Analytical and Synthetic Method
Analytical Method
1. It
proceeds from unknown to known
2.
Analysis means breaking up of the problems in hand so that it ultimately gets connected with something obvious or
already known
3.
It is a process of unfolding of the problem or of conducting its operation
to know its hidden aspects
4. It starts with what is to be found out
5.
In original sense the verb “to analyze “ means to loosen or
separate things that are together about
analysis
Merits
1.
It is logical
method
2. It leaves no doubts and convinces the learners
3.
It felicitates
(congratulates) understanding
4.
It also strengthens the urge (advocate) to discover facts
5.
The steps
in its procedure are developed in a general manner, no cramming of a
fixed step and a set pattern is
necessitated , each step has its reason and justification
6.
Students faced
different type of questions as, how to prove the equality of two angles? What are the possible ways of resolving a
statement into simpler elements etc?
7.
Students grapple (tackle, struggle) with
the problems confidently and intelligently
Drawbacks
1.
It is lengthy
method
2.
It is difficult to acquire efficiency and
speed through this method
3.
It may not be equally applicable to all topic
well
Synthetic Method
1.
It is the opposite to the analytic method
2.
It proceeds from known to unknown
3.
It is the complement of analysis
4.
To synthesize is to place together things
that are apart
5.
It starts with something already known and
connects with that part of the statement
6. It
starts with data available or known and connects the same with the conclusion
7. It
is the process of putting together known bits of information to reach the point
where unknown information becomes
obvious and true
Merits
1.
It is short and elegant method
2.
It glorifies the memory
Drawbacks
1.
It leaves many doubts in the mind of the
learner and offers no explanation for them
2.
Students feel perplex when new problem is set
to him because he does not get satisfaction in early stage
3. It does not provide full understanding
4. There is no scope for discovery and thinking
in this method
5. Memory work and home work are likely to become
heavy
Comparative study of analytical and synthetic method
|
Analytical method |
Synthetic method |
|
It proceeds from unknown to known facts |
It proceeds from known to unknown facts |
|
It starts from conclusion and goes to
hypothesis |
It starts with hypothesis and ends with
conclusion |
|
It is a process of thinking |
It is a product of thought |
|
It is process of exploration and demands
thoughts |
It is process of presentation of the
previously discovered facts |
|
It pulls apart or analysis and statement
under solution |
It pulls together or synthesis known facts |
|
It is general method |
It is a special device |
|
It is lengthy, awkward, slow, roundabout
and involves trial and error |
It is concise, elegant, quick,
straightforward and does without trial and error |
|
It answers satisfactorily any question that
may arise in the mind of any intelligent pupils |
It does not satisfy the doubts and
questions arise in the mind of the learner |
|
It is a method for discoverer and thinker |
It is a method for the crammer |
|
There are close contacts between the
teacher and the taught |
There is no such intimate contacts between
them |
|
It develops originality |
It develops memory |
|
The students can recall and reconstruct
easily any steps if forgotten |
It is not easy to recall or reconstruct any
forgotten steps |
|
It is informal |
It is formal |
|
It is psychological |
It is logical |
|
It is formational |
It is informational |
|
It is based on heuristic lines |
There is no heuristic approach in it |
|
It is fore-runner of synthesis |
It is the follower of the analysis |
Inductive- Deductive Method
Inductive Method
1.
Leads from concrete to abstract
2.
Particular to general
3.
Examples to general rules
4.
Used to construct formula with the help of
sufficient examples
5.
Provides universal truth by showing if it is
true for particular case then it is true for the adequate number of cases
6.
Students use many examples for doing
generalization
Merits
1.
Helps in understanding
2.
Gives better understanding about any
mathematical principle through many examples
3.
Clear doubts in very beginning
4.
It is a logical method so it suit mathematics
5.
It gives opportunity of active participation
to students in the discovery of any formula
6.
It is based on actual observation, thinking
and experimentation
7.
It curbs the tendency to learn things by
rote, and also reduces homework
8.
It gives freedom from doubts and helps in
understanding, it suits the child
Drawbacks
1.
It is limited in range
2.
It contains process of discovering but do not
tell, what would be next?
3.
Only discovery of formula does not complete
the study of whole topic
4.
Inductive reasoning is not absolutely
conclusive. Three or four cases are to be studied to generalize an observation
5.
It is likely to be more laborious (difficult)
and time consuming
6.
It is not useful at advance stage because
unnecessary detail may make the lesson dull
and boring
7.
Its applications are restricted and confined
to understanding of rules in the early stages
Deductive Method
1.
It is opposite of inductive method
2.
Learner proceeds from general to particular
3.
From abstract to concrete
4.
Formula to example
5.
Pre constructed formula is to be told to the
students to solve the problems
6.
