Optimal learning in schools – theoretical
evidence: Part 2 Updating Piaget
John Crossland
ABSTRACT Part 1 in this four-part series of articles discussed Piaget’s theories of learning and
development (Crossland, 2016). Part 2 explores how post-Piagetian researchers have addressed
criticisms of Piaget’s theories by linking recent evidence including that from neuroscience. The
outcomes show that good teachers make a difference by implementing classroom-based optimal
learning strategies. This new evidence brings Piaget’s theories into the 21st century and leads to a
clearer definition of optimal learning in the classroom.
Periods of transition
Several post-Piagetian researchers (neo-Piagetians)
have attempted to build upon Piaget’s theories.
Demetriou (2006) comprehensively summarised
five neo-Piagetian theories showing how the
criticisms levelled at Piaget’s theories are being
addressed in relation to the transition between
the types of thinking and doing. There are two
approaches with a strong neurological evidence
base, so these are the focus for this series of
articles. The first is Fischer’s skills-based approach
and the second is Demetriou’s semantic approach.
A few years later, updated outcomes from the
same two researchers (Fischer, 2008 and Demetriou
et al., 2013) have been brought together with
those of Piaget to shed light upon some aspects
of cognitive stability and dynamic variability of
school-aged-learner development. The fact that
the three studies used different methodologies,
measuring instruments and tools of statistical
analysis adds weight to the areas where they agree.
First, some broad aspects about the research
methods and outcomes used by Piaget, Fischer
and Demetriou:
l Piaget based his stages of development on
observing learning in a longitudinal study
with a small group of learners supplemented
by clinical interviews. The outcomes were
discussed in Part 1 (Crossland, 2016).
l Fischer’s data were drawn from the
development of the neo-cortex and worked on
longitudinal electroencephalography (EEG)
studies. These tested the development of
skills under the conditions of familiarity and
scaffolding (mediation) compared with no
help given at all. The EEG studies showed
the processes by which the brain undergoes
significant spirals of culling and rewiring and
these are related to surges of development
in skills. Fischer interpreted these results to
mean that the individual learner’s true level
of development can only be reached under
conditions of maximum mediation (see Box 1).
Under these conditions, development occurs
in spurts that affect a wide array of particular
skills and in line with the expectations of a
dynamic systems approach. Thus, supportive
teaching has a periodic accelerating effect,
which confirms that good teaching makes
a difference to the pace of development.
However, Fischer’s theory ignores the role of
processing capacity in the transition of types of
thinking and employs a very loose definition
of social mediation, such as reading books.
l Demetriou, in collaboration with many other
researchers over several decades, analysed
three studies, two of them longitudinal.
Demetriou’s data were drawn from the whole
brain, including the development of those
vital areas for learning: the hippocampus,
amygdala, thalamus, neo-cortex and working
memory. Also, Demetriou researched
individual differences, including gender. The
studies investigated the relationships between
age, processing speed, working memory
and fluid intelligence. From the results, he
developed a theory that looked specifically
at how the transitions between optimal
performances took place. Like Fischer, his
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Optimal learning in schools – theoretical evidence: Part 2 Updating PiagetCrossland
BOX 1 Mediation and the zone of proximal
development
The zone of proximal development (ZPD) has
been defined as ‘the distance between the actual
developmental level as determined by independent
problem solving and the level of potential
development as determined through problem
solving under adult guidance, or in collaboration
with more capable peers’ (Vygotsky, 1978: 86).
Using the metaphor of a brick wall with bricks
missing to represent the parts of a concept a
learner has not yet attained, the learner will not
be able to successfully use their concept to
solve a complex problem. If another learner also
has a deficit in full understanding but in different
parts of the concept (different bricks missing in
their wall) then, during exploratory talk (Mercer,
2000), the pair can copy and swap bricks so
that each of them attains a full brick wall and fully
understands the nuances of the concept. The
result is they solve the problem together when
neither of them can solve it on their own.
theory acknowledged the dynamics and selforganising properties of human action, feeling
and thought, and recognised that individuals
operate at multiple simultaneous cognitive
levels as the rule rather than the exception.
