Seems to me there's roughly 4 roles that ought to be covered in educational IT support. Whether you have the manpower or the need(re size of network) to fill these roles is another matter but I see them as:

1. Helpdesk ~ stay in the office, answer the phone, deal with incoming people, change kids passwords, make new accounts, tweak the helpdesk, maintain records, keep track of what needs doing,

2. Firefighting ~ roam with a radio, first responder, bring broken stuff back to the office, change mice, deal with wireless connection issues, printer jams, etc

3. Fxing stuff ~ reimaging computers/laptops, repairing broken stuff, referrals from helpdesk, general maintenance of rooms,

4. Sysadmin ~ Servers, forward thinking, R & D, Solving reoccurring problems, designing/implementing new network features etc

On smaller networks roles can be merged but the minimum ought to be 2. The greatest revolution in my work was employing a specific help desk person. Before this, even with a helpdesk application we always in a bit of mess keeping track of things, maintaining consistency and had limited records of stuff we had . Such a person need not be great technically. Primarily they need to be good with people & kids and good at organising. We're lucky ours is good at fixing stuff too.