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Thirty years on – a large anti-Flynn effect?
The Piagetian test Volume &Heaviness norms
1975–2003
Michael Shayer
1
*, Denise Ginsburg
2
and Robert Coe
3
1
King’s College, University of London, UK
2
Independent Consultant, Cambridge, UK
3
University of Durham, UK
Background. Volume & Heaviness was one of three Piagetian tests used in the CSMS
survey in 1975/76. However unlike psychometric tests showing the Flynn effect – that is
with students showing steady improvements year by year requiring tests to be
restandardized – it appeared that the performance of Y7 students has recently been
getting steadily worse.
Aims. A sample of schools sufficiently large and representative was chosen so that
the hypothesis of worsening performance could be tested, and estimated quantitatively.
Sample. Sixty-nine Y7 school year groups containing pupil data on the Volume &
Heaviness test and the University of Durham CEM Centre MidYIS test were located
giving a sample of 10, 023 students covering the years 2000 to 2003.
Method. Regression of the students’ school mean on Volume & Heaviness on the
schools’ mean MidYIS 1999 standardized score, and computing the regression at
MidYS ¼100 allows comparison with that found in 1976.
Results. The mean drops in scores from 1976 to 2003 were boys ¼1.13 and
girls ¼0.6 levels. A differential of 0.50 standard deviations in favour of boys in 1976 had
completely disappeared by the year 2002. Between 1976 and 2003 the effect-size of the
drop in the boys’ performance was 1.04 standard deviations, and for girls was 0.55
standard deviations.
Conclusion. The idea that children leaving primary school are getting more and
more intelligent and competent – whether it is viewed in terms of the Flynn effect, or in
terms of government statistics on performance in Key Stage 2 SATS in mathematics and
science – is put into question by these findings.
There has been much discussion, in recent years, as to whether standards have dropped
or have been allowed to drop – whether it be at A-level (Tymms & FitzGibbon, 2001),
* Correspondence should be addressed to Prof. Michael Shayer, 16 Fen End, Over, Cambridge CB4 5NE, UK
(e-mail: m.shayer@ukonline.co.uk).
The
British
Psychological
Society
25
British Journal of Educational Psychology (2007), 77, 25–41
q2007 The British Psychological Society
www.bpsjournals.co.uk
DOI:10.1348/000709906X96987
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GCSE, or in the various government statistics on Key Stage 1, 2 and 3 National
Curriculum Tests
1
(NCTs).
On the other hand, those concerned with constructing and monitoring tests of
general intelligence have found that, on retesting with nationally representative
samples, children’s responses have been improving – the Flynn effect. Thus, every 15
years or so the tests now have to be restandardized.
One might reasonably argue that, over the years, examination results are subject to
pressures that are mostly unperceivable by those setting examinations and evaluating
examination pass levels. If more students sit the examination, and the same proportion
are given A or C grades and above, on the principle of more means worse (Amis,
1959/1990) the standard must drop, even if the quality of the questions remain the same.
Such an argument could partially be countered by consideration of the Flynn effect.
In order to obtain a purchase on both of these kinds of problems it would be
necessary to obtain data on a criterion-referenced test that is also tied to a theory-base
which at least in principle offers an underlying scale that has measurement rather than
relative properties. This article presents such data – originally researched by Piaget and
Inhelder (1974) and in 1975 used in the CSMS
2
survey (Shayer, Ku
¨chemann, & Wylam,
1976) on a large nationally representative sample. The test Volume & Heaviness
assesses children’s concepts of physical quantities with, at the top end, their ability to
use simple mathematical modelling of weight/volume relationships. The comparisons
that will be offered here are for students just entering secondary from primary school in
Y7, average age 11/7.
The psychometric and Genevan literatures and applied research
In the 1920s two quite different approaches to the description of children’s cognitive
development were initiated: from Binet’s original test developed at the turn of the 20th
century the art of psychometric testing grew (Binet, 1975). However, parallel to this
Piaget (who had been a student of Binet’s), beginning with 5- to 8-year-olds, sought to
describe what, under the surface, the ‘rules of the game’ were for children’s thinking.
Until well after the Second World War the communication between these two arts – of
the psychometric assessment of intelligence and of rich descriptions of the
development of intelligence – was virtually zero. Yet they were both attempts to
describe the same thing.
The achievement of the psychometric tradition is well summarized in Cattell (1971).
Factor analysis on batteries of tests reveals a spectrum of different mental abilities,
together with a factor common to all, called g, following Spearman (1927). Moreover,
Cattell showed that there were two families of tests. Tests of crystallized intelligence
related to learned or culturally determined skills and knowledge, whereas fluid
intelligence tests were measures of ‘here-and-now’ thinking.
3
Raven’s matrices is the
most widely used of these tests of fluid intelligence (Raven, 2000).
