The Peninsula Daily News reports the board voted in favor of the ban this week and will take a final vote at its June 11 meeting.
The board member who voted against the ban, Sarah Methner, says, "It's a nanny state gone wild."
Superintendent Jane Pryne says the rule was prompted by complaints against a few teachers who let their dogs run in the hallways.
Board Vice President Lonnie Linn says a review by legal and insurance teams found that almost any animal in a classroom is an unacceptable risk, especially for disease such as salmonella.
Fish tanks and service animals would still be OK.
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