The student edition is for single users only (one install per serial number), and is not for use by schools.
Institutional use of SolidWorks Student Edition is prohibited. Schools interested in licensing use should contact an authorized SolidWorks reseller.
You can find network installation instructions here, but they are only for the full Educational edition.
I would recommend calling your local reseller and getting an evaluation version of the educational version.
It was the head of department who phoned for this trial, I would presume that he explained it was for a school. I will get back to him. Although not allowing a STUDENT version in a SCHOOL seems a little ridiculous to me. It is the STUDENTS who he wants to trial it with.
It does seam a bit strange but the idea is that the student version is to help the individual student to be able to obtain the software for their own computer so they can learn out of the class room and get better. Students typically can't afford to pay insane software costs like the businesses making profits from it can. So the software companies greatly reduce the cost (or even give it free) to students who they know are most likely not making substantial profits from it. In return they are helping saturate the market with people who know their software better. I'm disappointed that SW makes their student version as expensive as they do. AutoDesk gives free student versions! Come on SW! Kids tend to learn it more when they can play with it, and they will be influencing buying decisions later on.
Schools are really giant businesses and should have to pay, but like bigger businesses they should be able to get substantial volume discounts. I am sure SW is willing to work with your school, probably just a miscommunication as to how your school was going to employ the trial.
Good luck getting it sorted out. I wish my school (Lawrence Technological University) had this worked with SW. Last I heard they were working on it and had a few licenses they could give out.