Why is your educational coordinator involved in this at all? Is he also responsible for making the schedule? Did he try and implement a rotation for "educational" reasons and was rebuffed?
With only 4 stations and an area that size rotating through each truck wouldn't bother me that much...if it was done over the course of a year; every shift is excessive. There is something to be said for moving so that you remain familiar with the different geographies, roads, cities, fire departments, hospitals, police departments, nursing homes and so forth, although this only works for departments of certain sizes; if you work in NYC not much point to moving from Queens to Brooklyn to the Bronx every month or so. Conversely, if it's a small enough place there also isn't a point since you'll still cover the same ground no matter where you are stationed. There is something to be said for only working in one smallish area as you will come to know it very, very well. And if you are going outside that particular area often enough to keep some level of familiarity with the surrounding places, it's not a huge deal. Again, this is dependant on the overall size of the department.
Partnering up with people can be a tricky thing. When you've got a good partner it's great. But when you get a lousy one...I'm just going to shudder quietly in the corner for a bit. And if you have any lousy people where you work, somebody will draw the short straw. Of course, there is always the option of putting 2 lousy people with each other, but often the work tends to suffer when that happens.
There's no good answer really. Having a permanent home and partner is awesome...when it's a good spot and you like who you're working with. When you don't have that, less fun. At least with a rotation you know there's a definite end to the misery.
With a place with only 4 different trucks I'd suggest coming up with a rotation that will have you moving trucks and partners every month or two; you still hit each location and I'd guess work with most people, but at least you'll have more of a home than rotating every shift. If you can come up with a way that people can request to work together at various times/places, even better.