Not just Piaget; not just Vygotsky, and certainly not Vygotsky as alternative to Piaget

Abstract

There have been many interpretations published on the relative importance of the work of both Vygotsky and Piaget: often to the detriment of the latter. This article represents an attempt to discover the meaning and intention of the former by going back to the specifics of what he said and wrote. By reference to what they said of each other it is argued that by the early 30s they had reached almost identical positions regarding child development, and that the work of each is complementary to that of the other. The implications of this position for a theory of intervention for cognitive acceleration are then discussed.

Full text

Learning and Instruction 13 (2003) 465–485
www.elsevier.com/locate/learninstruc
Not just Piaget; not just Vygotsky, and
certainly not Vygotsky as alternative to Piaget
Michael Shayer
∗
King’s College, University of London, 16 Fen End, Over, Cambridge CB4 5NE, UK
Abstract
There have been many interpretations published on the relative importance of the work of
both Vygotsky and Piaget: often to the detriment of the latter. This article represents an attempt
to discover the meaning and intention of the former by going back to the specifics of what
he said and wrote. By reference to what they said of each other it is argued that by the early
30s they had reached almost identical positions regarding child development, and that the
work of each is complementary to that of the other. The implications of this position for a
theory of intervention for cognitive acceleration are then discussed.
2003 Elsevier Science Ltd. All rights reserved.
1. Introduction
As we know from investigations of the process of concept formation, a concept
is more than the sum of certain associative bonds formed by memory, more than
a mere mental habit; it is a complex and genuine act of thought that cannot be
taught by drilling, but can be accomplished only when the child’s mental develop-
ment has itself reached the requisite level. (1)
Throughout the history of the child’s development runs a ‘warfare’ between spon-
taneous and non-spontaneous, systematically learned, concepts. (cf. the Alternative
Conceptions movement). (2)
∗
Tel.: +44-1954-231814.
E-mail address: m.shayer@ukonline.co.uk (M. Shayer).
0959-4752/03/$ - see front matter 2003 Elsevier Science Ltd. All rights reserved.
doi:10.1016/S0959-4752(03)00092-6

466 M. Shayer / Learning and Instruction 13 (2003) 465–485
…the development of nonspontaneous concepts must possess all the traits peculiar
to the child’s thought at each developmental level because these concepts are not
simply acquired by rote but evolve with the aid of strenuous mental activity on
the part of the child himself. We believe that that the two processes—the develop-
ment of spontaneous and of nonspontaneous concepts—are related and constantly
influence each other. (3)
…recently psychologists have shown that a person can imitate only that which is
within her developmental level. (4)
Each school subject has its own specific relation to the course of child develop-
ment, a relation that varies as the child goes from one stage to another. (5)
Quotations from Piaget or from Western applied research from the 60s and 70s?—
No, all from Vygotsky, round about 1930
1
. Having laid down his framework of
thinking at the pure and applied level of research Vygotsky then goes on to make
recommendations for education at the applicable level (Belbin, 1979).
Formerly, it was believed that, by using tests, we determine the mental develop-
ment level with which education should reckon and whose limits it should not
exceed …It turned out that a teaching system based solely on concreteness—one
that eliminated from teaching everything associated with abstract thinking—not
only failed to help retarded children overcome their innate handicaps but also
reinforced their handicaps by accustoming children exclusively to concrete think-
ing and thus suppressing the rudiments of any abstract thought that such children
have. (MiS, p. 89) (6)
In thinking about the relation between ‘spontaneous thinking’, i.e. the kind of
thinking studied primarily by Piaget in the Genevan methodology, and ‘nonspon-
taneous thinking’, i.e. the explicit teaching of concepts and procedures characteristic
of normal school instruction, Vygotsky suggests there is a subtle relation between
the two:
Since instruction given in one area can transform and reorganise other areas of
child’s thought, it may not only follow maturing or keep in step with it but also
precede it and further its progress. (T&L, p. 177) (7)
In saying that:
…the development of scientific concepts runs ahead of the development of spon-
taneous concepts (T&L, p. 147) (8)
1
The first three quotations are from Vygotsky (1986),Thought and Language (T&L) pp. 149, 155,
157. The next two are from Vygotsky (1978),Mind in Society (MiS) pp. 88 and 91.

467M. Shayer / Learning and Instruction 13 (2003) 465–485
he is in no way saying that teachers may remain ignorant of children’s level of
mental development. Only three pages later he warns:
Practical experience also shows that direct teaching of concepts is impossible and
fruitless. A teacher who tries this usually accomplishes nothing but empty verbal-
ism, a parrotlike repetition of words by the child, simulating a knowledge of the
corresponding concepts but actually covering up a vacuum. (T&L, p. 150) (9)
His formulation of the learning paradox (Bereiter, 1985, pp. 201–226) begins:
…to introduce a new concept means just to start the process of its appropriation.
Deliberate introduction of new concepts does not precede spontaneous develop-
ment, but rather charts the new paths for it. (T&L, p. 152) (see quote 3 above) (10)
but
…scientific concepts, like spontaneous concepts, just start their development,
rather than finish it, at a moment when a child learns the term or word meaning
denoting the new concept. (T&L, p. 159) (11)
Thus far one may doubt whether Vygotsky is describing schooling as he has seen
it, or as he thinks it should or could be. It quickly becomes clear that more, much
more is needed, if learning, in relation to mental development, is to be optimal.
Given the dual and reciprocal relation between cognitive development and conceptual
learning within school subjects—that is, as the former develops it makes higher
levels of learning possible, but as children are challenged by new school learning
demands they may be stimulated to re-process the learning in their own spontaneous
manner of processing and hence receive a stimulus to further cognitive develop-
ment—it follows that revolutionary teaching methods are needed. A first step is sug-
gested: since
Scientific and spontaneous concepts reveal different attitudes toward the object
of study and different ways of its representation in the consciousness. (T&L, p.
161) (12)
it follows that:
The most promising approach to the problem [of reconciling laboratory studies
of cognition with school achievement measures, necessarily superficial] would
seem to be the study of scientific concepts, which are real concepts, yet are formed
under our eyes almost in the fashion of artificial concepts…To uncover the com-
plex relation between instruction and the development of scientific concepts is an
important practical task (T&L, pp. 161–162) (13)
In parentheses, I would claim that this is exactly what we undertook, and for the

