Jean Piaget was the leading psychologist to discover and
create a systematic study of cognitive development in children. Prior to this
discovery, it was thought that children are less knowledgeable thinkers than
adults. Through his findings, Piaget came to the conclusion that children think
and reason differently at four specific periods in their lives (Piaget, 1936). These
periods are, according to Piaget, structured from birth to 11 years onwards. Piaget
(1932) believes that the ability to learn any cognitive content is always
related to a child’s stage of intellectual development. Children who are at a
certain stage cannot be taught concepts of a stage higher than their current
intellectual stage. Much like Bloom’s Taxonomy, the child needs to follow each
stage in order to progress to the next stage and eventually the desired outcome.
Piaget concluded that children are inherently born with some existing schemas
(knowledge) and construct an understanding of the world around them. When new
information arises, and according to their specific developmental stage, they
reorganise their new schemas to fit in to what they already know. This process
is what Piaget coined accommodation and assimilation (Piaget, 1936).

Assimilating causes the individual to develop new outlooks,
rethink what were once misunderstandings, and evaluate what is important,
ultimately altering their perceptions. Accommodation, on the other hand, is
reframing the world and new experiences into the mental capacity already
present (Teachnology, d.u.).

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Piaget (1958) believed that problem solving
skills cannot be taught, they should be discovered. In order to discover these
problem solving skills, assimilation and accommodation require an active
learner.

Individuals conceive a particular fashion in which the world
operates. When things do not operate within that context, they must accommodate
and reframing the expectations with the outcomes. It is by adapting to things
that thought organizes itself and it is by organizing itself that it structures
things (Piaget, 1936:8).

According to Lev Vygotsky (1978) Piaget
failed to take into account the effect that cognitive development may be
influenced by a social and a cultural setting. Piaget’s studies show that
thought precedes language, however, Vygotsky (1978) argues that;

The development of language and thought go
together and that the origin of reasoning is more to do with our ability to
communicate with others than with our interaction with the material world
(McLeod, 2015:6).

This
brings us to discuss the movement of social constructivism. The leading
theorist of Social Constructivism is Lev Vygotsky. He not only criticised
Piaget’s work but more importantly developed his theories further.

Social constructivism emphasizes the
importance of dialogic space, where communication is not the transfer of
knowledge, but the interpretation of knowledge within a community of learners (Khourey-Bowers, 2006: p.u.).

Lev Vygotsky (1952) strongly believed that learning and social context
work hand in hand. Unlike Piaget, Vygotsky argued that all cognitive function
begins as a product of social interactions. The learner, as part of a social
group, is integral to the theory of social constructivism. Learning is an
actively engaging process, they share experiences and this emerges through
group interaction (McMahon, 1997; Derry 1999). Linking this back to what Piaget
would say is the interaction of assimilation and accommodation. However,
Vygotsky believes this process is achieved through dialogue. The learners match
new ideas to their existing ideas and then adapt it to make sense through
verbal discussion. Not only did Vygotsky emphasise the importance of a social
setting but he believe a cultural background also influences a child’s
learning. According to social constructivism, the culture in which a child is
brought up in gives much of the content of their knowledge. Culture provides
children with the ability of what to think, and how to think. This is guided
and facilitated by adults which influence a child’s language, social context,
cultural history and modern electronic sources (Draper, 2013). Vygotsky
introduced two developmental levels that show the process of learning within an
individual, he called this the Zone of Proximal Development (Vygotsky 1978). There
seem to be various arguments of what Vygotsky explicitly meant when he
described the Zone of Proximal Development (ZPD), but for the purpose of this
discussion we will infer that Vygotsky meant there is a direct correlation
between what a child learns and how it is being taught by a teacher. Vygotsky
described the ZPD as

The
distance between the actual development 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).

Vygotsky believes that the desired outcome of
learning takes place at the level of potential development. What a child or
learner already knows at the actual development is holding the child back from
learning anything new, so with the guidance of an adult or more knowledgeable
other a learner is able to progress to the potential development stage while
all taking place in collaboration with peers in a social setting.

