Harry could usefully collaborate with Hagrid, but Hermione or Draco may need to point that out. Hagrid has had limited access to practicing his magic, so provides something of a control to his classmates, to test whether magical strength is an increasing function of magical use, if magical strength is easily measured - Dumbledore seemed to be able to sense it. Hermione challenged by Fawkes, may see improving the performance of everyone in the class as the effective way of working harder. Asking Harry "Why are we different?" and based on "Great artists steal", what existing techniques should we look at could be both effective for both of them.
Update: Discussion has moved on to a new thread.
After 61 chapters of Harry Potter and the Methods of Rationality and 5 discussion threads with over 500 comments each, HPMOR discussion has graduated from the main page and moved into the Less Wrong discussion section (which seems like a more appropriate location). You can post all of your insights, speculation, and, well, discussion about Eliezer Yudkowsky's Harry Potter fanfic here.
Previous threads are available under the harry_potter tag on the main page (or: one, two, three, four, five); this and future threads will be found under the discussion section tag (since there is a separate tag system for the discussion section). See also the author page for (almost) all things HPMOR, and AdeleneDawner's Author's Notes archive for one thing that the author page is missing.
As a reminder, it's useful to indicate at the start of your comment which chapter you are commenting on. Time passes but your comment stays the same.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: