Dragged Down by Innumeracy

The current economic problems that the West faces were not purely a result of greed and dishonesty. Our business and government leaders chose to ignore the experts, and instead went by the whims of the public. Given that the average person cannot deal with large numbers and has trouble with logic, why are we surprised?

 It doesn’t help when I read pieces like http://www.washingtonpost.com/blogs/answer-sheet/post/when-an-adult-took-standardized-tests-forced-on-kids/2011/12/05/gIQApTDuUO_blog.html?wprss=answer-sheet and http://www.washingtonpost.com/blogs/answer-sheet/post/revealed-school-board-member-who-took-standardized-test/2011/12/06/gIQAbIcxZO_blog.html ,

which presents the argument similar to those given some years ago by Simon Jenkins in the Guardian and Richard Cohen in the Washington Post: “I can’t do mathematics, therefore it isn’t necessary”.

13 comments for “Dragged Down by Innumeracy

  1. Patrick Harris
    December 9, 2011 at 3:44 pm

    Technocrats – enter stage right.

    • Voice of Reason
      December 9, 2011 at 6:19 pm

      Is that positive, or negative?

      • December 9, 2011 at 9:02 pm

        Generally negative.

  2. December 9, 2011 at 5:09 pm

    Most of the arguments I have with people boil down to simple existing statistics, which don’t require much maths skills or doing simple calculations based thereon or even applying logic.

    But there appears to be some mental block that prevents people from accepting, for example:
    1. Rather less than ten per cent of the UK by surface area is urban.
    2. Welfare spending is rather less than 10% of all UK government spending.
    3. A bank’s balance sheet always adds up to the same amount on each side, for every financial asset there is a financial liability, and one man’s financial asset is another man’s financial liability.
    4. The tax which is withheld from public sector salaries is not really tax at all.
    5. If you add up all the ‘worthy’ public sector workers, nurses, doctors, teachers, coppers, bin men, social workers, border agency etc then the total is around two million – but there are seven or eight million on the public sector payroll.
    6. The UK is, or could be quite easily, self-sufficient in most food stuffs.
    7. Land values are almost infinitely higher in town centres than farm land, the factor is hundreds of thousands, if not quite a million.

    The list is endless, but people just go into Daily Mail-mode, or Guardian-mode and cling to some vague belief that none of the above is true. And if people refuse to accept basic existing facts and logic then it is impossible having any further discussion.

    And all this is before you expect people to plus, minus, times, divide, use percentages, express everything in the same units (i.e. per year, or per person, or per household) etc. That is completely beyond most people.

    • December 9, 2011 at 8:28 pm

      I’ve often wondered why some people seem to have no difficulty with sports statistics – rattling off batting averages or goal differences ad nauseam – but go blank whenever figures appear in any other context, or worse, simply accept without question the sort of preposterous statistics that crop up in the news.

    • December 9, 2011 at 9:31 pm

      I think many people who naturally prefer the herd, see facts and logic as something mavericks use to try and trick them.

  3. December 9, 2011 at 8:46 pm

    Well, I have agreement and disagreement with the two sides of this debate: hardly surprising, I know.

    Firstly for Voice of Reason.

    a. A science degree in education !?

    b. 15 hours’ credit for a doctorate. Well a doctorate might reasonably take 4,800 hours of work: so 15 is not something to brag about.

    c. If you think an exam is crap, the best persuasion is to give a fair example of the (allegedly crap) questions.

    d. Could not do any of the maths questions, and got 10% right by chance. Can that really be right for a well educated adult: we need to go back to ‘c’.

    My personal, though anecdotal, experience.

    e. In the 6th form (some 40 years ago, doing double maths and physics), I fell in love with IQ tests. On one book however, I improved my score through practice by 40 IQ points. Even the nerdish person that I was (and perhaps still am) viewed that as highly suspicious.

    f. Bringing 2 daughters through GCSE and A-levels (within the last decade for both and last half decade for one), I occasionally felt I could help with maths and science. Though most attempts ended in tears on their parts and frustration on mine, there was more substantive information, beyond my personal ability as teacher.

    f.1. Too often, the questions were so badly worded that they had no truly correct answer: only the ignorance of the pupil (and then not in many cases) would allow the questions to have (nearly unambiguous) meaning and answer.

    f.2. In some cases, my greater knowledge as an adult well educated in a narrow field (particularly physics and maths) rendered the case one close to ‘f.1’. On this, I’d say that the problems were exacerbated by the exam questions showing inadequate knowledge (in those setting the questions) of both the subject under examination and of English semantics and syntax – not very encouraging, really.

    g. On some questions, CAGW and other issues of more political correctness than science did raise their heads. I wonder how children did in the days of Copernicus, Galileo and Kepler when exam questions required a belief in Ptolemy’s theory of astronomy.

