“Leading is the work of
a teacher does to motivate, encourage and inspire the students, so that they
will readily achieve the learning”.
-
Davis,
I.K.
Introduction:
The entire system of education is geared towards the
realization of certain national goals.
The Indian Education Commission (1964 – 66) has recommended the
following to make education as a powerful agency of social, economic and
cultural transformation necessary for realization of the national goals.
Every subject/course included in the curriculum has
distinct and unique aims. The aims of
teaching mathematics and sciences will be distinctly different from those of
teaching languages and social sciences.
The aims of mathematics education are derived from and intimately
related to the broad aims of education or goals of education.
The
need and significance of teaching Mathematics:
Mathematics education provides:
F A
good mathematical background with the knowledge of concepts and theories.
F Ability
to apply mathematical concepts and theorems of new situations.
F Ability
to transfer the mathematical type of thinking and reasoning to daily life
situations.
F A
clear understanding of laws of nature.
F A
clear understanding of the culture and development of civilization.
F An
appreciation of the applications of mathematics for the scientific and
technological advancement.
F Sufficient
mathematical skills to meet the demands of daily life.
F A
better understanding of the world around.
F Ability
to make independent decisions in societal issues.
F A
good deal of self – reliance, self – confidence, tolerance and open –
mindedness.
F A
window for looking at the world and a framework for solving problems.
F Ability
to transfer the knowledge and skills learned through mathematics lessons to
other contexts in the work place and in everyday life.
F An
essential element of communication.
F A
powerful tool in the hands of the learners.
F Ability
to apply mathematics and make meaningful connections to life’s experience.
F Ability
to communicate mathematical ideas coherently and clearly to peers, teachers and
others.
F Ability
to think alternative methods of solving problems.
F Ability
to apply mathematical ideas and relationships in areas outside classroom such
as in art, science and other curricular areas and in everyday life, especially
physical phenomenon.
Aims
and Objectives of Teaching Mathematics:
Aims
of Teaching Mathematics:
Aims are general and long term goals and may be common to
more than one subject. Long term goals
refer to high level aims and tend to be related to broad reasons, why a
particular subject or activities are being organized or why a particular course
is being done. Thus aims or long term
goals can be regarded as expressions of strategy.
General
Aims of Teaching Mathematics:
The general aims of teaching mathematics are as follows:
š To
enable the child to understand the use of numbers and quantities related to
their daily life.
š To
enable the child to solve mathematical problems of his daily life.
š To
create a suitable type of discipline in the mind of the child.
š To
familiarize the child with the latest mathematical knowledge to fulfill the
existing needs of the society.
š To
give knowledge about the broad objectives of teaching mathematics such as –
knowledge, understanding, application etc.
š To
develop in the child fundamental skills and process of mathematics.
š To
develop in the child a sense of appreciation of cultural arts.
š To
prepare the child for elementary as well as higher education in science,
engineering etc.
š To
develop the habit of concentration, self – confidence, self – reliance and
discovery.
š To
develop in the child the mental powers like thinking, reasoning etc.
š To
develop scientific and realistic attitude towards life.
š To
give practical knowledge of mathematics to face the day – to – day problems.
š To
prepare the child for technical professions such as those of accounts, audits,
bankers, surveyors, cashiers, scientists, architects and mathematics teachers.
š To
bring an all – round and harmonious development of the personality of the
child.
š To
develop the sense of appreciation of mathematical knowledge and contribution of
mathematicians.
š To
develop the skills to use the modern mathematical devices like computers etc.
š To
develop the abilities of analysis, synthesis, reasoning, computation etc.
š To
develop interest in mathematics.
Different
Aims of Teaching Mathematics:
Aims of teaching mathematics can be classified under the
following heads:
Ø Utilitarian
or Practical Aims
Ø Disciplinary
Aims
Ø Cultural
Aims and
Ø Social
Aims
Utilitarian
or Practical Aims:
The following
are the practical aims of teaching mathematics:
F To
enable the students to have clear ideas about number concept.
F To
give the individual an understanding of ideas and operations in number and
quantity needed in daily life.
F To
enable the individual to have clear comprehension of the way the number is
applied to all measures but most particularly to those frequently used concepts
such as length, volume, area, weight, temperature, speed etc.
