Microsoft used to come around University telling the students that XNA is deprecated in favour of MonoGame (an open-source XNA clone). The VisualStudio IDE used to crash every time they did a demonstration of the content pipeline with MonoGame http://www.monogame.net
At risk of getting a lower grade because of minor differences between the two, I can't suggest that you use it. But you should probably evaluate it yourself and make the choice.
Your tutor might respect the fact that you are looking outside the box and towards solving issues of portability (a major topic within the game development industry).
For 2D you should find it pretty easy. For 3D naturally it becomes a more steep learning curve because you will be learning the fundamentals of modern 3D graphics programming rather than just scripting and automating products like Unity.http://www.opentk.com
Edited by Karsten_, 12 July 2014 - 05:34 AM.