To see more about GOAL-Oriented Problem Solving and the supporting research see On-line Articles: Robert Beichner.
For more information about Teaching Students to Solve Quantitative Physics Problems by Writing Their Way Into the Solution, contact Calvin S. Kalman.
The solution presentation shown emphasizes importance of gathering information in a coherent manner. The guiding idea is the NEED-TO-KNOW. For the case at hand we need to know the acceleration of the bucket. By simply asking "How would I find out?" Newton's law of motion provides an appropriate response. Now we NEED-TO-KNOW the net force. The idea of a free-body diagram provides a response. The process is continued, each step being a consequence of the previous step and a precursor to the next step. Problem solve themselves.