Unit 2- Aims and Objectives of Teaching Mathematics

 

Aims and Objectives of Teaching Mathematics

Values of learning mathematics

Values are the motive behind purposeful action. Values are the outcomes or results achieved after teaching according to the aims. Every subject in the curriculum has its own value system that makes a student a better person. They are the actual results of our teaching effort. The main Values of learning mathematics is to armour the learner with such knowledge which will help him to become a useful and efficient citizen of the society. The values of learning mathematics are classified as follows:

·        Practical/Utilitarian value

·        Intellectual value

·        Social value

·        Moral value

·        Disciplinary value

·        Cultural value

·        International value

·        Vocational value

·        Aesthetic value

·        Psychological value

Practical/Utilitarian value

The knowledge of mathematics is needed at every step or stage of our day to day life. Each and every person of society needs mathematical knowledge. It is very difficult for even a common man to lead his life comfortably without the use of basic operations of mathematics and skills. All natural phenomenon are based on mathematical principles. It is also required to study other school subjects especially science subjects. All scientific inventions and instruments which have made our daily life so easy smooth and happy are available only by mathematics.

Examples: A labour uses mathematical knowledge to calculate wages, to make purchases from market etc.

A business man uses the knowledge of percentage, average, stock and share to run his business efficiently.

Intellectual value

There is no other subject in the curriculum like mathematics which helps students to develop intellectual powers like power of imagination, memorization, observation, invention, concentration, originality, creativity and reasoning.

Social value

The study of mathematics should enable an individual to appreciate that man is a social being and he must play an important role in bringing about social progress. Mathematics plays an important role in the proper organization and maintenance of social institutions such as banks, co-operatives, railways, post office, transports and so on. The social values like tolerance, open-mindedness, co-operation, honesty, truthfulness and will power are also can be acquired by the study of mathematics.

Moral value

The knowledge of mathematics is helpful in character and personality development. Child develops the qualities of honesty, truthfulness, justice, punctuality, self-confidence, cleanliness and patience etc.

Disciplinary value

The nature of Mathematics helps the students to lead a well-disciplined life as it helps the students to imbibe values like honesty, truthfulness, open-mindedness, objectivity, self-confidence, patience and it trains the students in systematic and orderly habits namely concentration, punctuality, neatness, hard work, regularity, orderliness and so on.

Cultural value

Mathematics has great cultural values, it has helped in transmitting and enriching our culture. It has helped in the development of various subjects and occupations. It is mainly responsible for the progress of our civilization. Mathematics helps in promoting cultural heritage and transmitting it to future generation.

International value

The study of mathematics helps to create international understanding and brotherhood.

Eg: Any invention of a country reaches to the different countries.

Mathematics books and journals circulated among almost all the nations of the world.

Vocational value

Mathematics prepares the students to achieve suitable vocations. Almost all vocations need the knowledge of mathematics.

Example: Agriculture, accountancy, banking, carpentry etc.

Aesthetic value

Mathematics has great aesthetic value. Whenever a child discovers something new with the help of mathematical law, facts, principles and theorems a sense of joy is developed in his mind. He realize the aesthetic aspects of his findings. Mathematics is closely related with arts like drawing, painting, music and dance. Mathematical regularity, symmetry, order and arrangement are needed for the perfectness of these arts.

Psychological value

 Mathematics education is essential for developing scientific attitude among the children. It helps to develop positive attitude such as open mindedness, reasoning etc. among learners. Mathematics fulfills the psychological needs of the children.

AIMS AND OBJECTIVES OF TEACHING MATHEMATICS

Aims of teaching mathematics

The term aims of teaching mathematics stands for the goals, targets or broader purposes that may be fulfilled by the teaching of mathematics in the general scheme of education.

General aims of teaching mathematics

·        To enable the child to understand the use of numbers and quantities to daily life.

·        To develop mathematical curiosity and use inductive and deductive reasoning when solving problems

·        To create a suitable type of discipline in the mind of the child.

·        To enable the child to solve mathematical problems of his daily life.

·        To develop in the fundamental skills and process of mathematics.

·        To develop the habit of concentration, self-confidence and discovery.

·        To develop scientific and realistic attitude towards life.

·        To develop the abilities of analysis, synthesis, reasoning, computation etc.

·        To develop interest in mathematics.

·        To appreciate the usefulness, power and beauty of mathematics

Objectives of Teaching Mathematics

The objective are those short-term, immediate goals or purposes that may be achieved within the specified classroom situations. Objectives are easily attainable direct and practical in nature. The aims are broken into specified objectives to provide definite learning experiences for bringing about desirable behavioral changes.

Difference between aims and objectives 

Aims	Objectives
Broad and general	Specific and narrow
Give direction to the educational system	Directed towards aims
Common to more than subject	Specific to each subject
Not easily attainable	Easily attainable
Cannot be evaluated	Can be evaluated
Aims include objectives	Objectives are the part of aim
Philosophy and sociology are main source of aims	Psychology is the main source of objectives
Long term goals	Short term goals

 dObjectives of learning mathematics at elementary, secondary and senior secondary levels with respect to NCF and KCF

NCF- National Curriculum Framework

According to the National Curriculum Framework (NCF) 2005, the main goal of Mathematics education in schools is the 'mathematisation' of a child's thinking. Clarity of thought and pursuing assumptions to logical conclusions is central to the mathematical enterprise. While there are many ways of thinking, the kind of thinking one learns in Mathematics is an ability to handle abstractions and an approach to problem solving.

