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## 1.1 Meaning of Curriculum

**Introduction:**

The mathematics which deals the contents that should be taught in mathematics in order to achieve the aims and objectives. It tells the infinite solutions through the point-in-point digital method. It solves the critical numerous problems through mathematics.

**Definition of Curriculum:**

- Curriculum is the instructional and educative program through which the popular achieve their goals, ideas and aspirations of life.

- It is the soul process of education.
- It acts as pivot in organizing educational effort.

- The totality of experiences that the learners receive through all type of activities in and outside the classroom.

- Curriculum evolves from life itself and are such curriculum planning to life centre.
- It confirms to the needs of the state and the society at the same time.

- The curriculum is the tool in the hands of the artist to mould his material according to his ideals in his studio.
- Curriculum is the sum total of the experiences of the people that he receives through the manifold activities.
- Curriculum is all the activities respond by the school to the students for fulfilling its objectives.
- Curriculum is the sum of the educational experiences that children have in school.
- Curriculum decides exactly what activities to be provided according to the age of the pupils.

### 1.1.1 Characteristics of Curriculum

The specific characteristic of curriculum as given below:

- The contents should be choosen on the basis of its possible contribution to the objective.
- Subject matter should be considered primarily as a means to an end.
- The curriculum contains variety of physical and mental activities.
- The content of course fullfills of direct significance to life’s problems and activities.
- The order of difficulty of learning activities where students may get the satisfaction.
- Learning activities for interest of students should feel pleasure in completing them.
- The activities included in the curriculum of science, which provides the opportunity for exercise of creative activity of young students in fields of romance, adventure, discovery and invention.
- The activities should provide direct and concrete experiences.
- Curriculum should include abundant opportunities connected with skill and aptitude.
- Curriculum lead to easy comprehension of generalisation of scientific facts which important social implications.

### 1.1.2 Mathematics Curriculum Objectives

#### 1. Pre-Primary Stage

At the pre-primary stage:

- All learning ocours through play rather than throat didactic communication.
- The rote learning of the number sequence children need to learn and understand.
- It includes the context of small sets, the connection between words games and counting between counting and quantity.
- Making simple comparison and classification selling one dimension at a time and identifying safe and symmetries are appropriate skills to acquire at this stage.
- Encouraging children to use language to freely express one’s thoughts and emotions.

- The children develop a positive attitude towards and a linking for mathematics are the primary stage.
- Mathematical games, puzzles and stories help in developing a positive attitude and in making connections between mathematics and everyday thinking.
- Besides numbers and number operations due importance must be given to shapes, spatial understanding, patterns, measurement and data handling.
- Apart from computer computational skills, stree must be laid on identifying, expressing and explaining patterns.
- By estimation and approximation in solving problems on making connections and on the development of skills of language in communication and reasoning students will able to measure own knowledge.

#### 2. Upper Primary Stage

At the upper primary stage :

- Students get the first teste of the power of mathematics through the application of powerful abstract concepts.
- It enables them to revisit and consolidate basic concepts and skills.
- Students are introduced to algebraic notation and its use in solving problems and generalisation.
- It enhances the systematic study of space and shapes and for consolidating their knowledge of measurement.
- This stage also offers an opportunity to enrich students spatial reasoning and visualisation skills.

At the secondary stage:

- Students begin to save the structure of mathematics as a discipline.
- They become familiar with the characteristics of mathematical communication.
- They carefully define terms and concepts, use of symbols and justify prepositions.
- These aspects are developed particularly in the area of geometry.
- Students develop their facility with algebra in mathematics for providing justifications and proofs.
- Students integrate the meaning concept and skills that they have learnt into a problem solving ability.
- Mathematical modelling data analysis and interpretation taught at this stage can consolidate a high level of mathematical literacy.
- The use of appropriate tools that include concrete models as in mathematics laboratories and computers.

#### 3. Higher Secondary Stage

The aim of the mathematics curriculum at the higher secondary stage is:

- To provide students with an appreciation of the wide variety of the application of mathematics.
- To equip them with the basic tools that enables application.
- The rapid explosion of mathematics as a discipline and of its range of application.
- The communication of mathematical insights and concepts which is naturally interested and curiosity of students.

**Major Objectives of the Mathematics Curriculum:**

- Proficiency in fundamental mathematical skills.
- Comprehension of basic mathematical concepts.
- Appreciation of significant meanings.
- Development of desirable attitudes.
- Efficiency in making sound mathematical applications.
- Confidence in making intelligent and independent interpretation.

**Vision for School Mathematics Curriculum as Laid in CNF 2005:**

- Children learn to enjoy mathematics rather than fear it.
- Children learn important mathematics: mathematics is more than formulas and mechanical procedures.
- Children see mathematics at something to talk about, to communicate through, to discuss among them, to work together on.
- Children pose and solve meaningfull problems.
- Children use obstructions to process relationships, to see structures, to reason out things, to know the truth or false statements.
- Children understand the basic structure of mathematics: arithmetic, algebra, geometry and trigonometry.