After his initial work and publications in the 1920s Piaget restarted his life’s
programme by 1929–1931, describing the genesis of the first 2 years of his own
1
http://www.dfes.gov.uk/
2
CSMS: Concepts in Secondary Science and Mathematics. Research programme funded at Chelsea College by the SSRC
1974–1979.
3
This does not imply superficiality. Cattell (1971, p. 120) has ‘fluid ability:::a general, relation-perceiving span based on the
magnitude of a neurologically efficient mass, and appearing as an existing energy in any current behaviour’.
26 Michael Shayer et al.
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children’s life from 0 days, 2 hours onwards (Piaget, 1953, 1936). In the 1930s he
produced books, with many collaborators in Geneva at a rate of almost one a year,
containing descriptions of different aspects of thinking of children up to about 11 years
of age. These could be considered Piaget’s versions of differential mental abilities.
During the Second World War, isolated in Switzerland, he worked mainly on the
possibility of explaining his findings in terms of logical models of different degrees of
complexity (Piaget, 1949). This then made possible, together with Inhelder, the two
major works which summed, between them, the whole genesis of children’s thinking
between the ages of 5 and 16 (Inhelder & Piaget, 1958, 1964).
From the point of view of applied and applicable research in intervention studies
(Belbin, 1979) the psychometric tradition has a severe disadvantage. It rapidly dropped
the concept of mental age – with the implication that an absolute scale was possible – to
focus its methodology on comparing children with those of the same age in the
standardization process, typically to a mean of 100 and standard deviation of 15. Draft
test items are kept in, or ejected on the basis of their statistical properties rather than on
a theoretical model. Thus, if we know that an 11-year-old, on a test of mathematical
ability, has a score of 105, all we know is that he is slightly above average for his age. We
do not know what maths he can or cannot understand, except in very broad terms. It is
worse still if the question is asked of a score of 135, or of what he might do at 14.
Moreover, Embretson (1988) showed that the IQ scale does not reach even the level of
being equal-interval as described by Stevens (1946), which creates major problems in
interpreting intervention studies where children make big increases.
By contrast, Piaget’s work comes very close to having, in principle, a ratio scale as
described by Stevens (1946): that is, a set of observationally defined levels and sublevels
stretching back from Early Concrete, observed on 5-year-olds, to a hypothetical zero of
his first recorded observation at 0 days, 2 hours. Although found very controversial
Piaget’s descriptions do have an underlying logic-based theoretical model to
differentiate different levels of complexity. It also describes the same behaviours – for
example in the ability to control variables in experimenting – whether the subject is 9 or
16. So any Piaget-based test is, by definition, criterion-referenced, and can be given
equal-interval properties. The convenience of this for assessing school performance in
science was shown in great detail in Shayer and Adey (1981).
The problem of reconciling the psychometric and developmentalist approaches was
addressed in a monograph (Shayer, Demetriou, & Pervez, 1988) by scaling a battery of
Piagetian tests taken from the work of Piaget on children from 5 to 10 years of age, in
England, Pakistan, Greece and Australia using Rasch analysis (Rasch, 1980, 1960; Wright
& Stone, 1970), which confers equal interval properties to the scale. This showed that
children’s performance could be differentiated into mental abilities similar to those that
had earlier been described in the psychometric literature – a phenomenon unhelpfully
labelled ‘horizontal de
´calage’ in Geneva – as well as the broad logical levels corresponding
to the psychometric g. This led to two decades of important work by Demetriou, taking
from and unifying the two traditions (Demetriou, Christou, Spanoudis, & Platsidou, 2002;
Demetriou & Kazi, 2006), and the methods were also used on Piagetian tests used to
assess the outcomes of various intervention studies (Shayer, 1999; Shayer & Adey, 1993).
The Flynn effect
Flynn (1987, 1994) surveying data on the standardization and restandardization of
various psychometric tests from the late 1940s on, reported gains of about 9 points per
Thirty years on – a large anti-Flynn effect? 27
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generation for tests of crystallized intelligence, and 15 points or one standard deviation
for tests of fluid intelligence (Raven’s matrices). This general apparent improvement has
entered the literature as the Flynn effect. In a later review (Flynn, 1998), examining
evidence going back to the 19th century, he had become sceptical of claims that this
meant that people’s intelligence – children or adults – was improving generation by
generation. He wondered whether the concept of ‘intelligence’ was still viable.
Certainly, people’s test-taking ability has improved; but after discounting as minor
factors such as nutrition, urbanization and TV, and pointing out that children’s gains on
arithmetic reasoning, vocabulary, creativity and speed of learning were far less, he was
tempted to suggest that school and environmental stimulus in some undefined way were
improving children’s decontextualized problem-solving skills.