The NCF envisions school Mathematics as taking place in a situation where:

1. Children learn to enjoy Mathematics rather than fear it.

2. Children learn “important” Mathematics which is more than formulas and mechanical procedures.

3. Children see Mathematics as something to talk about, to communicate through, to discuss among themselves, to work together on.

4. Children pose and solve meaningful problems.

 5. Children use abstractions to perceive relationships, to see structures, to reason out things, to argue the truth or falsity of statements.

6. Children understand the basic structure of Mathematics: arithmetic, algebra, geometry and trigonometry, the basic content areas of school Mathematics, all of which offer a methodology for abstraction, structuration and generalization.  

7. Teachers are expected to engage every child in class with the conviction that everyone can learn Mathematics.

The NCF, therefore, recommends:

 1. Shifting the focus of Mathematics education from achieving 'narrow' goals of mathematical content to 'higher' goals of creating mathematical learning environments, where processes like formal problem solving, use of heuristics, estimation and approximation, optimisation, use of patterns, visualisation, representation, reasoning and proof, making connections and mathematical communication take precedence.

2. Engaging every student with a sense of success, while at the same time offering conceptual challenges to the emerging Mathematician.

3. Changing modes of assessment to examine students' mathematisation abilities rather than procedural knowledge.

 4. Enriching teachers with a variety of mathematical resources.

GENERAL OBJECTIVES OF TEACHING MATHEMATICS AS ENUMARATED BY N.C.F

• ·        Developing children’s ability for mathematics is the main goal of mathematics education.
• ·        The narrow aim of school mathematics is to develop useful capabilities, particularly those relating to numbers, number operations, measurements, decimals and percentage.
• ·        The higher aim is to develop the child resources to think and reason mathematically, to pursue assumptions to their logical conclusion and to handle abstraction.
• ·        It gives importance how a child do things, and the ability and the attitude to formulate and solve problem.
• ·        Children learn to enjoy mathematics rather than fear it.
• ·        Children learn importance of mathematics
• ·        Children see mathematics as something to talk about, to communicate through, to discuss among themselves, to work together on.
• ·        Children use abstraction to precise relationship to see structure, to reason out thing to argue the truth falsity of statement.
• ·        Children understand basic structure of mathematics, arithmetic, algebra, geometry and trigonometry.
• ·        Teacher engage every child in class with the conviction that everyone can learn mathematics.
• ·        The teaching of mathematics should enhance children’s ability to think and reason, to visualise and handle abstraction to formulate and solve problem.

 Objectives of Teaching Mathematics with respect to NCF

Elementary

• ·        To develop the concept of numbers, measurements, quantity, counting etc.
• ·        To give knowledge about shapes and symmetries.
• ·        To encourage children to use language to freely express one's thoughts and emotions.
• ·        To develop a positive attitude towards Mathematics.
• ·        To develop the ability of fundamental operations.
• ·        To develop cognitive skills and logical reasoning
• ·        To express and explain patterns
• ·        To develop critical thinking
• ·        To get the first taste of the application of powerful abstract concepts that compress previous learning and experience.

 Secondary

1. ·        To enable the child to perceive the structure of Mathematics as a discipline.
2. ·        To make the child logical and critical thinker.
3. ·        To integrate the many concepts and skills that they have learnt into a problem-solving ability.
4. ·         To give knowledge about Mathematical modelling, data analysis and interpretation.
5. ·         Individual and group exploration of connections and patterns,
6. ·        To develop the skills to visualize and generalize the mathematical concepts.
7. ·        Encourage the child to use appropriate tools that include concrete models as in Mathematics laboratories and computers.

 Higher Secondary

·        To provide students with an appreciation of the wide variety of the application of Mathematics, and equip them with the basic tools that enable such application.

GENERAL OBJECTIVES OF TEACHING MATHEMATICS AS ENUMARATED BY KCF

 

·        The basic characteristics mathematics is to analyze and interpret the world on the basis of mathematics.

·        Mathematics is a language that presence facts through figures

·        It help the child to develop logical reasoning.

·        Teachers should ask open ended questions. (ie, there  should be chances to generate many conclusions which can be directly or indirectly connected to the concept).

·        Teachers should promote divergent thinking of children. (ie,we move away from the conventional method of finding a single answer to a question).

·        It is a language in which children communicate and translate among themselves.

·        Children communicate with mathematics through figures, table and graphs.

·        Children come to conclusion by realizing the cause and effects of a problem.

·        Children do not learn definition or a formula by heart.

·        It gives children the ability to expand or given problem according to one’s own level of understanding and that of giving a new dimension to mathematical poses are instances of problem solving.