<p><pre><code>  Wayward paths can help us better understand the correct ones.
</code></pre>
Very true, IMO.  It's one of the reasons I love my algorithm textbook more than any other school textbook I've ever had: it not only explains why you choose a certain way of proving an algorithm, or how to construct an efficient one, <i>it gives you seemingly-logical, incorrect alternatives that people naturally fall into</i> and explains why they're wrong.  It actively helps you to recognize potential mistakes later, rather than having you stumble onto them without understanding why you made the mistake.