The document discusses various teaching techniques including simulation, concept mapping, and gradation. Simulation involves modeling real-world situations to teach concepts. Concept mapping visually represents relationships between mathematical concepts. Gradation refers to sequencing instruction from simple to complex, known to unknown, and concrete to abstract. Some key principles of gradation include proceeding from the known, simple, concrete, empirical, psychological, whole, near, and particular to the unknown, complex, abstract, rational, logical, parts, far, and general. Inductive teaching starts with specific examples and builds to general principles, while deductive teaching applies general rules to specific cases.

1. ONLINEASSIGNMENT

2. SUBMITTED BY
SRUTHY U S

3. Simulation, Concept Mapping &Gradation
Simulation
Simulation may be defined as the process of teaching
which is enacted artificially. In the world of Science and Technology,
Simulation is a must. Engineers build models, soldiers engage in moc
fighting etc are examples of Simulation.
Definitionof Simulation
R Wynn: “Simulation is an accurate representation of realistic
situation”.
Many topics in Mathematics that have immediate utility
value can be best introduced using the technique of Simulation. That is
enacting a real situation in the class. Topics that have relation with
commercial concern is an example. The functioning of a co-operative
society or bank can be cited as an example.
First students may be taken to such institutions to
observe the nature and techniques of the various activities going on
there. Notes may be taken. In order to reinforce and to make the activity
more familiar, the working of such institutions may be enacted in the
class. The Simulation should be carefully arranged so as to make the
insight as meaningful as possible.
For example, there is a school co-operative
society. The working of the society may be observed and the salient
features of how it was organized and what the activities taken up are
noted. Then imagine that the learners are planning to start a class co-

4. operative society. The steps such as selling of shares to pools, the capital
required, election of various office bearers, nature of transaction
involved (together with the mathematical skills), the style of keeping the
records concerning the various aspects including the account book, the
technique of preparing a balance sheet, calculation and dispersal of
dividends to the share holders etc can be simulated.
In the same way, the activities in a bank with special
reference to the Mathematical calculations involved (such as deposits
and withdrawals, calculations of interests at various rates other money
transactions giving loans etc) may be simulated in a realistic manner.
This will not only help in realizing the utility value of
Mathematics, but also will give realistic insights in to the related
commercial Mathematics. Further the roles played in simulation will
create interest among learners.
Advantages of Simulated Teaching
 Device for motivating students – Simulated Teaching is a device for
motivating students. It avoids the risk of actual classroom encounter.
 Analysis of teaching problems – Simulated Teaching provides
opportunities to student-teachers to study and analyze critical teaching
problems.
 Insight into behavioural –Simulated Teaching helps the students in
understanding behavioral problems of class-rooms. It helps in developing
an insight to encounter them.
 Acquisition of classroom manners –Simulated Teaching helps the
students in acquisition of classroom manners. It enables the students to

5. improve social skills and to gain confidence in their ability to use these
skills.
 Forging link between theory and practice –A major advantage of using
simulated teaching is that it forges close links between theory and
practice.
 Means to provide laboratory experiences –Simulated teaching serves
as a social laboratory. It provides opportunities to the students to
exercise the social skills acquired. It helps in utilizing an artificial
environment knowledge previously acquired. It helps in utilizing an
artificial environment knowledge previously acquired.
 Interesting and enjoyable –Last but not the least, the simulated
teaching of mathematics is interesting and enjoyable to the students.
Limitations of Simulation
 Difficulty for beginners – New participants may face some difficulty in
asking different kinds of questions. A simple task such as “open” and
“closed” questions may provide an introductory challenge.
 Incorrect recording –It is possible that during an exercise, the
observer may record incorrectly.
Concept Mapping
Concept Mapping was invented by Joseph Novak and Albert Canas in
1972. A Concept Map visually pictures Mathematical connections and
describes them in writing. In other words, it describes how concepts are
related.

6. Advantages of Concept Mapping
 Focuses on demonstrating how Mathematical ideas could be
represented.
 It helps students to see relationship between topics.
 It helps students to improve their problem solving ability.
Disadvantages of Concept Mapping
 Students with weak visual skills may not profit from Concept
Mapping.
 It will be less effective if instructor introduce them at the wrong
times.
 Instructor need to focus their time effectively.
 Use Concept Maps which are most effective.
Gradation
It is very helpful in obtaining the active involvement and participation of
the learners in the teaching-learning process. A good teacher should be
quite familiar with them.
 Proceed from the known to the unknown
 The most natural and simple way of teaching a lesson is to proceed
from something that the students already know to those facts which they
do not know. What is already known to the students is of great use to the
students. This means that the teacher should arouse interest in a lesson
by putting questions on the subject matter already known to the pupils.
The teacher is to proceed step by step to connect the new matter to the
old one. New knowledge cannot be grasped in a vacuum.

