PPT for Lecture 2 - Theories of How Children Learn.pptx

UNIT 1: HOW CHILDREN LEARN MATHEMATICS
THEORIES OFTEACHINGAND LEARNING MATHEMATICS
2 / 2 9 / 2 0 2 4
D R . A L D I N B E L L I N F A N T I E , R E F E R E N C E F R O M
H T T P S : / / L M S . K O M E N D A C O L L E G E . E D U . G H / W P -
C O N T E N T / U P L O A D S / 2 0 2 0 / 0 4 / U N I T 2 -
P Y C H O L O G I C A L - B A S I S . P D F
1

Objectives
By the end of the unit, the student will be able to;
• Discuss and explain the various theories of learning
• Apply teaching techniques to various topics in mathematics
• Analyze theories of learning about mathematics
• Deliver easier teaching/learning techniques to students
• Create interesting and meaningful teaching techniques
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2

Definitions of a theory
• A theory is a supposition or system of ideas intended to
explain something, especially one based on general
principles independent of the thing to be explain.
• A theory is a set of principles on which the practice of an
activity is based.
• A theory is an idea used to account for a situation or
justify a course of action.
• Learning theory therefore describes how students receive,
process and retain knowledge during learning.
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Key characteristics of learning
• Learning involves change
• All learning involves activities
• Learning requires interaction
• Learning is a lifelong process
• Learning occurs randomly throughout life
• Learning involves problem solving
• Learning is a process of acquiring experience
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The main tenets of Behaviourist theory of learning
• Learning is a connection between stimulus and response /
response and reinforcement
• Change in behavior as result of an individual response to
stimulus that occur in the environment
• Learning is acquisition of a new behaviour through conditioning
• Rewards and punishment
• Edward L. Thorndike, B. F.Skinner, Pavlov and Robert Gagne
are the main proponents of behaviourist
• The experiment by Pavlov which conditioned a dog to salivate to
sound of bell(classical conditioning)
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How will you define reinforcement from the
behaviourist point of view?
•Reinforcement is an event which increases
the frequency of the response that follows it.
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Robert Gagne
• Behavioural response of the learner follows some
form of instruction.
• Arranging the conditions to bring about the most
effective learning of intellectual skills, cognitive
strategies, verbal information, motor skills, and
attitudes (i.e. five categories of capabilities).
• Teaching and learning should be very specific or goal
directed. It must also be based on task analysis.
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How do we apply behaviourist learning theory in mathematics
classroom?
We can applybehaviouristlearningtheory in mathematics classroom by:
• Reinforcing the correct responses and discourage wrong responses.
• Controlling the stimuli, choose the correct response and providing
the appropriate reward.
• Providing feedback to learners immediately.
• Using marks, prizes and praise as different reinforcements.
• Arranging lessons into series of graded steps(i.e. programmed learning).
• Providing opportunities for practice(i.e. drill and practice).
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Gestalt psychology
• Gestalt is German word literally means
configuration or pattern or form.
• Gestalt psychology is a school of thought
that looks at the human mind and
behaviour as a whole rather than
attempting to break up into small parts.
• They perceived the whole of anything to be
greater than any of its parts.
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Cognitive /developmentalists Theory of Learning
Principles that underlie cognitivists learning theory:
1. Learning consists of changes in mental constructs and
processes; learning takes place when the learner
mentally reorganizes his/her inner world of concepts.
2. Learning is a personal experience and teachers only
need to serve as a facilitator.
3. Learning is something that happens as a result of thinking.
4. The child cannot learn the same content as adults and even
among children there are individual differences to consider.
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Cognitive /developmentalistsTheory of Learning (cont.)
• For meaningful learning to take place, new information
needs to fit in with existing cognitive structures.
• Learning is a process in the learner is actively involved.
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Effective application of cognitivism requires that the
teacher needs to:
• Know about the students’ previous learning.
• Assist the student in developing meaning by providing
puzzles and rules for the students to work with.
• Provide structures or help the students to create a
structure to which they can add a new information.
• Employ the inductive-deductive approach of teaching.
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Jean Piaget
• Jean Piaget was a Swiss psychologist who has provided numerous
insights into the development of human intelligence, ranging
from the random responses of the young infant to the highly
complex mental operations inherent in adult abstract reasoning.
• Piagetian theory indicates that in learning, children pass through
developmental stages and that the use of active methods which
gives scope to spontaneous research by the child helps him
rediscover or reconstruct what is to be learned “not simply imparted
to him”.
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Developmental stages according to Piaget
• Sensory motor(0-2 years of age): This stage is where children
begins to use imitation, memory and thought. The child
moves from reflex actions to goal- directed activity.
• Pre-operational (2-7 years) : This is the stage where children
gradually develop language and the ability to think in symbolic
form.
• Concrete operational(7-11 years): This is the stage where
children are able to solve concrete(hands-on) problems in
logical fashion.
• Formal operation(11-15 years): this is the stage where children
are able to solve abstract problems in logical fashion.
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Conservation of numbers , volume and length
• Conservation of numbers: This experiment was to see if a
child realizes that the number of elements in a set remains
unchanged even as the set is physically rearranged.
• Conservation of volume: This experiment determined
whether the child understands that volume is unchanged
under a certain type of physical rearrangement.
• Conservation of length has to do with the child being able
to recognize that the length of an object remains the same
no matter the different positions or inclinations
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Jerome Bruner
• Brunner was interested in the general
nature of cognition(i.e. Conceptual
development).
• Bruner was of the view that any subject can be
taught effectively in some intellectually honest
form to any child at any stage of
development(Bruner,1966).
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The three sequential phases of learning by Bruner
• Concrete which involves hands on activity.
• Semi concrete which involves the use of visual
medium.
•Abstract which involves the use of symbols.
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The three phase/levels of acquiring sequential thinking by Bruner
• Enactive level which involves hands on or direct experience: The
student is engaged in first-hand manipulating, constructing, or
arranging of real-life objects. In other words, students interact
directly with the concrete materials.
• Iconic level or imaginary phase: This phase is characterized by the
use of visual medium which is dominated by visuals and perceptual
organizations such as films, pictures, diagrams: It is semi-concrete
in nature.
• Symbolic level involves the students being able to use abstract
symbols to represent reality.
2 / 2 9 / 2 0 2 4 D R . A L D I N B E L L I N F A N T I E , R E F E R E N C E F R O M H T T P S : / / L M S . K O M E N D A C O L L E G E . E D U . G H / W P -
C O N T E N T / U P L O A D S / 2 0 2 0 / 0 4 / U N I T 2 - P Y C H O L O G I C A L - B A S I S . P D F
18

