Oddly, perhaps, one of my favorite Peanuts cartoon strips shows Snoopy in his usual nighttime position, lying on his back atop his beloved dog house.  His thought bubble says, “Yet another year has passed and I didn’t use algebra once.”
You might expect I’d hear that sentiment a lot, and you’d be right.  The most common version goes something like “I had algebra in high school and never used it again.”  I’m sure you’ve heard it.  In fact, I fear that at least 36% of you have said it yourselves.
Being a math educator, I used to cringe at those sentiments.  Years ago, it hit me:  from their perspective, those folks are probably right!  They took algebra in high school, and never factored another polynomial again.
The fault for the confusion there may belong to those of us who teach/taught math.  Did we teach them the skills of algebra and assume they would make the connection to the real world?  We might as well have taught them how to toss/catch tennis balls and expected them to juggle.
What we have here is a special case of one of the larger problems involved in trying to teach/learn almost anything, not just mathematics.  Where and how does one most efficiently make the jump (or help the student to jump) from learning necessary ‘basic skills’ of a subject to actually being able to master the broader subject itself?
Suppose Johnny wants to be a pianist and Jane wants to be a writer.  Obviously, Johnny will need lots of technique work, finger exercises, practice with scales, etc.  Jane will just as obviously need to learn lots of grammar, spelling, sentence structure, and more.
But we all know that Johnny can play scales to precision forever without ever playing music.  And Jane can make an A in English class and never write her best-seller.  Partly, there’s that elusive entity named ‘talent’, but part of it is making that jump from the individual ‘skills’ of a subject to blending of skills that produces mastery.
So, back to algebra/mathematics for a moment.  Math lovers and teachers know that algebra is more than factoring polynomials, but perhaps we haven’t effectively gotten that message to students.  In our haste to share our own music (algebra, e.g.) with students, have we focused too much on the ‘scales’ (basic skills)?
Another fascinating part of the situation is the differing public perception of these subjects.  The public does not confuse playing scales for playing music, nor do they confuse diagramming sentences for writing.  But, unfortunately, it seems they/we DO confuse factoring polynomials for ‘algebra’, and balancing checkbooks for ‘mathematics’ (as in ‘do the math’).
This confusion is most prevalent in the field of mathematics, but, once again, it can be a bugaboo for education in general.  The whole country, it seems, is confused and frustrated about declining test scores and even wonders how much our students, even our ‘brightest’ ones, seem to really know after high school graduation.
Could part of the problem be the picture we are giving our students of education and learning?  If they think that music is playing scales, then no wonder they don’t want to be musicians.  If they think history is memorizing dates, then no wonder they don’t want to be historians.
And, if they think being educated is just soaking up tons of skill, facts, techniques, and procedures, in isolation, then maybe it’s no wonder they become bored with learning.