Formula is to be accepted by the students as
a pre established and well established truth
Merits
1.
It is short and time saving therefore most of the teachers like this
method
2.
It glorifies the memory as students have to
memorize a considerable number of formula
3.
At “practice and revision” stage, this method
is adequate and advantageous
4.
It combines, with the inductive method to
remove the incompleteness and inadequacy of
the latter
Drawbacks
1.
It seems difficult for a beginner to
understand an abstract formula if it is not proceeded by the number of concrete instances
2.
Pure deductive demands memorization of a
large number of formula
3.
It causes an unnecessary and heavy burden on
the brain
4.
Memory becomes more important than
understanding and intelligence which is educationally
unsound
5.
It lets bad effect on the students if he
forgets the formula at the time of examination and he can not
recollect the formula again
6.
Students can not become an active learners
7.
It is not suitable for the develop of
thinking, reasoning and discovery
Heuristic Method
1.
Term Heuristic is derived from Greek word
means “ I find”
2.
Child is to be put in the place of discoverer
3.
Method involves finding out by the student
instead of merely telling of everything by the
teacher
4.
Aims at removing shortcomings attributed to
lecture method
5.
Demands complete self activity or self
education on the part of the learner
6.
Pupils learn to reason for themselves
7.
Few opinions are that child should be made a
discoverer and inventor
8.
When applied at extreme form, teacher stands
aside as an onlooker
9.
Child select his own path and proceed
according to his own light
10. Teacher
is not required to encourage, help or guide the student
11. No
need of teacher’s approval or disapproval in child’s work
12. If
students want to accomplish something, let them at their own way
13. No
stress for reasoning, arguments and product of thinking by the teacher on the students
14. No
emphasis of bookish, readymade and teacher made arguments
15. This
method make the student reliant and independent
16. It
imparts sound training in education
17. Teacher’s
job is not to solve the problem for the students, but to enable the students to solve the problems for themselves
18. Prof.
Armstrong was the originator of this method
19. He
advised it for the teaching of science
20. He
said school should develop thinking power of the students
21. Students
must be given opportunity to think
22. Specially
useful in teaching of mathematics
23. Used
to develop particular attitude of the learner
24. It is
also known as scientific method
25. Knowledge
is not primarily consideration in this method
26. Creates
self confidence, originality, independence of judgment and thinking power
27. Teacher
acts as passive observer
28. Mostly
child is considered ignorant
29. Students
seek guidance in certain cases
30. Student
may need help at each step
31. He
need proper time and help to develop proper acquaintance with new knowledge
32. Student
is given few hints in case of discontinuity or slow progress
Merits
1.
Student become an active participant in
learning process
2.
Student think for himself and does not merely
listen for information
3.
Hone study and memorization work become light
4.
It is certainly a psychologically sound
method
5.
Aims at utilizing the active, original,
creative and constructive tendencies of the learner
6.
After discovering student feels pride at his
own work which gives him happiness and mental
satisfaction
7.
It encourages the student for further
achievement
8.
Student require a real understanding and
clear notion of the subject
9.
Gives complete master of what he has learnt
10. Teacher
remain in constant touch with his students
11. Develops
scientific attitudes
12. Creates
sprit of enquiry
13. Student
becomes self-reliant
Drawbacks
1.
Demands extraordinary labor and special
preparation from the teacher who is already overburden
2.
Every teacher may not use it successfully
3.
Teacher must be gifted with the Heuristic
sprit
4.
It is slow method
5.
Too much time is taken up by the
investigation
6.
There is very little certainty that child
will make himself steady
7.
Every child cannot be expected to be gifted
discoverer because immature child has his
limitations and difficulties
8.
Early stages require little guidance
9.
In early stages students may get discouraged
and disgusted
10. Teacher should give well measured guidance to
the students. Over guidance may also
harm the initiative of the learner and make him dependent
11. If
students are tempted to consult books for the sake of discovery , this method
fails in its purpose
12. This
method is not valid for the teaching of all the topics
13. This
method demands small group of the class for individual discovery
14. It cannot
provoke (irritate) the real thinking if teacher does not frame good questions
Sometimes teacher fails to distinguish between false heuristic and true heuristic, as difference is below
|
False
heuristic |
True
heuristic |
|
Is it true that a square has all sides equal? |
What do you know about the sides of the
square? |
|
Do you remember that area of the rectangle
= length x breadth? |
How do we calculate the area of the
rectangle |
|
Tell me whether the profit or loss % is
calculated on the cost or selling price? |
On which price do we calculate profit or
loss %? |
Conclusion
1.
What we have concluded?
2.
Generally it looks as it is out of the
question
3.
Presence of the teacher is to stimulate and
inspire the student
4.
Its success depends upon good questioning
5.