F To
enable the individual to become proficient in the four fundamental operations
of addition, subtraction, multiplication and division.
F To
provide the basis of mathematical skills and processes this will be needed for
vocational process.
F To
enable the learner to acquire and develop mathematical skills and attitude to
meet the demands of (i) daily life (ii) future mathematical work and (iii) work
in the related fields of knowledge.
F To
enable the student to make appropriate approximations.
F To
enable the learner to understand the concept of ratio and scale drawing, read
and interpret graphs, diagrams and tables.
F To
enable the individual to apply his mathematics to a wide range of problems that
occurs in daily life.
Disciplinary
Aims:
The teaching of mathematics intends to realize the
following the disciplinary aims:
F To
provide opportunities that enable the learners to exercise and discipline
mental faculties.
F To
help the learner in the intelligent use of reasoning power.
F To
develop constructive imagination and inventive faculties.
F To
develop the character through systematic and orderly habits.
F To
help the learner to be original and creative in thinking.
F To
help the individual to become self – reliant and independent.
Cultural
Aims:
The cultural aims can be summarized as follows:
F To
enable the learner to appreciate the part played by mathematics in the culture
of the past and that it continues to play in the present world.
F To
enable the student to appreciate the role played by mathematics in preserving
and transmitting our cultural traditions.
F To
enable him to appreciate various cultural arts like drawing, design making,
painting, poetry, music, sculpture and architecture.
F To
provide through mathematical ideas, aesthetic and intellectual enjoyment and
satisfaction and to give an opportunity for creative expression.
F To
help the students explore creative fields such as art and architecture.
F To
make the learner aware of the strengths and virtues of the culture he has
inherited.
F To
develop in the individual an aesthetic awareness of mathematical shapes and
patterns in nature as well as the products of our civilization.
Social
Aims:
The important
social aims of teaching mathematics are as under:
F To
develop in the individual an awareness of the mathematical principles and
operations which will enable the individual to understand and participate in
the general social and economic life of his community.
F To
enable the student to understand how the methods of mathematics such as
scientific, intuitive, deductive and inventive are used to investigate,
interpret and to make decision in human affairs.
F To
help the pupil acquire social and moral values to lead a fruitful life in the
society.
F To
help the pupil in the formation of social laws and social order needed for
social harmony.
F To
provide the pupils scientific and technological knowledge necessary for
adjusting to the rapidly changing society and social life.
F To help the learner appreciate how mathematics
contributes to his understanding of natural phenomena.
F To
help the pupil interpret social and economic phenomena.
All
these aims are very broad and general in nature, without having any vital
relationship to the curriculum and the day – to – day classroom activities.
Objectives
of Teaching Mathematics:
The objectives imply the changes that we try to bring
about in the children. According to
NCERT’s Evaluation and Examination issue:
“An objective is a point or end in view of something
towards which action is directed, a planned change sought through any activity
what we set out to do”.
The objective is a statement or a form of category which
suggests any kind of change. It
indicates the direction of pupil’s growth and provides basis for selection of
evaluation procedures. Objectives
provide link between teachers, pupils, testers and parents by focusing their
attention with intended outcomes of learning.
Thus objectives validate the process of education. Hence objectives have the following
characteristics:
·
They provide direction to the
activities.
·
They help for the planned change.
·
They provide basis for organizing
teaching – learning activities.
The
objectives are classified into two categories:
i.
Educational Objectives
ii.
Teaching Objectives
i.
Educational
Objectives:
Educational
objectives are broad and philosophical in nature. They are related to the schools and
educational system.
“Educational
objective as a desired change in behaviour of a person that we try to bring
about through education”.
-
Furst,
E. J.
“Educational
objectives are not only the goals towards which the curriculum is shaped and towards which
instruction is guided, but they are also the goals that provide the detailed
specification for the curriculum and use of evaluation techniques”.
-
Bloom,
B. S.
The
educational objectives are achieved with the help of teaching or instructional
objectives. These include several
teaching or instructional objectives.
ii.
Teaching
Objectives:
The
teaching objectives are narrow and psychological in nature. Teaching objectives may be achieved in a
certain period in the classroom, for example a period of 30 or 35 minutes
duration. These are related with the
expected change in behaviour of the child.
