I think it's because you don't have quotes around the data fields in the sql statement. Using ',' may seem like you have the quotes, but that only creates a comma, you have to have "','"
function newSchool()
{
$sql_command = "INSERT INTO schools (school, country, city, state, zip) VALUES ('" . $this->school . "','" . $this->country . "','" . $this->city . "','" . $this->state . "','" . $this->zip . "')";
// by placing this in a variable you can test with
echo $sql_command;
$sql = mysql_query ($sql_command);
return $sql;
}