A few months ago, I wrote a couple of posts on my website mentioning that I was learning the Polish language. I still am learning Polish and enjoying it so much more than I first imagined that I would.

Even though I don’t subscribe to a particular fixed learning style or methodology I do like to find out how other people go about doing things that I want to be able to do – some people will do things that I really like and that I can incorporate into my learning technique and other people will go about things in a way that is the complete opposite to how I would like to learn and so, even though the technique may work for them, I may choose not to follow their example.

A name that came up during my reading and research was Stephen Krashen – Krashen is (according to Google) a linguist and educational researcher. I decided to find out more about his work and I’m so glad that I did!! In fact, my only regret is that I never came across his work before.

Much of Krashen’s work is focused on language learning and language acquisition (these two concepts are distinct) which, obviously, makes it highly relevant to my quest to learn Polish – but I believe that a lot of what he says regarding how language is acquired is applicable, at least in part, to learning mathematics.

Krashen says that for language acquisition (as opposed to language learning) to take place then the individual must receive large quantities of input that is both comprehensible and interesting (he even goes so far as to say that the input should be compelling and not merely interesting). Language acquisition is viewed as being the more permanent knowledge and makes the greatest contribution to fluency in a language; it may in many cases be a completely unconscious and effortless process. Language learning is stuff like grammar drills and vocab lists which Krashen says is almost completely worthless and unnecessary in the face of language acquisition.

Is it true that large quantities of comprehensible and interesting (if not compelling) input is required for mathematics to be ‘acquired’? looking back over my personal experiences of learning mathematics then I would have to say a huge yes in response to that question. In fact, I think it confirms some things that I often recommend to my students (and which usually get ignored) such as

  • Read around the subject
  • Use a range of different resources
  • Learn because you want to and not because you have to and not just to pass an exam

If you want to read some of Krashen’s work then you can download some of his older books and some of his journal articles from his own website for free at www.sdkrashen.com. Some of his more recent books you will have to buy but I highly recommend even if language learning and acquisition is not your thing then it’s still a real eye-opener.

Some of Krashen’s books that I’ve read over the last couple of months are

  • Principles and Practice in Second Language Acquisition
  • Language Two (written with two other authors)
  • Explorations in Language Acquisition and Use

Obviously, learning a language and learning mathematics are not the same thing and I’m not saying that everything that Krashen says regarding language learning and acquisition is applicable to mathematics but I think there is a lot of stuff in there that is very relevant and can be very useful to mathematics learners.

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