3. INTRODUCTION
• Laid foundation for Cognitive Psychology
• Focus not only on the external behavior of the learner, rather
importace is given to internal behavior of the learner
• Our thinking process change radically, though slowly, from birth to
maturity because we constantly strive to make sense of the world.
•Belived that learning is a function of certain process
4. Stages of cognitive Development
Piaget has identified four primary stages of development:
1. Sensori motor stage (birth-2 years old)
2. Preoperational stage (2-7 years old)
3. Concrete operational stage (7-11 years old) and
4. Formal operational stage (adolescence-adulthood)
1. Sensori motor Stage
(0-2 years)
• The child’s thinking involves seeing, moving, touching, tasting , etc.
• Develops object permanence
• Begins to recognise that objects do not cease to exist when they are hidden
• Moves from reflex actions to goal directed activity.
5. Children younger than 6 months of age do not grasp object
permanance, i.e., objects that are outof sight are also but of mind.
Learning Mathematics at sensorimotor Stage
• They have the ability to link numbers to objects (one dog,two
cats, three toys).
•To develop mathematical capability of a child in this stage,the
child’s ability might be enhanced.
• At this stage they have some understanding of the concept of
numbers and counting.
•It enhaces children’s conceptual development of number.
6. 2. Preoperational stage
(2-7 years)
• Ability to use symbols, words,gestures, signs, images,etc.
• difficulty with reversible thinking (thinking backward)
•They lack basic logical operational skills.
• Pre – operational children are egocentric
They think the world is created for them
Inability to see the world through others perspective
Should be gone by age 5
• They indulde in collective monologue
•Animism –belief that inanimate things are alive.
7. Piaget tested the concept conservation by pouring the same amount of
liquid into two similar containers. When the liquid from one container is
poured into a third, wider container, the level is lower and the child thinks
there is less liquid in the third container. The child is using one dimension,
height, as the basis for his judgement of onother dimension,volume.
Teaching students in this stage of development should employ effective
questioning obout characterizing objects.
•Child links together unrelated events,see objects as possessing life.
•Child should engage with problem -solving tasks that incorporate available
materials such as blocks,sand,and water.
•Children’s perceptions are generally restricted to one aspect or dimension
of an object.
• Eg. Concept of conservation. The child use only one dimension,height as
the basis for the judgement of another dimention, volume.
•Teachers should employ effective questioning about characterizing objects.
•For eg. A teacher could ask students to group the shapes according to
similar characteristics.
8. 3. Concrete Operational stage
(7-11 years)
conservation
• Children at primary level
• Understand the concept of conservation
• can think logically,use analogies, and perform mathematical
transformation (5+9 is the same as 9+5)
• Is also know as reversibility which promotes logical thinking
Learning mathematics at concrete operational stage
• Characterized by seven types of conservation : Number, length,
liquid, mass, weight,area , volume.
• Develop transitivity
• Eg. If A is bigger than B,and B is bigger than C then what is the
relation between A and C?
9. • They can consider two or three dimensions simultaneously
(Decentration)
• For eg. In the liquid experiment, if the child notices the lowered
level of the liquid, he also notices the dish is wider, seeing both the
dimensions at the same time.
• Concrete experiences are needed to explore concepts such as place
values and arithmetic operations.
• Materials like: patern blocks, cubes, tiles, geoboards,
tangrams,dice, etc....
• Teachers can use convenient materials in activities such as paper
folding and cutting
• Children tend to think that the manipulations they do with models
are one method for finding a solution and pencil-and paper math is
entirely separate.
• Creating opportunities for students to present mathematical
solutions by multiple ways (eg. Symbol, graphs, tables) is one tool for
cognitive development in this stage.
Formal operational stage
(11 or 12+ years)
Abstract Reasoning
• Thought process becomes quite systematic
•Imagination develops
10. • Develop experimental spirit
• Grater abstraction and metacognition
• Ability to judge truth of logical relationships
• Reflective thinking.
Learning mathematics at Formal operational stage
• The child is capable of forming hypothesis and deducing possible consequences
• Can allow the child to construct his own mathematics
• reasoning skills in this stage include :clarification, inference , evaluation and
application
1 . Clarification: It requires students to identify and analyse elements of a problem,
allowing them to interpret the information needed in solving a problem.
2. Inference : Students at this stage are developmentally ready to make inductive and
deductive inferences in mathematics
3. Evaluation : Evaluation involves using criteria to judge the adequacy of the problem
4.Application : Students connecting mathematical concepts to real life situation
• Thus the child can discover concepts through investigation.
•While the teacher studies the child’s work to better understand his thinking, the child
should be encourages to self check,appropriate , reflect and reason.
•In general the knowledge of piaget’s stages helps the teacher understand the
cognitive development of the child as the teacher plans stage appropriate activities to
keep students active.
11. Conclusion
• Piaget theory emphasizes interaction of children with
physical world.
•Biggest changes occur as a result of conflicts between what
is know and the problem encountering .
•Maturity procedes learning.
• teachers to plan developmentally appropriate activities
reaction.
