METHODS
OF TEACHING MATHEMATICS
Introduction
Teaching is more likely to
constitute the more informal part of the country, the part where they have greater
autonomy in the development of their work than involved in teacher directed
instruction.
Various methods of teaching Mathematics:
v Lecture Method
v Inductive Method
v Deductive Method
v Heuristic Method
v Project Method
Ø Lecture Method
The
lecture method is the most widely used form of presentation. Every teacher has
to know how to develop and present a lecture.
Delivering a lecture
Suitable Language:
In the
teaching lecture, simple rather than complex words should be used whenever
possible. The teacher should not use substandard English. If the subject matter
includes technical terms, the teacher should clearly define each one so that no
student is in doubt about its meaning. Whenever possible, the teacher should
use specific rather than general words.
Tone and Pace:
Another
way the teacher can add to the lecture is to vary his or her tone of voice and
pace of speaking. In addition, using sentences of different length also helps.
The teacher should normally use sentences of short and medium length.
Use of notes:
For a
teacher notes are a must because they help keep the lecture on track. The
teacher should use them modestly. Notes may be written legibly or typed, and
they should be placed where they can be consulted easily.
Advantages of the Lecture Method:
§ Lecture method gives the teacher
the chance to expose students to all kinds of material.
§ Can be used to arouse interest in
a subject.
§ Can complement and clarify text
material.
§ Complements certain individual
learning preferences.
§ Facilitates large-class
communication.
Disadvantages of Lecture Method
§ Places students in a passive
rather than an active role, which hinders learning.
§ Encourages one-way communication;
therefore, the lecture must make a conscious effort to become aware of student
problems and student understanding of content without verbal feedback.
§ Requires a considerable amount of
unguided student time outside of the classroom to enable understanding and
long-term retention of content.
Scopes and limitations of Lecture Method
§ Lectures are used to introduce
new topics, summarizing ideas, showing relationships between theory and
practice, reemphasizing main points, etc.
§ This method is adaptable to many different settings.
§ It may be used to introduce a
unit or a complete course.
§ Finally, lectures can be
effectively combined with other teaching methods to give added meaning and
direction.
The teaching
lecture is favored by most teachers because it allows some active participation
by the students. The success of the teaching lecture depends upon the teacher’s
ability to communicate effectively with the class. The teacher must develop a
keen perception for subtle responses from the class-facial expressions, manner
of taking notes, and apparent interest or disinterest in the lesson.
Preparing the Teaching Lecture
Planning:
The following four steps are followed in the
planning phase of preparation:
·
Establishing
the objective and desired outcomes;
·
Researching
the subject;
·
Organizing
the materials; and
·
Planning
productive classroom activities.
In all stages of preparing for
the teaching lecture, the teacher should support any point to be covered with meaningful
examples, comparisons, statistics, or testimony. While developing the lesson,
the teacher also should strongly consider the use of examples and personal
experiences related to the subject of the lesson.
Rehearsing:
After completing the preliminary
planning and writing of the lesson plan, the teacher should rehearse the
lecture to build self-confidence. It helps to smooth out the use notes, visual
aids, and other instructional devices.
Ø Inductive Method
Inductive method is that form of
reasoning in which a general law is derived from a study of particular objects
or specific processes. Students use measurements, manipulators or constructive
activities and patterns etc to discover a relationship. They later formulate a
law or rule about that relationship based on their observations, experiences,
inferences and conclusions.
ü Example 1: Ask pupils to draw a
number of triangles. Ask them to measure the three angles of each triangle and
find their sum. They will find that the sum of the three angles of all
triangles is 180⁰.
ü Example 2: Ask pupils to find the
sum of two odd numbers like 3+5=8, 5+7=12, 9+11=20, etc. They will find that
the sum of two odd numbers is an even number.
Steps in the Inductive method:
1. The first step is clear
recognition of the problem. It should be clearly understood and defined by the
pupils.
