How can a student revise his lessons without feeling the whispers of showing off (riyaa'), and how can he purify his intention for Allah Almighty in his work?

Seeking knowledge is one of the best ways to draw closer to Allah. The whispers and distracting thoughts you experience during study are from Satan, aiming to deter you from seeking knowledge. Beware of these whispers and strive to rectify your intention and attain sincerity for the sake of Allah the Almighty, by intending through your pursuit of knowledge Allah's pleasure and drawing closer to Him, and by worshipping Him with insight and removing ignorance from yourself. To correct your intention, intend humility through knowledge, not arrogance, and intend to remove ignorance from yourself. As for the method of revision, it is by repeating what you have memorized to yourself or to others, and by frequent repetition until it becomes firmly embedded and established in the mind.