7.  Proceed from simple to complex
The simple task or topic must be taught first and the
complex one can follow later on. The word simple and complex are to be
seen from the point of view of the child and not that of the adult.
 Proceed from easy to difficult
Student’s standard must be kept in view. This will help
in sustaining the interest of the students. There are many things which
look easy to us but are in fact difficult for children. The interest of the
child has also be taken in to account.
 Proceed from the concrete to the abstract
Children in the beginning cannot think in abstractions.
Small children learn first from things which they can see and handle. A
child understands an aero plane with the help of a model.
 Proceed from particular to general
Before giving principles and rules, particular examples
should be presented. As a matter of fact, a study of particular facts
should lead the children themselves to frame general rules.
 Proceed from indefinite to definite
Ideas of children in the initial stages are indefinite,
incoherent and very vague. These ideas are to be made definite, clear,
precise and systematic. Effective teaching necessitates that every word
and idea presented should stand out clearly in the child’s mind as a
picture. For clarifying ideas, adequate use must be made of actual

8. objects, diagrams and pictures. Every possible effort should be made to
make the children interesting in the lesson.
 Proceed from empirical to rational.
Observation and experience are the basics of empirical
knowledge. The general feeling is that the child first of all experiences
knowledge in his day to day life and after that he feels the rational bases.
For instance, plane geometry makes better sense when taught in the
context of everyday life instead of it in the format of a highly abstract
theory. It is always better to begin with what the children see, feel and
experience than arguing and generalizing.
 Proceed from psychological to logical.
Logical approach is concerned with the arrangement
of the subject matter. Psychological approach looks at the child’s
interest, needs, mental makeup and reactions. When we treat a subject
logically, we are usually thinking of it from our own point of view and not
from the point of view of the child. In psychological approach ,we
proceed from the concrete to the abstract, from the simple to the
complex and from known to unknown. We start reading by teaching the
child to read a whole sentence, as for him, the unit is the sentence, not
the word or the letter as it is for the adult. This is psychological approach.
In a drawing lesson a child has little sense in lines and curves. Logically
we start with simple lines and curves but psychologically we start with
drawing a whole animal.
 Proceed from whole to parts.
Whole is more meaningful to the child than the parts
of the whole. The learner sees a relationships between the central idea of

9. the material to be learned. The ‘whole’ unit or passage for slow learners
should be smaller than the ‘whole’ for the fast learners.
 From near to far.
A child learns well in the surroundings in which he
resides. So he should be first acquainted with his immediate
environment. Gradually he may be taught about things which are a far
from his immediate environment.
 From analysis to synthesis
Analysis means breaking a problem into convenient
parts and synthesis means grouping of these separated parts into one
complete whole. A complex problem can be made simple and easy by
dividing it into units.
 From actual to representative
When actual objectives are shown to children, they
learn easily and retain them in their minds for a long time. This is
specially suitable for younger children. Representative objects in the
form of pictures, models etc should be used for the grownups.
 Proceed inductively
This maxim includes almost all the maxims stated above.
In the inductive approach, we start from particular examples and
establish general rules through the active participation of the learners. In
the deductive approach, we assume a definition, a general rule or
formula and apply it to particular examples. An example will make this

10. distinction very clear. The farmers in India are very poor is a general
statement in the deductive type of reasoning. The inductive will follow
thus: Ram is a farmer. He is very poor. Shyam is a farmer. He is very poor.
Krishan is a farmer. He is very poor. In this way from several such
examples it will be evident that farmers are poor. Thus we derive
generalizations. Both of the approaches i.e., the deductive and inductive
have their own importance. However in general, inductive approach is
considered a better one.
Conclusion
Simulation may be made as a powerful tool in solving
some of the problems that hinder effective teaching. It may also impart
teaching of certain skills which are necessary for teaching and its
effectiveness. Concept mapping is a technique for representing the
structure of information visually. Different maxims suit different
situations and different children. It is therefore, essential that a judicious
use should be made of each maxim.
Reference
 Mathematics Education : Dr.K.Sivarjan
 Principles and Techniques of Education : Dr.R.N.Sharma