Wednesday, March 12, 2008

Rethinking traditional academics

One good thing about the Constructivist revolution is that it provokes fresh thought about the grade school traditions we all take for granted.  Why, for example, should we bother teaching English grammar to native English speakers?  

Why, indeed, I thought last night as I watched my daughter mechanically underline the verbs (or "action words") in a vocabulary list for her language arts homework.  What was she learning that she didn't know already?

Modern linguistics tells us that we master the grammar of our native languages automatically, without explicit teaching.  This, indeed, is one of the first lessons of linguistics 101.  But there's grammar, and then there's grammar.  

On the one hand, there's basic, intuitive grammar. Even if we native English speakers don't know the labels "subject," "verb," and "object," we know to put the subject first, then the verb, and then the object.  This is the focus of linguistics 101.

Then there's grammar as style, or what distinguishes good syntax from bad.  This is--or should be--the focus of writing 101. For it's where we native speakers make mistakes--all the time. Dangling our modifiers, we say "returning home, the front door was ajar." Failing to keep conjoined phrases parallel, we say "a time not for thinking about it but acting on it."  Many of us don't master good syntactic style automatically, but depend on explicit teaching.

To see a dangling modifier as such, you need to identify the subject of the main clause (e.g., the front door), infer the tacit subject of the modifier (e.g., whoever is returning home), and notice that they differ. To see a lack of parallelism as such, you need to group the sentence into phrases, notice which phrases are conjoined (e.g., "for thinking about it" and "acting on it") and determine whether they have the same basic syntax (e.g., do they both begin with prepositions?).

Here it helps to visualize sentences as trees.  Traditional grammarians use the diagrammed sentence, but I prefer the more transparent syntax tree of modern linguistics. To construct such trees, you need to be able to identify the different parts of speech, just as my daughter was starting to do last night.

Recognizing good style, in other words, means becoming consciously aware of the grammar we all know intuitively.

What about long division?  This is one of the traditional algorithms of arithmetic that our right-brained Reform Math has marginalized. Ever fewer students can automatically, effortlessly, work their way through its many steps.  Does it matter?

Just like fractions, long division resurfaces in algebra.  It's often the easiest way to turn improper rational expressions into sums of proper ones.

So later last night, watching my son attempt to long-divide (x + 2) into x to the 4th, I asked myself whether it helped that he already knew how to long-divide 12 into 10,000. As soon as he started to flounder, the answer became obvious.  Just as I'd reminded him last week how common denominators work, I was able to reboot him on long division--in both cases by revisiting what we'd already helped him master back in arithmetic.

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