5. bruner inductive theory
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Cognitive Theory
Jerome Bruner
Dr. Joharibin Surif Department of Science and Mathematics
Faculty of EducationUTM
SPN1022
Learning Science and Mathematics
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Three ways to understand
• Enactive: through action andmanipulation
• Iconic: Through the formation of imagesand organization of learning, seeing andkinesthetic perceptions.
• Symbolic: through words and symbols.
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Spiral Curriculum
• Whatever skill or knowledge can be taught to the pupilat each age level if that skill or knowledge is adapted tothe pupil’s development.
•
It is necessary for the teacher and pupil to revise whathas been learnt from time to time, acquiring deeperunderstanding each time.
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Spiral curriculum in school
PRIMARY LOWER
SECONDARY
UPPER
SECONDARY
Experience onobjects that float and
sink
Measurement ofmass and volume;
calculation ofmass/ volume
Calculation ofspecific gravity,
Archimedes’Principle
Observation ofchange of colorindicator by acid or
base
Neutralization ofacid and base bymixing measured
volumes of acid andbase
Titration: the use ofconcepts of volumemol and related
formula
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Inductive learning
• Pupils are not passive hearers, but can learn wellif their minds act on what they study.
• Inductive learning can motivate active learning
as well as the formation and understanding ofconcepts.
• It start s with the specific experience of thepupils which is then consolidated with more and
more ideas until a general idea or concept isformed.
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INDUCTIVE LEARNING
• 1: The pupil is introduced to anexperience and learns specificexamples for the concept to bediscovered.
• 2: The teacher helps the pupil toexamine these examples and
identify the similarities anddifferences.
• 3: The teacher guides the pupil toform a concept and general idea.
• 4: The pupil develops anunderstanding of the concept
examined and applies the conceptin different situations.
GENERAL
SPECIFIC
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Discovery Learning
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Discovery learning in Science
• Children should be give the learningopportunity to discover a conceptthemselves.
• The teacher prepares the atmosphere andfacilities and only helps if necessary.
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Benefits of discovery learning
• Increase of intellectual potential.
– Helping student learn how to learn.
– Learn the skills of problem-solving and inquiry,
enables them to arrange and use what they learn innew situations and learn further concepts.
• Shift from extrinsic reward to intrinsic reward.
– Self-satisfaction
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Benefits of discovery learning
• Opportunity to learn the heuristic of discovery(inkuiri terpimpin).
– Heuristics is the method of training a person to
discover things for himself.• Helps the process of memorizing.
• Knowledge that produced through discovery iseasier to remember and more easy to recall.
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Discovery learning in Mathematics
• Most mathematics knowledge of today have
been discovered and not created
• Al khawarizmi: discovery of 0
• Pythagorean theorem
• Fibonacci sequence:
• Golden ratio
• Euler circuit
3,1,1221
nF F F F F nnn
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Euler’s circuit
AC
D
B
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Golden ratio
a b
618.1a
ba
b
a
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Discovery learning defined
• Learner makes a discovery through a variety of
learning activities
• In mathematics, the learner may make a
conjecture, formulate a hypothesis or find amathematical truth through inductive or
deductive process
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Induction process
• Induction is a process of making a
generalization from specific cases
• Example:
3+4=4+3
5+6=6+5
7+8=8+7
Therefore, a+b=b+a
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Deduction process
• Deduction is a of making a specific conclusion
based on a given general statement
• Example:
• Volume V of a right prism is Ah, A=base area,
h=height.
• Given solid P is a right prism,
• Therefore volume of P, V=Ah
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Why discovery learning in
mathematics?
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Purposes of discovery learning
• Students will learn some procedures that are
necessary in figuring things out themselves
• Develop attitudes and practice strategies used
in problem-solving, inquiry and research
• Increase students’ ability to analyze,
synthesize and evaluate information
• Intrinsic rewards such as satisfaction when
making a discovery motivate students in math
classroom
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• Students are actively involved
• Learn to find patterns in abstract and concrete
situations
• Develop effective ways in working in a team
• Skills and concepts learnt in discovery lessons
are more meaningful to students
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Discovery learning strategies
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Discovery learning strategies
• The best is guided discovery where the
teacher:
i. Encourage students to discuss with one
another
ii. Direct discussions towards useful outcomes
iii. Monitor the flow of ideas and activities in
the classroom
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iv. Teachers should answer students’ questions
v. Ask leading questions
vi. Provide some useful information when
students need help
vii. After a discovery has been made, the teacher
should help in formulating an understandable
statement and to test its reliability and validity
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Fears for discovery learning in class
• Take too much time
• Lead to frustration when students cannot
discover• Discover the wrong thing
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Guide to create a guided discovery
lesson class
• Have specific small objectives
• Ask leading questions
• Give useful resources to students
• Be prepared to guide students and give
information
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Class Activity
• Create a discovery lesson for your class
• Discuss in 2-3’s
• Present to your classmates