468 M. Shayer / Learning and Instruction 13 (2003) 465–485
same reasons, for secondary school mathematics and science in the five-year Con-
cepts in Secondary Mathematics & Science (CSMS) research Programme at Chelsea
College, London in the 70s (Shayer & Adey, 1981; Hart, 1981). I say this because
Vygotsky was never able to undertake this programme of research before his early
death in 1934. But he did work on the other major problem: Just how may schooling
be optimised so as to overcome the learning paradox? His answer was:
‘…the only ‘good learning’is that which is ahead of development. (MiS, p.
89) (14)
…the only good kind of instruction is that which marches ahead of development
and leads it; it must be aimed not so much at the ripe as the ripening functions.
(T&L, p. 188) (15)
This presupposes reconciling all the statements cited above. On the one hand,
mere ‘cognitive level matching’leaves the children’s mental development stagnant
(quote 6); on the other, empty verbalism may result if the concept is too far ahead
of the children. Moreover a whole programme of applied research is needed first to
enable teachers, in each school subject, to know just how far ‘ahead of development’
the learning they choose for their students should be. I think I would add, too, that
we need to know a great deal more about differential cognitive development in the
child population than either Vygotsky or Piaget were aware of in the early 30s.
Perhaps the most important implication of the CSMS survey of 14,000 children
between the ages of 10 and 16 on Piagetian tests (Shayer, Ku
¨chemann, & Wylam,
1976; Shayer & Wylam, 1978) is that the range of mental development in any one
year group is far, far wider than anyone dreamed, as those teaching in Comprehensive
schools have learnt empirically the hard way. In Fig. 1 this is shown both in terms
of the CSMS survey and also in a recent whole population assessment of 14-year-olds
(KS3 Maths). Any Y7 class is likely to contain pupils ranging from early concrete to
mature formal in Piagetian terms.
Bearing in mind his creative contribution to special education in the USSR, I am
sure that this would have been taken very seriously by Vygotsky, had his research
revealed it.
But most important of all, without a theory of how ‘spontaneous development’is
related to the progressive inculcation of the child into the culture as embodied in
school learning, there is no way in which Vygotsky’s‘new formula’for teaching
(his words) could be implemented: hence the notion of the ‘Zone of Proximal Devel-
opment’(ZPD).
2. The zone of proximal development
It is a strange fact that both Piaget and Vygotsky were introduced to research in
psychology by being asked, in their respective countries, to undertake the replication
of the new Binet test of intelligence in the 20s. It is also strange that a concept tied

469M. Shayer / Learning and Instruction 13 (2003) 465–485
Fig. 1. ‘12-year gap’shown in two independent sources of evidence.
specifically to the testing of individual children should be treated, later, by some
authors (e.g. Lerman, 1996) as a theory of the social origin of children’s develop-
ment. The essence of the method is this. The child is first given a standard intelli-
gence test, such as the Binet, and his mental age estimated from his score. The
psychologist then takes the child through some of the easier items on which he had
failed, giving various hints and/or discussing the problems with the child. With this

470 M. Shayer / Learning and Instruction 13 (2003) 465–485
assistance the child can then solve more of the items, and hence a new mental age
can be calculated relating to the limit of the child’s success with the mediation of the
psychologist. The difference between the two scores represents the ‘zone of proximal
development’of the child: in Vygotsky’s words:
The zone of proximal development of the child is the distance between his actual
development, determined with the help of independently solved tasks, and the
level of potential development of the child, determined with the help of tasks
solved by the child under the guidance of adults and in cooperation with his more
intelligent partners
2
. (16)
Note that ‘his more intelligent partners’is just speculative on Vygotsky’s part:
the research which was actually done was with the psychologist and the child only.
Hence one aspect of the solution to the problem of teaching ‘ahead of development’
is the recommendation: Teach to the limit of the ZPD of the students, but not further.
Note that this presupposes the availability of the applied research of the cognitive
demand level of the specifics of the school curriculum, which had not been done
either at the time when Vygotsky was working, nor, indeed until the 70s, and is far
from being universally accepted as feasible even now (Shayer & Adey, 1981; Hart,
1981; Collis, 1975).
It is interesting that in the original paper/lecture in which the ZPD was presented
Vygotsky gave an interpretation of it that has shown to be, at least partially, wrong:
Taking an example of a child, tested at the age of 4 giving an independent mental
age of 4.5 years, but having a ZPD extending to 7 years after mediation, Vygotsky
predicted that over the next three years the child would reach an unassisted mental
age of 7, as predicted from the earlier ZPD, but that the ZPD of 7 would have
remained static at 7 (van der Veer & Valsiner, 1991, pp. 343, 344).
When this process of dynamic testing was initiated to children in a special school
at the age of 12, it was found, two years later, that the ZPD of control children had
indeed moved up but little (Beasley & Shayer, 1990). But those who had received
the Feuerstein Instrumental Enrichment (IE) intervention (in other words, taught just
as Vygotsky recommended) had reached the level predicted from their ZPD two
years earlier, but now they had a new ZPD reaching about 2 mental age years even
further ahead of their new unassisted score.
The educational application Vygotsky cited was this: with children tested by his
clinical interview at ages 10, their unassisted score on the Binet predicted less well
their school achievement two years later than their ZPD score, that is the difference
between their unassisted score and their post-mediation score. Hence the theory that
the ZPD is a better predictor of potential achievement than the child’s IQ score
2
Note: this is not taken from the more usually quoted Mind in society, but from a (partial) translation
of the original by van der Veer in van der Veer and Valsiner (1991), p. 337—see Vygotsky, 1933/1935.

