&gt; Then ask harder questions that show the value of the harder (more complicated, less intuitive) methods.<p>It&#x27;s not clear to me that there&#x27;s an obvious right answer here, but I do believe that most obvious answers are, to some degree, wrong.  Namely, saying &quot;just ask harder questions&quot; doesn&#x27;t take into account that then the student is trying to solve hard questions <i>and</i> learn a new method at the same time.<p>Teaching a more general method on easy problems gives time to become acclimatised to the method, while also offering sanity checks (by easier, faster, and &#x2F; or approximate methods) to make sure that it&#x27;s not going wrong.  On the other hand, as you say, this approach seems unmotivated, and bores or frustrates students—there&#x27;s no obvious right answer!  I think that all that can be said is that one must find the appropriate balance for each individual student, or class.