Yet this may be only a historic effect: in Grissmer et al.’s chapter in Flynn (1998,
pp. 262–265) there is some evidence suggesting that gains are levelling off from the late
1980s. In this country the nferNelson CAT test showed no change in norms between the
1984 and 2000 standardizations (see the Endnote for details). Flynn (2006) wonders
whether IQ gains will cease in all highly industrialized nations, citing Sundet, Barlaug,
and Torjussen (2004) as evidence that gains have ceased in Norway, and Emanuelsson,
Reuterberg, and Svensson (1993) and Teasdale and Owen (2000) that gains have
flattened since the late 1980s in Sweden and Denmark, respectively.
The Volume &Heaviness test
The Science Reasoning Test II Volume & Heaviness (NFER, 1979), used in the original
CSMS survey (Shayer et al., 1976) has been used, since the early 1990s, as a pre-test for Y7
pupils entering secondar y schools subsequently to be given the CASE intervention
4
(Adey
& Shayer, 1990; Shayer, 1999). The median values for all studies in Flynn (1987) was 0.59
point a year for tests of fluid intelligence and 0.38 point a year for tests of crystallized
intelligence. Thus in the 30 years since the standardization of the Volume & Heaviness
test in 1975, the anticipated increase in performance might have been expected to be
1.18 standard deviations were it a test of fluid intelligence, or at least 0.76 standard
deviation if a test of crystallized intelligence, if subject to the Flynn effect.
On the other hand, given that it is a criterion-referenced test, it is possible that these
considerations do not apply. Although two of the tests used in the CSMS survey – SRT 1,
Spatial Relations and SRT III, Pendulum – test essentially here-and-now thinking (fluid
intelligence), SRT II, Volume & Heaviness is somewhat different. Ten of the items
concern the concrete operational schemata of conservations of quantity of substance
(mass), internal volume, external volume, weight, displacement volume and intuitive
density. Only four of the items relating to the formal operational level, concerning density
as a weight/volume relation, test here-and-now (fluid) thinking, but for these there is
probably a crystallized component as well. The crucial period for the attainment of most
of the conservations tested is the period from 5 to 8 years of age. If the children have them
at 11 þyears old they will pass the items without having to think, as ‘obvious’: the test
content mostly relates to children’s past experience in school and home.
Increases in achievement reported in government statistics
Whether it be NCTs at Key Stages 2 or 3, or GCSE, or A-levels, each year’s published
statistics show improvements (with the occasional exception) from one year to the next
4
CASE: Cognitive Acceleration through Science Education. Research project funded by the SSRC, 1984–87.
28 Michael Shayer et al.
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in science and maths. On the other hand, a study published by the Engineering Council
(2000) where teachers at 60 university departments had used their own means of
testing their incoming students’ mathematical competence, showed a decline in basic
mathematical skills in relation to the same A-level grades, the drop starting in 1985.
Evidence that just such a lowering of standards has occurred is published in Tymms and
FitzGibbon (2001). By using the International Test of Developed Abilities as a
benchmark measure it was shown that just between 1996 and 1999 grade inflation in A-
level maths was nearly one grade.
For NCTs at Key Stage 2, two studies, Tymms (2004) and Brown, Askew, Millett, and
Rhodes (2003) present evidence which is more tricky to interpret. Between 1995, when
the National Numeracy and Literacy Projects were introduced and the year 2000, rises of
0.7 standard deviations were reported by the DfES on both English and Maths Key Stage
2 NCTs. However then, post 2000, the levels plateaued. This could be interpreted as
being due to schools – themselves subject to extreme pressure to show improvement –
professionally teaching to the test and also giving their children test practise. Once this
adjustment had taken place generally, the system, post 2000, would have no further
scope for showing an increase in standards. However the evidence is different for the
two subjects. Tymms and FitzGibbon (2001) show evidence from many large research
sources that little or no increase in reading had taken place right from 1975 to 2000, yet
in the last 3 years the KS2 English results had shown the rise mentioned above. Tymms
continued the story: from 1997 to 2004 on the PIPS test
5
the gain was only 0.16 standard
deviation (SD) on reading. For maths the evidence conflicts. Tymms, taking the period
1998 to 2002, cites effects sizes of 0.41 SD for KS2 maths, 0.2 SD for the maths
component of PIPS and 0.18 SD from Brown et al.. This does suggest that at least half of
the KS2 improvements in maths represent a real gain for the pupils, possibly due to an
increased time of exposure to maths teaching.
The research presented
Since 1995 Ginsburg has offered schools a report service (NFER, 1979) initially for
King’s College PD only, but later independently for many LEAs in the UK. Schools send
her the Y7 Volume & Heaviness test results in EXCEL file, and also the Y8 end-of-year
tests on the formal operational SRTs Pendulum or Equilibrium in the Balance, and she
gives them a class by class assessment of the effects of 2 years CASE teaching, related to
the CSMS norms. She also compares the item analysis for each class with the item
pattern from a good research sample, in order to highlight evidence for occasional faulty
administration of the test. Her finding that the Y7 means of new schools from recent
years have appeared to be unexpectedly low led to the research reported in this article.
