Conservation refers to the idea that “certain physical characteristics of objects remain the same”, despite their perceptual differences (Berk, 2009).
In Piaget’s theory on conservation, children gradually acquire various conservation abilities, such as understanding the conservation of numbers, weight, and volume to name a few. Piaget asserts that until they successfully acquire these abilities, they have no real understanding that quantity remains unchanged despite perceptual changes of the objects with respect to their appearance.
This paper aims to reconsider the accuracy of Piaget’s assertion, which is supported by alternative views of other theorists. Piaget’s conservation task goes like this. Children were first shown two objects that were both equal in quantity and appearance. They were then asked to judge whether the objects were still quantitatively equal after having seen one of the objects being transformed, where it stays quantitatively unchanged while its appearance is altered.
Piaget’s evidence on children’s acquisition of understanding conservation was based on the their verbal explanations, which demonstrates their understanding of– (a) reversibility (“If you transform it back to its original state it will be the same”), (b) compensation (“Reduction in one aspect is compensated for in another”), (c) identity (“Nothing was added or subtracted, so it is the same”) (Elkind, 1967).
The Review on Gender Differences In Mathematical Understanding In Children part 1
Gender Differences in Mathematical Understanding in Children The issue of gender differences in mathematics has been debated since 1970s. Then the numerous research projects investigated the nature and extend of the differences between the achievements of boys and girls and proposed different kinds of reasons of such disparities. In my essay I will continue the discourse on mathematics and gender ...
However, other theorists such as Elkind disagreed with Piaget. Piaget and Elkind had different views on conservation.
According to Elkind (1967), conservation tasks involves two types of conservation, identity conservation and equivalence conservation. Identity conservation refers to equivalence between the before (V) and after (V1) state of the variable object. Equivalence conservation refers to equivalence between the standard (S) and variable object (V1).
Elkind (1967) argues that Piaget’s discussion of conservation only deals with identity conservation as it only revolves around reversibility and compensation.
For example, in the liquid conservation task, Piaget emphasised how children understood the quantity equivalence between liquid in a tall, narrow glass and liquid in a wide, shallow glass, by recognising that change in its height was compensated by a change in its width (compensation) (Berk, 2009).
What Piaget failed to explain was how children knew the equivalence of the two immediately present objects (S & V1).
In the form of verbal explanation, a child who fully solved the task would say “Since S was equal to V, and transformation of V to V1 did not change anything, S will be equal to V1” (Elkind, 1967), therefore exhibiting equivalence conservation. Piaget also assumed that identity and equivalence conservation acquisition occurs simultaneously in time. Other theorists argued that identity conservation emerges prior to that of equivalence conservation.
For example, children could complete the task of adjusting the height of the water level of a container to match that of another container of different dimensions, at a time when they have yet acquired equivalence conservation (Elkind, 1967).
At this stage, children had an incomplete concept of liquid quantity, which was based only on the water level. In Feigenbaum and Sulkin and Frank’s experiment, a 4-year-old could recognise that quantity was unchanged when they did not see the variable object’s transformation.
The Essay on Piagetian Tasks: Number Conservation
I interviewed both my children separately with the conservation of number tasks. I used 14 pennies; 7 pennies in 1 row and the other 7 pennies in a row spaced farther apart than the first row of pennies. First, I interviewed my 4-year-old daughter; I asked her if there are the same amounts of pennies in both rows. She did not ask me anything she just began to count. After she counted both lines, ...
However, if they did, their anticipation of water level conflicts with the outcome as they anticipated the water level to remain unchanged because nothing was added or removed. This caused them to be fooled into making an incorrect judgement by the perceptual illusion and hence fail to recognise conservation, up until they understand compensation (Acredolo & Acredolo, 1979), like what Piaget had proposed.
Another example is when children were asked whether the clay sausage (transformed from a clay ball) weigh more/ less/ equal to the standard clay ball, they might think that the apparent increase (perceptually) in weight of the sausage is compensated for by the larger size of the ball, when the size was actually constant (Elkind, 1967).
Clearly, children failed to show an understanding of the conservation of weight despite knowing that they were quantitatively unchanged.
Hence, identity conservation is insufficient for passing conservation tasks which assess equivalence conservation. Therefore, children do have some degree of understanding of quantity constancy before they fully acquired conservation abilities, though their lack of understanding of compensation confuses and obstructs them from the correct evaluation that the objects were quantitatively equivalent.
In all, theorists disagreed on Piaget’s point on children’s inability to recognise quantitative constancy when there was change in appearance, assuming that they did not see the transformation. However, even if they do have the ability, they still could not grasp the concept of equivalence conservation involving other abilities such as understanding conservation of weight, hence agreeing with Piaget. Theorists agree with Piaget on children’s gradual acquisition of conservation abilities as well.
For example, in the course of learning number conservation, it is important to note that their concept of quantity emerged before their concept of conservation, and was based on perceptual cues such as height and length (Zimiles, 1963).
As they learn how to count and other mathematical skills, they add on to this original concept of quantity and start to rely more on these skills for better accuracy. Therefore, at least in this concept, Piaget’s idea was unanimously agreed upon by other theorists.
The Essay on Two Theories Of How Children’s Understandings Of Mathematical Develop
In this task I am going to describe Jean Piaget’s and Tina Bruce’s theories about how children’s understandings of mathematical develop. Piaget Jean Piaget’s research led him to believe that we develop by taking in information, which is then processed by the brain and as a result of this our behaviour changes. He started that there are staged of development that children move through. The ages are ...
In conclusion, theorists do agree with Piaget in some of his ideas on conservation, such as children’s gradual acquisition of conservation abilities, and that for a complete understanding of conservation (comprising of both identity and equivalence conservation), children must fully grasp all the various types of conservation such as weight and number. There was also some debate on how Piaget discussed his theory of conservation, such that he explains only using identity conservation by stating children conserve by comparing V and V1, which only shows their understanding of compensational changes within one object (V and V1).
Elkind (1967) disagreed on the grounds of the difference between identity and equivalence conservation, both of which are needed to pass Piaget’s conservation task. Equivalence conservation is based on a child’s understanding of the relations between the objects that are immediately present, not the relations between the same object before and after transformation. Nevertheless, Piaget’s theory still serves as a useful guide on children’s cognitive development, although it has been proven that it is not completely accurate.
