I had a student once. They* had memorized their math facts through the tens before they became my student. But they seemed to understand those facts as unrelated pieces of information - unconnected data islands.
Nine times three is 27. Eight times six is 48.
If I asked them for seven times 11, or for two times 12, they gave me a blank look. They didn't know, and they didn't know how to find out. The idea of a pattern of numbers, a pattern that could be extended beyond what they already new, seemed foreign.
I'll come back to that...
I recently came across a page on Constructivism by Bonnie Skaalid done while she was a doctoral student in the late 1990's at the University of Saskatchewan. She wrote something that struck me as epitomizing one of the problems, I think, in the articulating Constructivist theory.
It is impossible to discuss constructivism without contrasting it with its opposite, objectivism.
And down the road we go to an "either/or" discussion of whether I'm a Constructivist or an Objectivist....
I'm willing to be both. When we set those positions up as opposites, we set up extreme positions as straw men that we can beat the stuffing out of in order to prove that our position is right. It seems more productive to me to think of those extremes as ends of a continuum.
The problem with objectivism is that no one is objective. Science builds safeguards against bias into its methodology because objectivity is so difficult to come by. So, assuming reality is real, that doesn't mean you see it accurately. Acknowledge some inaccuracy in your perception of reality and you've moved a notch down the continuum toward Constructivism. You don't really even have to acknowledge an inaccuracy; you just have to acknowledge that sensation (which happens at the finger tips) and perception (which happens in the brain) are different things.
Let's go back to my student.
It wasn't a problem I ever solved. We parted company at the end of a school year. They knew 100 math facts, I knew they thought of them differently than most students. And I felt like that they managed to learn those math facts without learning the process of arriving at them or the connections between them.
I come back to my experience with that student often. I use that experience to consider definitions for terms like meaning and knowledge.
I think when enough people share some experience, especially if it can be quantified, the chance become good that it is an objective reality. I think I could win an argument with most reasonable people about whether nine times three is 27. The biggest problem would be finding someone who wanted to bother to argue about it. The idea that nine times three is 27 is, well, reality. Objective reality, I'd say. There are first and second graders at my school who don't know that. It’s knowledge they'll get later.
For the student we've been talking about, though, something other than knowledge was involved. They knew what nine times three was, but knowing didn't hold much meaning for them - at least nt in the context of math. And because it wasn't meaningful to them, they couldn't really use the knowledge very often.
The student had a disability. Their disability served to illustrate the profound difference between knowledge and meaning. And seeing that difference in them makes me consider what it is that we construct - knowledge, or meaning.
-----------
*I use the plural "they" instead of "he" or "she" on purpose as a way of protecting confidentiality. English doesn't have gender neutral singular pronouns in the third person like (for example) Finnish. So I use the plural because, in the setting of the small schools where I've worked, doing so makes it hard for a reader to guess a student's identity...
No comments:
Post a Comment