471M. Shayer / Learning and Instruction 13 (2003) 465–485
itself. It follows from this that the experimentally grounded source of the theory of
the ZPD is in terms of the behaviour of the individual child, and so this sense of
the concept is indicative only of partially formed skills or schemes possessed by that
child itself (not in his/her social milieu, but mostly derived therefrom), as revealed
in the dynamic assessment interview. In the mediation process the children—admit-
tedly in social interaction with the psychologist—construct from their partially achi-
eved skills or concepts the completed skill or scheme required to solve the test items.
The less the mediation required for success, the nearer to 100% competence the
child is. In our replication of this testing process it was possible to differentiate 10
different levels of mediation (ranging from ‘Just look again’at one end to giving
the solution and the reason for the solution at the other end), and also to describe
the qualitative cognitive functions in which the child was strong or weak (Beasley &
Shayer, 1990; Beasley, 1984). We also verified the better predictivity of the ZPD,
but with the proviso: only with those children who had received the IE intervention,
that is, only on those children who had received the kind of instruction designed to
realise the children’s potential, aimed ahead of where they presently are (Shayer &
Beasley, 1987).
So what is the connection between this testing process, conducted on individual
children, and a theory of optimal teaching in school, and with classes, and also with
a more general theory of child development? Unfortunately chapter 6 in Mind and
Society is somewhat unhelpful for answering this question because it appears to
consist of extracts from at least two different papers, given on different occasions
and with different contexts, with no indication of where one begins or another ends.
Nor is the reference given (we have only a mention, in the preface, of a 1935 book
with an English title, which I was unable to locate in English). The only further hint
of a connection (MiS p. 90) is the recommendation:
We propose that an essential feature of learning is that it creates a zone of proxi-
mal development, that is, learning awakens a variety of internal developmental
processes that are able to operate only when the child is interacting with people
in his environment and in cooperation with his peers. Once these processes are
internalised, they become part of the child’s independent developmental achieve-
ment. (17)
Here the ZPD is taken out of the context of individual testing, and displaced to
the context of school learning as a social process. We may then perhaps make the
further connection to the thought in a paper with a quite different context, The genesis
of higher mental functions (in Wertsch, 1979, p. 163) in which Vygotsky states:
We could formulate the general genetic law of cultural development as follows:
Any function in the child’s cultural development appears twice, or on two planes.
First it appears on the social plane, and then on the psychological plane. First it
appears between people as an interpsychological category, and then within the
child as an intrapsychological category. This is equally true with regard to volun-
tary attention, logical memory, the formation of concepts, and the development
of volition. (18)

472 M. Shayer / Learning and Instruction 13 (2003) 465–485
In this paper (I guess written several years earlier) the distinction Vygotsky made,
in T&L, between spontaneous and nonspontaneous was not there in his thinking,
and ‘development’is being taken rather globally. But the following statement seems
to link the previous two quotations:
…the connection between the child’s natural behavioural development based on
organic maturation and the types of development we have dealt with …has a
revolutionary rather than an evolutionary character. Development does not take
place by gradual alteration or change, by the accumulation of small increments,
the sum of which finally provides some kind of essential change: from the very
beginning we observe a revolutionary type of development. In other words, we
see sharp and fundamental changes in the very type of development, in the motiv-
ating factors of this process. (Wertsch, 1979, p. 171) (19)
The kind of ‘jumps’in performance one sees when mediating children in the
dynamic assessment of their ZPD are revolutionary (although the child may be
already three-quarters of the way there, even if one could not see it) like, possibly,
similar jumps made by individuals when collaborating with their peers when they
internalise some successful performance to which they may have contributed but
have, nevertheless, witnessed in a peer and immediately internalised (completed their
individual ZPD). Between collaborating peers it would be meaningful to postulate
a collective ZPD from which each child can draw as from a collective pool, and the
first of the three quotations above is suggesting that it should be part of the teacher’s
art to offer a learning situation in which the instruction ‘…marches ahead of develop-
ment and leads it: aimed not so much at ripe as at the ripening functions’(T&L, p.
188). This is the point where it is necessary to compare Piaget’s and Vygotsky’s
position on development.
3. Piaget and Vygotsky’s view of mental development
A major difficulty in interpreting Vygotsky’s work derives from what, in my opi-
nion at least, is his major virtue. Each time he gave a lecture or wrote a paper he
updated his thinking according to the particular context he was inquiring into at the
time. Instead of trying to make himself consistent with what he may have published
earlier, or trying to defend himself against other academics (or anonymous referees!),
he thinks afresh according to how he saw things at the time (Piaget, I am afraid,
was quite different, appearing to show he had always thought of everything and was
never inconsistent, only evolving). This dialectical method is quite delightful, but it
means the reader has to try to gauge what were the issues Vygotsky was trying to
address, and to what extent his thinking had become more powerful. It is more like
trying to compare the Verdi of La Traviata with the Verdi of Otello and Falstaff,
asking the question, What has been deepened and developed, but also What has
been lost?
In Vygotsky’s papers from around 1926 until his death in 1934 two closely related,