In his opinion, these variations are caused by
differences in the experience that individuals
have with different domains of knowledge and
skills, and also by differences in the support
(teaching) that they receive when interacting
with the various domains.
Optimal performance is a plateau in
consolidating a particular type of thinking and
performance. The period of growth or transition
that follows moves the learner to increasingly
more advanced thinking and performance. Table 1
summarises developments according to the
different researchers at different ages of children.
For example, Piaget sees children in a period of
development from ages 2 to 6 that can be assessed
as achieving a best performance at age 6 to 7.
These research results show common patterns
for the ages of transitions followed by spurts
in development. They also dismiss a long-time
argument with Bruner’s idea of development
being continuous (McLeod, 2008).
When their results are compared, a major
difference is that Piaget’s formal period of
operations was completed by the age of 15, but
both Fischer’s and Demetriou’s research showed
significant reshaping of the brain up to the age of
25, and the changes continued to correlate with
improved performance.
The main conclusion from the table
is, however, that this new evidence from
neuroscience supports the broad idea from
Piaget that, as learners of school age grow older
and develop, they add more advanced types of
thinking to their repertoire.
What is not supported is Piaget’s original
concept of a whole-brain stage of development. It
is what happens in each transition/growth period
that is disputed. The transitions are contextspecific and the contexts include conceptual,
social, emotional, cultural and individual factors.
Social factors
Piaget is famous for his interest in how individual
learners develop their own thinking through a
constructivist approach. However, Piaget also
argued that, ‘children construct schemes of social
reaction just as they construct schemes relating
to the world of objects … Unfortunately, the
abstruseness of his conceptions interferes with his
effective communication. Also, uncharacteristically,
Piaget provided few examples.’ (DeVries, 1997).
As a result, Piaget’s social theory had little impact
on classroom practice.
However, Piaget’s contemporary, Vygotsky,
was more influential. Vygotsky (1978) focused
Table 1 Broad school-age results brought together
Researcher
Piaget
Fischer
Demetriou
78
Development period (ages)
Transition
(growth)
Optimal
performance
Transition
(growth)
Optimal
performance
Transition
(growth)
2–6
4–6
2–6
6/7
6
6
7–11
6–9
6–11
11/12
10
11
12+
11+
12+
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Optimal learning in schools – theoretical evidence: Part 2 Updating Piaget
Figure 1 Exploratory talk accelerates cognitive
development
on the social and cultural aspects of learning,
known as ‘social constructivism’. It laid emphasis
on the part played by language and other people
in enabling learning. His ideas of the zone of
proximal development (see Box 1) and teacher–
learner mediation have had a significant impact on
improving classroom practice (Crossland, 2010a).
Vygotsky in his last published work introduced
the concept of an affective (social and cultural)
dimension to the zone of proximal development.
The article (Crossland, 2010a) also highlights the
importance of promoting cognitive development
through the affective aspects of exploratory talk
and learner–learner mediation in small groups,
with teacher non-intervention (Figure 1). So, in
terms of the social aspects of learning, Vygotsky’s
ideas are just as useful as Piaget’s for informing
optimal learning.
Emotional factors
‘Neuroscience provides substantial evidence
for the fundamental role of emotion in learning
that settles long-standing ideological debates
about whether educators should be responsible
for emotional development’ (Hinton, Miyamoto
and della-Chiesa, 2008). In a meta-analysis of
213 mainly US social and emotional learning
programmes, Durlak et al. (2011) found
significant improvements in social and emotional
skills, attitudes to learning and school, and
academic performance, compared with the
control groups.
In a small-scale study Morra, Parrella
and Camba (2011) found that emotional
comprehension develops with age. The capacity
of working memory (Baddeley’s model, as
discussed in Part 3 (Crossland, 2017)) itself can
be developed through teaching (Gathercole and
Alloway, 2008). Emotional comprehension is
considerably impacted by the development of
working memory through its decisive role in
transforming external stimuli into understanding
mental aspects of emotion: for example, the
reaction to an unusual noise. Sitting alone in the
daytime, the unusual noise leads to the body’s
heightened awareness of the senses and is
interpreted through working memory as curiosity.
