<p><pre><code>  &#62; How do you motivate basic maths, though?
  &#62; Not everything can be directly connected
  &#62; to drug couriers and what not.
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So far I've always succeeded, and I don't even think I'm especially gifted.  On current experience, if you name a topic or technique, even in basic math, I can probably relate it to and motivate it by (comparatively) real world requirements at an appropriate level.<p><pre><code>  &#62; Ultimately I suspect the only way to succeed
  &#62; in maths early on is to consider it to be a
  &#62; kind of game. That is, puzzle solving for fun.
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I agree entirely that people who are going to go and do science or math probably have an element of problem-solving enjoyment, and for them, such motivation not only will work, but is the most appropriate.  Getting such people to puzzle over why something happens, and getting them curious about how it works is probably the best thing you can do for them.<p>When I'm talking to people I show them a couple of things and gauge their reactions.  Here are two:<p><a href="http://www.fieggen.com/shoelace/ianknot.htm" rel="nofollow">http://www.fieggen.com/shoelace/ianknot.htm</a><p><a href="http://news.ycombinator.com/item?id=604347" rel="nofollow">http://news.ycombinator.com/item?id=604347</a><p>Any given person will react in one of two ways.  One is to half-shrug as if to say "who cares?" and then move on, the other is to look closer and say "Do that again."  People in the former group are most likely to need motivating with things that matter to them <i>which might (but might not!) include games.</i>  The others can just have their curiosity poked and you're off and running.<p>YMMV, personal opinions only, <i>etc, etc.</i>