In pre-calc 12, I think that permutations, combinations, and binomial theorem will be the most challenging and difficult for students to understand. After emailing my sponsor teacher, she agrees completely. Last year was her first year teaching this topic and she found that she had to go at a much slower pace than anticipated. In addition, she had to explain the concepts with more detail and precision in comparison to other topics. So some basic tips from her were to adjust the pace accordingly and to make sure students understand what information is key when reading word problems.
I think probability(perms, combs, binomial theorm) is a difficult topic in general because types of problems and the concepts are extremely different from what students are used to. There are formulaic, logical, and common sense aspects to probability which make it difficult. I think understanding what information to look for in word problems is a skill that needs to be developed so before introducing probability we should make sure to incorporate word problems throughout the year. Also, the Khan academy had a couple of great videos on permutations and combinations that explain the concepts in a clear way.
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