2. Once the problem has been
defined, the child should start searching for data from all possible sources
like books, magazines, journals, making visits to certain places etc.
3. Under the guidance of the
teacher; the pupils organize the data which they have collected from various
sources. They select relevant data and discard irrelevant material.
4. By studying particular instances,
the pupils frame possible solutions.
5. These solutions are discussed,
argued and judged. Thus tentative solutions are eliminated and only the
probable solutions remain.
6. The solutions are applied to the
situation and results are verified.
Merits of Inductive Method
§ This method is psychological. The
student fees interested in experiments, experiences and discoveries.
§ This method fosters independence
and self-confidence in the pupil which proves very useful in later life.
§ In this method, children discover
the solution themselves. Hence it develops and encourages and creative
thinking.
§ All that is learnt using
inductive method is remembered easily as it is self-acquired.
§ In this method, the pupils
observe and analyze particular objects of similar and different nature and try
to arrive at general truth.
§ Inductive method takes into
consideration all the maxims of good teaching. The process of induction calls for
perception, reasoning, judgment and generalization.
Ø Deductive Method
Deductive is the method in which the
law is accepted and then applied to a number of specific examples. The child
does not discover the law but develops skills in applying the same, proceeds
from general to particular or abstract to concrete.
Steps involved in Deductive Method
1. Like the inductive method, the first
step is the clear understanding of the problem.
2. It may involve the study of a
particular thing and phenomenon.
3. Principles and generalizations
are reviewed to find the one which may be applicable to find a solution.
4. In this step the rule, principle
or generalization is applied to a problem and inference is formulated that the
problem falls under such rule, principle of generalization.
5. Verification of the inference is
done by applying it to a case. If itsolves the problem then it is accepted
otherwise the procedure is repeated to find the correct one.
Merits of Deductive Method
§ Deductive method is short and
time-saving. It takes little time to solve the problem by predetermined
formulae.
§ In the deductive method, the
teacher’s work is very much simplified. He/she simply gives a rule and asks the
pupils to verify it by application to several concrete examples. For example, students
are told that the area of rectangle = length * breadth. Then a few sums are
solved before the students. The studentsapply these formulae to solve these
problems and they memorize it for future use.
§ This method is very useful for
small children because with smallchildren wegenerally use story or telling
method.
§ This method is adequate and
advantages during practice and revision stage.
§ This method glorifies memory, as
the students have to memorize a considerable number of formulae and
definitions.
Comparison of Inductive-Deductive Method
|
Inductive method
|
Deductive method
|
|
1.
It
proceeds from particular to general; concrete to abstract.
2.
It
takes care of the needs of the pupils. It is a developmental process and
takes them through easy to difficult phase.
3.
It
encourages ‘discovery’ and stimulates thinking.
4.
The
generalization or rule is formulated by the child; therefore he remembers it
with ease.
5.
The
how and why of the process is made clear through reasoning.
6.
It
starts from observation and direct experience and ends in developing a rule
in abstract form.
7.
It
encourages child participation and group work.
|
1.
It
proceeds from general to particular; abstract to concrete.
2.
In
this method facts are thrust upon the pupils. The principle of growth is to
concrete.
3.
The
authority decides or gives the formula and encourages memorization.
4.
The
rule is given to the child. He does not appreciate its nature and is likely
to forget it easily.
5.
The
process is taken for granted and accepted without reasoning.
6.
Does
not encourage learning but it starts with a rule and provides for practice
and applications.
7.
It
demands individual learning and treats the child as a passive recipien.
|
So
it concluded inductive method provides self-reliance and confidence in the
students.This method is slow and safe as the general law is reached
step-up-step. Students climb up the stairs of thought leadings to definitions,principles
or rules.can give us the formal validity because the rule is taken for granted.
The aim of deduction method is to fit
the pupil generally for the battle of life. The laws should be discovered by
pupils inductively and they must be further verified through applications .