Since 1983 the Curriculum, Evaluation and Management Centre (CEM), based at the
University of Durham, has offered schools an extensive testing service, enabling many
checks to be made on their children’s ability, achievement and potential. Durham
possesses well-established and up-to-date national norms on various tests, and in
particular the MidYIS test, being a general test of developed ability used for Y7 pupils
and standardized in 1999. There were 69 matches between schools that have used
Volume & Heaviness in Y7 and are on Ginsburg’s database, and have in the same year
used the MidYIS
6
test, with the results on the same children in the CEM database, giving
5
PIPS. Performance Indicators in Primary Schools test run by the CEM Centre at Durham University.
6
See www.midysproject.org
Thirty years on – a large anti-Flynn effect? 29
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a sample of 10,023 with approximately the same number of pupils in each year from
2000 to 2003. Thus, the MidYIS norms can be used to estimate what would be the
national mean on Volume & Heaviness for each of these 4 years.
Both the paper and pencil MidYIS test and Volume & Heaviness are administered by
teachers to whole classes. However, although there is a pupil response sheet, Volume &
Heaviness consists of a number of demonstrations and all the questions are read out by
the teacher, who is encouraged to make sure that all pupils understand what the
questions on the paper mean, and have enough time to decide on their responses. Both
tests occupy about 50 minutes of pupil time.
Details of the sample
In Table 1 the locations of the schools covered by the research are shown.
Among the 39 schools in the table, there were 63 Y7 year groups, as some schools
provided data on more than one of the 4 years sampled. Comprehensive school year
groups range from 160 to 200 in number of pupils, independent schools less. Each year
supplied over 2000 pupils, as can be seen in Table 2.
Although it cannot be claimed that the sample of schools is in proportional relation
to the total population of schools – in particular the south-west is not represented – they
do represent both the areas of England and Wales and also state and independent
schools.
Table 1. Types and locations of schools providing test data
Comprehensive Independent
Area Girls Mixed Boys Girls Mixed Total
London and the Home counties 4 4 1 1 10
East Midlands 1 1
West Midlands 11 11
North East 1 1
North West 2 1 3
South 1 1 2
South Wales 9 9
North Wales 2 2
Total 4 29 1 2 3 39
Table 2. Representative sample distributions of Volume & Heaviness over 28 years
6 and above 3.9 to 4.6
NYear Boys (%) Girls (%) Boys (%) Girls (%)
2,350 1975/76 33.4 23.9 12.6 17.3
2,816 2000/01 15.2 8.1 37.3 43.2
2,569 2001/02 10.8 8.4 39.3 46.1
2,456 2002/03 9.9 6.9 41.9 45.2
2,162 2003/04 5.7 4.7 41.8 45.3
30 Michael Shayer et al.
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The analysis of data
A general drop in students’ success on VH: 1975–2003
In Figure 1 the distribution of scores of the original CSMS data on all Y7 students are
compared with all the students in the 2003 sample, separately for boys and girls. Neither
is an exact national sample: The MidYIS mean for 2003/04 is 105, and the NFER Calvert
Non-Verbal mean for CSMS 1975/76 is 101.8, and so the difference is slightly
underestimated. However the qualitative contrast is clear.
The data in Figure 1 are reported on a Piagetian scale of 3 ¼2A, Early Concrete;
4¼2A/2B, Middle Concrete; 5 ¼2B, Mature Concrete; 6 ¼2B*, Concrete
Generalization; and 7 ¼3A, Early Formal. Wylam and Shayer (1980) give the
psychometric properties of the Volume & Heaviness test, and Shayer and Adey (1981)
give information on its school use in relation to science teaching. In order to make a
quantitative comparison of the two distributions two score ranges were selected: 6 and
above – the 1975/76 modal value for boys – in order to compare high performance, and
3.9 to 4.6 as characteristic of the modal performance of both boys and girls in 2003. The
proportions of the students in each range in each school were regressed on the school
MidYIS mean, separately for boys and girls, and computed from the regression equation
at MidYIS ¼100. In Table 2 the proportions in each range are compared year by year.
It can be seen that in 1975/76, as reported in Shayer and Wylam (1978), there was a
substantial difference, in favour of boys, in performance on Volume & Heaviness, which
has disappeared by 2003. In addition, although both boys and girls have shown great
drops in performance, the relative drop is greater for boys. Moreover, there was rapid
change between 2000 and 2003.
