Saturday, 5 October 2013

Numbers and languages

When my children became initiated in the arts of school homework, they welcomed assistance from us parents in revising, among other things, their times tables. It didn’t take me long to start suspecting serious innumeracy in all three children: they took unsettling amounts of time to reply to my questions, whether toughie ones like Seven times eight...? or easy-peasy ones like Three times two...?

It took me a bit longer to realise that the problem had nothing to do with number skills, and all to do with languages: I naturally used Portuguese in these drilling sessions, but the children were learning their times tables in English, their school language, and were therefore computing the sums in this language. Which meant that they had to mentally translate my questions into English, and then re-translate the answers into Portuguese, which does indeed take ages. Which in turn meant immediate revision of home language policies: English became the language of homework, because homework comes in tongues. Part 3, ‘Acquiring a Third Language’, of my book Three is a Crowd? has more on multilingual division (and revision) of language-based labour.

Now, you may be wondering that the reason I naturally used Portuguese to drill times tables was that this is “the language in which I count”, since I am Portuguese. Well, not really. First, my times tables became forever etched in my brain in both Portuguese and French, through similar school-bound drilling. I used Portuguese with my children because this is the default mummy-child language in my home. Second, there’s no denying that numbers associate with languages, because everything else that matters to us does, too. But not necessarily with a single language: numbers, like homework, also come in tongues. In my case, for instance, I can only recall phone numbers (or recipes, for that matter) in the language in which I memorised them. Ask me to tell you, say, a Swedish phone number in another language, and watch me jotting it down in mental Swedish so I can read it to you in spoken non-Swedish, much like my children were doing with their times tables. And third, language names and nationality names don’t designate coextensive concepts, and never have. It makes as much sense to ask South Africans or Singaporeans which language they count in, as it does those of us who happen to have a nationality which happens to have the same name as a language.

Most of us know our times tables – and our other sums – in the language(s) in which we were made to drill them, in school. Whatever we learn in school, number goodies included, we learn through some language. Unless we want to claim that school-trained behaviours represent “the” essence of overall multilingual cognition, and that the language(s) of schooling play “the” core role in it, I don’t see the relevance of questions like In which language do you count? for our understanding of multilingualism. Several years ago, Marguerite Malakoff made this clear in The effect of language of instruction on reasoning in bilingual children.

Numbers, it turns out, aren’t essential to our languages, because numbers aren’t essential to human beings.

Numbers rule?

The interesting questions are whether numerical skills relate to numbers at all. For example, does numeracy depend on command of number words? Researching Numerical thought with and without words: Evidence from indigenous Australian children, Brian Butterworth and colleagues compared numerical concepts of child speakers of languages with restricted vs. broad number-related vocabularies, to find no correlation between numerical thought and number words, a finding that they extend to claims about adult numeracy and vocabularies. Christine Nicholls also turned to child users of Australian languages, to show that numbers aren’t at the core of mathematical reasoning (even discounting the common confusion between arithmetic and mathematics). Quoting from her article It’s time we draft Aussie Rules to tackle Indigenous mathematics, “Aboriginal mathematical systems are largely founded upon spatial relationships rather than on numbers, which is the case in Australia’s dominant culture.”

“Dominant culture” is the key phrase here. The association of numeracy and/or maths skills with languages which feature number vocabularies, and are featured in mainstream schooling, draws on misguided and misguiding dominant, Western, monolingual models of language use and language education. So does the related assumption in meaningless questions like In which language do you X?, where X variously stands for “higher-level”, “fundamental”, “spontaneous” and/or “emotional” exponents, believed to be descriptive of what we are, such as thinking, dreaming, swearing or being miserable and happy.

Finally, in case you’re feeling that something is surely missing here, because numbers must lay bare essential findings about us in that they’re factual and therefore indisputable, then don’t: numbers are no more than what we do with them – whatever our languages. Darrel Huff said so in his enduring pearl of a book, How to Lie with Statistics, and so did Sebastian Wernicke in his TED Talk Lies, damned lies and statistics.

I’ll keep to ways of deceiving, in my next post.

© MCF 2013

Next post: Multilingual liars. Saturday 2nd November 2013.


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