QUESTION 1:
In our quest to understand how children master basic mathematical concepts,
we need some basis from which to build our understanding. Many approaches
to teaching and different theories on how children develop and learn, have
been documented through the years
1.1 Identify THREE (3) of the child development theorists.
Jean Piaget
Lev Vygotsky
Jerome Bruner
1.2 Evaluate these child development theories and explain the applicability of
each one to the teaching and learning of mathematics in the Foundation
Phase.
Cognitive Constructivist Theory Jean Piaget
Piaget Maintained that a child's learning is a contentious process of
constructing knowledge.
He believed that children acquire information by interacting with objects, ideas
and other people.
According to Piaget , children construct knowledge through two processes of
adaptation,namely, assimilation and accommodation.Assimilation happens
when children add new information to their existing thought structures.
-in other words, the new information or experience fits in with what they
already know.
Accommodation takes place when children when children make changes to
their existing thought structures so that new information from environment can
fit in better. Piaget(1936) proposed a series of stages through which
intellectual maturity moves. Piaget claimed that these stages are fixed and
followed each other but accepted that there was no fixed time for each stage.
Piaget suggested that children proceed through stages of development and
that these stages are same for all children according to their ages.
The social Constructivist Theory of Vygotsky
Vygotsky focused on the importance of language in learning. According to him,
Children make sense of their world through shared experiences and learning
occurs in the zone of proximal development. The ZPD encompasses the
different between what a child knows and what a child can learn with the
assistance of a more knowledgeable other ( a peer or an adult).In this social
interaction, the child learns significantly more and learns deeper concepts
than she/he would on her/his own. Scaffolding is a process through which a
teacher adds supports for learners in order for them to learn and master tasks.
The teacher builds on the learners’ experiences and knowledge as they are
learning new skills.
, The social Constructivist Theory of Bruner
Jerome Bruner (1915 -2016) believed that children learn by actively engaging
with their environments but they require guided assistance, called
scaffolding,to enable them to learn optimally. According to burner
(1978),learning is an active process in which learners construct new ideas or
concepts based upon their current and/past knowledge. A learner selects and
transforms information,constructs concepts and makes decisions,relying on a
cognitive structure(Schema)to do so.The following principle that underpin
Burner's theory have implications for the teaching and learning of
mathematics:
Learning is an active process
Learners select and transform information. They use prior experiences to fit
knew information into pre-exist structures. Good teaching relies on scaffolding
to achieve optimal learning.
Scaffolding is the process through which able peers or adults offer support for
learning. This assistance gradually becomes less frequent as it becomes
unnecessary.
The stage of intellectual development
Bruner identified three stages of development, namely, the inactive stage ,
which refers to learning through actions, the iconic stage, which refers
learners use of pictures or models, and the symbolic stage ,which refers to the
development of the ability to think in abstract terms.Burner advocated the
notion of s spiral curriculum,which is that a curriculum should revisit basic
ideas,building on them until learners have grasped the full concept.Bruner’s
Learning theory has direct implications for teaching practice.
Bruner’s theory focuses on level of knowing and operates on the tree levels,
namely enactive,iconic and symbolic knowledge (Clements,DH&
Sarama,J.2014.
Enactive Knowledge is derived from the physical manipulation of objects
and the childs own movement. This involves all that the young child is
doing, for example,sorting or counting objects. Examples of enactive
learning are moving around in the classroom to touch something that has
the same shape as,say,a boy,or children using their fingers to count.
Iconic knowledge involves mental operation where the child uses
representations of concrete objects,for example, using pictures thereof.