When did the decline start? Boy/girl differences: 1976 to 2003/04
Figure 2 shows various data. The data points joined by solid lines from the year 2000
to 2003 represent the major data presented in this paper. VH means for each school
were regressed on the school MidYIS means, separately for boys and girls, and
national values read off at MidYIS ¼100. The way in which this, and other data
analysis reported was done is illustrated in the Appendix. The 1976 CSMS data points
were recalculated from the original CSMS data by regressing the school VH means on
the NFER Calvert Non-Verbal Reasoning test means and reading off at Calvert
NV ¼100. In Shayer and Wylam (1978) the mean levels were reported as
0.16
0.12
0.08
0.04
0.00
123456789
Proportion of pupils at level
0.16
0.12
0.08
0.04
0.00
Proportion of pupils at level
Piagetian level
1976
2003
Early
concrete
Early
formal
Mature
concrete
123456789
Piagetian level
Early
concrete
Early
formal
Mature
concrete
Boys Girls
Figure 1. Comparison of performance for boys and girls on Volume & Heaviness 1976 to 2003.
Thirty years on – a large anti-Flynn effect? 31
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boys ¼5.67 and girls ¼5.13. However this testing was done in the Spring term, at
an average age of 12/1. In order to compare the original CSMS data with those tested
on the MidYIS test from 2000 to 2003 with average age 11/7, early in the school year,
the CSMS values were corrected for the age difference, using curves for the relation
between age and mean score computed from the original CSMS data. The error bars
here are the mean regression errors: that is they represent the actual school-to-school
variation in the phenomena in question. In assessing the year-on-year fluctuations the
standard error of the estimates of the means is around 0.07 level, so although there is
no doubt about the significance of the changes from 2000 to 2003, the fluctuations in
the girls’ means from 2000 to 2002 are within sampling variation. Table 3 shows the
data used in Figure 2, and also the effect sizes of changes.
In order to address the issue of when the decline from 1976 began other data were
sought, and are represented on the graph from 1995 to 1997. The error bars here are
based on school sample numbers and represent the statistical expectation of variation in
the means.
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
5.0
5.1
5.2
5.3
5.4
5.5
5.6
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Boy
Girl
Piagetian Level
Year
1976
ABCD
CSMS
Figure 2. Boys/Girl means on Volume & Heaviness in various data 1976 to 2003.
Table 3. Effect-sizes of change on Volume & Heaviness from 1975 onwards
Mean level Effect-size (SD) of drop
Year Boys Girls Boys Girls B/G difference
1975/6 5.42 4.88 – – 0.5
2000/01 4.59 4.45 0.76 0.39 0.13
2001/02 4.49 4.43 0.85 0.41 0.06
2002/03 4.43 4.45 0.91 0.39 20.02
2003/04 4.29 4.28 1.04 0.55 0
32 Michael Shayer et al.
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The values for 1995 were obtained from one school in the research reported in
Shayer and Adhami (in press). This school had given us nferNelson Cognitive Ability test
(CAT) scores as well as the VH scores for their students. The CAT mean percentile was
given as 50.8, and the VH mean, based on the original 1976 standardization of the test, as
48.6. Since neither of these were outside sampling variation of the 50th percentile this
school (A) was taken as estimating the national average.
The values for the three schools (B, C, D) from 1996 to 1997 were computed from
data on the school nferNelson CAT means supplied by Fernandez (see Endnote). In
order to represent the data from these four schools – all with below-average intakes –
their VH means were adjusted. This adjustment made use of the original Rasch scaling of
the CSMS VH data that gives an equal interval exact linear relation between logit
percentile and VH scale score. The logit difference between the VH scale value based on
the CAT logit percentile, being the best current estimate of the school intake level, and
the VH scale value for logit ¼0 (50th percentile) was added to the school mean VH
level to compare the school’s data with other data estimating the national average. The
original data are given in Table 4.
The dashed lines on Figure 2 represent an interpretation of the data: they are not
regression lines. The error bars allow the reader to gauge the reasonableness of the
interpretation. It is suggested that the data indicate that there may have been no change
in the VH norms until a year or two of the year 1995 and that the decline from 1995
onwards was consistent with the more accurate estimates from 2000 onwards.
Nevertheless, it is acknowledged that this is based only on an opportunity sample:
schools that should have been able to provide several years’ data had already destroyed
their CAT test records.
Inspection of the concepts involved in the Volume & Heaviness test
In Figure 3 the mean facilities of the 15 items in VH obtained in the CSMS survey in
1975/76 are shown. They were determined by regressing the schools’ mean
facilities on the schools’ NFER Calvert Non-Verbal mean score, and computing the
facility at Calvert ¼100. For the schools from the year 2003/04 their mean facilities
on each of the items were regressed on the MidYIS school mean, and their values
read off at MidYIS ¼100, for comparison with the CSMS survey. A drastic drop in
performance can be seen comparing 2003 with 1975, and by comparing 2000/01
with 2003/04 it can be seen that the deterioration was continuing in the 3 years
following 2000.