So they are also called behavioural objectives. Teaching objectives are directly related with
the learning process and they are well defined, definite, clear, specific and
measurable. These give direction to the
learning process, learning experiences and teaching. They provide the foundation of the entire
educational structure. Therefore,
teaching objectives are also called instructional objectives. The teaching strategies methods and
techniques are selected on the basis of teaching or instructional objectives.
Comparison
between Aims and Objectives:
For a teacher it is practically impossible to realize all
the aims of mathematics education within the framework of curriculum, for they
involve a total programme of education encompassing even out – of – classroom
experiences. The part of the aim that
can be achieved within an institution is an objective. While aims give directions to education,
objectives are directed towards the aims.
|
AIMS
|
OBJECTIVES
|
|
1. Aims
are very broad and comprehensive.
|
1. Objectives
are narrower and specific.
|
|
2. Philosophy,
sociology is main source of aims.
|
2. Psychology
is the main source of objectives.
|
|
3. They
are not definite and clear.
|
3. They
are definite and clear.
|
|
4. They
are difficult to achieve.
|
4. They
can be achieved conveniently.
|
|
5. Long
time duration is needed in order to achieve aims.
|
5. They
need short duration i.e. in the period of class room teaching.
|
|
6. They
are subjective.
|
6. They
are objective.
|
|
7. These
cannot be evaluated.
|
7. These
can be evaluated.
|
|
8. These
include objectives.
|
8. Objectives
are a part of aims.
|
|
9. They
are related with the whole education system and whole curriculum.
|
9. These
are related with the teaching and any specific topic.
|
|
10. It
is the responsibility of school, society and nation to achieve them.
|
10. Generally
teacher is only responsible.
|
|
11. These
are theoretical and indirect.
|
11. Objectives
are direct and concerned with the teaching learning process.
|
|
12. Aims
are formal.
|
12. These
are functional and informative.
|
Sources
of Objectives:
The following are the sources of objectives and the
teacher can make use of these sources while writing objectives.
·
Aims of education
·
Institutional aims
·
Aims of mathematics education
·
Opinions of subject experts and
associations
·
The nature of the learner, and the
course subject
·
The psychology of teaching and learning
·
Societal requirements
·
List of objectives developed by SCERT,
NCERT etc.
Instructional
Objectives – Definition and Meaning:
An instructional objective is a statement of expected
result. It is a description of the
learning outcome that the teacher expects as a result of his/her
instruction. Bloom et al state,
“By
educational objectives, we mean explicit formulation of the ways in which
students are expected to be changed by the education process; that is the ways
in which they will change in their thinking, their feelings and actions”.
Thus the objectives are
statements describing the expected change in behaviour as outcomes of
instruction. It is a statement of what
students should be able to do at the end of the learning period that they could
not do before hand. Thus the term
‘Objective’ may be defined as:
“An objective is a point or end view of the
possible achievement in terms of what a student is able to do when the whole
educational system is directed towards educational aims”.
An instructional objective is a statement that describes
what pupil will do or be able to do, towards the realization of an educational
aim. When a pupil attains an objective
he realizes a part of the broad aim.
Importance
of Stating Instructional Objectives:
When the teacher plans the instruction based on the
objectives then the focus of the entire instructional process gets shifted from
the teacher to the student. The
instructional objective not only guides, teacher in designing her instruction
but also helps the examiners in selecting the suitable evaluation tools. The objectives are useful for the students in
knowing what is expected of them after completing the period of learning.
The
objectives help the teacher to:
v Define
clearly the expected behaviour modification of the students after a period of
instruction.
v Plan
appropriate learning experiences.
v Proceed
in the right direction to realize the aims.
v Convey
clearly the instructional intent to others.
v Provide
the basis for the decisions regarding selection and organization of the
content, the mode of instruction and evaluation techniques.
The
objectives give directions to the examiner in:
v Selecting
appropriate evaluation tools.
v Selecting
relevant test items to test the expected change in behaviour of the tests.
The
objectives are helpful to the students.
The objectives:
v Tell
the student what is expected of him after a period of instruction and thereby
enables him to use his study time more efficiently.
v Tell
the student how he should be able to use the material from the syllabus and in
what ways he is expected to display his mental skills and abilities.
v Tell
the student what will be the minimum level of acceptance for his performance
and under what conditions it could be achieved.
