4 stages of development

Sensori-motor period (birth – 2 years)

As discussed in Flavell’s Developmental psychology of Jean Piaget (Flavell, 1963), there are six sub-stages within the sensori-motor period. Piaget studied the sensori-motor phase with his own three children.

Stage 1 and 2 (0-4 months) In the first two stages, the child shows reflexes provided at birth and some inter-coordination of these movements as he progresses towards 4 months.

Stage 3 (4-8 months)
The child begins to show attention towards objects, people, and occurrences outside of their own body.  In this stage, the infant begins to show intentional movements and goal-directedness.  As we saw in week 6’s video (Piaget’s Developmental Theory: An overview, Davidson Films), the baby in stage 3 was interested in the set of keys, but when hidden under the blanket she began to cry, unable to think to look under the blanket.

Stage 4, (8-12 months)
In this stage the child is building on their intentional movements, and goals, but the child is simply building upon their habitual movements shown in stage 3. Stage 4 can be differentiated from the previous stage by looking at a game of peek-a-boo.  A baby of 6-7 months will watch someone appear and disappear out of sight several times without searching for where they have gone.  It is not until they reach stage 4 that they will begin to crawl and search for the hidden person, or in other cases objects.

Stage 5 (12-18 months)
This stage shows the child beginning to experiment with their own environment and “pursue novelty for its own sake” (Flavell, 1963).  This means the child is now interested in objects, and people simply because it is like they are seeing them for the first time. Objects now take on a new meaning and seem new to the child.

Stage 6 (18-24 months)
During stage 6, “the child begins to make internal, symbolic representations of sensory-motor problems, inventing solutions by implicit rather than explicit trial-and-error behavior” (Flavell, 1963).

Pre-operational stage (two-seven)

Within this period there are three sub-stages.

Beginning of representational thought (2-4)

Piaget refers to this period as preconceptual intelligence (Piaget,1950) and describes this as the first beginnings of reasoning. Piaget describes preconepts as “the notion [with] which the child attaches to the first verbal signs he learns to use” (Piaget, 1950. p. 140). This period is thought of being when language first begins to appear, but it may begin earlier or later than 2 years of age.

Simple representations or intuitions (4-5.5 or 6 depending)

Piaget describes this next stage as intuitive thought (Piaget,1950) and describes this stage as what a child goes through when they expand and go from preconcepts to actual operations. He very clearly notes here that there is the absence of logic. Cohen makes reference to this absence of logic when he refers to pink cows in the example below

Articulated representations or intuitions (5.5 or 6-7)

There is only a very subtle difference between the simple representations or intuitions phase and the articulated representations or intuitions phase.  A child in the simple representation phase will go about tasks asked of them without making any connections.  The example Piaget references is the asking a child in the simple representations versus the articulated representations to put a line of blue counters after a line of red counters has been put on a table.  The child at 4-5.5/6 will put their blue counters in a simple line without establishing a connection between the red and blue.  A child of 5.5-7 will put their blue counters opposite of the red establishing an identical line and “connecting” the two, but an operation has not been acquired as Piaget states, as all you need to do is move the counters closer together or further apart for the 5.5-7 year old child to no longer believe in their equivalence.

Part of what has yet to occur in the pre-operational stage is the ability to recognize what Piaget’s referred to as transitivity:

Example: 

“A child will grasp that:

If there are brown cows;
If there are black cows;
There are more cows than black cows

And

There are more cows than brown cows.

The same would go for pink cows, since once of the lessor pleasures of formal logic is peppering equations with absurdities. (Cohen, p. 38).”

The above analysis would confuse a child between the ages of 4-7.  Piaget’s findings, however, indicated that this example regarding the number of cows would no longer confuse a child between the ages of 6-7 and beyond as they are now able to recognize transitivity.  If the relationship holds between the 1^st and 2^nd element (brown and black cows), the 2^nd and 3^rd element (black cows and total cows) then the relationship must hold between the brown cows and the total cows.

This is the central theme of this stage of operations in Piaget’s mind. “It is the failure of children to grasp logically necessary relationships that Piaget often focused on. 2x 3 must equal 3 x 2.  There cannot be more brown cows than the totality of cows. The inability to order relationships between the part and the whole, between all and some, eludes children at this stage” (Cohen, p. 42)

It was in this 2nd stage of development that Piaget focused on irreversibility, conservation, and egocentrism.  Egocentrism in children, as part of Piaget’s developmental stages, is central to this stage of development as Piaget believed children still lacked the ability to see other points of view, which hampered them from beginning to see the bigger picture.  Egocentrism prevents children from fully learning from adults, as such educators want to take this into consideration in the passing of knowledge to children.