473M. Shayer / Learning and Instruction 13 (2003) 465–485
interweaving but not identical themes are, What is the relation between children’s
‘spontaneous’thinking (which is what he claimed Piaget studied) and their ‘non-
spontaneous’or learning-related thinking, and What is the relation between Action
and ‘the Word’?
If you look at quotations 2, 3, 7, 8 10 and 11, and couple them with 4—
…recently psychologists have shown that a person can imitate only that which is
within her developmental level
—you can see a paradox: from quotation 6 one sees rejected the idea that one should
teach only at the level of children’s current competence. Likewise quotation 9 rejects
as useless teaching too far ahead of where the children are. But if it is true that
…the development of scientific concepts runs ahead of the development of spon-
taneous concepts
it is also true that teaching at what has been called the ‘N+1’level, where N is the
child’s current mental level, can challenge the children’s thinking in such a way that
their ‘spontaneous’thinking moves ahead:
…to introduce a new concept means just to start the process of its appropriation.
Deliberate introduction of new concepts does not precede spontaneous develop-
ment, but rather charts the new paths for it. (T&L, p. 152) (20)
So on the one hand it is conceded that ‘natural’or ‘spontaneous’thinking inevi-
tably lags behind the intellectual challenge of schooling, but on the other it is asserted
that in providing children with new tools for thinking the learning demands of school
act as a kind of leading edge impelling their spontaneous thinking to more powerful
schemes (to use Piaget’s word). Vygotsky never resolved this paradox, but sometimes
to locate a valid antithesis to a thesis is itself a great achievement which others can
then benefit from
3
.
With action and ‘the Word’(Vygotsky did use the Greek and biblical sense often
in his thinking) one thinks first of Vygotsky’s criticism of Piaget in T&L, and of
Piaget’s later response to that criticism in 1962 (retranslated in Piaget, 2000). It is
rather pointless to try to takes sides on that exchange, because on Vygotsky’s part
he had access only to the work Piaget had done up to 1924, and Piaget did not read
Russian so had even less access to the bulk of Vygotsky’s later thinking. Piaget’s
early work was open to the criticism of being focused too much on children’s words
and too little on their action. He admitted this later in his life (see footnote 15 in
Piaget, 1962/2000 for references), and Piaget (1962/2000, p. 242) admits by impli-
cation that it was only after he had completed the study of his own three children’s
3
cf. Newton—thesis: heavenly bodies attract each other with an inverse square law; antithesis: action
at a distance is an unsatisfactory mystical concept—it would be over 200 years until Einstein resolved this.

474 M. Shayer / Learning and Instruction 13 (2003) 465–485
development from birth, as reported in The Origin of Intelligence—during much of
which time there were no words to observe and study—that he was able ‘…to locate
the beginnings of thinking in a context of adaptation which has a more and more
biological sense’.
I claim instead that by 1933 the two had reached an almost identical position—
in the case of Vygotsky a synthesis achieved possibly by further reflection on his
criticism of Piaget taken as antithesis—in the case of Piaget the antithesis being the
activity of meticulous recording of his children’s actions before they were able to
speak. Under the heading, Word and Action (in Tool and Symbol In Child Develop-
ment, pp. 166–170 in van der Veer & Valsiner, 1994) Vygotsky begins by rejecting
‘In the beginning was the Word’as applying to the development of children’s minds.
He then quotes from Goethe’s Faust, but with the subtle change of italicisation:
...... in the beginning was the deed
and goes on to reject the idea that speech and action evolve independently of each
other or in parallel. He objects (to the positions others had taken):
Yet we were able to observe on a factual basis how, in the process of development,
the child’s action becomes social, and how, in losing speech because of aphasia,
its practical action falls to the level of its elementary zoopsychological form.
Finally he says:
We cannot dwell …on either the evangelical or Goethean formula, no matter
which word we accentuate.
and hence
We have attempted, throughout the article, to show how the word, itself intellectu-
alised and developed on the basis of action, raises the action to a higher level,
subjects it to the power of the child, puts upon the action the stamp of will. But
since we wanted to express all this in one short formula, in one sentence, we might
put it thus: if at the beginning of development there stands the act, independent of
the word, then at the end of it there stands the word which becomes the act, the
word which makes man’s action free.
4
(21)
Although Piaget would never have expressed himself like that, I can hardly slip
a piece of paper between this position and that of the man involved in researching
The Growth of Logical Thinking (GLT) (Inhelder & Piaget, 1958), and The Early
Growth of Logic (EGL) (Inhelder & Piaget, 1964).
4
Note that this quotation differs from that given in van der Veer and Valsiner (1991). It was retrans-
lated from the Russian by Mundher Adhami, and van der Veer confirmed that this is a correct translation.

475M. Shayer / Learning and Instruction 13 (2003) 465–485
4. For cognitive development, follow Piaget
Cole and Wertsch (2000) in an interesting position paper placed on the Internet
assert:
There is little doubt in our view that there is still much to be learned from both
Vygotsky and Piaget, and in many cases the strengths of one theorist complement
the weakness of the other. However, we believe that discussions of these two
figure’s accounts of mind and its boundaries are not well served by overly
rehearsed debates about the primacy of the individual or the social. Instead, we
have argued that the more interesting contrast between them concerns the role of
cultural artefacts in constituting the two poles of the individual–social antinomy.
For Vygotsky such artefacts play a central role in elaborating an account of what
and where mind is. In pursuing the line of inquiry, he focused on a set of issues
and phenomena that do not appear to have any clear counterpart in Piaget’s think-
ing, and consequently may be more appropriately characterised as being different,
rather than directly in conflict with those at the centre of Piaget’s project.
In this spirit, I claim that, provided one takes The Origin of Intelligence as marking
the beginning of the thoroughly well-grounded life-work of Piaget studying all stages
of development (excepting ages 3–5) of children from birth to the end of adolescence,
then it is the strength of this person that one should rely on. But first it is necessary
to clarify what it was that Piaget had described. Vygotsky (T&L, p. 154) claimed
that Piaget only described the genesis of children’s‘spontaneous concepts’. But in
the previous section we have seen that the relation between ‘spontaneous and non-
spontaneous, systematically learned, concepts’—as Vygotsky rightly states—is an
interaction in the process of development. Piaget never presented these concepts as
‘firmly divided and self-contained entities whose interaction is impossible’—Vygot-
sky was wrong about that (T&L, p. 154). What can be said is that Piaget selected
tasks for children little likely to be contaminated by the children parroting ‘teacher’s
right answers’. But the purpose of this was to get below the surface of younger
children’s performances to find the extent to which they can construct classes,
relations etc. in a wide variety of contexts. If one looks at Piaget’s sampling unit as
being not the individual but as a set of children sufficiently varied both in age and
ability to elicit both successful understanding and all the steps in the ZPD leading
up to the achievement of the scheme studied, one can then view the Genevan method-
ology as focused on the qualitative detail of the study of the ZPD phenomenon, as
distinguished from the quantitative side which Vygotsky described in his psycho-
metric phase. It is interesting that both used the term ‘genetic’to describe their
approach to development. Piaget’s own view of his methodology as being the study
of ‘the epistemic subject’(but see Shayer, 1993) is compatible with this description
of his sampling unit, within which enough detail can be given to describe all steps
or alternatives of development of that ‘subject’.
Looking then on Vygotsky and Piaget’s approaches to development as different
in the way suggested by Cole and Wertsch, one can see that Vygotsky’s emphasis

