Tuesday, 1 March 2011

curriculum development for Nunavut schools

Ever since I was taught how to read English I've basically taught myself almost everything that I know today. It started out simple and simply, without any discernible direction as I gained familiarity with the words and how they're arranged in a sentence, into paragraphs, etc. (largely by consequence for it was sheer love of reading that compelled me and took hold me).

But as time went on my reading (and thinking) became more directed and purposeful. When I was in elementary school I chanced upon an encyclopedia and before I knew it I had read through the whole collection from A to Z within a school year. Over a period of years I would read the whole encyclopedia over and over again. But it was not to memorize - memorization is boring - for accident-like, a conceptual landscape began to form in my head. My greatest interest was in the sciences and philosophical thought (I didn't know it was philosophy at the time).

In my adulthood I've become a natural analyst with a very broad range of interests from linguistics, philosophy, politics to mathematics. It's not, contrary to people who know me, that I'm a know-it-all but that I know where to seek out information, to discern patterns of argument and think about first principles that generate them.

As a policy analyst for the Inuit Organizations my areas of concern were education and language. In my capacity I was involved in some exercises at the formal level where I met people who specialize in education and was introduced to some of thinkers on education I've come to admire greatly: Vygotsky, Northrop Frye, John Dewey.

One of the things that greatly concern me though in North American society is this disconcerting anti-intellectual attitude which a few generations of students from quasi-bohemian sixties on have acquired. The whole world-view seems to comprise of: if they don't understand something immediately it is not worth learning and, more importantly, not worth getting an understanding of. Native intelligence can only carry one so far; making and acquiring knowledge explicit and aware goes much further.

In terms of curriculum development as according to my experience in learning, I'm very much a believer in history-based pedagogy. What I mean is that learning about historical developments in any field is the best way to learn the subject, be it history (HA!), political thought (thru civic studies), science, and mathematics.

In terms of "mathematics" what gets passed as it in Nunavut is really mindless rote-teaching of the four basic arithematic operations: adding, subtracting, division and multiplication -which is really nothing more than counting numbers. Most of my career as a student I thought I was bad in "mathematics" but it turns out that my mathematical thinking abilities were always quite servicable, in fact, quite advanced. My introduction to real mathematics came by way of linguistics where I learned mathematical notation in grammatical analysis.

It turns out that mathematics is less about computation than about "discovering" characteristics of numbers and relationships between these properties of numbers (collections (sets) of numbers).

As a believer in history-based pedagogy I would suggest that teaching mathematics should introduce numerical analysis of ancient Greeks called "pebble notation". Pebble notation is about how numbers can be arranged into geometric patterns, such as triangular forms:

*
**

*
**
***

*
**
***
**** ;

squares:

**
**

***
***
***

****
****
****
**** ;

and oblongs:

***
***

****
****
****

*****
*****
*****
*****

(my apologies for the shoddy layouts) and looking at possible shapes and allowable arrangements of the pebbles (which is the notion behind "properties of numbers" and the beginning of number analysis). The oblong numbers, for example, can be split into two triangular numbers by cutting a diagonal line to divide them into triangles. Prime numbers, being odd numbers except for two, cannot be arranged into perfect oblong patterns because there will always be one pebble left over. The ancient Greeks called prime numbers "linear numbers" because the only satisfying way of arranging them is a line (though some can be arranged into triangles not all of them can be so arranged).

Constructing arrangements and talking and asking questions about the pebble arrangements is much more fun and intuitive than memorizing arithematic "tricks" for quick computations. Arrangement thinking also cultivates the mind to organize "information" and abstract thought in a more intuitive way using first principles. Insight is the mother of originality, and, once "original" thought is arrived at, the student is hooked for life.

I can tell you that the "aha" moment is pure bliss and addictive. The thoughts are at first cloudy and amorphous but when understanding comes the blobs take shape and arrange themselves into productive forms. That is real learning. Guidance, though, is absolutely necessary for learning to happen.

Jay

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