Through most of my career as a mother, I have made it a point of aligning my interests with my children's interests. This has taken me to many interesting places, taught me many interesting things, and even gotten me published in the science magazine Nature (reprint on Fantastic Metropolis).

I have made an exception for annoying fads, especially the Pokémon thing. (See my May 18th, 2003 post, "Pokémon Infestations and Other Matters.")

I realized in the middle of the night, night before last, that there was something big I had been missing about the whole phenomenon. Here is an out-take from what I wrote about it:

One puzzling phenomenon I've observed watching 2nd graders is how kids, who are only just getting basic addition and subtraction of multidigit numbers by the tail, can spend literally hours trading Pokemon cards (by which I mean 2 or 3 hours at a time). The decisions of whether or not to trade are based on multiple factors, some of which are linear functions like how many hit points does a given card have (or is the sum of the hit points of the two cards you are offering me equal to or greater than the hit points of the card of mine you want), and some of which are binary (is it a "shiny", i.e. a holographic card).

. . .

I spot-checked Peter's sense of the relative value of cards back in February. I had him show me what he thought of as his three best cards. I priced them on Cardorder.com. The cheapest of them came in at $47.00. I then had him show me three of his cards that he thought of as "not-so-good." Cardorder.com priced those between 75 cents and $3.00.Given what I know of the scholastically measurable of the math skills of the kids in question, there has to be some kind of pre-verbal calculation going on. They seem to me to be carrying out complex calculations involving multiple variables of different types, and arriving at basically correct conclusions via some kind of folk-math.

. . .

One other implication of this phenomenon, it seems to me, is that the equals sign, as a piece of mathematical notation, is highly socially embedded. I remember something about a second grade playground bead market at Ravenna during recess that spontaneously emerged and then spread until teachers banned it after a few weeks. It may be that there is a developmental phase around 7 or 8 in which the social embedding of trade is explored.

I would be interested in your anecdotes about young kids and card trading. I've decided to investigate further.

I should also say that this realization was inspired partly by Munir Fasheh's essay "Can We Eradicate Illiteracy Without Eradicating Illiterates?", an expansion on a paper given at a UNESCO meeting in Paris, on 9-10 September, 2002, to celebrate the International Literacy Day. The meeting was entitled "Literacy as Freedom."

In it, he dscribes his realization of his illiterate mother's mathematical sophistication:

My 'discovery' of my illiterate mother's mathematics, and how my mathematics and knowledge could neither detect nor comprehend her mathematics and knowledge, mark the biggest turning point in my life, and have had the greatest impact on my perception of knowledge, language, and their relationship to reality. Later, I realized that the invisibility of my mother's mathematics was not an isolated matter but a reflection of a wide phenomenon related to the dominant Western worldview. In this sense, the challenge facing communities everywhere, is to reclaim and revalue the diverse ways of learning, teaching, knowing, relating, doing, and expressing. This reclaiming has been the pivotal theme of my thinking and work for the last two decades.

My concern is not about statistical measures - for example, how many learn the alphabet - but about our perception of the learner and what happens to her/him in the process of learning the alphabet. My concern is to make sure that the learner does not lose what s/he already has; that literacy does not replace other forms of learning, knowing, and expressing; that literacy is not considered superior to other forms; and that the learner uses the alphabet rather than be used by it. My concern is to make sure that in the process of eradicating illiteracy, we do not crush illiterates.

In the 1970s, while I was working in schools and universities in the West Bank region in Palestine and trying to make sense out of mathematics, science and knowledge, I discovered that what I was looking for has been next to me, in my own home: my mother's mathematics and knowledge. She was a seamstress. Women would bring to her rectangular pieces of cloth in the morning; she would take few measures with colored chalk; by noon each rectangular piece is cut into 30 small pieces; and by the evening these scattered pieces are connected to form a new and beautiful whole. If this is not mathematics, I do not know what mathematics is. The fact that I could not see it for 35 years made me realize the power of language in what we see and what we do not see.

Her knowledge was embedded in life, like salt in food, in a way that made it invisible to me as an educated and literate person. I was trained to see things through official language and professional categories. In a very true sense, I discovered that my mother was illiterate in relation to my type of knowledge, but I was illiterate in terms of her type of understanding and knowledge. Thus, to describe her as illiterate and me as literate, in some absolute sense, reflects a narrow and distorted view of the real world and of reality. A division, which I find more significant than literate and illiterate, would be between people whose words are rooted in the cultural-social soil in which they live - like real flowers - and people who use words that may look bright and shiny but without roots - just like plastic flowers.

(It's a neat essay. Read the whole thing.)