476 M. Shayer / Learning and Instruction 13 (2003) 465–485
on ‘nonspontaneous’concepts was a concern with the dynamics of development—
that which drives it—and Piaget’s with the statics of development, where they actu-
ally are when removed from sources of stimulus: exactly what Vygotsky said one
needed to know in order to have a good model of ‘instruction’(quotations 4, 13,
14 and 15). Hence the Genevan methodology where the psychologist, while support-
ing the children by approving all they do and say, deliberately avoids mediation,
and in fact by offering counter suggestions to gauge the stability of a child’s concept,
could be described as sometimes offering negative mediation. In this sense one could
call the Vygotskian dynamic assessment process, where a variety of mediation is
offered to each child, as being focused on the individual, and Piaget’s as focused
rather on the population. Yet, paradoxically, a point which is very obvious—although
I have never seen it expressed by any commentator, be they either pro or anti Pia-
get—if you want to see the detailed specifics of what is present in various children’s
ZPDs, if you want evidence that partially achieved schemes are present in children’s
minds before they finally achieve them, you will not find Vygotsky ever bothering
to show you: instead you will see them recorded in fascinating detail in every work
associated with Piaget.
Although there could have been some justification at the time in Vygotsky viewing
Piaget”s work with younger children thus:
In schoolchildren of eleven to twelve, the nonspontaneous concepts completely
replace the spontaneous, and with this, according to Piaget, intellectual develop-
ment reaches its port of arrival. The real culmination of the developmental process,
i.e. the formation of mature, scientific concepts in adolescence, simply has no
place in Piaget’s model. (22)
this could only have been true with respect to the development of concrete operations.
I don’t recognise this myself as a valid description, but if one looks at the character-
istics of the concrete generalisation level one might be forgiven in interpreting it as
children having the capacity to use all the concrete operational schemes that Piaget
describes fluently in any school learning they are offered, and hence the gap between
development and learning capacity to have disappeared. But as soon as one looks
at GLT, 20 years later, it is possible to see that many of the aspects of development
which Vygotsky described apply more to the development of formal operations than
to concrete operations.
In the various chapters researched by Inhelder and Piaget in GLT one can see,
exhibited within the specifics of well-chosen contexts, the major underlying schemes
(Reasoning Patterns) required for effective thinking in the biological and physical
sciences. These presuppose without any doubt (the research was done on the selected
population of Swiss gymnasia schools, perhaps the upper 20% or less of the
population) adolescents whose development had already long been established in a
complex interaction between their mental development and their exposure to and
(partial) mastery of the reasoning patterns needed to make their own the concepts
of science. As Vygotsky put it:

477M. Shayer / Learning and Instruction 13 (2003) 465–485
…the development of nonspontaneous concepts must possess all the traits peculiar
to the child’s thought at each developmental level because these concepts are not
simply acquired by rote but evolve with the aid of strenuous mental activity on
the part of the child himself. We believe that the two processes—the development
of spontaneous and nonspontaneous concepts—are related and constantly influ-
ence each other. (T&L, p. 157) (23)
Thus all Inhelder and Piaget are doing in GLT is to present adolescents with
investigations, related to quite complex thinking underlying genuine mastery of
science concepts, which reveal their development of reasoning patterns such as con-
trol and exclusion of irrelevant variables required in biological thinking, and pro-
portion and equilibria of systems needed to model physical science. Vygotsky’s criti-
cisms of the limitations of spontaneous thinking all vanish as we see they relate only
to the middle phase of the development of concrete operations in younger children.
The ‘spontaneous’thinking of the adolescent is a very different animal to that of
the 8–10 year old. As Inhelder and Piaget show in delightful detail, the ‘spontaneous
concepts’exhibited by these adolescents have already been brought:
…up to the level of development which would guarantee that the scientific con-
cepts are actually just above the spontaneous ones. (T&L, p. 195)
In claiming that if one needs the specifics of the levels of mental development
then it is to Piaget that one should turn, then one should remember that this delivers
only the statics. To give Vygotsky the last word in this section:
It became clear that the functioning of intelligence depends upon the structure of
thought. Piaget’s works are but the most explicit expression of the concern with
the structural aspect of thought. (T&L, p. 207.)
5. Fostering the dynamics of development: Vygotsky and Piaget in tandem
Piaget has been represented as studying (and promoting) only the individual, and
Vygotsky as focusing on (and promoting) the primacy of social processes of learning
(Lerman, 1996). But this is to confound investigational method with intention.
Neither engaged in applicable research in the classroom. I have already presented
the paradox that Vygotsky’s own reports of his work in dynamic assessment were
focused only the individual, whereas as Piaget notoriously once said, truly, of the
Genevan method ‘I am not interested in individuals’, for in fact his selection of a
good sample of children was typical of the methodology of the biologist seeking to
describe a species. I would claim, though, that the delightful human specifics detailed
in every book present the same implicit love of children as a good biologist has for
the animals he studies.
Les Smith (Smith, 1996;Piaget, 1995) has shown in meticulous detail that—at
the abstract level at least—Piaget and Vygotsky occupied very similar territory with