## 1.2 Principles of Curriculum Construction in Mathematics

**1. Principle of Utility**

All that which is useful should be included in the curriculum of mathematics.

Mathematics curriculum should incorporate all those topics which are:

- Helpful in day to day life.
- Helpful in learning of other subjects.
- Helpful in providing common ground for a fairly good number of vacations.
- Helpful in the proper understanding and progress of one’s culture and civilization.
- Helpful in acquainting the students with the contribution of mathematics in the improvement of heavy industry, engineering, trade and commerce.
- Helpful in the realization of the aesthetic and artistic value of the subject.
- Hlpful in inspiring the students with biographies and history of discoveries.
- Helpful in understanding the scientific and technological progress.

**2. Principle of Disciplinary Value**

- It disciplines and trains the faculities of mind.
- The topics and contents of mathematics which help in the task of discipline in the mind.
- It has been experimentally prove that the real useful problems.
- The mathematics curriculum we should not include it simply, because it has disciplinary value.

**3. Useful for Higher Education**

- The child aims to go higher and higher on the education ladder.
- The education at one stage must aim to prepare the child for the education at the highest stages.
- Curriculum of mathematics at any stage most connected to the needs of the higher classes.

**4. Child Centeredness**:

- We must give proper weightage to the needs and requirements of the students.
- In any scheme of curriculum construction, the needs ability, interest and other developmental characteristics of the children of a particular age, interest and society should be kept in view.

**5. Integration of Theory with Practice**

- It is essential to have a proper integration of theory and practice in mathematics.
- The teachers should have to eye on mathematics for a fair representation.

**6. Flexibility**

- A curriculum by all means should have a flexible nature.
- So that it can be modified and reshaped according to the circumstances and demands of the resources in hand.

**7. Community Centeredness**:

- A curriculum should serve the community of a particular place by educating the children according to the needs.
- Community should be constructed and except for the welfare of the local community.

## 1.5 Recommendations of NCF 2005 with Reference to Mathematics Education

**Introduction**:

The National Curriculum Framework, NCF 2005 is one of the four national curriculum framework published in 1975 1988 2000 and 2005 by the National council of educational research and training NCERT in India. It provides the framework for making syllabus, textbooks and teaching practices. NCF 2005 document draws its policy basis from earlier government reports on education. The NCF 2005 in its position paper on “Teaching of mathematics describes the higher secondary stage as the launching pad from which the student is guided towards career choices.”

**The recommendations of NCF 2005 on mathematics curriculum are as follows:**

- The primary goal of mathematics education should be “Mathematisation of the child’s thought process” and the development of “inner resources of the growing child”.
- Mathematics empowers an individual to think logically handle abstractions, generalize patterns and solve problems using a variety of methods.
- Mathematics tought in the school should be “important”.
- The teaching of mathematics at all levels should be activity oriented and student centred.
- Students should understand the basic structure of mathematics and learn how to think mathematically and how to relate mathematics to life experiences.
- The emphasis is largely on developing manipulative skills to solve problems and they are is relativly on visualising concepts and exploring applications.
- Mathematics modeling should be introduced at this level making it possible to include the applications of some mathematical concepts.
- The content and the approach to dealing with the topic should be long term.
- The applications of each topic in mathematics should be focused.
- The senior secondary mathematics curriculum needs to have adequate emphasis on the understanding of mathematics as well as a problem solving.
- Mathematics curriculum should be interesting and importance but not limited objectives.
- Opportunities should be provided to the students to believe that mathematics is an exact science.
- The application of mathematics should be developed from primary stage.
- Students should be helped in understanding proper direction in career options.
- Highlight the relevance of mathematics as a discipline.
- Shift the focus of mathematics education from achieving narrow goals to higher goals.
- Engage every student with a sense of success.
- Cange the modes of assessment to examine mathematician abilities.
- Emphasis should be given to problem solving skills.
- Mathematics at the pre-primary stage should be in play way method.
- Importance should be given for correlating mathematics with other school subjects.
- The beauty and asthetic aspects in logics should be identified.
- Mathematical expression should be clear and brief.

### 1.5.1 Recommendations of APSCF 2011 with Reference to Mathematics Education

- Understand and develop skills related to number and space.
- Importance should be given to logical proof.
- Mathematical skills should be taught.
- Gometry and Trigonometry should be completely understand.
- Complete understanding should be provided in algebra.
- Clear understanding should be developed about abstract concepts and their uses in daily life.
- The problem solving abilities should be developed in the student.
- Higher level data analysis and substitution should be emphasized.
- Conducting experiments in mathematics laboratories and formulating new concepts should be taken.
- Emphasis to creating and solving a problem.
- Mathematics club should be established and mathematical programs should be organised.
- Research projects should be taken up.
- Interest should be around in the students by explaining and research.

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