Table 4. Data for Figure 2
VH mean
VH means
adjusted
Year School Boys Girls Boys Girls CAT Mean
1995/96 A 5.44 4.97 – – 100
1996/97 B 5.27 4.73 5.32 4.77 99.3
1997/98 C 4.43 4.43 5.03 4.9 91.3
1997/98 D 4.49 4.45 4.93 4.78 94.9
Thirty years on – a large anti-Flynn effect? 33
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Items 1, 2 and 3a test the earliest of the conservations – that of quantity of liquid
material. A narrow cylinder is filled with water and poured into a wider glass cylinder.
The narrow cylinder is refilled and children are asked how the quantities of water in the
two cylinders compare. It can be seen that there is relatively little change on these items.
The majority of 7-year-olds possess this conservation. Item 3b tests the harder
conservation of weight.
Items 5, 6 and 7, on the other hand, test the conservation of internal volume. For
item 6 students are shown a rectanguloid block of plasticine, dimensions 5 by 4 by 3 cm.
A glass cylinder is filled to the brim with water, and the block is lowered in by a thread
just under the surface so the students see the water overflow. The cylinder is then
refilled, and the students are asked whether more, less or the same amount of water
would overflow if the block is lowered in (a) to half-way down and (b) right to the
bottom. They are being asked implicitly whether they understand that since the volume
of the block has not changed the position of it under the water should make no
difference. The drop in performance on these items to half that of 1976 shows students
have a much weaker concept of physical quantities.
Items 8 and 9 test a similar concept to items 1, 2 and 3a, except in this case the
material is solid, not liquid. The plasticine block is first rolled into a ball, and then into a
sausage shape.
The most drastic drop is on item 10, testing the concept of displacement volume. A 5
by 4 by 3 cm block of brass and a block of plasticine of identical dimensions are quickly
passed around the class, and students are asked to heft them in their hands. They are then
asked whether the metal block would displace more, less or the same amount of water
than the plasticine. Here they need to have established that it is the volume of the blocks,
not their weight that determines how much water they will push aside. In 1976 many
more girls than boys had an implicit model that the weight is the determining cause. The
average success rate on this item in 1975/76 was 54% for boys and 27% for girls, and by
2003/04 the differential had completely disappeared, with the success rate for both at 17%.
1.0
0.8
0.6
0.4
0.2
0.0
1 2 3a 3b 5 6 7 8 9 10 11 12 13a 13b 14
Volume and heaviness items
1976
2000
2003
Proportion of pupils succeeding on item
Conservation
of quantity
(liquid)
Conservation
of quantity
(solid)
Conservation
of weight
Conservation
of volume
Displacement
volume
Intuitive
density
Weight/
volume
ratio
''Archimedes''
volume density
Proportion
Figure 3. Item facilities on VH test for representative samples 1976, 2001 and 2003.
34 Michael Shayer et al.
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Item 11 in effect tests conservation of intuitive density, which is that density is a
property of the material, not of its size or shape. Students are shown that the plasticine
block sinks in water. Part of it is then rolled into a flat disc and they are asked whether it
will float. Finally, a piece the size and dimensions of a penny piece is held up, and the
same question is asked.
Thus far VH is only testing the conservations and concepts of physical quantities
children have already developed over the last 5 or 6 years. In the items that follow they
need both to be able to handle the weight/volume relationship as a concept of physical
quantities relating to floating and sinking, and also carry out mathematical modelling
on the spot. In item 12 they are shown a 10 by 10 by 10 cm box of thin Perspex, open
at the top. In one question they are told that full of dry-cleaning fluid it would weigh
1,500 gm, and in the other full of alcohol it weighed 850 gm. They are asked to say
whether each would float or sink if lowered into water, and to show how they got
their answer. To assist them the same box is drawn on the paper, with another, just
twice as tall (10 by 10 by 20 cm) immediately below it, which they are told holds
2,000 gm of water.
For items 13a and 13b the teacher tells them the whole story of Archimedes and the
king’s crown. They are told that copper is lighter than gold, and that Archimedes first
found out the old and the new crown’s weights and then their volumes. In 13a they are
asked how he got their volume (with a visual hint of him in a full bath), but in 13b they
are told that the new crown weighed more than the old, and yet Archimedes still proved
there was some lighter metal in it. They have to show what his proof strategy was – a
very difficult item! Typical strategies are either to argue from the weight/volume ratios
in each, or to say that ‘for the same volume the old crown weighed more’.
Finally, question 14, although involving density as a quantitative concept, is an
archetypal mathematical proportion problem, depending more on students’ abilities in
maths. Two brass blocks are illustrated, one over twice the size of the other. They are
told A weighs 60 gm with a volume of 15 cm
3
, and B weighs 160 gm. Given that they are
made of the same brass, what is the volume of B?
