I’m aware that considering I plan on studying engineering I will need a math and science recommendation, thankfully two teachers I’m very close with have been 2 of my AP teachers, one in Physics, the other in Statistics. This being said, something I really want to pop in my application is my leadership ability, the teachers I believe that can best attest to this would be my sophomore year English teacher and my student government instructor, despite my major, could I be able to viably use recommendations from these teachers? Also there is one teacher for whom I’ve worked for as a class officer and NHS officer but I’ve never had her as an academic teacher, would I be able to use her as well?
TL:dr
Can I use teachers that aren’t math or science oriented for my application to engineering colleges if they can beat attest to my leadership? Also can I use someone who has not taught me in an academic setting?
You can submit a third recommendation from someone (teacher or non-teacher) who can specifically talk to aspects of your personality or skill set that neither of your teachers can address. Just beware redundancy. Reviewers have to get through a lot of documentation. And don’t send more than 3 (plus the guidance counselor rec) - it’s overkill.
Read with care the application process for each of the colleges on your list. There may be exceptions regarding which teachers they prefer as references so in some cases you may be able to pick any of the teachers you mention. Most often however they prefer “recent” teachers and ones with whom you’ve had an “academic” relationship. So a sophomore year teacher may not be suitable. That said many colleges allow you to add a supplemental reference, and for that you may choose a teacher with whom you have not had an academic relationship.
If you need a math and science recommendation for engineering school I’d use the two teachers you mentioned. It is usually OK to add a third recommendation (teacher or other) but only if they will discuss attributes that would not appear in a typical teacher recommendation so I’d say at most add one of the other two you mentioned (English teacher or student govt instructor) – pick the one you think knows you best and can talk to your extracurricular/leadership the best.