Mathematics Curriculum

Unit-1 | Unit-2 | Unit-3 | Unit-4 | Unit-5

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.

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1.3 Approaches of Curriculum Organization

The topics aur contents selected for inclusion in the curriculum should have a proper order and arrangement as to facilitate the teaching and learning officer concerned subject like in mathematics what office or contents should be reserved for the curriculum of one status or the other or what should be the scope and limit of the content in a particular class or steps in a particular class or stage should be properly decided in developing curriculum for a particular class or stills the following principles need to be considered for this purpose principle of logical and physical order principle of activity criterion of difficulty principle of correlation principle of topical arrangement principle of constructed concentric arrangement principle of spiral arrangement

1. Principle of Logical and Psychological Order

there are two different view points for the organisation of the contents of topics in mathematics 1 psychological and the other logical the former advocates the organisation according to the development of the mind of the child is needs and interest etc consider systematic knowledge more important than the child it demands that the topics should be taught in a logical order depending upon the fundamental process and modes of thinking in this way logic recommends that volume should be studied after studying all topics related to area but practically the volume is simpler than many topics in area that is area of circle etc therefore psychological it is improper to 30 in the way as logics orders on the other hand we cannot do away with logy as the systematic organisation of the subject cannot be sacrificed.

Psychology suit decide what type of logic is suitable for the students of a certain age and abilities and what kind of topics will be most suitable for the development of such logical thinking.

Psychological and Logical Arrangement

logical arrangement leads to the rigorous treatment of the subject matter which is based on logical reasoning where as psychological assessment is from the point of view of the students it seems that both the approaches are different what these can be easily most the organisation can both be psychological and logical all thinking is psychological psychology throws light on the power of understanding of students at a particular stage we can be logical in various ways psychology so decide which logical approach will show it for a particular topic logic will help in maintaining proper sequence of topics so I should organise the topics in such a way that we may follow psychology and logic at the same time the happy combination of the two is always desirable.

the nature of the subject mathematics is mostly logical and the subject matter requires rigorous treatment the subject grows on definitions rules and reasoning processes if we decide to deliver the content to the child it is Mela subject centred approach which is not located in the interest of the learner.

psychology throws light on the use of a topic for the people from the academic as well as practical point of view it takes into consideration the power of grasping and understanding of couples in a particular age group the order in which topics are to be tekken ok will largely depend on its findings similarly logic most with their psychology so decide what kind of logic is appropriate for the people of certain age and what type of topics will be most suitable for the development of social logical thinking logical help in maintaining the link and sequence of topics found in school and meaningful for the child.

2. Principle of Activity

child is active by Nature resorts in the field of pedagogy child learns through direct experiences more than the indirect expenses he should be given more opportunity for using concrete things in a major class in order to learn skills and aqua useful knowledge a topic which gives greater scope of practical work experiences and handling of concrete objects appear in liar classes and it should be alert to grow gradually into the abstract school of mathematics to be studied in successive higher classes.

3. The Criterion of Difficulty

Indore Ganesh song of the contents for topic we must try to follow the maximum from simple to complex what we put in terms of topics and contents in curriculum of any class or stage so sweet the mental capacity and development of the age group of the classes hostess it means that they are sold neither be too easy North to difficult topics in a curriculum the topic of the beginning classes should be within the comprehension of the children without involving any complication of the students go higher and higher on the land on the topic may take a more and more difficult for it should also be considered that what is simple for mathematics teacher may not necessarily be simple for the student therefore in every case the difficulty of a topic must be judge from the point of view of the pupils.

4. Principle of Correlation

While organising topics for contents of a curriculum one must be careful to see the maximum possible correlation of the topics of contents

With the life activities of the puppies b e with the techniques teachings of other subjects of the school curriculum c topics of the other branches of mathematics d with the topics are contents of the branch to which they themselves belong experience activities of the work experience areas

in seeking the above 5 types of correlation the following kinds of information need to gather about the students for home curriculum is being constructed

social physical and cultural environment of the students day to day life activities of the students nature of the other subjects taught and the possibility of seeking correlation with them of the topics are contents of the difficult branches of mathematics being taught in the different grades nature of the experiences gained in work experience areas of difficult grades and possibility of seeking correlation with them.

