For numerous reasons, I daven at home before going into school, but then I put on tefillin at school again for chinukh reasons. I should say a berakhah, right?
If there is hefseik of siluk hada’at or that you go into a place where you cannot be wearing your tefillin – i.e., the bathroom (although, whether that is really true with today’s bathrooms is a different question) – then you say another berakhah. If you were to take them off, go into the car, go straight to school and into the room where people are davening and put them on again, then you would not say another berakhah. I am assuming that that is not the case. So, yes, you make a berakhah again.