Problem Solving Strategies Crossing the River with Dogs and Other Mathematical Adventures Why Teach a Course in Problem Solving? The NCTM Principles andStandards state that problem solving should be integrated throughout all courses and grade levels. For example, guess-and-check is a natural strategy to apply in algebra. Advanced math students often use finite differences to study functions and sequences. And drawing a diagram and using physical representations are commonly employed strategies in many contexts. However, many students never encounter valuable strategies such as matrix logic or unit analysis. And in content-crowded math classes, few students get the concentrated practice or time necessary to fully develop their problem-solving skills. By taking a semester course in problem solving, students can master a multitude of strategies while developing confidence in their problem-solving abilities. Your students will be better prepared to meet the challenges of school and life by taking this course.