Tuesday, April 5, 2011

Between the basic elements and the fuzzy abstractions...

One of the biggest disconnects in education is the leap that so many K12 classes make between the low-level elements of a given subject and certain fuzzy heights of abstraction or fuzzy breadths of big picturism.


In math, it's either low-level "math facts" and terminology (7 + 8, 7 × 8, "liter," "ray," "kite," "box and whiskers," and "number sentence"), or "meta-cognitive" reflection and interdisciplinary/arts & crafts projects (explain why your answer is correct; reflect on what you still need to work on; invent a game using everything you know about math).

In social studies, it's either memorizing names, places, and terminology (who was William Penn; where is New England; what does "colony" mean) or broader themes (genocide; racism) or big projects (choose a country and write a travel brochure; invent a culture). 

In K12 writing classes, it's either individual words (spelling words, learning their definitions, or identifying their parts of speech), or paragraphs and beyond (the 5-paragraph essay, the personal reflection, the narrative, etc.).

In foreign language, there's a similar leap from word-level (vocabulary) to the level of conversational utterances (what's now called "communicative competence").

And, looking beyond the classroom and backwards into the pre-K years to therapies for autism, there's a parallel leap between the words and categories of Applied Behavioral Analysis and the naturalistic conversational pragmatics of DIR/Floor Time and Sally Rogers.

What lies between? What links the levels together and is all-too-often ignored by today's teachers and therapists? Structure

There's the mathematical structure of arithmetic and beyond, complete with the conceptual connections among addition, subtraction, multiplication and division; the standard algorithms of arithmetic; the base 10 number system; and the interrelationships between them all.  

There's the chronological, causal, and geographic structure of history (it's telling that while memorizing names and terminology is still popular, memorizing dates and sequences and global and relative locations is not): the matrix into which all the facts fall and become meaningful and memorable, and from which the broader themes emerge. 

There's sentence structure or syntax: the multiple ways to structure sentences and what to consider in picking the one that best delivers the message and best links up with and flows into the adjacent sentences. 

And there's the overall grammar of language: the multi-tiered structure that combines words together in the specific ways that make communication possible.

Why do so many educators (and autism experts) neglect these things? Is structure too dry and abstract; too hard to teach; presumed to be too hard to learn? Or, in our right-brain world, do people simply forget, or want to forget, that structure even exists?

So here's to making structure the centerpiece of instruction. After all, the route to mathematical understanding is understanding mathematical structure; the route to understanding history is acquiring an organized, fact-rich, core knowledge of history; the route to writing well is choosing among the myriad ways to structure sentences (for any given message, there are almost always more syntax-level options than there are options at the level of word choice); and the route to learning a new language (or mastering your first language) is understanding how the words fit together into grammatical structures.

Without structure, the basic elements are meaningless, unmemorable dross; the abstractions and big picture are a messy, uninteresting blur; and conceptual understanding--true conceptual understanding--however promisingly it sparkles in the distance, remains forever out of reach.

5 comments:

Jerrid Kruse said...

My first reaction was that you haven't defined structure well enough so it ends up being this abstract concept - like the ones you lament. Then, I figured out what you mean by structure and your post makes much sense. (Examples are great, but are not a definition, sometimes the abstract is a very very good thing).

However, this structure you long for is most often reduced to a set of rules to be memorized rather than a set of understandings. Because the structure is interpreted this way, it rarely leads to the big ideas you are talking about. But hey, I was just glad to see you care about the big ideas.

Hainish said...

Excellent post.

I don't think it's that teachers forget or want to forget structure, I think that it's below the radar for them. It doesn't even register. Instead of seeing the structure, they see the "lower-level" things--the names and dates and individual words--so they write it off as being too trivial to care about.

But, maybe I'm being uncharitable.

FedUpMom said...

Katharine, good point. At my younger daughter's school, they use Trailblazers math.

They've had a lot of complaints, of course, so in response they make the kids do a lot of very low level stuff -- computerized drill of adding and subtracting whole numbers, stuff like that.

The problem is that there's a whole layer of conceptual stuff that they still don't cover.

So they've got the airy-fairy "what's your favorite number?" level covered, and the bog-level drills covered, but none of the necessary concepts in between.

Barry Garelick said...

However, this structure you long for is most often reduced to a set of rules to be memorized rather than a set of understandings.

You don't teach a "set of understandings". The understandings are first about the procedures--presented in proper context, the understandings will follow. Sometimes the conceptual underpinnings will occur in a later grade/course. It wasn't until I took algebra, for example, that I understood why the invert and multiply rule for fractional division worked. In the meantime, however, I certainly knew when to apply fractional division to solve problems.

The hang-up over "big picture" is a continual confusion between epistemology and pedagogy. Novices don't learn to become experts by being given problems that only experts can solve.

Sweller talks about this in his article "Why Minimal Guidance During Instruction Doesn't Work":

According to Kyle (1980), scientific inquiry is a systematic
and investigative performance ability incorporating unrestrained
thinking capabilities after a person has acquired a
broad, critical knowledge of the particular subject matter
through formal teaching processes. It may not be equated with investigative methods of science teaching, self-instructional teaching techniques, or open-ended teaching techniques. Educators who confuse the two are guilty of the improper use of inquiry as a paradigm on which to base an
instructional strategy.


http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.169.8810&rep=rep1&type=pdf

LynnG said...

The cumulative building of knowledge in the various disciplines (and they are called "disciplines" for a reason) is under-appreciated in k-12 education.

In an effort to make everything relevant right now, the structure of knowledge has been lost.

I asked a couple 9th graders "which came first, the Vietnam War or the Civil War?" they had no idea. But they could all reflect at length about the evils of slavery and discrimination, without reference to any of the major events in the history of civil rights.

Our children have been taught that their feelings about big issues is far more important than knowledge of the these things.