The answer is a LOT.
It always surprises me that we need more and more research to prove this to many people, given how intuitive and obvious it should be to anyone who has ever attended school. Regardless of what children bring with them to school in terms of home experiences, previous learning, expectations -- WHATEVER -- if the teacher in the classroom IS NOT teaching, or is not teaching effectively, or -- and this does happen -- is actually telling the students that they are not capable of learning .....well, NO learning will happen.
Whereas a good or great teacher, armed with only paper and pencils can do amazing things. Give those teachers even better resources and they will arrange miracles. Fortunately, most teachers fall in this category (and are feeling quite dispirited by the polarized discussion that labels all participants as either "anti-" or "pro-" teacher, as if all teachers are equal in quality).
Alas, today's education debates are such that we need hardcore research to prove that the quality/ability/effort of the teacher in the classroom has a tremendous impact on whether kids learn or not.
Additional research is showing that when there are ineffective teachers in the system, they are disproportionately placed in front of low-income, minority students in communities where the parents have the least power to do something about it. Then we blame those parents, students and communities for the resulting lower academic performance.
The question is, why do we allow this to continue?
Some reading on the matter: