Elemental Arcane Schools and Monster Summoning

[Smaugnolia]

In a game I am currently playing a sylphan wind mage (School of air), and have been wondering about the spell list. Every even numbered Summon Monster spell appears as a school spell for the arcane school of air, and the other elemental schools' lists. I always interpereted this as being you can prepare that spell in the school slot, but have to summon an air elemental with it. Looking around I am having trouble finding anything that states this explicitly though.
I assume I'm playing in the spirit of the rules but is there anything mechanically keeping me from using my school slots to summon grizzly bears?

[Gilarius]

As far as I can tell, yes you can summon anything from the appropriate summon monster spell.

Is that rules as intended? Who knows?

[Rhorik Hogsvard]

...even earth elementals?

[Dafydd]

Elemental Arcane Schools wrote:

Unlike a normal arcane school, each elemental school requires the wizard to select his opposed element as his opposition school (air opposes earth, fire opposes water). He does not need to select a second opposition school. He must expend two spell slots to prepare a spell from his opposed elemental school as normal.

Summon Monster 1 wrote:

When you use a summoning spell to summon a creature with an alignment or elemental subtype, it is a spell of that type.

So while I do not see anything directly against it, it is against the spirit of the school. That said, there is no notation you must summon elementals of your school (like there is in the elemental bloodline for sorcerer).