Stuck on applying mathematics?!

Cross Posted from The Pai Intersect

So here’s my recent struggle with math education. I came to this realization a while ago, and it’s been bugging me:

Have I been focusing too much on applying mathematics and expanding the concept of “relevance?”

Ok let me give some context to this.  Drawing on the idea of relevance has been a big topic all around math education.  It boils down to the need to get students engaged, and motivated to learn and develop their own mathematics.  I think there is essentially two methods for doing this, that focuses on the intellectual aspects of students (I am not including “cool things,” or emotional encouragement for students…etc.).

First, the idea of getting students to think about situations (real situations) that they can relate to, and motivate them to do mathematics, following questions they come up with.  The “three act” concept, recently popularized by Dan Meyer, (I say recently popularized, because it’s not a completely new concept, but definitely an important one) is one way to go about it.  A huge feature of this type of engagement is the idea of relevance.  Relate the situation to students, make them the players who invest in, and consequently explore, their own questions.

Second, engagement can also be developed without relevance.  Of course, I am talking about the specific definition of relevance where it relates to reality (and sometimes lives of students).  An example could be something like what @jamestanton often tweets:

Among any 51 2-digit nmbrs there must be 2 that sum to 100(Why?).How many 3digit nmbrs must one have to be sure there are 3 summing to 1000?
— James Tanton (@jamestanton) January 28, 2013

Over the past few semesters, I find myself more and more focused on looking for applications for mathematical concepts — making it relevant for students.  Make no mistake: I love this.  I love taking pictures of situation where math jumps out at me.  I love creating videos where math jumps out at me.  101qs is an excellent place to find some existing ones as well.  But I am still left with the same question and struggle:

Have I been focusing too much on applying mathematics and expanding the concept of “relevance?”

Have I been expending too much energy on looking for relevance when I should play off of the interesting and awesome world that is mathematics?  I had one student who became more disengaged throughout the year as everyone else was loving the relevance and exploring their own questions.

He said “I just don’t really like these application types of questions.  I prefer questions that are just fun and have nothing to do with anything.  Like puzzles or games, or just abstract numbers.”

That really troubled me for a while, and still do.  He was not using his statement as an excuse to not do work.  He was genuinely adverse to coming up with his own questions and seeking answers.  He was never perplexed because he was never intrigued enough by the situation or question.  He also did not like the openness — the fact that he has control over the kind of questions he asks.

There were lots of other (non-academic) factors that contributed to his decreasing engagement level.  There’s a lot to be valued in showing him the fun and importance of developing his own questions and curiosity.  There is certainly a lot of other issues that deserves attention.  But I know that there’s also worth in taking his comment as the way it came.  That perhaps he isn’t engaged by the idea of relevance.  Perhaps he prefers other methods of engagement.

Well it’s still an interesting question that strikes me sometimes.  I am unsure as to how to overcome this struggle, and I am unsure that there is an answer.

Am I too stuck on the concept of relevance, and should explore additional venues of engagement?