(b) Authorization to perform certain solo flights and cross-country flights. A student pilot must obtain an endorsement from an authorized instructor to make solo flights from the airport where the student pilot normally receives training to another location. A student pilot who receives this endorsement must comply with the requirements of this paragraph.
(1) Solo flights may be made to another airport that is within 25 nautical miles from the airport where the student pilot normally receives training
The student must be endorsed with something along the lines of:
I certify that (First name, MI, Last name) has received the required training of section 61.93(b)(1). I have determined that he/she is proficient to practice solo takeoffs and landings at (airport name). The takeoffs and landings at (airport name) are subject to the following conditions: (List any applicable conditions or limitations.)
Emphasis on the word TO, in (1). I interpret this as "You must be endorsed to fly solo TO another airport for takeoffs and landings." However, my instructor, and it would seem the majority of the instructors at my school interpret it as "You must be endorsed to fly solo AT another airport for takeoffs and landings." The FARs seem to imply my interpretation, and the recommended endorsement seems to imply the opposite (in fact the endorsement doesn't even mention the 25nm part except in title).
The situation it is used in most commonly is the towered-field TO/LDG practice. There is a towered field about 10 miles north of our airport where we all go to practice. However, the instructor is required to fly dual up there, solo the student, and fly dual back. Is this endorsement required in that case?