To improve your understanding of a proof, there is a series of techniques you should apply.
After reading each line:
Try to identify and elaborate the main ideas in the proof.
Attempt to explain each line in terms of previous ideas. These may be ideas from the information in the proof, ideas from previous theorems/proofs, or ideas from your own prior knowledge of the topic area.
Consider any questions that arise if new information contradicts your current understanding.
Before proceeding to the next line of the proof you should ask yourself the following:
Do I understand the ideas used in that line?
Do I understand why those ideas have been used?
How do those ideas link to other ideas in the proof, other theorems, or prior knowledge that I may have?
Does the self-explanation I have generated help to answer the questions that I am asking?
Below you will find an example showing possible self-explanations generated by students when trying to understand a proof (the labels ‘‘(L1)’’ etc. in the proof indicate line numbers). Please read the example carefully in order to understand how to use this strategy in your own learning.