The emphasis here is on visual and perceptual information (Schultz,
Colarusso & Strawderman, 1989).An example of this kind of knowledge is
when children are provided with a picture of three butterflies and are
asked to draw a flower for each butterfly
Symbolic knowledge refers to the ability to use abstract symbols. The goal
in mathematics is to reach the highest level of symbolic knowledge. This
means that the child will start off by counting 2 real apples(enactive), then
In our quest to understand how children master basic mathematical concepts,
we need some basis from which to build our understanding. Many approaches
to teaching and different theories on how children develop and learn, have
been documented through the years
1.1 Identify THREE (3) of the child development theorists.
Jean Piaget
Lev Vygotsky
Jerome Bruner
1.2 Evaluate these child development theories and explain the applicability of
each one to the teaching and learning of mathematics in the Foundation
Phase.
Cognitive Constructivist Theory Jean Piaget
Piaget Maintained that a child's learning is a contentious process of
constructing knowledge.
He believed that children acquire information by interacting with objects, ideas
and other people.
According to Piaget , children construct knowledge through two processes of
adaptation,namely, assimilation and accommodation.Assimilation happens
when children add new information to their existing thought structures.
-in other words, the new information or experience fits in with what they
already know.
Accommodation takes place when children when children make changes to
their existing thought structures so that new information from environment can
fit in better. Piaget(1936) proposed a series of stages through which
intellectual maturity moves. Piaget claimed that these stages are fixed and
followed each other but accepted that there was no fixed time for each stage.
Piaget suggested that children proceed through stages of development and
that these stages are same for all children according to their ages.
The social Constructivist Theory of Vygotsky
Vygotsky focused on the importance of language in learning. According to him,
Children make sense of their world through shared experiences and learning
occurs in the zone of proximal development. The ZPD encompasses the
different between what a child knows and what a child can learn with the
assistance of a more knowledgeable other ( a peer or an adult).In this social
interaction, the child learns significantly more and learns deeper concepts
than she/he would on her/his own. Scaffolding is a process through which a
teacher adds supports for learners in order for them to learn and master tasks.
The teacher builds on the learners’ experiences and knowledge as they are
learning new skills.
, The social Constructivist Theory of Bruner
Jerome Bruner (1915 -2016) believed that children learn by actively engaging
with their environments but they require guided assistance, called
scaffolding,to enable them to learn optimally. According to burner
(1978),learning is an active process in which learners construct new ideas or
concepts based upon their current and/past knowledge. A learner selects and
transforms information,constructs concepts and makes decisions,relying on a
cognitive structure(Schema)to do so.The following principle that underpin
Burner's theory have implications for the teaching and learning of
mathematics:
Learning is an active process
Learners select and transform information. They use prior experiences to fit
knew information into pre-exist structures. Good teaching relies on scaffolding
to achieve optimal learning.
Scaffolding is the process through which able peers or adults offer support for
learning. This assistance gradually becomes less frequent as it becomes
unnecessary.
The stage of intellectual development
Bruner identified three stages of development, namely, the inactive stage ,
which refers to learning through actions, the iconic stage, which refers
learners use of pictures or models, and the symbolic stage ,which refers to the
development of the ability to think in abstract terms.Burner advocated the
notion of s spiral curriculum,which is that a curriculum should revisit basic
ideas,building on them until learners have grasped the full concept.Bruner’s
Learning theory has direct implications for teaching practice.
Bruner’s theory focuses on level of knowing and operates on the tree levels,
namely enactive,iconic and symbolic knowledge (Clements,DH&
Sarama,J.2014.
Enactive Knowledge is derived from the physical manipulation of objects
and the childs own movement. This involves all that the young child is
doing, for example,sorting or counting objects. Examples of enactive
learning are moving around in the classroom to touch something that has
the same shape as,say,a boy,or children using their fingers to count.
Iconic knowledge involves mental operation where the child uses
representations of concrete objects,for example, using pictures thereof.
The emphasis here is on visual and perceptual information (Schultz,
Colarusso & Strawderman, 1989).An example of this kind of knowledge is
when children are provided with a picture of three butterflies and are
asked to draw a flower for each butterfly
Symbolic knowledge refers to the ability to use abstract symbols. The goal
in mathematics is to reach the highest level of symbolic knowledge. This
means that the child will start off by counting 2 real apples(enactive), then