In fact, the pattern of relative success of these last four items is the same in 2003 as it
was in 1976 – showing their inter-connection – only now students are coming up from
primary schools with far less grasp both of physical causation and the ability to use
mathematical modelling of the causal relationships.
However, perhaps the drop for items 5 to 10, testing conservations of quantity, weight
and volume is yet more disturbing. In a general way, work in science and mathematics in
primary school would be expected to provide the experience base for the development
of these concepts, and yet this seems to have happened far less than in 1976.
Interpretation of findings and discussion
Originally VH was chosen as a pre-test for much assessment of the effects of the CASE
intervention because it has substantial predictive validity for both science and
mathematics achievement (Shayer, 1999). Also its administration in secondary schools
was a very effective way of alerting science teachers, who would be administering it, the
range of abilities in their pupils – interpreted both in terms of Piagetian levels and also
simply in terms of difficulties they encounter with what teachers sometimes see as easy
conservation and density concepts.
However the significance of the results presented in this paper can only properly be
assessed if this test is located within the whole field of psychometric and other testing of
Thirty years on – a large anti-Flynn effect? 35
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intelligence and abilities. Since the monograph of Shayer et al. (1988), Demetriou has
published further research on generalized models of development (Demetriou, 2004;
Demetriou et al., 2002) – now strategically divorced from reference to Piaget, but, as
with VH, criterion referenced so as to specify the age-related hierarchy of behaviours.
From brain research he has taken account of working memory and from information
processing he looks at how processing efficiency relates to performance. From
differential or psychometric psychology he has refined the concept of mental abilities.
Thus, with five domains as shown in Figure 4 – each specified in terms of behaviours
described as typically characteristic of the top 20% of the population – in a table
consisting of seven 2-year steps from age 3–4 to age 15–16, he describes the whole
course of development from early childhood to the end of adolescence (Demetriou,
2004). Each of the five domains is related to a second order factor, psychometric g.
However, then the issue arises, to what extent is ga factor-analytical artifact, or does
it relate to activity in a separate part of the brain from those where the specifics of the
domains are processed? Measures of processing efficiency, including speed of
processing and executive control, and working memory account for most of the
variance in g, and then between 60% and 65% of the variance on the items testing the
five domains. This does suggest that gmay correspond to parts of the brain where
information, and also strategies for obtaining information, are more generally and even
abstractly processed. Indeed, Duncan et al. (2000) has shown, by use of PET scans on
adults working on spatial and verbal reasoning tests, each with high gloadings, that
while each show brain activity in the different areas known to relate to the task
specifics, nevertheless the same area of the left lateral frontal cortex was active during
both tests. This is in a part of the brain concerned with concepts of executive control,
strategy formation and monitoring the contents of working memory – just those
represented by tests in Demetriou’s research. Perhaps the two disparate specifics are
abstracted to a level at which some kind of abstract decision-tree is tested against the
chunks being processed in working memory? It may be that McCullough and Pitts’s
(1943) original suggestion and Piaget’s (1949) symbolic logic model are closer to brain
processes than has been thought.
Quantitative
-Relational
Causal
Spatial
Categorical
Propositionnal
G
DOMAINS
Figure 4. Demetriou’s model of mental abilities.
36 Michael Shayer et al.
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Whatever view is taken on this, it is clear that any use of any general intelligence test
(including VH) is conceptually faulty if it is used as implicitly measuring one and only
one thing. In terms of Demetriou’s model, a general gmeasure, which in some cases is
approximated by an overall test-score average, needs to be accompanied by measures on
each of the domains sampled by the test items. Some students will always score
relatively high on spatial items and low on verbal items, and vice versa (Shayer et al.,
1988), and the description of a student needs to be represented accordingly. VH relates
to Demetriou’s quantitative-relational and causal domains and has substantial predictive
validity for science achievement as well as mathematics and so relates to an important
part of children’s spectrum of learning achievement. Nevertheless, there is a difference
between tests based on Piaget’s description of cognitive development and other
psychometric tests. It may be that they form a third category to Cattell’s distinction
between fluid and crystallized intelligence. The conservations assessed in VH are not
directly teachable, yet they lie deep beneath the surface of what is potentially teachable,
or testable by a psychometric test performance item. If a child does not conserve
quantity he will not interpret any teaching on measuring volumes (Piaget, 1952,
pp. 223–230). Only if a Y7 student does have the concept of displacement volume,
thinking about relationships between the weight and the volume of solids or liquids
begins to be possible. Most of the test items in VH require neither fluid nor crystallized
intelligence, but it could be argued that they are necessary conditions for success on
tests of crystallized intelligence featuring quantitative reasoning.