Sources
of Objectives:
The following are the sources of objectives and the
teacher can make use of these sources while writing objectives.
v Aims
of education
v Institutional
aims
v Aims
of mathematics education
v Opinions
of subject experts and associations
v The
nature of the learner, and the course subject
v The
psychology of teaching and learning
v Societal
requirements
v List
of objectives developed by SCERT, NCERT etc.
Criteria
for Judging Instructional Objectives:
In choosing general instructional objectives, it is
helpful to have criteria against which to judge whether or not the objectives
are relevant and useful.
§ Attainability - within
the realm of possibility
§ Validity -
in line with the aims of the education
§ Comprehensiveness - cover fully all the
behaviour and content
material
§ Precision
-
clear and unambiguous
§ Feasibility
-
for application
§ Appropriateness
- for
yielding specific outcomes
§ Reasonable
in number
§ Consistent
with one another
General
Instructional Objectives (GIOs) and Specific Outcomes of Learning (SOLs):
The GIOs are for a course and can apply to any item of
the curriculum/syllabus. They are
intended to assist in defining and carrying out broad educational aims. By specifically stating the kind of outcome
of student learning desired, these objectives can be used to clarify teaching
methods, learning experiences and material needed for particular content and
course.
Examples
for GIOs:
Ø The
pupil acquires knowledge of mathematical terms, facts, concepts,
principles, theorem etc.
Ø The
pupil understands the meaning of mathematical terms, facts etc.
Ø The
pupil applies mathematical principles to new and unfamiliar
situations.
These
objectives are also known as non – behavioural objectives as they
do not depict an overt behaviour of the learner.
SOLs
consist of statements defining the specific performances, which we adopt as evidence
that a student has actually reached his objective, all of which are precise and
measurable. These objectives are also
known as behavioural objectives as the statement of these objectives
contains an action verb which displays an overt behaviour of the learner.
Examples
for SOLs:
Ø The
pupil recalls definitions of mathematical terms or concepts.
Ø The
pupil recognizes mathematical symbols.
Ø The
pupil lists properties of geometrical figures.
Ø The
pupil classifies geometrical figures.
Ø The
pupil gives reason for mathematical statements.
Ø The
pupil establishes relationship among mathematical concepts.
Ø The
pupil formulates a hypothesis for solving a given problem.
Ø The
pupil selects principles relevant to the problem presented.
Writing
GIOs and SOLs:
Listing objectives is a time consuming
process, which requires careful thought.
It is best done over a period of time in order to be able to review and
revise. But for having once prepared and
refined a list for a course, it can remain as a guide from year to year with
only minor revisions.
For each general instructional objective it is necessary
to write SOLs that will state the precise behaviour or performance that is
expected of a student. Each general
instructional objective can have many specific outcomes of learning under
it. These are smaller unit’s performance
and can be precisely measured by tests of various kinds.
There are five elements which when used in writing an SOL
give the clearest definition for student performance that can be used for both
teaching and testing. The five elements
are as follows:
a)
Performer (The Student, The Trainer, The
Learner, etc.)
b)
Action Required (An action verb. Example:
identifies, compares, describes, distinguishes, analyses, classifies
etc.)
c)
Task (Include a task to be
performed. Example: compares the properties,
explains the derivation)
d)
Conditions (Include any condition that
may be required. Example: compares the
properties of the given triangles)
e)
Criteria for judgement (any relevant
criteria for clarity. Example: explains,
the phenomena with at least two examples, computers with speed and accuracy)
Example
for SOLs:
Ø The
pupil recalls the formula for the area of an equilateral triangle.
Ø The
pupil constructs the triangle according to the given specifications.
Ø The
pupil selects an appropriate method/formula to solve the given problem.
Ø The
pupil computes the area of the given equilateral triangle with speed and
accuracy.
Ø The
pupil lists the properties of an equilateral triangle.
Ø The
pupil states Pythagoras theorem.
Three
Qualities to be maintained:
In writing an SOL, there are three qualities which must
be maintained, if SOL is to serve the purpose of communication between teacher,
pupil and examiner.
Ø Use
clear, precise action verbs.
Ø Must
be feasible in terms of student’s level, nature of the content and learning
experiences.
Ø Must
be observable and measurable.