Jerome Bruner, another prominent constructivist also emphasized the
social nature of learning and attaches great
importance to language in determining cognitive development. He, much
like Piaget and Vygotsky, believed that other people should assist a child or
learner in developing skills. However, he called this model scaffolding. There is a very close relationship
between scaffolding and the zone of proximal development. Bruner (1961),
believed that scaffolding exists between the process of actual development and
potential development with the guidance of a more knowledgeable other.
Therefore, scaffolding takes place in Vygotsky’s Zone of Proximal Development.

Scaffolding refers to the steps taken to
reduce the degrees of freedom in carrying out some task so that the child can
concentrate on the difficult skill she is in the process of acquiring (Bruner,
1978: 19).

Bruner likens his scaffolding model to
scaffolding on a building. It is there to aid the builders but eventually it gets
taken away once the desired outcome has been achieved. Scaffolding is temporary
but necessary. Learners are dependent and need help from a more knowledgeable
other but once the desired outcome has been achieved, learners become
independent and are then placed in groups where they can assess and aid each
other in accomplishing tasks. Vygotsky’s theory of social learning has been
expanded upon in recent years by Douglas Barnes and Neil Mercer.

Douglas Barnes believes that as we grow up and learn, we relate what we
are learning to what we already know. We evolve our current thoughts or schemas
to include new thoughts based on previous thoughts. Barnes calls this “working
on understanding” (Barnes, 2008: 1). Working on understanding can be likened to
Piaget’s ideas of assimilation. Accommodating new ideas is daunting, one simply
does not just accept a truth or idea. Barnes believes the best way of working
on understanding is often through talk, because talking makes it easy for us to
arrange or rearrange new ways of thinking from what we already know. If
something does not seem quite right as you are saying it, or hearing it, one
would deem it inadequate, or hopefully, much like a puzzle piece, one would
rearrange it until it makes sense and ‘fits’ (Mercer and Hodgkinson, 2008). Barnes
states that there are two forms of talk. They are exploratory talk and presentational
talk (Barnes 1976/ 1992);

“Exploratory
talk is hesitant and incomplete because it enables the speaker to try out
ideas, to hear how they sound, to see what others make of them, to arrange
information and ideas into different patterns … in presentational talk the
speaker’s attention is primarily focused on adjusting the language, content and
manner to the needs of an audience” (Barnes 2008: 5).

Barnes believes that there are numerous ways to come to an understanding
of an idea but through talk it is easier and impermanent. There is much leeway
to make mistakes and reorganise your thought in your head and then verbalise
it. It is not finite where it is on say, paper. There is room for mistakes and
of course this could bring its downfalls. Learners not wanting to embarrass
themselves may not engage in exploratory talk, but I will discuss more of this
later on. Exploratory talk is quite literally exploring thought, your own and
others, by way of verbal communication. One would process, sort and organise
ideas to accommodate a new idea. Exploratory talk is much more advantageous
than presentational talk. Presentational talk lends itself to the idea that you
are talking to express the correct answer or idea. Barnes claims that some
teachers rush into presentational talk before they have had the chance to work
on understanding through exploratory talk. Short answers, as given in
presentational talk does not allow the learner to gain a deeper level of
understanding.

Thinking Together (Mercer et.al. 2012), a dialogue-based
approach integral to the development of children’s thinking and learning,
suggests that there are three ways of talking and thinking; disputational,
cumulative and exploratory: Disputational talk is identified as short answered,
disagreements with little to none collaborative decision making. Few attempts
are made to pool resources together to make suggestions as well as no constructive
feedback given to each other. Cumulative talk on the other hand, is where there
is more agreement but still little to none explanation of answers or ideas. Cumulative
talk results in agreed answers and no constructive criticism is involved.
Exploratory talk, however, when manifested in a secure environment involves,   

Partners
engaging critically but constructively with each other’s ideas … Partners all
actively participate, and opinions are sought and considered before decisions
are jointly made. Compared with the other two types, in Exploratory Talk
knowledge is made more publicly accountable and reasoning is more visible in
the talk (Mercer et al, 2012: 2).