5. Principle of Topical Arrangement

Topical method is based on the unity of the topic that is complete education of the topic it means it topic one starter should be completely exhausted in the same class in doing so the entire topic the persons it’s difficult should be completed in the sentence this method has so many drawbacks

Merits:

It is possible to complete the hole in it due to less number of units in the syllabus it will be easy to complete the syllabus.

Demerits:

in every topic there will be easy as well as difficult persons on the ability of the locals which is highly on psychological view of the bookings you need it takes to 3 months time for its completion who is lead to develop hurting you feeling of boredom in the learn the topic for only one year after few years they may her get the topic and retention of knowledge is not possible there is no your to your revision of the event keeping in view all the adverb stated drawbacks it could be calculated that topical method is best on the principle of difficulty and it is not at all suitable for the organisation of mathematics curriculum.

6. Principle of Concentric Arrangement

This method was introduced in order to avoid the demerits of topical method rajmantri ko start every topic should be divided into parts subunits those parts should be graded according to the difficulty and each part should be introduced at a proper stage concern tree method is formed framed in accordance with these aspects concentric method is based on the principle of widening of knowledge just like the concentric circles with the same centre and different ready go on extending the knowledge of the same unit will be spread throughout in number of years for example the unit algebra is divided into types of units and introduce to s b i b i v i IAS and IPS classes in concentric arrangement song introductory knowledge will be given in the first year somo hire knowledge will be given in the second year and so on as the subunits are so arranged according to the age and ability of the Konkan couples can learn easily care should be taken in individual the unit into subunits so that the subunits should hire dete hue small not too lengthy because if the subunit is true length it will take the form of topical method and if it is too small it will not create any permanent impression on the mind of the learner.

therefore it could be concluded that concentric method is most suitable for organising the mathematics curriculum and most of the units in the present days secondary school mathematics curriculum are arranged according to concentric method only.

7. Principle of Spiral Arrangement

this is almost similar to concentric method got the only difference is that in concentric method the gap between two consecutive subunits is 1 year age in spiral method it will be from three to four months it means that two parts of the unit will be arranged in the same class

this method came into existence in order to avoid the comment by some psychologist that in concentric method due to 1 year gap between two parts of unit there is every possibility for the popular to forget about the previous subunit this method could be compared with spiral or spring which indicates that the learning could be continuous without any kya power brake.

for example in 8th class mathematics test book unit 1 is real number and unit 5 is elementary number theory finally it could be concluded that spiral environment is the best ointment for mathematics curriculum.

1.4. Curriculum and Syllabus

the words curriculum and syllabus are used as contemporary works by some educational trust consider as separate.

syllabus is considered as the content part in the curriculum it should be repaired basing on the curriculum it may fairy from local to local ATI class for class it should be prepared under 30 30 gallons of teachers supervisors and publishers syllabus Syndicate content teaching aids methods and evaluation system in unorganised it should be useful in school for practical purpose syllabus consented with content in the curriculum syllabus is the topics to be studied in each subject for a column includes curricular activities and co curricular activities which helps for the development of all round personality of the child it comprises the syllabus of all subjects apps for a particular class.

through these figure it can we say that syllabus is the subset of curriculum.

The ideas to be kept in mind while framing the curriculum:

The age And Nature of the Child: The general loading capability capacities and the child attitudes towards the subject should be kept in mind along with the child age.
Nature of the Content: The learners should be able to study the basic is used along with the methods of study and the broader concepts of the subject.
Nature of the Society: the topic should be selected basing on the type of life thoughts and attitudes which are required for a successful democratic life.

Need for Curriculum

It is an essential for an educational structure not only the objectives of education portal source path to teach how to teach to whom to teach and where to 30 it serves as a way for the students to achieve their educational goals different items in the school life like different subjects curricular and cocurricular activities the atmosphere and the social life is thing they are find a place in the curriculum provides the knowledge required for the school children and repairs them as a good citizen.

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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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1.6 Discussion of Important Concepts Principles and Process

(A) Teaching of Arithmetic

Hindi SI unit teaching of arithmetic is discussed branch of mathematics need for a system of counting it is to be efficient and successful living the teaching of responsibilities

in calculation of appreciative understanding of power number system and an intelligent proficiency in its fundamental process of number experiences

Nature of Mathematics

arithmetic is the science of numbers in the art of computer some mathematical is the queen of science and arithmetic the queen of mathematics most having maximum value to almost all human in all walks of life is utility and cultural and disciplinary values upto August to need any argument or explanation.

there is need of good command of arithmetic by skilled mechanic by the modern farmer bye the process progressive professional person is successful merchant and efficient housewife and buy a citizen in general automatic is both a light bearing and fruit bearing subject it sharpens our intelligent broadness board on our mental origin develop the power of sowing a problem logically in brief of a sound knowledge of arithmetic the fast branch of mathematics is very much essential for becoming an intelligent useful and efficient citizen.