Ø Heuristic Method (Discovery / Inquiry Method)
Discovery through Inquiry adapts
the Scientific method. It organizes investigation
of
realworld phenomena into four steps. Each step has a series of tasks that lead
to the next step or the conclusion of the investigation. The process involves
an inquiry strategy that uses questions and the seeking of answers to guide the
investigation as it proceeds. The teacher becomes a facilitator and guide,
making it possible for the learner to reach mutually-agreed-upon goals. The
teacher servers as a resource person to stimulate, motivate, clarify, and
explain.
Step 1:Wondering:
What
do we want to discover?
1. Make observations on real world
phenomena related to topic of study.
2. Connect observations to topic and
possibly subtopic of study.
3. Identify questions to be answered
or problems to be solved.
Step 2:Designing:
How
can we find out?
1. Create hypothesis.
2. Design methods to test
hypothesis.
3. Develop means to collect and
analyze data.
Step 3:Investigating:
1. Conduct experiments to test
hypothesis.
2. Record data.
3. Organize and analyze data.
4. Prove or revisit and revise
hypothesis.
Step 4:Discovery:
1.
State
conclusions after analyzing data.
2.
Determine
validity of conclusions.
3.
Construct
meaning by connecting to real world.
Discovery teaching brings four basic components of the educational setting into interaction:
·
Student
·
Teacher
·
Environment
·
Content
ü The student is an active
participants who solves problems which
he understands through the process of structuring his own learning experiences.
ü The teacher plays the role of
resource person and a facilitator.
ü The environment includes both
freedom and structure with freedom having the upper hand.
ü The content may very well be
propositional truth in a general context, and capture it for his own.
Importance of Heuristic Method:
·
Allows
for individualistic accomplishments.
·
Is
highly adaptive and versatile, limited only by the imagination of the participants
at both the teacher and student level.
·
Allows
for free expression of individual creativity. It is a concept of learning about
which we talk much and do little.
·
Develops
the relationship of students to teachers and of students to students.
Problems of teaching in Heuristic Method:
Many studentsfeel insecure in an
unstructured environment of learning. It is much more comfortable tobe able to
listen to a lecture and take notes in orderly fashion than to be confronted
with the haunting question, “What do you want to learn about this subject, and how
do you propose to learn it?”. If responsibilities are not taken seriously by the
participants, the whole process could get out of control. It is also a
time-consuming method.
Principles for Heuristic Method
§ To get best results, a teacher
must encourage the questioning mind, and equip students with skills.
§ Suggest resources, but refrain
for doing the research for the learner.
§ Train the students to
think.Challenge the answers they suggest and not be satisfied with the easy
answer they are ‘supposed to get’.
§ Teach the students how to use
various resources as they their solutions through books, articles, films,
recordings, maps, experiences, projects, and most important, other people.
Ø Project Method
This method aims to bring
practically designed experience into the classroom. Often
conducted
over a period of three to six months, the projects give students an opportunity
to work in a team environment and apply theory learned in the classroom. There
are some parts of the curriculum in which children are necessarily dependent on
the teacher and others in which children can work more independently.
Project work can be seen
as providing complementary learning opportunities to children in which they not
only need to know how to use askill but also when to use it. They need to learn
to recognize for themselves the contexts in which the skill might be useful and
the purposes which it can most appropriately serve.
In project work they
apply those skills in meaningful contexts. The project work can be seen as the
part of the curriculum which is planned in negotiation with the children and
which supports and extends the more formal and teacher directed instructional
elements.
Scopes and Strategies
This method is appropriate for any
level, but is often employed for senior levels of education. Using projects
usually requires a lot of preparation by the teacher.
Some tips in this regard are as follows:
§ Realize that the product of the
project is not as important as the processes.
§ It is not important that the
students determine an optimal design. What is important, however, is that they
experience the design process.
§ It is important that the scope of
the project is reasonable; care must be taken to ensure that the students are
not overloaded.
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