Recently I ran into a quote on a t-shirt that makes a perfect segue for our earlier thoughts about thinking and right answers, and our recent detour into calculator thoughts. The quote happens to be about mathematics, but don’t run away.  We’ll quickly generalize to all fields of education.
The quote goes like this:   “Good mathematics is not about how many answers you know – it’s about how you behave when you don’t know the answers.”
This is more than clever wording.  Think about it:  Would we rather have a student in algebra who can eventually factor every polynomial (‘right answers’) or one who can recognize when algebraic concepts might be helpful in tackling (and maybe solving) a real-world problem involving math?  Or, to revisit our last topic, would you rather have a student who can take a square root by paper/pencil, or would you rather have one who knows when a square root is called for in the solving of a problem?
As mentioned, we need not restrict this idea to mathematics.  Would we rather have a history student who knows that Abraham Lincoln was assassinated by John Wilkes Booth (who) at Ford Theatre (where) in April 1865 (when), or a student who might have forgotten one or two of those ‘facts’, but could thoughtfully think and write about the effect of the assassination on our country after the Civil War?
Numerous examples abound. You get the idea.  The point is that becoming educated is NOT about collecting ‘right answers’, which is to say information. At least not entirely.  It is more about how we use the information we learn.  Are we satisfied only with ‘right answers’ or do we want our students to learn to think as well?
Obviously, it’s not either/or.  We want the ideal blend of both.  We want students to learn basic information, and ALSO to learn to use it effectively when they need it.  But there are two traps here that can be VERY subtle:  First, there’s always the question of what’s ‘basic’ (often controversial, by the way!).  And then there’s this very subtle by-product:   More is not always better.
It is not unusual for school systems, colleges, and/or state school boards to require MORE courses from students.  More years of math, more years of English, more specific courses, etc.  This is usually done in the name of ‘high standards’, which is fine.  But, if not considered carefully, it can also be counter-productive.
In the first place, ‘more’ is not always needed for all students.  I’m about to commit possible heresy in my own discipline, but it simply not the case that everyone needs three or four years of math in high school, e.g.  Another classic example here is the university that ‘requires’ college algebra of all students to graduate, rather than a more helpful “Math in The World” type survey course for some less-math-oriented career paths.
Second, requiring more ‘stuff’ of all students can severely limit students’ chances to try other areas of inquiry, and to discover a passion or interest they didn’t realize they had.   Limiting these opportunities at this crucial juncture in their lives can be damaging not only to the students, but to society as a whole.
As always, a final word of perspective:  this column is not about ‘math’ or ‘history’ or ‘course requirements’ specifically.  Instead, it yet another example of asking ourselves continually what we think education is, and what that means for our classrooms.