Concrete operational stage (7-12)

It is Cohen who sums us this stage, and differs it from formal operations by stating:

“Piaget’s choice of labels remains important here.  Concrete operations differ from formal operations in that they handle the here and now.  The child can manoeuvre the logic of the situations in front of him, but he cannot envisage myriad possibilities.” (Cohen, p.44)

Children now have the ability to recognize groupings and equivalency even with objects of different heights, widths etc. The ordering of the objects is no longer a problem for children. They understand that regardless of whether you take 2 x 3 or 3 x 2 you will still yield the answer of 6.

One of Piaget’s most famous experience is providing a child with different liquids.

“One study dealt with giving a subject four numbered bottles, each holding a colourless fluid. No. 1 was a catalyst; no. 2 was water; no.3 was oxygenated water; no. 4 was another catalyst. There was a fifth bottle, labelled ‘g’ and a pipette. Mixing 1, 3, and ‘g’ produced a yellow liquid.  Subjects were then shown one bottle with a mixture of 1 and 3 and a second bottle which was simply bottle no. 2. Into each of these bottles, some drops of ‘g’ were poured.  1 + 3+ ‘g’ gave yellow; 2+ ‘g’ remained colourless.  The children were then instructed to recreate the yellow liquid.”

The result of this study illustrated to Piaget that a children in concrete operations stage (a typical 7 year old was chosen) would eventually produce the yellow liquid, but it was through trial and error.  Once the child eventually did recreate this yellow liquid he was unable to state exactly how he had done it demonstrating a lack of problem solving skills which do not arise until the formal operations stage.

Formal Operations (12 and up)

This experiment was also done with a 13 year old child.  As referenced in Flavell (Flavell, 1963. p.207) the 13 year old begins by trying each liquid 1-4 with g.  When this does not work he immediately determines that you need to combine g with not just one liquid but potentially two or three of the liquids.

“Maybe you have to mix them [he tries I x 2 X g, then 1 x 3 X g]- It turned yellow. But are there other solutions? I’ll try [1 x 4 X g; 2 X 3 X g; 2 X 4 X g: 3 X 4 X g; with the two preceding combinations this gives the six two-by-two combinations systematically]. It doesn’t work.” (Flavell, 1963, p.207)

When he determines all of the possible solutions he is still not content.  He begins to wonder what is liquid 4, and what is liquid 2?

The child in this experiment above is not focused solely on what actually occurs, but is hypothesizing on what the liquids are, what they mean, and what are all of the different possibilities.  The 7 year old in the concrete operations is very focused on the end objective of turning the water yellow with no care as to why or how this is occurring, whereas, the 13 year old in the formal operations is interested in all of the combinations that could turn the water yellow.

It is important to note the limitations of the child in the concrete operational stage as discussed by Flavell (1963):

1. The child’s thinking is tied to the immediate and they are focused solely on the concrete objects in front of them.
2. It is because the child is tied to the here and now that they must go through what Flavell describes as “vanquish[ing] the various physical properties of objects and events (mass, weight, length, area, time, etc.) one by one because his cognitive instruments are insufficiently “formal”” (Flavell, 1963, p.204).  This limitation and interpretation of Piaget’s work becomes important as the child going from concrete operations to formal operations will not grasp all of the concepts of mass, weight etc. at once.  They may begin to understand the concept of mass, but still struggle with the concept of length etc. suggesting that children do not progress from one stage to another in a fluid motion, but may regress to prior stages or will be in-between different stages.
3. The third limitation is that the child is unable to integrate their own knowledge to solve problems that may involve more than one variable. They have not consolidated their knowledge into one system, but are rather operating using numerous subsystems, therefore missing links between their own knowledge.

These limitations are shed as the concrete operations child makes their way into the formal operations stage. Piaget describes the formal operation’s stage in The Principles of Genetic Epistemology as “it is this power of forming operations of operations which enables knowledge to transcend reality, and why by means of a combinatorial system makes available to an infinite range of possibilities while operations cease to be restricted, as are concrete operations, to step-by-step construction” (p.47)

What stage are you in?

25 blue and 25 red trinkets are put in two buckets as shown below. 5 blue trinkets and 5 red trinkets are then taken from each bucket and put in the opposite colour’s bucket.  The buckets are then shaken up.  If you then randomly take 5 trinkets from one bucket and 5 trinkets from the other bucket, this leads us to a the question which bin has more of the other colour?