# Educational styles for writing proofs

Can someone please point to research papers that analyze different ways of expressing informal proofs from an educational point of view? I am particularly interested in proofs by induction but I would like to read about different ways of expressing logical inferences in a way that students understand them better.

For example, a commonly used one is the calculational style. Are there any others? How do they compare to this one?

• Generally my sense is that students simply haven't had logic. In particular for induction, the inductive step is proving an implication $P \rightarrow Q$, and if they've never practiced that and are jumping into it in the midst of an induction discussion, that's a lot of moving parts to pick up on at once. So a modification to the search might be "does teaching logic improve success in later proofs courses?" – Daniel R. Collins Feb 19 '16 at 5:31
• Along the lines of DRC's comment, of the basic methods of proof, induction is probably the most difficult. If you haven't mastered other, simpler methods, induction will be somewhat hit-and-miss. You might Google "software to teach methods of proof." – Dan Christensen Mar 21 '16 at 13:46
• I don't know about so-called learning styles as avenue of research, especially for something as abstract as proofs by induction. I have seen some postings here attempting to debunk the whole notion saying that there is really no science behind it. Look into it before putting a whole lot of time into it. – Dan Christensen Mar 21 '16 at 13:55
• – Dan Christensen Mar 21 '16 at 14:05
• Probably not what you're looking for, but I like The Grammar According to West. – Austin Mohr May 19 '16 at 3:38