professor at Stanford University (among other universities). Much has been written since 1945 to explain these steps in more detail, but the truth is that they are more art than science.
As you solve more problems (and learn how other people solved them), you learn strategies and techniques that can be useful. George Pólya was a great champion in the field of teachingeffective problem solving skills. He wrote many mathematical papers along with three books, most famously, “How to Solve it.” Pólya died at the age 98 in 1985. This is where math becomes a creative endeavor (and where it becomes so much fun).
, helped ignite a movement of visual innovators and problem solvers.
Since then, Dan has written four more books about visual thinking and even launched an online “napkin academy” to help unlock all of our potential to give visual form to ideas.
Ask yourself “what if” questions: You need to be sure to go back to the original problem at the end, but wishful thinking can be a powerful strategy for getting started.
This brings us to the most important problem solving strategy of all: If you are really trying to solve a problem, the whole point is that you do not know what to do right out of the starting gate. Put pencil to paper (or stylus to screen or chalk to board or whatever! This is often an important step in understanding the problem; just mess around with it a bit to understand the situation and figure out what is going on.
Assume that each piece has at least two numbers and that no number is damaged (e.g.
12 isn’t split into two digits 1 and 2.) Sometimes the problem has a lot of details in it that are unimportant, or at least unimportant for getting started.
This is all well and good, but how do you actually do these steps?!?! We will articulate some useful problem solving strategies, but no such list will ever be complete.
This is really just a start to help you on your way.