Aims and Objectives of Teaching Arithmetic

The following are some of the aims of teaching arithmetic:

To develop mathematical thinking in the students to make the students gain interest in the quantities aspects of the world to give knowledge of the practical utility of arithmetic in everyday life to provide and facility in simple computer science of the fundamental process to prepare students for a study of higher mathematics.

The following are the major objectives of teaching of arithmetic:

Ability to perform various number operations skillfully to provide variety of experiences to enable the students to apply quantitative procedure effectively in society.

General objectives of teaching arithmetic:

to lay the foundation for understanding of number operations equipping the students with the competence to enable them to understand the mathematical statements to develop the ability to have correct analysis and reach proper conclusions to develop proper idea of different measures to develop the ability of performing computational jobs with speed and accuracy to give the students a clear idea of practical utility of arithmetic in daily life to enable the students to make dependable estimates and approximations to develop among students the quality of resourcefulness and ingenuity.

Principles of the Study of Arithmetic

the story of unity is to be regarded mainly on the requirement of the learner is to mastery in a certain spear of activity is new approach is considered as a tool in the first row 3 stage the four pillars to grow dexterity in the use of his tools then only the people on the scientific principle on the living in new rule childhood is the period of activity adolescence is the period of enquiry and manhood is the period of application the creative is mechanical abstract treatment of arithmetic is to be avoided in the early stages the task of the teacher is to 30 the profiles not alphametic it should be born in mind that finds its place in the curriculum due to the practical value cultural value and mental discipline the Kapil should feel that he is working arithmetic not because it is used but because he finds it is useful for him from the earliest the learners should be encouraged to think arithmetical and written work should not be introduced soon while framing the syllabus emphasis should be given to the fundamentals the learners should appreciate the need for arithmetic rules and implications the keynote for the teacher of arithmetic is cooperation which can result in the willingness response of cookies a rule for a special case should not be given which can be included in his general cash to be taught later on.

Approaches of Teaching Arithmetic:

The following four approaches generally used in the teaching of arithmetic:

Incidental Approach: In this approach teaching is done in rotational rational and incidental manner this approaches opposed to the traditional or drill approach.
Drill Approach: In this approach the teacher continuous repeat the task before the students till it gets fixed in the mind of the students.
Social Approach: The experiences of the teaching of arithmetic is done in such a way that it is closely with the experiences of the student in his daily routine.
Meaningful Approach: In this approach the whole program of the teaching work is systematically workout.

One basic thing that has to be kept in mind while teaching arithmetic is that it is a means of developing the child’s natural ability and teaching school lead to the method the best thing in the teaching of arithmetic is that two months of emphasis should not be put on the theory that students should be made to do things in a practical manual and their ability is to be assessed.

Place of Drill in Teaching of Arithmetic:

The students must be given a good drill to make the teaching of arithmetic effective and successful drill enables them to have the reputation of the knowledge that ultimately strengthens their experiences drill is nothing but exercise however a careful and systematic planning of the exercise and what is needed items should be made to correlate the drill of the exercise with the facts of life lesson will have permanent and lasting effect.

Following points are to be kept in mind about exercises and drill:

Drill should be clear and vivid it should have association fast and atoms and association in future there should be an element of motivation in there should be no scope for gas work.

Teachings on Specific Units of Arithmetic:

Teaching arithmetic in auto to be effective has to be guided by certain rules and regulations these rules and regulations are properly put forward the students are not be able to understand things properly the teacher needs to explain the general principles of understanding of the topic of the lesson which is to be taught the teacher should keep in mind the minimum levels of learning of the topics the students should be allowed to work independently the teachers should provide help keeping in view the individual differences exercise and drills should be provided the teachers should do the correlation very carefully in order to provide guidance to pupils.

