First of all, I am well aware of that there are many of questions regarding this topic. I have read them, but still could figure out an appropriate answer for my situation.<
I don't think you can easily do that. What you can do is using public key authentication instead.
Something along these lines
ssh-keygen -t rsa ssh school mkdir .ssh/ cat ~/.ssh/id_rsa.pub | ssh school "cat >>.ssh/authorized_keys"
(or dsa).
dsa
But hey, it's not serverfault, is it? ;-)