There is very little difference between a child using the Scientific Approach to problem solve and a mathematician using it to do research.Hence through problem solving, children get a much better feel for what mathematics is actually about than they get in the more traditional type of teaching.
Most of the problems used in problem solving have more than one solution.
The more traditional approach to teaching mathematics sees the child as an empty vessel that has to be filled.
Correspondingly we have two contrasting models of "the guide on the side", the coach trying to encourage the learner along, and "the sage on the stage", the lecturer imparting knowledge.
Over time, and from seeing what other children have done, you should be able to develop and extend the range of strategies that the children have at their disposal.
So, starting with the members of your own class in mind, problems can be found that can give every child in the class the chance of making some progress toward a solution, either on their own or with the assistance of others in their group.