Questioning used as a spirit behind this
method
6.
The teacher no longer teaches
7.
The learner no longer listen
8.
Teacher should frame hints and instructions
very carefully to avoid over feeding
9. In
time assistance and removal of difficulties
Laboratory Method
1.
Learnt by doing rather than by reading
2.
Also called activity method
3.
Used to discover mathematical facts
4.
Based on principles like, “learning by
doing”, “learning by observation”
5.
Proceeding from concrete to abstract
6.
It is extension of the inductive method
7.
Pupils not only listen but also do
practically
8.
Principles have to be discovered, generalized
and established
9.
Makes the subject interesting
Merits
1.
Interesting and joyful for the learner, he
likes to do with his own hand
2.
Based on two sound psychological principles
i.e., “proceed from concrete to abstract” and
“learn by doing”
3.
Gives clear understanding of the subject to
the learner
4.
Provides great scope for independent work and
individual development
5.
Helps in growth of self reliance
6.
Inculcates spirit of cooperation and exchange
of ideas in lab
7.
Gives encouragement on successful experiment
8.
Removes shyness by using and handling of
apparatus
9.
Impart skills to use mathematics in practical
life
10. Make
subject functional and meaningful for the students
11. Few
topics are better understood through this method
Drawbacks
1.
This method is very expensive
2.
Laboratory work is not typical mathematical
work
3.
Does not give any training to the learner in
true mathematical thinking
4.
It acquaints the student with facts and not
with mathematical reasoning
5.
Needs thorough planning and supervision
6.
Needs individual attention
7.
Exceedingly laborious and slow method
8.
Not easy to find facts specially in lower
classes
9.
Sometimes generate manually training to the
learner
Conclusion
1.
Difficult and lengthy method
2.
Prove exceedingly profitable if properly
employed
3.
A lot of depends on facilities available as
staff, laboratory accommodation and equipment
Project method
1.
It is based on John Dewey’s philosophy of
pragmatism
2.
Dr. Kilpatrick said, “ A project is a
unit of whole hearted purposeful activity, carried on preferably , in its natural setting”
3.
Stephen soon defined it as, “ A
project is a bit of real life that has been imported into the school”
4.
Project plan is a modified form of an old
method called, “concentration of studies” which
means some subjects are taken as
core or centre and all other school subjects, as
they arise, are studied in connection with it
5.
It is based on the principle of learning by
doing
There are two types of projects
a.
Individual
project,
carried out by a single individual
b.
The social
project which is carried out by a group of individual
To complete any project we have five stages
in actual practice
- Providing
a situation
- Choosing
and purposing
- Planning
of the project
- Executing
the project
- Judging
the project
There is no
rigidity about these stages. Modifications can be made according to the nature
of the project; project should be given to the students according to their
abilities and stamina
Example
Project: “Celebration of republic
day”
The project
can have the following different aspects
1.
Why do we celebrate this day?
2.
The school programme of its celebration
3.
Estimated expenditure for different items,
budget preparation
4.
From where to arrange for the expenses?
5.
The account of collection from the locality,
if any
6.
The account of collections from amongst the
students, if any
7.
The preparation and organization of different
items of the programme
8.
Making purchases for the programme
9. Keeping
accounts of the expenses incurred (invited, deserved)
10. Execution (completing, finishing) of the
different programme
11. Preparing the report of the programme
12. Evaluation of the entire celebration
Merits of the
Project Method
1.
It is based on psychological laws of
learning. Education is related to the child's life and is acquired through
meaningful activity
2.
It uploads (give) the dignity of labour
3.
It introduces democracy in a education ,
because it necessitates cooperation among students
and their activity together for a common cause
4.
It brings about concentration of studies and
correlation of activity and subject
5.
It emphasizes problem solving rather than
cramming or memorizing
6.
It inculcates social discipline through joint
activities
7.
It develops self confidence and self discipline
8.
A project tends to illustrate real nature of
the subject and produce spirit of enquiry
9.
Project can be used to arouse interest,
justify the study of the topics, encourage initiative and give the students joy at the
successful completion of the given work
10. There
is no opportunity for mutual exchange of ideas
Drawbacks of the
project method
1.
Mathematics cannot be taught purely by this
method , incidental teaching will not suffice
, planned teaching will have to be added to it
2.
Students will not acquire skill and
efficiency without collective and individual drill which will be possible through planned teaching
only
3.
There is no saving of time, energy and
efforts
4.
A single opportunity for practical experience
cannot develop or promote computational ability
5.
Systematic and continuous teaching is not
possible
Some suitable
projects are,
- Purchase
of craft material
- Running
the hostel mess
- The
sports day
- A
variety programme
- Model of
the village
- School
bank
- Use of
mathematics in a large business
- Mathematics
in the kitchen
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