Thus the large drops in competence by 11- to 12-year-olds on Volume & Heaviness
between 1975/76 and 2000/01, and the continuing fast drop in the 3 years following
represent an important and objective finding – that is free from any process of adaptation
to changing circumstances – that needs to addressed in assessing the overall impact of
primary schooling on children. In addition, the much higher drop by boys in this period
seems to tie up with other evidence on the deterioration of boys’ learning, relative to girls,
in schools. It makes it difficult to believe in the validity of the year on year improvements
reported nationally on Key Stage 3 NCTs in science and mathematics: if children are
entering secondary from primary school less and less equipped with the necessary
mental conditions for processing science and mathematics concepts it seems unlikely
that the next 21
2years KS3 teaching will have improved so much as more than to
compensate for what students of today lack in comparison with 1976.
On the reasons for the decline reported in this article one can only speculate. Piaget
believed that it was the whole everyday environmental experience of the child that
drove cognitive development, with schooling possibly playing only a minor part in the
process – Vygotsky believed that schooling should change to play a major part (Shayer,
2003). Passive exposure to many hours of television a week has increased since the
1960s when 1975 CSMS students entered primary school. Computer games may have
usurped what might have been, for boys, many hours playing outside with friends with
things, tools and mechanisms of various kinds rather than virtual reality. However, it is
possible that a decline in the use of activity methods in the early years of primary
schools, in favour of an increased proportion of the time dedicated to the 3Rs as
instanced by the National Numeracy and Literacy projects, may be partly responsible for
the continuing decline from 2000 to 2003.
In saying that the conservations are not teachable, it is not implied that schooling
cannot affect their development. Indeed, although primary schooling may only be a small
factor in our reported decline, perhaps only the primary school can begin to remedy this
major problem. There is recent applicable research addressing the learning of children in
Thirty years on – a large anti-Flynn effect? 37
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the first 2 years of primary education (Adey, Robertson, & Venville, 2002; Fawcett &
Garton, 2005; Shayer, 2005), but much more than this is required. Perhaps the next major
government objective in education should be to address the question: in focusing
teachers’ attention on the specifics of the 3Rs only, What has been lost from the earlier
primary practice of attending to the development of the whole person of the child?
Acknowledgements
We are grateful to Dr Cres Fernandez of nferNelson for searching his database for matching school
files of the Cognitive Abilities Test. We acknowledge also the work of Nicola Forster of CEM,
University of Durham both for finding the 69 matches between CEM and our own data-files, and
also getting them safely to our database.
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Appendix
The method of data analysis used for relating the MidYIS standardized scores to the
Volume & Heaviness scores is instanced for the boys from year 2002, and relies on the
substantial correlation between the two tests (r¼:78 for Pearson’s correlation
between the school means). Figure A1 shows the regression line linking the two mean
test scores.
In effect the regression line establishes a running mean of the scores when Volume
& Heaviness is predicted by MidYIS. The line is computed such that the mean of all
the squares of all the vertical distances between the line and the data points has
become zero. Thus, reading off the V&H score from the line when MidYIS ¼100
estimates the mean national average for V&H since 100 is the defined national average
for MidYIS.
80
6.0
5.5
5.0
4.5
4.0
3.5
3.0 85 90 95 100 105 110 115 120
Mean Midyis standard score
Mean Piagetian level
Figure A1. Year 2002: Regression line for estimating national mean for boys on Volume and Heaviness
from schools using the the MidYIS test.
40 Michael Shayer et al.
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Endnote
Dr Cres Fernandez, nferNelson: personal communication. The second edition of the
Cognitive Abilities Test (CAT2) was standardized in autumn 1984. The latest version
(CAT3) was standardized in autumn 2000. An equivalence study was conducted to see
the relationship between the CAT3 and CAT2 scores. Schools in the equivalence study
were asked to administer both versions of one battery, with the order of administration
being counter-balanced within each battery and level. That is, half the schools were
asked to give the CAT2 version first and half the CAT3 version first. In 422 schools
10,240 pupils took part in the equivalence study. The number of pupils tested in each
battery and year group varied between 250 and 850 pupils. The overall results from the
equating study shows that an average performing pupil in 2000 with a standardized
score of 100 in CAT3 Verbal would have expected to score 97 on CAT2 Verbal. Similarly,
a pupil scoring 100 in CAT3 Quantitative would have expected to scored 99 on CAT2
Quantitative. A pupil scoring 100 in CAT3 Non-Verbal would have expected to score 98
on CAT2 Non-Verbal. The language used in a few questions for the CAT 2 Verbal battery
may have dated over the period and may have contributed partly to the decline in the
verbal scores. One other possible explanation is that the overall ability of the population
of pupils in mainstream schools now is slightly lower than before as it includes many
SEN pupils that used to be in special schools. More details are given in the technical
manual: Smith, P., Fernandes, C., & Strand, S. (2001). Cognitive Abilities Test Third
Edition: Technical manual. Windsor, UK: nferNelson.
Thirty years on – a large anti-Flynn effect? 41
