Problem-Solving vs. Exercise Solving


  1. Involves a process used to obtain a best answer to an unknown, subject to some constraints.
  2. The situation is ill defined. There is no problem statement and there is some ambiguity in the information given. Students must define the problem themselves. Assumptions must be made regarding what is known and what needs to be found.
  3. The context of the problem is brand new (i.e., the student has never encountered this situation before).
  4. There is no explicit statement in the problem that tells the student what knowledge / technique / skill to use in order to solve the problem.
  5. There may be more than one valid approach.
  6. The algorithm for solving the problem is unclear.
  7. Integration of knowledge from a variety of subjects may be necessary to address all aspects of the problem.
  8. Requires strong oral / written communication skills to convey the essence of the problem and present the results.

Exercise Solving

  1. Involves a process to obtain the one and only right answer for the data given.
  2. The situation is well defined. There is an explicit problem statement with all the necessary information (known and unknown).
  3. The student has encountered similar exercises in books, in class or in homework.
  4. Exercises often prescribe assumptions to be made, principles to be used and sometimes they even give hints.
  5. There is usually one approach that gives the right answer.
  6. A usual method is to recall familiar solutions from previously solved exercises.
  7. Exercises involve one subject and in many cases only one topic from this subject.
  8. Communication skills are not essential, as most of the solution involves math and sketches.