Annin, S. A., & Lai, K. S. (February 2010). Common errors in counting problems. Mathematics Teacher, 103(6), 402-409.

This article was about the easily confusing differences within algebra combinatorics especially those in combinations and permutations. Giving 3 examples of problems where kids that have been taught the material and understand what is being asked of them but misread the problem and have faulty logic when creating solutions. It concludes with the idea that a variety of problems can help students gain a better conceptual understanding of the problems and become familiar with potential errors that they are then mindful of creating consistency and success in solving these problems.

This was a great article in the field of combinatorics and the presentation of the problems given. The main point of the paper was clear and interesting with a great answer to the problem posed; it was a great insight into student understanding and posited a simple solution to the main point. It stated that combinations and permutations are taught to be categorized into 4 separate groups: Permutations where repetition is allowed, permutations where repetition is not allowed, combinations where repetition is allowed, and combinations where repetition is not allowed. But in 3 given scenarios these 4 clear-cut categories are breached where the problem given could fall into several different groups, thus the solution method is not obvious. However, by knowing what is required from the problems, students could solve them based on understanding rather than even needing to categorize the problem. So I thought this was a great article on it's topic and would recommend it to anyone.