When my children were toddlers, my mom (a wise grandma) would always complement them whenever they are able to take one basic skill and apply it to another area of life. She used the term "ban jia", which means in Chinese "move to a different home". Now that I am in teacher education, I look back and recognize that this ability is a nice thing to complement a child for ... well, most of the time.
Once my 3-year old son saw a gorilla standing all alone in the corner of the zoo compound. He said sympathetically, "Look Mama, that grandpa monkey is having a time-out!". For my son, he was learning how to adapt his knowledge of the "time-out" strategy (someone standing in the corner alone) to describe that gorilla in the zoo. At the same time, he was trying to describe the gorilla based on his previous knowledge of what a monkey and a grandpa looks like.
Using "creativity", "flexiblity", and "adaptivity" to learn is a natural part of how human beings shape their understanding of the world. We often see that in young children. I guess you can call it a form of educated-trial-and-error. When children make mistakes whereby the strategy they have chosen does not "solve the problem", adults think it's cute and laugh about it. However when adults make mistakes we are in danger of not being able to reverse out of a certain mental mode, which could lead to frustrations of being unable to solve the problem.
I was talking to a grade 9 math student recently who said he does not like substitute teachers. So naturally, I asked him "why?". One reason is that substitute teachers might show them how to do a problem using another technique that is different from what his teacher has used. Maybe he was so focussed on his old method, that a new method disturbed him. That's too bad.
As teachers, we should frequently emphasize to students that are are many ways to approach a problem. If we can illustrate the value of being open to adapting different strategies, our students will be able to extend their problem solving skills far beyond the classroom. Our mathematical training should equip us to solve not just text-book, but real-life problems.
In our UBC math education class, I have come to appreciate the way we examine different ways of solving the same puzzle on the board. It has illustrated to me the incredible value of being creative, flexible, and adaptive when chosing a strategy to solve problems.