Thinking back to Vygotsky’s theory of the ZPD, Neil Mercer (2002) introduced
the idea of an intermental development zone (IDZ). This notion relies on the
fact that what is being learned, and whether this was achieved or not, is
dependent on all parties involved creating, maintaining and sharing knowledge
with a common frame of reference in their learning activity. Along with Vygotsky,
Mercer believes collaboration, specifically using exploratory talk, is what enables
a learner to fully access and achieve a learning outcome. Exploratory talk,
Mercer suggests,

Represents
a way in which partners involved in problem-solving activity can use language
to think collectively — to ‘interthink’ effectively, with their activity
encapsulated in an intermental zone of their own construction (Mercer, 2002:16).

Once all partners have achieved interthinking, they are then able to
achieve the intramental zone of development. I see it as very similar to
Vygotsky’s ZPD where one begins with actual development then progress to the potential
development. Once one interthinks, they are then able to intrathink.

These studies have
not gone unnoticed, according to the DfE National Curriculum (2014), pupils
should be taught to:

Listen and respond
appropriately to adults and their peers, ask relevant questions to extend their
understanding and knowledge, articulate and justify answers, arguments and
opinions, give well-structured descriptions, explanations and narratives,
participate actively in collaborative conversations, staying on topic and
initiating and responding to comments, use spoken language to develop
understanding through speculating, hypothesising, imagining and exploring ideas,
participate in discussions, consider and evaluate different viewpoints,
attending to and building on the contributions of others (DfE, 2014).

However, the DfE fail to recognise how this should be achieved.
Researchers have spent many years and found ways to enable successful learning
which, most importantly, involve exploratory talk as the heart of higher order
thinking.

For a
teacher to teach and a learner to learn, both partners need to use talk and
joint activity to create a shared framework of understanding from the resources
of their common knowledge and common interests or goals (Mercer, 2002: 143).

Robin Alexander (2000; 2004), who coined the term ‘Dialogic Teaching’ has
developed a strategy to ensure teachers are specifically trained according to
four frameworks. Once these teachers have been trained in ‘dialogic teaching’
they are then able to aid a learner in developing a higher order of thinking
and articulacy. Thus improving pupil engagement and attainment (Alexander 2015).
These strategies enable learners to reason, discuss, argue and explain their
thought process and opinion, rather than just respond to a closed-ended
question. Alexander builds on previous researchers to suggest a
cross-curricular pedagogic model. Alexander (2004) suggests that
dialogic teaching is indicated by certain features of classroom interaction
such as:

Questions are structured so as to provoke
thoughtful answers … answers provoke further questions and are seen as the
building blocks of dialogue rather than its terminal point; individual
teacher-pupil and pupil-pupil exchanges are chained into coherent lines of
enquiry rather than left stranded and disconnected (Alexander, 2004, p. 32).

One of Mercer’s main focus was
specifically on interthinking between learners thus achieving intrathinking
through exploratory talk. He did not place importance on the teacher’s type of
talk thus aiding students to achieve desirable outcomes. Mercer acknowledged
that a teacher needs to facilitate and guide a collaborative discussion,
however, there was no indication that the teacher plays a crucial role in teaching
learners how to use talk to learn. Alexander introduces the dialogic teaching
framework and expresses the need for;

Every
teacher to develop a broad repertoire of talk-based pedagogical skills and
strategies and to draw on these to expand and refine the talk repertoires and
capacities of their students (Alexander 2017: 3).

The dialogic teaching
framework lies on four interlocking components; these components are, justifications,
principles, repertoires and indicators. For the purpose of this essay, a quote I
believe so eloquently describes dialogic teaching can be summed up as,

If an answer does not give rise to a new
question from itself, it falls out of the dialogue. (Bakhtin 1986: 168).

