Monday, August 28, 2017

Street math and diglossia

In "Mathematics in the streets and in schools" (Carraher et al. 1985), child street vendors were given a paper and pencil and asked to calculate multiplications that they had, in fact, already done in their heads in the course of selling their wares. The results were often sobering, as in the following case:
Informal test
Customer: OK, I'll take three coconuts (at the price of Cr$ 40.00 each). How much is that?
Child: (Without gestures, calculates out loud) 40, 80, 120.

Formal test
Child solves the item 40 x 3 and obtains 70. She then explains the procedure 'Lower the zero; 4 and 3 is 7'.

As you can see, the children were perfectly capable of doing (some!) multiplication their own way, but when faced with school-style problems, this ability frequently deserted them. Confronted with a piece of paper, they attempted to apply the algorithm they had learned at school, without so much as checking their answers against the algorithm they had mastered as part of their daily life. In daily life, conversely, they presumably weren't getting much out of the multiplication algorithm they had learnt at school, even though it would let them tackle a much wider range of multiplication problems. School-learning that stays at school, and never affects real life despite having an obvious potential to be useful there: it's an educator's nightmare.

What this immediately reminded me of is diglossia. In a schoolroom or an essay, you obediently attempt to use Standard Arabic, and all the grammatical rules and vocabulary you learned for it. Almost anywhere else, you carefully avoid it, even while claiming to accept that Standard Arabic is correct and that what you actually make very sure to speak is wrong. To me, that seems to send a fundamentally problematic message: that what you learn in school is not supposed to be useful outside of some limited institutional contexts. I hope that's not the message most people get from it, but it would be great to know for sure. I don't suppose anyone knows of a study addressing the question?

12 comments:

Unknown said...

In The School and Society, John Dewey wrote: "While I was visiting the city of Moline a few years ago, the superintendent told me that they found many children every year, who were surprised to learn that the Mississippi river in the text-book had anything to do with the stream of water flowing past their homes." He tried to design schools that connected instruction with lived experience, as did Paulo Freire in Brazil. If you search for "child-centred education", you'll find a lot about this issue. But I'm not aware of anything that relates it specifically to diglossia. This looks like it might be relevant:

Brosh, H. "Arab Students’ Perceptions of Diglossia." Al-ʿArabiyya: Journal of the American Association of Teachers of Arabic, vol. 48 no. 1, 2015, pp. 23-41.

Benjamin Geer said...

Sorry, that comment from "Unknown" was from me.

Lameen Souag الأمين سواق said...

I keep coming across Freire's name - I should probably read one of his books some time...

Thanks for the article suggestion. Unfortunately, on examination it turns out not to have much to offer - and the very atypical context investigated, "one of the Arab cities in the center of Israel", further reduces its wider applicability - but the topic certainly deserves a more able investigation.

David Marjanović said...

Is "40, 80, 120" even multiplication, or is it (repeated) addition?

Tim said...

@David - to dodge the question, yes, multiplication is indeed a way of iterating addition!

David Marjanović said...

Sure, but in school these days we learn to do it in one step rather than by iteration, as if it were something completely unrelated. In "40, 80, 120", the iteration seems to be there, without recourse to memorized information like "3 x 4 = 12".

petre said...

David - I can do arithmetic in my head in both English and Belgian French. I can (just about) do it in Flemish/Nederlands, but not really in French French, certainly not in German. Am I a bad linguist, a bad mathematician, or both?

Anonymous said...

Lameen not everyone uses standard Arabic only at school or when writing essays. This is an oversimplification and generalization that you've chosen to make to minimize standard Arabic and make it seem like it's only ever used by force in school. Just as one example, my father (Egyptian) whatsapps me and emails me only in standard Arabic. Always has. I recently brought this up when hanging out with some friends (mostly Levantines), and many of them said their parents also text them in standard Arabic.

So that hardly counts as forced usage at school like you're trying to portray it as. We discuss everything from dad jokes to flight tickets to news articles in standard Arabic. When I have kids of my own I intend to do the same with them.

David Marjanović said...

David - I can do arithmetic in my head in both English and Belgian French. I can (just about) do it in Flemish/Nederlands, but not really in French French, certainly not in German. Am I a bad linguist, a bad mathematician, or both?

Why me?

And linguist doesn't mean "fluent in a lot of languages"...

Anonymous said...

I certain don't know a lot about how Arabic diglossia works, but ...
it sure can't as bad as 3 x 40 = 70, can it?

At least if a student is able to form Standard Arabic sentences that are not only (close to) correct, but also might make sense (in a way), then they are certainly far that school-math-gone-awry level.

The liguistic equivalent of that blind and wrong application of ununderstood algorithms would be repeating magical formulae without understanding any (or most) words.

Anonymous said...

I certainLY don't know a lot about how Arabic diglossia works, but ...
it sure can't BE as bad as 3 x 40 = 70, can it?

Ahem.

Lameen Souag الأمين سواق said...

Anonymous 1: Good for you! Yes, Standard Arabic is pretty common in even quite informal writing, like letters and messages. There is no taboo on using it in that context, quite the contrary. But have you ever had a casual conversation in Standard Arabic? Would you dare to use it to ask directions from a stranger? Both those things do happen occasionally; I've even met teachers who spoke Standard Arabic with their children on a routine basis at home. Nonetheless, that's really not socially acceptable as far as general Arab society is concerned, and their children suffered for it outside home. The naive idea of diglossia is that it's the state imposing Standard Arabic on a dialect-speaking society, but that's not really accurate: society, by and large, is strongly in favour of teaching and writing in Standard Arabic. A better way to look at diglossia is that it's society at large enforcing a ban on the use of Standard Arabic in most everyday contexts, whether the state likes it or not.

Anonymous 2: No, it's not as bad as that, I'm glad to say! What the two cases share is simply the idea that the rules you learn at school are only for school-like contexts, not for the street.