478 M. Shayer / Learning and Instruction 13 (2003) 465–485
respect to the social origin of thinking. Any reader who doubts this is invited to sit
the self-test given in Smith (1996) where one is requested to attribute to the right
author 20 brief quotations, there being an equal number from each. Among a score
of ‘experts’who were given the test unseen at the time, none did better than 16
right, and their mean score was 13 (mine was 12, but then I dodged two items, my
uncertainty helping to make Smith’s case). Both, in their own ways, stressed the
importance of ‘construction’by the individual (see quote 3)—in Vygotsky’s case
covered by the global term ‘internalisation’, which sometimes means immediate
appropriation of a concept made available by another collaborator in learning, and
sometimes means (quotation 3) subsequent work by the individual. This second
meaning overlaps Piaget’s contribution to the art of ‘cognitive conflict’, the pain and
challenge that follow a person finding that his present concepts are not powerful
enough to solve a dilemma.
This may be stated more strongly: If Vygotsky was right in conceding Piaget as
the Master vis-a
`-vis ‘the structural aspect of thought’, how was it that Piaget, setting
out in the early 1920s to discover ‘How does knowledge develop?’(by implication
a dynamic process), in fact spent all his time and that of his scores of co-workers
up to 1955 in what was essentially a structuralist enterprise? To answer this it is
necessary to imagine the state of our knowledge without Piaget’s life-work. It is like
medicine before detailed anatomical knowledge was available: before you can inter-
vene to remedy a dynamic function you first must know what it is that is in motion
and interaction. First Piaget had to describe, like a series of stills from a movie, all
the steps of knowledge development all over the psychological spectrum from birth
to adulthood. The famous ‘Genevan method’crystallised at just about the same time
as physicists like Heisenberg realised that there was a problem about describing a
system which you have to disturb to observe. Piaget and his assistants had their own
solution to describing children’s present thinking: it might be expressed ‘above all
avoid mediation’’, and by counter-suggestion, if need be, try to elicit only the child’s
present powers. Hence ‘the method’vetoed intervention, vetoed any attempt to
change the phenomena until the descriptive work was done.
Vygotsky on the other hand studied only the dialectics of change, and in his pro-
cess of dynamic assessment involving the concept of the ZPD adopted a different
solution to the Heisenberg problem. This was: mediate, and then measure the extent
of the child’s performance increases as a result of the mediation—essentially a
dynamic process (measuring the extent of the mediation as well was a further gloss
on the method, developed by Feuerstein).
The complementarity of their respective work then follows (cf. the wave and par-
ticle aspects of electrons and photons). Vygotsky would have needed Piaget’s
descriptions of development had he gone on in the work of improving schooling,
and had Piaget wanted to convert his (correct) intuitions about the importance of
collaborative learning among peers (see Smith, 2001 on Piaget’s views on education)
into school practice he would have needed to draw on the work of Vygotsky.

479M. Shayer / Learning and Instruction 13 (2003) 465–485
6. Evidence from intervention studies
This view of the complementary aspect of the work of Vygotsky and Piaget has
since 1981 implicitly underlain a substantial programme of intervention research.
Those with a taste for statistics will find the evidence in the papers cited.
First it was necessary to see whether intelligence can be enhanced at all. Shayer
and Beasley (1987) reported a replication of Feuerstein Instrumental Enrichment (IE)
over a two-year period (1982–84) on a class in a Special School. Part of the evidence
came from the use of a Piagetian test battery, adapted from the monograph by Shayer,
Demetriou, and Pervez (1988), where large-scale evidence on a stage interpretation
of Piaget’s work was argued. Although by definition Special School pupils are selec-
ted from the bottom 5% of the population on standardised tests of English and Maths,
it was interesting to see that on Pre-test at the age of 11 the children were assessed
at the 35th percentile of the CSMS norms (see Fig. 1). At post-test 20 months later
the children were at the 65th percentile, now above the National average for their
age. But this was very small-scale evidence.
6.1. Cognitive Acceleration through Science Education (CASE)
The original applied and applicable research was funded by the SSRC at Chelsea
College from 1984 to 1987. A summary of subsequent large-scale research on the
effects of this two-year intervention set within the context of science learning can
conveniently be inspected in Shayer (1999)—itself a response to a challenge offered
by Jones and Gott (1998). The first group of eight schools (pupil N=1486) offered
PD from King’s College from 1991 were given pre- and post-tests of two of the
Piagetian class-tasks used in the CSMS survey. The school effect-sizes showed an
average increase of 34 percentile points on the CSMS norms. In effect this amounted
to a doubling of the proportion of pupils with formal operational thinking.
Evidence for the meaning of these increases in thinking ability in terms of school
achievement is given by the Key Stage 3 results of those 12 schools beginning CASE
in 1992 (N苲4500). Not only did the pupils have enhanced results in Science com-
pared with those in control schools: they showed similarly large increases in Maths
and English. The results for all subjects indicate that it was the general learning
ability, intelligence in fact, which had been affected by the CASE intervention, rather
than specific science skills.
Evidence for the transmittability of the CASE methodology was given by the
results of five Sunderland schools given PD by Marion Jones, herself one of the
teachers initially trained at King’s in 1991. These results averaged the same as those
of the seven schools given PD at King’s.
Finally the GCSE 1999 results from 11 schools beginning CASE with PD from
King’s in 1994 feature in Shayer (2000). Added-value estimates averaged 1.02 grades
for Science, 0.95 grades in Maths, and 0.90 grades in English, with increases in the
proportion at C-grade or above of the order of 20%. This is the final evidence that
the effect of the CASE intervention is permanent.

