[Just a student, don't mind me :) ]
When we talk about people, we normally use he/she (with a few exceptions, for example babies). A student is a person, not an object, so I'd say it's natural to speak of his or her mind, not its mind.
My grammar is very bad, so I can't explain to you why we use "at" instead of "to" her, but your colleague is right.
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