One of the challenges that many students face when making the transition from mathematics courses in high school to ones in college is learning to read and dissect a complex problem. Most students achieve success in high school by learning and applying standard methods to solving problems. When in college, the hardest thing for students to learn is the process of struggling with a problem over an extended period of time. Too many teachers, in a misguided effort to boost the students' confidence, avoid assigning problems that have no clear path to the solution. Worse, they only assign problems that are closely modeled on examples, for which step-by-step solutions have been provided. As a result, students learn that it is acceptable not to read a problem carefully, and to follow a previously learned procedure. Students develop the view that understanding what a problem is asking and why the procedure for obtaining the answer works is unnecessary and even a distraction. Most students trained in this way are prone to making mistakes due to memory lapses and often misapply formulas or procedures when faced with novel problems.
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