One connection for each Thread??

I can't post all of my code, but here is the basic layout (well, the important stuff):

I've got a Threaded app, that calls a new instance of a class, basically, well, forever.

while (running)
{
    // poll a database table, check some values
    if (CONDITION CHECKS OUT)
    {
        new Test().start(); // <-- do some db transactions in here
    }
}

So...I could possibly have 10 or so Threads going at once...maybe more.

Now here is now I'm doing my connection to the database:

private static Connection conn = null;

public static Connection getConn()
{
    if (conn == null)
    {
        try
        {
            DriverManager.registerDriver(new oracle.jdbc.driver.OracleDriver());
            setConn(DriverManager.getConnection(dbUrl,dbUid,dbPwd));
        }
        catch(Exception e)
        {
            logger.error("Get Connection failed: " + e.getMessage());
        }
    }
    return conn;
}

public static void setConn(Connection conn)
{
    logger.debug("Setting new connection...");
    FlashClient.conn = conn;
}

Basically I get the connection ONE TIME, and keep it, so whenever the Thread touches the db, it uses the connection that I created above....

Now someone was telling me EACH THREAD needs to have it's own connection to do work.

TRUE OR FALSE???

And isn't that alot of overhead?  Opening a new connection, closing it...opening another one, closing it...blah blah blah??

What should I do???

I know nothing about Thread pooling..and I don't think that's an option for me.