Learners should be trained in oral alphametic work learners interest survi and ask and mental what not to be diminished develop systematic return work neatly and correctly roquefort should be done separately orderly to promote systematic return work problems should be selected by the teachers so as to help the learner to understand the use of the topic in day to day life the language of the work should be simple understandable and correct an effect should be made to develop order list accuracy and speed the teacher should follow the maximum of preceding from simple to complex the plane way devices in mathematics each child is to be provided with a mathematical kit accounting box there’s use trance type of screws toys animals toy money plastic roads napkins cars and the like using this keeps the child will learn in mathematical concepts children learn fundamental operations accountancy throws shopping games incidentally they may also be useful in measuring articles.

Few specific units

i. Numbers

The number concept is the most fundamental task in learning arithmetic in teaching it purposeful experiences with concrete object objects should be provided there should be no rote learning.

The number concept: Number to count individual things number to count cruise objects number as a symbol number as an operation and number as abstract.

Stages of number concept: The object the pictures tells the semi concrete stairs and the abstract simple steps each style has a little or more number sense before entering the school children are the cells have pre mathematical concepts and can distinguish between big and small more and less especially when they have some significance to them teachers should make use of real and concrete experiences for teaching numbers the play way method gives a good start in this connection teacher may make use of mathematical games play stories nursery rhymes toys and individual operators for this purpose.

Formally for teaching numbers the following steps are suggested:

Developing concept of more or less teaching accounting teaching numeration and teaching notation.

ii. Teaching of four fundamental operations:

Addition subtraction multiplication and division on the best or structure of learning in mathematics the proficiency in these operations is a fundamental necessity the basic unity among these operations is to be provided to the learners since they are mostly but only for different ways of counting in addition 1 kaunse forward where as in service tax on accounting is don’t required in multiplication or division counting is done for backward by leap of uniform length so what the initial stage these rules should we met relised in a closely integrated and correlated with the help of counting concrete objects.

iii. Percentage and its applications:

Percentage is a basic idea in business it is a fraction with denominator 100 it is denoted as % the concept of percentages is very closely in discount of 8% on loans and deposits dividends commission profit loss interest Excel it is so the topic can easily be introduced to the popular by referring to its use in daily life the story of percentages to begin with comparison of fractions as in school attendance performance of school results with another school results.

iv. Averages simple and compound interest insurance for sales of stocks and shares:

These topics aap direct during in the lives of citizens while teaching these topics learn mathematics club activities involving buying agencies and other commercial agencies so that the salesman know the advantages of self and high yielding investments.

v. Perimeter areas and volumes:

Throw hands on experience make the students class the concepts of linear square and cubic units with proper and cardboard cutouts models of different geometrical shapes and solids in the students in calculating their perimeters areas and volumes by measuring and computing.

Importance of mental arithmetic:

Doing without using paper and pen under mental arithmetic eating process mental abilities like constitution attention memory self confidence and self dependence mental arithmetic is stimulating making the popular skin and alright the Poppins effect in their knowledge and skills of calculations so mental drill serve as a useful purpose.

(B) Teaching of Algebra

David algebra Arabic in its origin it is distortion of the world all all all means the Java reference to the operation of transferring a quantity from one side of an equation to another coil macular means the process of subtracting similar quantities from both side of an equation.

algebra is nothing but generalised arithmetic and arithmetic is centralised algebra with the introduction of algebra the student learns to proceed from concrete to abstract.

Meaning and Nature of Algebra:

algebra is one of the important branches of mathematics symbolism and generalization are the two important characteristic observed in the structure and process algebra provides its language of symbols and power of generalisation to geometry trigonometry and all the branches of pure and applied mathematics it is a generalization of Walter Mitty cute animals The lost to expand extend the number system of alphabetic and perform the four fundamental operations in all cases algebra is primarily torch for manipulative skills solution of problems by equations for the power of generalization and use of formula on the idea of functionality algebra can be related to geometry algebra is the written geometry and GMT is the pixel algebra according to a and whitehead algebra is the intellectual instrument for rendering the quantitative aspects of the world in algebra arithmetical hacks for principles are denoted through abstract science and symbols in constant common size income form and expressed in an extended and generalized home for example of simple interest is equal rupi by hundred and volume of his softwares is equal to l X into b into X.

The Major Aims of the Teaching Algebra

removal of ambiguity and deficiencies of language to help in solving typical problems in arithmetic to simplicity the calculations to present the abstract relationship using new language and new symbols in calculate the power of analysis to check the results to make use of inductive method in order to evolve new knowledge.