An unusual noise in the middle of the night also
raises the body’s awareness and it is interpreted as
anxiety or fright.
These views corroborated the action
research (Crossland, 2010a), where advanced
skills teachers (ASTs) were convinced that
teaching learners group-working skills, using
a hierarchical framework developed and tested
in their classrooms, accelerated the emotional
development of the learners (greater detail will
be given in Part 4). The framework was found to
be a good match to Goleman’s model (1996) of
emotional intelligence.
In Crossland (2010b), the big picture model of
the brain showed that teachers must consciously
plan the emotional context for learning as a
prerequisite for effective cognitive development.
So, teachers who believe they are only involved
in teaching a subject must reassess this belief and
plan the involvement of both social and emotional
development to produce optimal learning. For a
range of evidence from nine different countries,
see OECD (2015) and the EEF Toolkit ‘Social
and emotional learning’ (+4 months progress)
(EEF, n.d.).
Cultural factors
Humans arrive in the world with a brain that is
predisposed to learn and store useful patterns
of experience that soon evolve into concepts
and expertise. In normal conditions, most
children are highly inquisitive and naturally
attentive to whatever they find interesting.
Instinctively, they attend to what humans around
them are doing. Human voices and faces have
an irresistible attraction; within a year most
children are expert at reading intonations and
expressions and copying and tuning their own
interactions accordingly.
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79
Figure 2
Optimal learning in schools – theoretical
evidence: Part 2 Updating PiagetCrossland
Cyclical Model of the Mind and Brain Development for School Aged Learn
(Adapted from Demetriou 2014)
Through networks of mirror cells, human
adulthood
brains are ‘hard wired’ to copy the actions and
intentions of others (Crossland, 2010b). So,
modelling by the teacher is a powerful way to
14
both introduce and consolidate learning. Learners
are very adept at picking up the hidden messages
from modelling, even if this was not the
secondary cycle of
education
principles
teacher’s intention. For example, non-specialist
teachers may inadvertently intimate by gesture
11
and demeanour that physics is analytical and
difficult; females in the teenage years, being
primary
cycle of
more attuned to emotional nuances, may pick up
education
concepts
6
this message more than boys and choose not to
age
study physics post-16.
Although each of us has a unique genetic
alignment
inheritance and an increasingly understood
flourishing
subcycle
subcycle
epigenetic inheritance, there is a great deal of
correlates with
correlates
with
evidence confirming the phenomenal flexibility
increased
increased speed
working
(plasticity) of the brain to evolve dynamically
of processing
memory
within a specific cultural setting. Learners all
capacity
bring a set of cultural understandings, perspectives
Figure 2 Cyclical model of mind and brain
and expectations to school.
development
for Mind
school-aged
learners
(adapted
Every school also has a cultural landscape
Figure 2. Cyclical Model of the
and Brain
Development
forfrom
School Aged Lea
Demetriou, Spanoudis
and Shayer,
2014)
(Adapted from
Demetriou
2014)
within and outside the community. The ways in
which learners learn cannot be separated from
these cultural contexts. So a clash between the
step forward in redefining the development of
learner’s culture and the school culture will
the mind and brain in terms of relevance to the
adversely affect learning. How the teacher
classroom (Figure 2).
in the classroom alleviates this is extremely
In terms of the general population, Demetriou
complex. There are the well-known problems in
(Demetriou, Spanoudis and Shayer, 2014)
teaching evolution to learners from families with
summarised neo-Piagetian research by identifying:
creationist views. There are similar problems
when teaching about rocks and minerals and
a number of powerful phenomena in intellectual
how they were formed, because these learners
development, including:
will have difficulty believing that the age of
1. Thought develops systematically from
the Earth is older than 5000 years. However,
birth to adulthood through a series of
for those individual learners, the resolution
cycles. Each begins with a new kind of
of this cultural conflict is a major factor in
representation at the beginning. There is
planning their cognitive development to produce
general agreement that there are four cycles,
optimal learning.
which start approximately at birth, 2, 6 and
11 respectively.