480 M. Shayer / Learning and Instruction 13 (2003) 465–485
7. Intervention toward a theory of instruction
One important insight from Vygotsky is that in ‘spontaneous’thinking the move-
ment in the child’s mind is from particular instances toward some more general
concept which links them, whereas in school learning—particularly that of science—
the child first receives the concept at the abstract level, and then has to struggle to
find out how it may be applied to different specific contexts. Quoting from West
and Pines (1985),Howe (1996) describes this:
The metaphor is of two vines; one vine representing spontaneous concepts grows
upward while the other vine, representing scientific concepts, grows downward.
Under the influence of instruction that encourages integration and consolidation
the two vines intertwine and grow together as conceptual understanding develops.
How then is one to draw on these various insights to create a general strategy for
effective teaching in school? In different ways both Feuerstein through the Instru-
mental Enrichment programme (IE) and the workers involved in the CASE and
CAME
5
interventions have chosen an intermediate tactical solution (Feuerstein,
Rand, Hoffman, & Miller, 1980; Adey, Shayer, & Yates, 1995; Adhami, Johnson, &
Shayer, 1998). Although they express it differently (Feuerstein through the concept
of ‘cultural deprivation’) I believe that both sets of workers addressed the problem
shown by the CSMS survey quoted above that in any one year-group or in any one
class of 12-year-olds in a neighbourhood High School with a mixed-ability policy,
maybe no more than 20% may be functioning at the level of their true mental poten-
tial, so that in Piagetian terms their mental levels may range from early to middle
concrete right through to mature formal. Before one could dream of an ideal solution
to school learning, first one must tackle the problem of the Western environment
that has produced ‘cultural deprivation’and hence so many people that cannot benefit
from schooling once it goes beyond the Primary level. Hence the notion of inter-
vention (drawn from medical terminology) as an intermediate tactic to increase the
proportion of children by a large amount to a mental level at which they can process
their learning during the course of ordinary instructional teaching It is claimed that
ample evidence has already been established to show that this tactic can be successful
(Shayer, 1999). Perhaps in 30 years time when intervention methodology has been
practised with all age groups from 5 through to 14, and most children realise their
genetic potential, ‘good teaching practice’will have evolved to a seamless integration
of instruction and intervention.
Given the twin vine concept on the one hand, and the CSMS survey evidence of
wide ranges of mental levels among the pupils on the other, then the first general
principle one can enunciate is that any good intervention activity should be in a
context that allows processing at several different levels. In this way there are opport-
5
Cognitive Acceleration in Mathematics Education Projects, funded at King’s College, 1993–1995 by
the Leverhulme Trust, and 1995–1997 jointly by the Esme
´e Fairbairn Foundation and the ESRC.

481M. Shayer / Learning and Instruction 13 (2003) 465–485
unities for all children in the class possibly to make ‘revolutionary’jumps in thinking,
each from where they presently are. ‘All shall get prizes’would then not be a patron-
ising observation.
But in order to design activities having this characteristic (such as the IE ‘Instru-
ments’and the CASE and CAME lessons) it is essential that designers—and those
who teach the lessons—are able to look at their curriculum through mental develop-
ment (Piagetian) eyes, as Vygotsky originally argued was essential. If you cannot
assess the range of mental levels of the children in your class, and simultaneously
what is the level of cognitive demand of each stage of the lesson activity, how can
you plan and then execute—in response to the minute by minute responses of the
pupils—tactics which result in all engaging fruitfully?
There then arises the question: How should the teachers conduct these intervention
activities? Statements 17 and 18 are suggestive that some kind of collaborative learn-
ing should be beneficial, and in case a Western reader is put off by the language of:
Functions are first formed in the collective
6
as relations among children and then
become mental functions for the individual. (Wertsch, 1979, p. 165).
—who can totally resist using the jargon of the times?—he/she could also interpret
it in the spirit of a later statement:
…play also creates the zone of proximal development of the child. In play the
child is always behaving beyond his age, above his usual every day behaviour;
in play he is, as it were, a head above himself. Play contains in a concentrated
form, as in the focus of a magnifying glass, all developmental tendencies; it is
as if the child tries to jump above his usual level. The relation of play to develop-
ment should be compared to the relation between instruction and development …
Play is a source of development and creates the zone of proximal development.
(Vygotsky, 1933, quoted in van der Veer & Valsiner, 1991, p. 345).
Thus the abstract formulation:
Research shows that reflection [by the individual] is spawned from argument [in
the collective]. (Wertsch, 1979, p. 165, 5 lines later)
implies a process nicely specific, indicating that the main source of mediation for
adolescents is their peers, rather than ‘scaffolding’by adults.
Thus the second general principle used both in the CASE and CAME interventions
is that the social conditions must be set up in the classroom/laboratory to allow a
communal ZPD to operate with further consequences for the promotion and com-
pletion of individual pupils’ZPDs.
6
My Russian translator assured me that the Russian word is used much as ‘group’is used in English,
without carrying as heavy political overtones as the word ‘collective’does in English.

