Why is math fun? Why is math hard?

Today in class, I tried to help break the ice and reduce some of the anxiety related to taking a university mathematics course (Math 231). I asked students for examples of why they might find mathematics fun and why they might find mathematics hard. Here are some of the responses.

Why fun?

• It's fun when you struggle with a concept and then it finally clicks and you understand.
• It's fun to see mathematics actually being applied to a real problem.
• It's fun when you are able to spot trends and make predictions based on data.
• It's fun why you really understand why instead of just the "required" steps.
• When you understand, it becomes easy.
• It can be a lot like a game or solving a puzzle.
• It's fun to develop things logically.

Why hard?

• Later material builds on earlier material, so missing something early is permanent hardship.
• It can be really hard when the teacher goes too fast.
• It can be really hard when the teacher is unclear, especially if they can't give alternate ways of thinking about an idea.
• It can be hard if the teaching style is very different from your learning style.
• There are so many formulas, it can be overwhelming to try to memorize them.
• The theorems, rules and definitions are full of little details.
• It can be difficult to understand the many conceptual ideas that interact.
• Learning related technology can be challenging.
• Only one answer, so you can't fake it.
• Very hard to cram for exams.
• It can be really hard to find a little (stupid) mistake when proofing your work.
• Lots of homework, and problems can take a lot of time.

I'd welcome more comments, including examples of when you found mathematics especially exciting or examples of how your relationship with mathematics soured. Feel free to post a comment.