The developing mind and brain
2. Processing speed, working memory and
Demetriou’s latest thinking (Demetriou,
executive control develop systematically
Spanoudis and Shayer, 2015) builds on his
during this age range. Processing becomes
previously peer-reviewed publications that are
increasingly faster, working memory stores
based on substantial and long-term research
increasingly more information and executive
studies. He explores the relationship between
control becomes increasingly more focused,
the developing mind and the developing brain
flexible and efficient.
in terms of the general school population. The
3. The awareness of mental processes [such as
(difficult-to-follow) logical progression in the
metacognition: my connotation] becomes
detail of his research shows that this is work in
increasingly accurate and refined.
progress, but the model produced is an important
80
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Optimal learning in schools – theoretical evidence: Part 2 Updating Piaget
However, these phenomena do not develop
in direct and linear causal relationships, they
interweave within the cycles of development in
Demetriou’s 2015 theoretical model.
The mind and brain have synchronous
development, occurring over four major cycles.
Each major cycle has two further subcycles of
development. The model is based on equating
a large number of learners aged 4–16 on
processing speed, type of thought and workingmemory performance. Baddeley’s model of
working memory (as explained in Part 3) is
extremely important for teachers to understand
because of its central relevance to learning and
therefore its implications for classroom practice
(Crossland, 2010a).
In general, the first subcycle is a flourishing
of development related to an increase in brainprocessing speed. This flourishing is heavily
influenced by experiences and therefore drives
individual differences (discussed in Part 3).
The second subcycle is an alignment of the
flourishing experiences to each other and related
to increases in working memory that prepares the
brain for the next major cycle of development.
However, the cyclical influence of both working
memory performance and speed of processing
are themselves mediated by the phenomenon
of mental awareness. So working memory and
speed of processing may be correlated to the
subcycles but, as mentioned earlier, they do
not cause the changes: deeper mental processes
are involved.
Demetriou named these processes
cognisance, although he did not provide a clear
definition of the processes of cognisance. From
my perspective, cognisance is the dynamic
system driving development and must have
substantial genetic and epigenetic components
combined with first-hand experiences from
the environment as well as influence from the
individual self. Cognisance also drives learning,
operating substantially at the pre-conscious
level but with an added consciously organised
accelerating effect. The preconscious and
conscious mechanisms for accelerating learning
include metacognitive monitoring, control
and evaluation.
So, like Demetriou, I define metacognition as
happening during and after the action, which is an
expansion of Piaget’s definition.
Concepts cycle
For the majority of learners, the concepts cycle
continues developing through early secondary
school. Early primary school learners (from
6 years of age) begin the third major cycle of
development named ‘concepts’. It is characterised
by the flourishing of language-based mental
representations integrated into rule-based
concepts as the result of experiences. For
example, at the water table or sink at school or
in the bath at home, these experiences lead to the
rule in floating and sinking that heavy objects
sink, a single variable solution. The alignment
subcycle (from 8 years of age) is characterised
by an alignment of the concepts to produce
systematic logical inferences. For example, in
floating and sinking, the outcome depends on
the weight and in some circumstances the shape
(volume). However, they do not understand
how the two variables weight and volume work
in combination. Also, they cannot associate
the logic behind the inferences, so, although
they can explain problems in familiar concrete
circumstances, they cannot explain unknown
contexts such as floating a pin on water or a
floating cruise liner weighing 100 000 tonnes.
Learners are aware of the mental processes
involved in development and learning and they
are better at being metacognitive about others’
thoughts and actions rather than their own (to be
discussed in Part 4).