Understanding
that Dialogic teaching is able to be applied across the curricular sheds light
on the ability of teachers to create a classroom rich in dialogue to aid
students in developing higher order thinking in any subject. As I previously
mentioned, this atmosphere needs to be a safe and confident environment.
Learners will unlikely give opinions and reveal their thoughts if they feel
they will be judged. Bowkett (2015) believes that,

Two of the greatest inhibitors to the
development of effective thinking are: children’s fear of the wrong answer …
and teachers doing the children’s thinking for them (Bowket, 2015: xii).

Dialogic
teaching is evident in subjects such as english, drama and debating, however,
applying it to the sciences or mathematics could be highly beneficial. A key
theme throughout Mathematics Explained
for Primary Teachers (Haylock 2014) is the importance of the development
and correct use of mathematical language. As a teacher, not only should one be
able to teach a specific unit of work but one should also teach children the vocabulary
and how to articulate themselves when expressing an opinion. Haylock goes on to
say,

Mathematics is effectively a language,
containing technical terminology, distinctive patters of spoken and written
language, a range of diagrammatic devices for organising and presenting data
and a distinctive way of using symbols to represent and manipulate concepts
(Haylock, 2014: 16).

A lot of
research suggests that mathematics is simply a rote-learning subject. A learner
does not make cognitive connections with existing networks of information and
does not seek to understand new material (Haylock 2014). The learner would
simply rather learn through memorisation. This thought needs to change and
Haylock (2014) suggests a meaningful-learning mind set will enable the learner
to want to understand what is being taught and to make cognitive connections
between existing schemas. Should a teacher incorporate Mercers’ Thinking Together, or Alexanders’ Dialogic Teaching, this will enable a
learner to gain a higher level of understanding that can be used across the curricular.
Thinking collaboratively, with peers, guided by a more knowledgeable other who
is equipped with specific questioning skills, is the perfect recipe for a
learner to discuss ideas and opinions, and, if necessary to accommodate new
ideas and eventually come to an independent understanding of what is being
taught. This gives the learner confidence knowing that he came to the
conclusion by himself, with full knowledge that all possible ideas have been
discussed and debated.

I conducted my own study with a small group of
children in Year 2. The study was based upon a unit of mathematics that was
taught in class. Seven students of varying ability were taken out of the lesson
and asked a question based on the unit they were learning. I wanted to see how
they would interact with each other and find a solution to the question. Initially
children were hesitant to discuss their ideas with me, however, after some prompting,
the conversation started to flow and all three different types of talk (Mercer
et al 2014) started to show. Appendix ___ shows the children working in a group
to answer the question: Does two odd
numbers added together give an even number? Even though the children are
very comfortable with each other, initially they are not able to demonstrate constructive
criticism, backed with their own idea, for fear of insulting someone. They do, however,
display confident disputational talk;

C5: Look, with the Numicon,
if you have a 9 and 9, you find the number and its 19 which is, uh, even number

C6: No

C1: No

C6: That’s an odd
number

C5: Yeah I knew that

Child 5 confidently gives an answer and when is
told by more than one other child that he is wrong he quickly agrees with them.
Child 5 was embarrassed and mostly kept quiet for the rest of the discussion. An
example of cumulative talk; this time the question was does three odd numbers added together give an even number?

C3: How about 3 plus 3
plus, um, plus 3… that’s 9

C1: Oooh…

C1: I know that’s never
true

Child
1 initially doesn’t have an opinion and after hearing what child 3 has to say child
1 then agrees. Child 1 does not give an explanation of why she has chosen to
agree. Child 3 on the other hand shows exploratory talk, he uses pauses and you
can see he is trying to work it out in his head and then verbally express his
answer with explanation. Another example of exploratory talk;

C4: I think it’s
sometimes true because 5 add 9 add 1 is, umm, no that’s not right

Exploratory
talk is shown here. The child is comfortable giving an opinion as well as
verbally expressing that he was incorrect. The environment shows that this
level of confidence has been achieved. This is the type of talk that teachers
nowadays are looking to find. They want children to explore different ideas
with each other. I must admit I was not the best facilitator in the discussion
as I could have been. Had I used Alexander’s strategy of Dialogic Teaching I would have been able to prompt the children
more using detailed strategies as well as ending up with a variety of
exploratory talk that would have mostly be led by the children themselves.

