Yes. A teacher with talent can steer even an elementary school student to "real math" insights. Something like Pascal's triangle is very interesting and conta

Yes. A teacher with talent can steer even an elementary school student to "real math" insights. Something like Pascal's triangle is very interesting and contains a lot of patterns, relations, and theorems, which open out very wide and deep in the right hands. Without contortions, you can go all the way to the rudiments of information theory if you want to.