Implication of Bruner’s work in teaching and learning
• Textbooks can hardly provide enactive experiences but they are
exclusively iconic and symbolic containing pictures of
things(physical objects and situational problems or tasks) and the
symbols associated to the things are not the things themselves.
• Mathematics programmes that are dominated by textbooks are
inadvertently creating a mismatch between the nature of the
learner’s needs and the mode in which content is to be learned by
students.
• A mathematics programme that does not make use of the environment
to develop mathematical concepts eliminates the three levels of
representing mathematical ideas.
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Implication of Bruner’s work in teaching and learning (cont.)
• Textbook activities need to be supplemented with
real-world experiences. Mathematics programmes
should include more manipulatives and more
experiences in applying mathematical ideas in the
real world.
• Manipulatives aids help learners to move from
concrete situations and problems to abstract ideas.
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Zoltan P
. Dienes
 Dienes’ theory combines some ideas of Piaget
and Bruner. He describes how mathematics is
to be learnt and how it should be taught (both
prescriptive and descriptive).
 Every learning should start with applications
which the learner can actually experience and
then progress to formal mathematical summary.
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Dienes’six-stage theory of learning mathematics
Stage 1 - Preliminary free play stage: Children interact with physical
materials within the environment. Different
embodiments provide exposures to the same basic
concepts but at this stage few commonalities are
observed.
Stage 2 - Structural activities stage: Following the free experimenting,
some regularity appears in the situation, which can be
formulated as rules of the game.
Stage 3 - Intuitive abstraction activities or comparing stage: At this
stage, patterns, commonalities and regularities are observed
and abstracted across the models.
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Dienes’six-stage theory of learning mathematics (cont.)
Stage 4 - Representation of activities stage:
This involves the use of images and pictures to provide representations.
Stage 5 - Examination and descriptive activities or symbolization stage:
This stage involves the description of the representation in mathematical
symbols and checking or verifying results.
Stage 6 - Axiomatic Formulation of activities or formulation stage:
This where the fundamental rules and properties are recognized as structures
of the systems.
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Implication of Dienes’work
• The whole class or large group lesson would be greatly
deemphasized in order to accommodate individual differences
in ability and interests. Individual and small group activities
will benefit students learning.
• The role of the teacher would include exposition as well as
being a facilitator where students’ role would be expanded to
assume a greater degree of responsibility for their own
learning.
• The newly defined learning environment would create new
demands for additional sources of information and direction such
as a learning laboratory containing materials such as computers.
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Constructivism learning theory
Constructivism states that learning is an active process
in which learners construct new ideas or concepts based
on current /past experience.
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Application of the constructivist learning theory
• Teachers should tailor teaching strategies to student responses and
encourage students to analyze, interpret, and predict information.
• Teacher and learners can negotiate meanings of actions and words
as they interact.
• Learners must be encouraged to verbalize mathematical thinking, to
explain and justify mathematical solutions and to resolve
complicating points of view.
• Learners are to be allowed to assess themselves and have regular
dialogue with teachers. They should feel free to comment why they
are have not achieved a particular learning goal.
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The teacher in a constructivist teaching and learning
environment should:
• Orchestrate discussion among learners.
• Encourage learners to verbalize the mathematics they
are constructing when doing activities.
• Encourage learners to make connections between
different aspects of mathematics.
• Encourage learners to explain and justify their
solutions.
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Theteacherina constructivistteachingand learning environment should:
• Orchestrate discussion among learners.
• Encourage learners to verbalize the mathematics
they are constructing when doing activities.
• Encourage learners to make connections between
different aspects of mathematics.
• Encourage learners to explain and justify
their solutions.
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END
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