The problem solving, or application level, and exercise solving levels differ. At the exercise solving level, a student can correctly demonstrate a procedure when asked to do so. Problem solving demands more from the student. Given a problem that is foreign to the student, he will be able to select the appropriate procedure to use without guidance from the teacher, and then correctly use the procedure. Problem solving level objectives promote critical thinking.
Problem solving requires a four-step cognitive process.
First, the problem's ambiguity forces students to search for familiar problem elements. Second, students determine the novel problem elements that make the problem different and thus more difficult from those seen in the past. Finally, students apply their solution strategy to solve the problem. Problem solving objectives require all four steps. Exercise solving objectives only require the final step where the solution strategy is obvious to the conscientious student.