Approaches of Teaching Algebra

big in teaching algebra to mental process generalisation abilities abstract thinking and reasoning power imaginative power powers of logical treatment and systematic analysis are developed in the learners start teaching algebra at the upper primary or secondary stage save from class 6 onwards when the students feel the necessity of learning to solve the problems of arithmetic in simple and logical method teacher algebra start teaching algebra and students started thinking in an abstract way with imagination and intuition make the learners know the way of expressing relations with the help of algebraic science converting the problem into an equation McDonald student known the meaning and significance of director numbers and their fundamental operations to start with most used concrete examples from arithmetic.

Example 2 apples plus 5 apples is equal to 7 apples or 2A + 5 is equal to 7:00 a.m..

There are three stages of development of algebra:

Dare re toruk synagogue and symbol area of a rectangle is obtained as the product of length and breadth psycho area equal length into breadth symbol a l into b.

Special methods of teaching algebra:

Formal method of teaching algebra four fundamental operations taught in arithmetic with letters replacing the numbers equation and problem method of teaching algebra these two methods are difficult to distinguish in teaching of algebra 2 starts with problem and equation method be used because it helps to develop interest in the subject teaching of algebra and literal numbers of quantities in algebra we use letter or literal numbers instead of numbers order of operations in algebra it is certain mathematical operations and a definite order to be followed in teaching these operations we should start with addition and subtraction and so till then take of multiplication and division use of brackets brackets occupy an important place in the teaching of algebra so it is very important to explain the use of crackers and the method of there in the students are to be given a clear idea of the meaning of brackets the students are to be trained as to interpret correctly mathematical expressions are in the brackets are used the students are to be trained to use the brackets correctly they should know when the brackets are to be used and when they shall be helpful the students are to be trained to transform expressions involving brackets into equivalent aspirations who is do not have brackets the term that are enclosed within a pair of crackers are one quantity just as if takat of books or a bundle of boxes etc crackers are like on 10 hours are the lemmings or areas that confirm certain things that students should be given a throw training in removing brackets.

Teaching Some Specific Units of Algebra:

i. Teaching director for signed numbers:

the major contribution of algebra lies in dealing with directed or sign numbers in arithmetic numbers relate only to magnitude or amount while in algebra numbers with positive or negative sign Syndicate magnitude and direction also the fast need is to attach certain meaning to the science Plus and minus. Kind of operation + r miner software direction + right word of God above negative leftword downward below opposite direction directed or sign numbers positive negative effect on direction + continuation indirection already established negative reversal of south direction.

ine number scale is used to represent director numbers by making a start from an arbitrary zero point ine number having no prefix sign is considered as positive by mathematical induction many rules could be able relating to the four fundamental operations with director numbers.

ii. Teaching simple simulators and quadratic equation:

Teachers should apply the principle of correlation in teaching various problems related with topics such as percentages averages profit and loss interest areas and volumes to cite a few these problems could be solved by using algebraic equations are the terms of equality used in solving equations when equal quantities are added to equal quantities the sum will be equal day and equal quantities are subtracted from equal quantities the differences will be equal when equal quantities are X equal quantities the product will be equal equal quantities are divided by the presence will be equal.

ability to translate the verbal problems in to algebra questions should be developed after gaining sufficient practice in solving simple equations equation in one on teaching of solving simultaneous equations in two unknowns are to taken out and equations in two unknowns are to be reduced to simple Little Champs in 11 and solve.

ability to translate the verbal problems into algebra questions should be develop development then factorising the expressions is to be taught with the help of ultrasonic number power of observation and systematic analysis involved in the process of fertilization should be developed.

different algebraic identities and formulae are to be arrived using fundamental operations launched in arithmetic the laws of indices should be developed using inductive method while solving quadratic equations graphic method inspection method using factorisation completing the square and quadratic formula could be used.

iii. Teaching of graphs:

This may be taken off under geometry in general and analytical for co-ordinate geometry in particular teaching of graphs should begin at largest in education in the middle of the upper primary stages or in High school stage secondary stage graph bring in natural correlation among all the branches of mathematics modern world is the world of started the entire structure of the country is economic planning population control eradication of diseases preparation of budget and others needs statics and graphs provide help in studies as well as in expressing and solving algebraic equations graphs compare the attributes graphs are in school in the concrete illustration of various mathematical facts and relations algebra questions can be solved and properly integrate graphs are very useful and concrete digital assets making the learning of mathematics more easy and effective graphs helps in developing aesthetic sense alternating educated and uneducated persons in general and students in particular the knowledge of graphs helps long hairs of institutions to know and register the progress.