Principles cycles
This is the final major cycle and begins in
secondary school (from 11 years of age). At the
beginning of the flourishing subcycle only the
top 5% of the ability range are fully aware of
Archimedes’ principle for floating and sinking,
that is, the outcome depends upon the relative
densities of the entities involved. This subcycle
is characterised by a flourishing of abstract
concepts being integrated into higher-order
language or arbitrary (mathematical) conceptual
systems (principles) allowing each concept to
be viewed from another’s point of view and
evaluated for validity. Learners are aware of
logical constraints and principles. The alignment
subcycle (from 14 years of age to adulthood) is
when these abstract concepts are progressively
related to each other and reality. This leads
to higher systems of principles containing
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Optimal learning in schools – theoretical evidence: Part 2 Updating PiagetCrossland
counterintuitive logical relations, including an
explicit grasp of metalogic, that is, the study of
the properties of the logical systems. Learners
are able to construct valid and sound arguments,
for example analysing and explaining the
stability of direction for a spinning gyroscope,
explaining the control of blood glucose levels
by the α and β cells in the pancreas or using
Raoult’s law for explaining melting and
boiling points.
Demetriou et al. (2015) found that the
‘type of thought was more closely related to
age than working memory, performance or
processing speed’. So, in development terms,
the parts of working memory he tested did not
have a great influence on development. To be
fair to Demetriou, he states in the discussion
section that much more research is required. For
example, he did not collect data for all parts of
Baddeley’s model of working memory, such as
the development of the spatial aspects of visual
working memory. There are other parts of working
memory that it is not yet possible to test because
there are no generally accepted methods for
testing all of the distinct parts (discussed further
in Part 3).
Demetriou’s model of development may
not yet be the complete story but it is of great
interest to teachers in understanding the broad
development changes taking places in the learners
they are teaching.
Summary
Following the historical fate of many theories,
Piaget’s ideas are not being thrown away
but brought into the 21st century. Piaget was
correct in identifying different types of thinking
accumulating with age and experience. However,
his original idea about whole-brain stages of
development is not fully compatible with the
current evidence from cognitive psychology
and neuroscience and has been replaced by
the concept of cycles of development. In the
general population, these cycles are statistically
significant periods of optimal performance leading
to spurts in transitions to new types of thinking
and performance.
Many aspects of Piaget’s theory of learning
are still important for teachers in order to improve
their classroom practice. The conclusions so
far have been based on population-related
82
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statistics with implications for providing
increased opportunities for optimal learning
in the classroom. In addition to those items
summarised at the end of Part 1, recent evidence
has added that:
l reshaping of the brain and mind continue their
l
l
l
l
l
cyclical development from early school age,
throughout puberty to the mid-20s (Demetriou
et al., 2015) (educational and curriculum
implications are covered in the remaining
parts of the series);
as learners grow older they add more advanced
types of thinking within specific contexts
(Demetriou et al., 2015);
planning emotional learning is a vital
prerequisite for optimal lear ning (EEF Toolkit
‘Social and emotional learning’ (+4 months
progress), EEF, n.d.);
the way learners learn is difficult to separate
from their cultural heritage;
an essential prerequisite when planning tasks
for optimal learning to accelerate cognitive
development is the encouragement of social
construction (Vygotsky, 1978) through
discussion in collaborative groups;
good teachers make a difference to the
rate of cognitive development (Demetriou
et al., 2015), and for Hattie (2015) the most
important barrier to school improvement is
the variability in effectiveness of teachers
within the same school. The most important
factor for improving achievement is when
teachers increase the range of their styles of
teaching (Hattie, 2015: 16). So far, this series
of articles is asking teachers to experiment
with adding:
 a Piagetian constructivist approach;
 cognitive conflict (see Part 1) not
undermined by teacher intervention that
explains/tells the solution or the method
for reaching a solution;
 collaborative group work (Hattie, 2015:
13) using Vygotsky’s social construction
with its learner mediation and exploratory
talk (EEF Toolkit ‘Collaborative learning’
(+5 months progress), EEF, n.d.).
Acknowledgement
I am grateful to Michael Shayer, King’s College
London, and Sue Crossland (MFL teacher) for
commenting on an earlier draft.
Crossland
Optimal learning in schools – theoretical evidence: Part 2 Updating Piaget
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