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