(C) Teaching of Geometry

Geometry jee combination of two hours Plus which means measurement of Earth it has two whole values it provides knowledge and animals students to two things logically the geometry teaching provides a mass of geometrical forms the geometric principles of equality symmetry and similarity are implanted in the nature of things it is used in engineering machines of construction industries landscape architecture interior decoration ctg it is the key to mathematical thinking.

Nature of Geometry

Geometry is a branch of mathematics it is the science of space and extent it dominance the learning of mathematics in High school classes you know that both arithmetic and algebra are sciences of numbers where are giving tree is the science of lines figures sizes saves and measurement of this tree is pictured arithmetic for algebra geometry is the key to mathematical thinking geometry comprises demonstrative geometry and practical geometry demonstrated geometry deals with the shape size and position of the figures by pure reasoning based on definition self evident trust assumptions and other established geometrical to Euclid a Greek mathematician iron was the father of demonstrative geometry many methods for handling is problems his methods are institutional observational invention and constructive informal creative experimental and son.

practical geometry covers the construction aspects of course based on the former namely demonstrating geometry however it may be observed that demonstrative geometry employees demonstration of analytical reasoning by synthetic presentation.

Aims and Objectives of Teaching Geometry:

to enable dalna not to occur lot of geometrical facts to synthesise synthesizer the awkward information to make the students understand the geometrical principles of equality symmetry and similarity to enlarge geometry box to help the poles in understanding fundamental techniques of using geometrical instruments to develop a test for geometry to extend the knowledge to the Potter and more general aspects of daily life to make the learner developed culturally to make the learner more disciplined to make apples draw geometrical constructions correctly and neatly to make the students apply the backwards knowledge of geometry in day-to-day life and in understanding other branches of mathematics and other subjects to install in the profiles and appreciation for the significance of the geometrical proof to provide training in analytical reasoning to stress extension and accuracy in mathematical reasoning.

Stages of Teaching Geometry:

Geometry is to be taught in sequence the following three stages are suitable and useful for its teaching:

1. The practical stage or experimental stage:

Examining and handling the motorcycle models and copper lines angles triangles and so on experiencing symmetry variety regularity beauty of forms in nature and practical hours keeping and handling geometrical instruments the geometry box observing and drawing common geometrical figures emphasis on classroom and environment experiments on observation recognization and institute instruction.

hear the people will accountant himself with the common geometrical concepts and figures the people will be taught how to keep and handle the instruments of a geometric box the work will centre around the observing and drawing of, geometrical or geometric figures it should not be taken to mean that practical geometry and with distance but the practical geometry is only to lead to the study of geometry.

2. The Deductive Stage/Stage of Reasoning:

It is dost to learn to prove theorems and exercises the process will have to be presented in both practical and theoretical to provide flawless understanding in the later part of distance the students will be expected to get used to reasoning without dependence on real and concrete instances informal reasoning will be encouraged and made interesting and attractive are the stage the field will be unable to know the theorems of lemon tree and to solve easyriders.

3. The Systematizing Stage:

It is the stage of equation of mystery in reasoning reasoning here will be more so what properly sweetheart to the mental age of appeals practice in logical reasoning will be more important than answering them are the answer to dependence on exams will also be reduced.

Kinds of Proofs in Geometry:

dholana should be alert to follow different kinds of rocks in different cases it may be that one kind of proof is more agreeable and is your than the other so insisting on any one type of exclusively is not accessible.

i. Experimental proof: it involves practical work like measuring angle size etc in this case theoretical argument is placed replaced by practical process in increases the interest of the child is experimental proof is taught record the logical proof of any proposition.

Ex: in any triangle the greater side has greater angle opposite to it.

ii. Logical proof: it is a pure abstract argument given systematically in 5 district steps:

Hypothesis reference to particular figure conclusion construction if any proof

in giving a logical proof the learner has to recall the axiom postulates and the previous relevant propositions the proof process prominent unone analytic method.

the actual proof is presented in the synthetic way from known to unknown this is applicable to all theorems.

Ex: the sum of two interior angles of a polygon of n sides to 1 – 4 right angle.

iii. Intuitive proof: This is useful in obvious cases, needing no experimental or logical proof.