Creative problem solving is needed to work on problems for which an approach to solve the problem is not clear initially. On such problems, chances of not being able to solve the problem are high. Our national instincts are to avoid such problems. If problems are selected where at least partial progress can be done, then that is likely to be encouraging to students. There can be multiple objectives in working on problems: to gain insights about the situation described in a problem, to learn about problem solving, to come up with a solution to the problem and to communicate problem progress to others on the team. It is not necessary to have 'coming up with a complete solution' as the only purpose for working on the problems. Given the right motivation, it is possible to enjoy the process of solving problems even if one does not succeed in it.
Mathematical thinking can be motivated by surprise, contradiction or a gap in knowledge. Kids can also be motivated by using appropriate problem solving contexts that interest them.
Following are examples of problems that can be used to motivate students
Mathematical thinking can sustained using challenging, questioning and reflecting atmosphere.
With the right attitude and practice, one can enjoy the process of mathematical thinking that involves thinking about mathematical problems, observing beautiful mathematical patterns, coming up with elegant insights, facing hard problems that you may or may not be able to solve, thrill of progressing on such problems and solving these, reflecting mathematical thinking and learning from your successes and failures. Then, you have an activity you can enjoy wherever you areand joy of creative thinking is all you need to motivate yourselves to get going on any challenging math problem.