Over the past year or so I’ve started to make my daughter do daily arithmetic practice in German. My reason for doing so stems from my dissatisfaction with the ways in which rote learning and memorization as a learning style are neglected and disdained in Australian education. By contrast, I am convinced they have an important place in a mix of learning styles. As my daughter doesn’t want to do additional math practice outside school, I had to package this little project as a form of German practice. German is not a school subject and she therefore agrees that additional practice is necessary for her to keep up.

Practicing addition, subtraction, multiplication and division may seem language-neutral. However, in the course of practicing them with my child I’ve discovered that they are not and that the different word formation patterns of English and German number words partly defeats my purpose of achieving greater automaticity. In contrast to English number words, German number words between 20 and 100 are constructed by saying the second digit first (e.g. “twenty-one” = “einundzwanzig” = lit. “one-and-twenty”).

As far as the times tables are concerned, I’m pretty sure my daughter has now two different systems in her head – Einmaleins in German and times tables in English. I’ve timed her a couple of times responding to a set of simple multiplications in English and in German. In German, she’s consistently performing the same task a minute or two faster. The fact that she’s faster in German (learnt at home by rote) than in English (learnt at school by exploration) establishes the superiority of rote learning for this particular task (well, really, I always knew that …).

However, the more intriguing observation is that while she’s doing well doing arithmetic problems on paper, she’s lost her automaticity in reading numbers out loud, particularly when it comes to 3-digit numbers. 3-digit numbers in English are basically formed by reading the first digit first, the second second and the third third, i.e. 438 is “four-hundred-and-thirty-eight.” In German the order is digit 1, digit 3, digit 2, i.e. 438 is literally “four-hundred-eight-and-thirty.”

As a matter of fact, I’ve discovered that I’m suffering from the same affliction: I’ve lost the automaticity to read out numbers in German “without thinking” and when I hear numbers in German I have to visualize them or “translate” them into the English order in my head.

When I reflect on this experience, it’s easy to see why formerly popular opinion would have been so focused on the negative cognitive effects of bilingualism. In the first half of the 20th century academic and popular opinion agreed that bilingualism was a social ill and that, wherever possible, young minds should be shielded from the confusing exposure to more than one language. Nowadays, of course, the pendulum has swung wide in the other direction and academic and popular opinion agree that bilingualism is a wonderful thing and carries all manner of cognitive, academic, creative and social benefits.

I’ve always found this ideologisation of bilingualism irritating but hadn’t understood how it has stunted our ability as bilingualism researchers to actually formulate a productive research agenda on the interrelationship between bilingualism and mathematical learning, for instance, until I read Aneta Pavlenko’s new edited volume Thinking and Speaking in Two Languages. I will explain why the study of bilingualism and cognition is such a new field in my next blog post but in the meantime maybe someone wants to venture a guess?

ResearchBlogging.org Aneta Pavlenko (Ed.) (2011). Thinking and Speaking in Two Languages Multilingual Matters

Author Ingrid Piller

Dr Ingrid Piller is Professor of Applied Linguistics at Macquarie University, Sydney, Australia. Ingrid’s research expertise is in the fields of intercultural communication, bilingual education and the sociolinguistics of language learning and multilingualism in the contexts of migration and globalization.

More posts by Ingrid Piller
  • Ahmad

    Thanks Ingrid. It is amazing that you value the use of rote learning in education. I wish you elaborate on this issue more, but in the meantime I will pass your story to our educators who consider rote learning as a bad thing although it is inherently part of our literacy practice.

  • Thanks, Ahmad! Obviously, you can have too much of a good thing and many educational systems suffer from on over-reliance on rote learning. However, just because it is used excessively in some context doesn’t mean it’s bad per se. It’s a very efficient way to acquire some sorts of knowledge such as the multiplication tables. Will try and elaborate in a future blog post 🙂

  • Great post, Ingrid, on a topic of great interest to me! I used to work in maths education here in Australia and then lived overseas for some years; since I’ve come back and now have a baby, I’ve heard that they no longer teach the times tables by rote and I was a little shocked. I am a major supporter of non-rote-learning *except* in some situations, and surely the times tables are something that should be learnt by rote. (It sounds like you need no convincing!). It seems like rote learning has become the devil unnecessarily. Anyway my additional interest is that our family language is German (my husband is German) so it’s interesting to see your perspective. Thanks!

  • Angela

    Your experience of having to mentally translate German numbers into the English order is interesting, Ingrid. I had always accepted the notion that when a multilingual person performs any kind of mathematical calculation they will always revert to the language through which they first became numerate. That is until I met my husband, whose mother tongue is Persian but uses his second language of Japanese for everything numeric, even though he did not encounter that language until he was in his 20s, and despite the fact that Japanese uses 10,000 as a basic unit. My son, on the other hand, became numerate first in Japanese, up to three digits and beyond using the Montessori golden beads. Now, after two years in an English educational setting, he seems to be functioning in English for all mathematical work, though I suspect there is still a process of translation happening.

  • Clare Maree

    When my son started school (here in Australia) 6 years ago, I was similarly dissatisfied with the lack of rote learning in maths in the early grades (and yes, I think your choice of word, disdain is spot on), which I think has made progress in maths learning here unnecessarily slow. Thanks to attending Japanese school on Saturdays, however, my two children learned the times tables up to nine in a matter of weeks in 2nd grade by learning the ku-ku, a super efficient way of reciting the times tables that is drummed into all Japanese school children in the 2nd year of primary school. They are now able to solve multiplication and division problems must faster than their peers and they are both high achievers in maths in general at their day school. This was not a conscious aim when we started our childrens bilingual journey (my husband is Japanese, I am Australian, our children were born in Australia but we speak only Japanese at home), but it is certainly an added benefit.

  • Grace

    I’ve always been passionate about how the structures of languages influence people’s cognition and perception. Mathematics is one of the hot topics in the debate of Linguistic Relativity. As for my own experience, I also need to translate English to Mandarin to do math, especially when it comes to 10,000 and the multiples of 10,000, because we have a word for 10,000 in Mandarin and we treat it as a unit in calculation. There is also study showing that English children are slower when learning irregular numbers such as eleven and twelve, while Chinese children are not because numbers in Mandarin are very consistent. The forms of languages, the carriers of meanings, are analogous to the notation of math. In Calculus, Newton and Leibniz were major contributors; however by using Newton’s notation the development of mathematics in Britain stagnated for 150 years, while Leibniz’s notation has been widely used until today. The forms of languages significantly affect the way we think, and as a

  • Grace

    The forms of languages significantly affect the way we think, and as a second language learner I sometimes feel like I should think with a different brain.

  • Grace

    I met a Chinese girl, who has been in AU for 5 years since high school and speaks English highly fluently. She told me she still uses L1 to do calculation in her accounting classes. However, the interesting phenomenon is while she speaks Mandarin, the structure of L2 is brought into L1. For example, 10,000, which should be Yi-Wan (one-unit for ten thousands) in Chinese, become Shi-Chian (ten-thousand) and so as the numbers upwards. To my surprise, it is not only her personal change but also the media in Australia. The Chinese newspapers in AU adopt this English-way whenever mentioning numbers. The pervasive change seems very functional. Immigrants live here, receive education, earn money and purchase here. It is much easier to just adopt English way of numbers and save the mental process of changing the unit back and forth because of the difference of languages, although it sounds so odd to other native Mandarin speakers.

  • Alida

    I’m currently teaching my daughter in America to do math in both English and Spanish. I felt it was a better way for her to understand math and be able to express it in more than one way.