Mathematics is hard

Tuesday 24 October 2006 at 10:43 am | In Articles | 3 Comments

A number of blogs have picked up on a US report that says:

    that countries with students who say they enjoy mathematics scored much lower than countries that rank lower in mathematics enjoyment

    The nations with the best scores have the least happy, least confident math students

    We might want to focus on the math that kids are learning and just be a little less obsessed with the fact that they have to enjoy every minute of it

    Other countries do better than the United States because they seem to expect more from students. That could also explain why high performers in other nations express less confidence and enjoyment in math. They consider their peer group to be star achievers.

    Even efforts to make math relevant may be irrelevant, says the study

    Nations that try to teach math in terms of daily life have the lowest test scores.

(the full report is available here)

These ideas may seem astonishing, yet to many battle-scarred maths teachers it is what they have been saying for years. Mathematics is hard and it requires dedication, effort and time to understand it. This is not popular so in the UK we have decided to get round the problem by making the subject easier, delivering it in small easily-digestible lumps and as formulaic as possible so anyone can follow it. To prove we are delivering (ha!) we test and re-test making sure that the questions we set are virtually identical each year and again, divide up into little pieces.

It’s a bit like teaching someone to ride a bike by ensuring that they always use stabilisers. Learning to maintain balance takes lots of time and practice and the same is true of mathematics. Yet in the end we lose out. The cyclists never discover the excitement and freedom of cycling alone and the mathematics student never discovers the beauty of mathematics, forever imprisoned by having to apply the same tedious but not understood methods to the same problems.

Ian Stewart in Concepts of Modern Mathematics puts it this way:

    the technical grind is not just an afterthought: it is an absolutely essential part of the process … The problem with the hard technical grind is that there is no way to appreciate it except by doing it … If we can get away from the alarming habit that has grown up of shying away from anything that is the least bit difficult, then we may make real progress.

Mathematics is hard and we do ourselves a disservice by denying or avoiding it. More, not less, time should be devoted to it in schools and colleges so that students have time to practice and have the opportunity to really think; only then will come understanding.

You can (and should) read more about this topic at
Mathematics Under the Microscope
NeverEndingBooks (from Belgium, top western country for mathematics according to a survey on which the report is based)
The Reference Frame
You may wish to contribute to this discussion on Gooseania’s blog.

PS Today’s Education Guardian has an article Four steps to being chucked on the scrapheap which describes the problems that arise with the formulaic approach to teaching any subject. The author, an experienced teacher, writes very well. I have always said that OFSTED inspired teaching plans are bollocks but now I can put it so much better and say

    a lesson plan goes together with good teaching like a horse and gherkin

3 Comments »

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  1. I just got Stewart’s book Concepts of Modern Mathematics that I hope to work through in my self-study of mathematics. Time to do away with my get-solutions-at-expense-of-understanding mentalitiy!

    Comment by egm — Monday 19 February 2007 12:08 am #

  2. That’s an excellent book from a very good author which should be on lots of people’s reading list.

    Comment by Steve — Monday 19 February 2007 12:21 am #

  3. I heard that it is a great book, I ordered myself a copy. I hope it is going to be fun

    Comment by Simon — Tuesday 11 August 2009 4:41 am #

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