482 M. Shayer / Learning and Instruction 13 (2003) 465–485
Fig. 2 summarises the abstract structure of a typical CASE lesson. Given a context
where multiple levels of understanding, say of controlling variables, or of ratio and
proportion, are involved, the teacher needs in Act 1 (8–12 min) to introduce the
pupils both to what will be involved in the investigation to come and to any technical
vocabulary they need. This needs to be done at a thinking level such that at least
80% of the class can enter into a dialogue with the teacher that creates a common
understanding of the work to come. In Act 2 (10–15 min) the working groups—
typically 3–5 in number—are to work at the task within their group ZPDs.
If Act 2 is to be successful the teacher needs to be mindful of Act 3 to come in
the class management strategies he/she uses toward the end of Act 1. In Act 3
(typically 15 min for CASE) each group is to report their ideas to the rest of the
class. If, in relation to one concept, a pupil in group 5 needs to complete her partially
formed ZPD, a strategy or idea created within group 2, then only Act 3 gives her
a chance to witness and internalise it. Act 3 is also the opportunity for the whole
class, having established a common ZPD in relation to the investigation, then to
reflect metacognitively on what has been achieved. The pupils already know from
past experience that they had better have something worth saying
7
when it comes
to Act 3, so the teacher will already have induced the flow of some ideas in the pupils
in Act 1 and will then have challenged all the groups to use the time announced to
Fig. 2. Technical terms used to describe phases of CASE and CAME lessons.
7
Otherwise you’d feel a right pratt, as one pupil said when interviewed on Radio Cambridge.

483M. Shayer / Learning and Instruction 13 (2003) 465–485
collaborate in finding as much as they can to show and say (’Don’t ask me, I shan’t
answer—it’s your ideas that are important’).
The teacher processes are described in more detail in a recent publication
(Shayer & Gamble, 2001) intended to show science teachers how they can extend to
their ordinary science teaching the teaching skills they employ in their CASE lessons.
During Act 2 the teacher’s main task is the class scan. He/she only intervenes to
enhance group energy where it flags, or to drop in the right question to induce
cognitive conflict where a group has become complacent at too low a level of pro-
cessing. Otherwise she notes all the ideas of interest coming up in different groups
(some teachers note names on the whiteboard for reference in Act 3), decides when
sufficient has occurred in Act 2 (it is not necessary for all groups to have completed
the task), and also makes a plan for how to manage Act 3. Implicit in all of this (but
consciously so on the teacher’s part) is that it is the peer–peer mediation occurring in
the group construction in Act 2, and in the exchange of ideas in Act 3, that is the
major driver of intellectual development in the CASE interventions. It is her job to
manage the lesson so that peer–peer mediation is maximised, a very different skill
from ordinary instructional teaching. Note too the qualitative difference between this
art and much that is featured in Newman, Griffin, and Cole (1989), e.g. p. 67:
…we would propose that the constructive work occurs as much in the interaction
between the adult and the child as in the child’s internal processes.
No, we argue, the teacher’s art is to manage all aspects of peer–peer construction
and mediation, a more indirect managerial process. “How do I know what I think
until I hear what I say?”(last page of Howards End, E.M. Forster) applies even
more to a group of children trying to find an idea which will illuminate a science
problem, or to find a strategy by which to attack a maths task, and could be comp-
lemented by, “How do I know what I think until I hear also what the others say?”
In fact, even “…until I hear what I say”implies the response and stimulation of the
others and the presence of ‘the collective’. Hence the importance of Act 3 of the
cycle (Whole class discussion,orMetacognition) where each group quickly reports
to the rest of the class the high points of their discussion, and others are allowed to
comment (‘I don’t agree with what John said, because…’). Bearing in mind the issue
of different levels of mental development in the class, and also different depths of
interpretation of the agenda, the teacher would be wise, at this point, if she ask first
the less able children to present any solutions to the lower level aspects of the task
she has seen and heard during the Construction period. It is not always the less able
pupils who benefit from this! Sometimes the more able say that worried them too,
but they didn’t want to ask. If each group only present what hasn’t already come
up, this exchange can be brisk and not tedious. Ideally every idea or strategy which
has come up in the group discussion then becomes available, for any or everyone,
increasing by a large factor the number of opportunities for each to complete their
ZPD in respect of this or that concept.
With the maths activities featured in CAME, typically there are not one but two
3-Act cycles, with Act 3 of the first becoming a preparation for Act 2 of the second.

484 M. Shayer / Learning and Instruction 13 (2003) 465–485
This is because any maths activity draws, more than is the case for science, on other
strands of maths processes, each of which needs addressing.
Lest it be thought that the above description implies dropping Piaget in favour of
Vygotsky, remember that every moment of the lesson management involves the
teacher being aware both of the processing levels of different aspects of the activity,
and also how each pupil’s response indicates the level that they are processing at,
and hence where they are presently moving up towards. In Shayer and Gamble (2001)
and also in Primary CAME (Y5/6) each lesson is presented in a diagram cast in
Piagetian space, where the hierarchy of concepts is displayed (Adhami, Johnson, &
Shayer, 2002).
It is not suggested that this teaching art, integrating the Piagetian (mental level)
and Vygotskian aspects (class management) is as easy as current announcements by
the British Government office (DfES) about ‘Thinking Skills’seem to suggest. You
cannot hope of any success—previous research data show this (Adey & Shayer,
1994, chapter 3)—by giving teachers a few days of abstract training and then asking
them to go away and apply it to their own subjects. Hitherto—whether it be Feu-
erstein IE, CASE or CAME—it has required several years with subject specialist
research teams to generate portfolios of lesson contexts which fulfil all the criteria
mentioned above. In a forthcoming book (Shayer & Adey, 2002) three different
recent developments of the art are presented: to Mathematics in the last two years
of Primary school, to Performing Arts subjects for 12–14 year-olds in the first two
years of secondary school and in the CASE@KS1 intervention for 5- to 6-year-old
Primary children (Adey, Robertson, & Venville, 2001, 2002). Each of these teaching
programmes only become effective through Professional Development delivered over
a period of at least a year, where feedback is given to the teachers as they gain
increasing experience of the problems which arise from the lesson activities.
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