In Mormonism, do persons ordained as Teachers in the Aaronic Priesthood have actual teaching duties? In the LDS faith, the offices of the Aaronic Priesthood are Deacon, Teacher, Priest, and Bishop. Current practice in the LDS church is to ordain most teenage boys in the church to the first three offices as they progress through their teenage years.

Do LDS Aaronic Priesthood Teachers have actual teaching duties in a practical sense in the 21st century, or are they teachers in an abstract or theoretical sense (e.g. if all priesthood holders except for 15 year old Billy were killed or incapacitated, he would be allowed to take over classrooms, but until then, he is expected to be quiet and let the adult professionals do the actual teaching)? Do they design curricula, lecture, hold office hours, grade papers, administer exams, evaluate students, or otherwise engage in practices associated with professional educators nowadays? Do Aaronic Teachers  have divine authority to teach a wide variety of courses, content, or curricula but in practice don't because there are usually more qualified, professional teachers available at whatever level is being discussed (e.g. college, high school, etc.), or are their actual teaching competencies sharply limited in both theory and practice (e.g. they are authorized only to teach Sunday School, and that only for Grade 5 and below, anything else requires a further ordination, and/or a non-priesthood teaching certification).
EDIT: As of this annoucement, some parts of this answer are out of date. I'll keep it as it is now though for historical purposes.

Yes

Teachers usually do not teach on Sunday (unless assigned to teach a class), but are assigned as home teachers.

All teachers are assigned one or more families to home teach. A new teacher is usually assigned a more experienced Priesthood holder (such as an Elder or High Priest) to mentor them, but they usually give the lesson half of the time. (This lesson could be considered a "lecture"). For example, in the New Era (a magizine for the youth of the Church), in Watching over the Church


  One of the most important parts of a successful home teaching visit is
  preparing and sharing a lesson. Every other month Brandon Stewart
  gives the lesson. Brandon has learned how to prepare a lesson by
  watching his senior companion, his father. Thanks to his dad’s good
  example, giving the lesson is Brandon’s favorite part of home
  teaching.


They might even create the lesson themselves (under the direction of the older Priesthood holder), although usually they do not. Home teachers also have other duties, which can be said to be "teaching by example", although I guess you would consider this more "abstract".

Some teachers are also assigned as the president of a teacher's quorum (in particular, one per quorum). This will usually be a 14 or 15 year old. They also might teach (in particular, they would teach other teachers), again under the direction of older priesthood holders.

It should be noted as well than any member can be assigned to give a talk on Sunday.

Is a teacher in the Aaronic teacher the same as college professors? Sadly no. Do they teach? Yes.