In the second study I conducted (see appendix
___), there were three less children than the first, however, there seemed to
be more confidence within the group as they collaboratively worked together.
The question, what holds more, 4 packets
with 5 cupcakes each or 3 packets with 10 cupcakes each, was discussed.
Evidence is shown of exploratory talk;

C2: It’s definitely 3 packets with 10 in
each

T: Why?

C2: Because… three… wait, what was the
other one?

T: 4 packets of cupcakes with 5 in each
packet

C2: 5 add 5 is 10 and add 2 more 5s is 20.
But 10 add 10 add 10 is 30

Child
2 immediately gives an answer before anyone else, and when asked to explain,
loses confidence and has to think about it. Once child 2 has thought about why
he said what he said he is able to explain himself. Cumulative talk transpires
when child 3 agrees;

C2: 5 add 5 is 10 and add 2 more 5s is 20.
But 10 add 10 add 10 is 30

T: Is anyone working it out a different
way?

C3: I think, I agree with C2 because 10 is
bigger than 5

T: That is true, 10 is bigger than 5 but
there are 4 packets and with 10 there are only three packets…

C3: So 5 add 5 add 5 add 5… 4, so that is,
40

C3: And then just 10

C3: Three packets of 10 is 30

Child
3 is agreeing with child 2 but fails to justify his answer. Child 3 is showing
exploratory talk but he is not making connections cognitively. I question
further to see if child 3 is able to adjust his thought process;

T: And
then 4 packets of 10 or 4 packets of 5?

C3: 4
packets of 5

T: Equals
how many?

C3: 40

C1: I
think three packets of 10 are bigger than….. 4 packets of 5

T: And
what is 4 packets of 5? C3 says its 40

C1: 4
packets of 5 are… can you wait a minute while I work this out?

C4: I
think 4 packets of 5 are 20.

Child
3 does not see the error in his ways. Later on I sit with child 3 and ask him
to show me his working out with physical objects which he then comes to the
conclusion that four packets of five cupcakes equals 20 cupcakes. It is
interesting to note that when a question is rephrased child 4 finds it difficult
to adjust to the new phrasing of the question;

C1: 4 packets of 5 are… can you wait a
minute while I work this out?

C4: I think 4 packets of 5 are 20.

T: How did you work that out?

C4: Because 5 plus 5 is 10 and 10 plus 10
is 20

T: Okay, so you are adding 10 twice
instead of 5 four times?

C4: whoa … it’s tricky

C1: The biggest pack holds 30 and the
other one is 20

It is
comforting to see that exploratory talk is evident in the group and can be
shown when child 1 asks for some thinking time and then comes back with an
answer in a very confident manner. Although the children are very comfortable
with each other, they do not work collaboratively with each other. They work
alongside each other, give an opinion, and are happy to leave it at that.
Overall, the study does not show that the children developed higher order
thinking with the exception of child 1.

Recent studies emphasise keywords such as
collaboration, community, collective thinking and democratic engagement
(Peacock 2016). The idea is that working together one is able to achieve a
higher level of thinking than the level that is achieved when working alone. Working
collaboratively relaxes the learning environment and allows for misconceptions
to be debated and discussed. A learner no longer suffers in silence if he or
she does not understand something. When working in a group you are more likely
to hear a thought that you can agree with and comprehend. You are also able to
see other points of view. Mathematically, working collaboratively is highly advantageous
as you are able to see that there is usually more than one way to figure out an
answer. Luke Rolls, a teacher at the University of Cambridge Primary School
says;

When
we stop cutting off conversations and really listen, pupils seem to follow suit
and their ideas can be truly heard and responded to. As the dialogue develops,
what often becomes evident is how pupils’ perspectives cab surprisingly be
different within the class. This communicates an important aspect of learning
maths; being open-minded and looking onwards. As students and as teachers, our perspectives
do not limit us to that which we are already familiar with but open up
possibilities of new ideas, new thinking and new understanding (Peacock 2016:
38-39).