Common Errors in Counting Problems

Mathematics teachers are often asked, "What is the most difficult topic for you to teach?" Their answer is teaching students to count. The concepts can be challenging and slippery to apply in problems. Many times, no rigid procedures or formulas can be used to solve the problems directly, and students simply do not know where or how to approach them. Further, subtle differences in how questions are posed can necessitate entirely different solution techniques. This article will draw attention to some errors that students fall victim to when solving counting problems, examine the differences between correct solutions and solutions often given by misdirected students, and provide some problems to encourage practice in this challenging area. (Contains 6 figures.)