The diagram cannot logically be drawn in its entirety before the solution is commenced. A particular example of preemptive drawing is the instruction to show all the forces acting in a particular problem. In the case of two connected masses, for example, only the forces acting on one of the masses are necessary to begin the solution. The solution will, at the appropriate point, ask for inclusion of the details of the effects of the second mass on the first mass. There are two free body diagrams involved and one is developed before the other.
Problem solving is a linear process.
Rapidly developing technology confronts an ever-growing population with the need to function in more sophisticated areas of thought and application. A part of this is the use of mathematics as a communication tool. Problem solving using mathematical methods has strong training and application attributes. In order to meet this challenge it is necessary to modernize the teaching and use of problem solving as a tool to understanding and applying ideas. Teaching students to be effective problem solvers, instead of training them to be poor problem solvers, will contribute much to making physical and mathematical ideas available to a broader population.