Observers of the ongoing "standards in maths" debate may have been puzzled to compare two recent reports. One, The Teaching of Number in Three Inner-urban LEAs, is the Office for Standards in Education's look at numeracy in the London boroughs of Greenwich and Newham and the Merseyside district of Knowsley. The other is the latest from the Third International Maths and Science Study.
OFSTED's report, which follows on from a similar, hotly contested, report on literacy published last year, looks at maths lessons in 15 primary schools in each of the three boroughs. It compares performance using tests for Years 2 and 6 devised by researchers at Leeds University. The TIMSS study looks at 12 practical maths and science tasks in tests administered by the National Foundation for Educational Research (NFER) in 1995 to 450 pupils aged 13-14 in 50 schools.
OFSTED found a wide variation in teaching and outcomes in the three boroughs. This variation - unacceptable, according to Chris Woodhead, chief of the inspection service - could not, apparently, be accounted for by deprivation, as neighbouring schools differed widely. In one, only four per cent of Year 2 children could write a two-digit number expressed in words whereas in another 93 per cent did so correctly.
Dissenters might point out that even deprived areas contain pockets of affluence, but nobody seriously doubts that, as a recent report from King's College substantiates, the effectiveness and coherence of teaching varies widely within and between schools.
OFSTED is optimistic and says the Government's target of 75 per cent of 11-year-olds achieving level 4 or above on the national curriculum by 2002 is attainable. This is despite identified weaknesses in time management, differentiation, use of mental arithmetic, memorisation of routine number facts and the creativity of problem-solving (taught well in only nine of the 45 schools).
Many teachers also complained they had not been taught how to run primary maths lessons. Perhaps this explains why there was much "low-level filling in of worksheets", why only one in four schools set mental tests and one in three had no written maths policy. On the other hand, some of the best work involved Year 6 pupils using now-unfashionable calculators to estimate and record square roots and squares, and Year 2 pupils being introduced to the language and notation of fractions through work on rotating shapes.
Mr Woodhead, in later interviews, scuppered the positive tone of the OFSTED report by remarking that if it looked as if English children were on course for targets, perhaps the targets were too soft, as English children did less well in international comparisons. But is this true?
The TIMSS report is the necessary complement to the one published last year. That international comparison of 19 countries seemed to show England slipping, and performing less well in written computations and knowledge retrieval. This new report shows England at or above the mean in practical tasks in both skills areas - performing mathematical procedures (such as making a scale drawing) and problem-solvingmathematical reasoning.
In part, no doubt, this comparison reflects the different biases of national curricula worldwide. In part it reflects English teaching styles. Pupils in England may be less familiar than those in Pacific Rim countries with routine written computations - they may be more adept at using their knowledge in the context of solving an investigation or working to a practical application.
Tasks included the geometry involved in packaging sets of equal-sized balls in different boxes and an exercise in fitting a bed and coffee table in a room. Number tasks included making number patterns with a calculator and using a rule to change the number pattern obtained when throwing a pair of dice.
So what is going on? Are we doing better or worse than other countries? Are we doing better or worse than we used to? Perhaps the report from the new numeracy task force on the teaching of number, due in November, will make it all clear. Above all, perhaps it will suggest a means of bridging that gap between high and low achievers identified by OFSTED, which national average scores will not display.
The Teaching of Number in Three Inner-urban LEAs is available from OFSTED, Alexandra House, 33 Kingsway, London WC2B 6SE. Tel: 0171 421 6800 Performance Assessment, TIMSS International Study Center, School of Education, Boston College, MA 02167, US