    Some issues against the view of Voice of Reason.

    h. From my points ‘f’ and ‘g’, it seems to me that the quality of examiners (and especially those setting the questions) is no longer what it was 40ish years ago. Thus the results of the exams are less useful.

    i. There is an attempt now to score pupils on some unified scale of ability.

    i.1. This is particularly problematic when the range of ability is large and the exam time is short. It is more difficult (in a fixed period) to score and rank pupils over a large range of ability than it is to score and rank them over a smaller range of ability. By widening the range of ability over which any exam applies, either the cost of examination must rise, or the quality of discrimination must fall.

    i.2. On this, the use of dual, or even triple, exams (as in the GCSEs to cover the range previously in GCE O-level and CSE) with ‘normalisation’ is so prone to error that it is most likely pointless: another exercise in politically correct education.

    j. In addition, there is too much of an attempt nowadays (especially in the UK) to score pupils at a specific age in a way that affects the whole of their future life. This is worse than it was 40 or so years ago. Where grammar schools still exist, the concept of the 13+ exam, as well as the 11+ exam, has (as far as I can see) been phased out. This and similar (even greater) reliance on more exams of less and less discrimination is not helping people, who are individual in their rates of progress.

    k. The modern politically correct view is that failure is not socially acceptable, and so must be avoided. Likewise, all must have prizes; as time has gone on, all must have first prizes. The actual primary requirement of examinations is to rank the pupils for reward: and reward through further and higher level education, employment or other acknowledgement of societal worth.

    l. Finally, I note the socialist requirement is to avoid nepotism; and I’d like to value pupils for their own worth rather than that of the bank balance of their parents. However, continuous assessment is not the way to do that, at least up to the age of somewhere between 16 to 18. One should examine the pupils, not the diligence of their parents.

    So the problem is vastly bigger than some influential people (innumerate members of the so-called intelligentsia) believing that the world needs nothing but their personal choices of ability, wrong though that clearly is.

    Best regards

    • Voice of Reason
      December 10, 2011 at 3:52 am


      a. There are lots of odd degrees in education in the US
      b. He means 15 semester/quarter hours, typically about 1/8 of a doctorate
      c. I agree, as with your later comments. The questions might be crap, but all 60 of them?
      d. Degrees in education in the US make one well-educated in theory, completely un-educated in practice. Many teach that pedagogy trumps content. In other words, if you know how to teach, you don’t need to understand material to teach it.
      I also have 3 degrees in mathematics, so am somewhat sensitive about crap like these pieces.

  4. December 9, 2011 at 9:33 pm

    The media is innumerate so it should be no surprise that there is no longer any shame in innumeracy.

    Every day I froth over some Today item that has meaningless percentages or incoherent statistics.

    The CAGW scare is based on the same innumeracy. People think a one degree temperature rise is significant because 20 degrees is a comfortable temperature. However 0C is actually 273K. So instead of 1 degree rise in 20 it’s 1 in 293, a very different magnitude of change.

  5. Ian
    December 10, 2011 at 3:21 am

    Conducting its own self-assessment, the Office of National Statistics found that three quarters of its staff could not add up, and that the other half couldn’t subtract.

  6. December 10, 2011 at 1:45 pm

    “I fell in love with IQ tests. On one book however, I improved my score through practice by 40 IQ points. Even the nerdish person that I was (and perhaps still am) viewed that as highly suspicious.”

    I don’t see why. I’d have thought that with practice, you can improve in problem-solving as you can in other activities.

    • Voice of Reason
      December 10, 2011 at 8:06 pm

      Experience suggests that each is limited by their natural capacity. Some people literally cannot process numbers. Unfortunately, all too many become managers.

    • December 12, 2011 at 8:42 am

      Just for clarity, I am assuming Sackerson’s question is that he does not see why such variation in IQ test score by one person is highly suspicious.

      I am sure he and I agree that the variation (or at least some variation) through practice is not suspicious at all.

      What I find suspicious is the great weight, within society, placed on such scores. This is especially with such a large variation for so little effort (IIRC a modest part of my ‘fun time’ over 1 or 2 weeks).

      Maybe such tests are too simple to be reliable for the purpose to which they are put.

      Best regards

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