CURRICULUM AND RESOURCE MATERIALS FOR TEACHING MATHEMATICS

CURRICULUM AND RESOURCE MATERIALS FOR   TEACHING MATHEMATICS

Curriculum construction and organization in mathematics

Meaning of Curriculum:   According to Cunningham “The curriculum is the tool in the hands of the artist (the teacher) to mould his material (the pupil) according to his ideals (objectives) in his studio (the school)”.

CURRICULUM

1)   Curriculum is “ A general overall plan of the content  or specific materials of instructions that the school should offer the students by way of qualifying him for graduation or certification or for entrance into a professional or vocational field”.(Good,1959).

2)  “All experiences a learner has under the guidance of the school” (Foshay, 1959).

3)   “Curriculum consists of all the situations that the school may select and consciously organize for the purpose of developing the personality of its pupils and for making behavioural changes in them” (Payne).

PRINCIPLES OF CURRICULUM CONSTRUCTION

1)    Principle of Disciplinary value: The topics and contents of mathematics which help in the task of disciplining the mind.

2)   Useful for Higher Education: The child aims to go higher and higher on the Education ladder. Therefore education at one stage must aim to prepare the child for the education at the higher stages. Therefore, curriculum of mathematics at any stage must cater to the needs of the higher classes.

3)    Principle of utility: According to this principle all that which is useful should be minded in the curriculum.

Mathematics curriculum should include all those topics which are,

i)    Helpful in day to day life.

ii)    Helpful in learning other subjects.

iii)   Helpful in realization of aesthetic and artistic value of the subject mathematics.

iv)    Helpful in understanding the scientific and technological progress and rendering help for the further research work in the field of mathematics and science.

4)   Child centeredness: In curriculum construction we must give proper weightage to the needs and requirements of the students for whom we are going to prepare a curriculum. Therefore   in any scheme of curriculum construction, the needs-ability, interest and other developmental characteristics of the children of particular age, interest and society should be kept in view.

5)    Integrity of theory with practice: Mathematics curriculum requires the topics, contents, experiences and activities in such a way that we may have enough opportunities of integrating theory with practice.

6)    Principle of flexibility: 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)  Principle of community centeredness: Curriculum be constructed and shaped for the welfare of the local community.

Principle of consulting experts: Curriculum construction needs the help and guidance of those persons whose interests are to be served by a particular curriculum

Principles of curriculum organization:

The following methods in general are adopted while framing the curriculum of a subject.

1)    1)  Topical and Spiral method:  Topical approach suggested by its name advocates to cover a topic as a whole in a particular grade. Here a few topics of the subject mathematics may there by marked for being included as in the curriculum of one grade or the other then it is expected to cover all the content or learning experiences related to that very topic only in that very class and not to repeat it in any way in the junior or senior grades. Thus a topic marked for a particular grade should have its beginning and end it that every grade without having its need to be taught in the earlier and later grades. We have different sets of topic for their inclusion in the curriculum of different grades of secondary stages of school education.

      It has been described under the head criterion of difficulty that easier topics should be dealt with earlier than the difficult ones. Certain portions of a topic are always easier than the other portions of the same topic. Thus Square Measure is easier than cubical measure. Again V=LXBXH is easier than the area of a circle or a triangle. Similarly in profit and loss, certain problems are easier than other. Inverse problems are generally more difficult than the direct ones.

     Spiral system is based on the principle that a subject cannot be given an exhaustive treatment at the first stage. To begin with, a simple presentation of the subject-matter is given, gaps are filled in the following year and more gaps a year or two later, in accordance with the amount of knowledge which pupils are capable of assimilating. Spiral method demands the division of the topic or the subject into number oif smaller independent units to be dealt with in order of difficulty suiting the mental capacities of the pupils, while the topical method demands that a topic once taken should be finished in its entirety. Spiral method is more natural and less tiring to the pupil. The child loses nothing in accuracy and gains considerably in the power of intelligent application of rules to problems.       

     Spiral approach may run contrary to the topical approach there we do not include topic as a whole and finish it entirely in a particular grade as practiced in topical approach but try to spread it over to different grades by covering easier portion   in the lower grades and the difficult ones in the higher and higher grades. In this way while expecting concentric (Spiral) approach in any single topic may find its place in the curriculum of different grades on that school education in accordance of the difficulty level of the subject matter/learning experience suiting to the mental level of the students.

     The chief defect in the topical plan is that it introduces in the curriculum a large mass of irrelevant material for which the pupil finds no time and no immediate need or the use of which cannot be appreciated by the pupil at that stage. They are introduced with a view to making the teaching of the topic complete and thorough.

Ex. –Multiplication and division with 6 or 7 digits in the first or second standard.

2)      2. .Logical and Psychological Arrangement:  Logical arrangement leads to the rigorous treatment of the subject-matter which is based on logical reasoning whereas psychological arrangement is from the point of view of the students. It seems that both the approaches are different but these can be easily merged. The organization 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 should decide which logical approach will suit for a particular topic. Logic will help in maintaining proper sequence of topics, so we should organize the topics in such a way that we may follow psychology and logic at the same time. The happy combination of two is always desirable.

Psychology should decide what kind of logic is appropriate for the pupil of a certain age and what type of topics will be most suitable for the development of such logical thinking. Logic will help in maintaining the link and sequence of topics found useful and meaningful for the child.

3)      3. Principle of correlation: While organizing the content in mathematics the principle of correlation should always be given due weightage. Correlation may be of different varieties. The following types of correlation must be kept in mind while organizing curriculum in Mathematics:

                                                                                I.            Correlation of Mathematics with the problems of everyday life.

                                                                              II.            Correlation of Mathematics with other subjects.

                                                                            III.            Correlation between different branches of Mathematics.

                                                                            IV.            Correlation between different topics of a particular branch of Mathematics.

                                                                              V.            Correlation with craft or work experience.

           For correlating subject-matter we must know the following:

Ø  Day to day life activities of the students.

Ø  The nature of topics included in other subjects at the same stage.

Ø  The topics included in different branches of the subject e.g., Arithmetic, Algebra, Geometry etc.

Ø  The sequence of topics of the same branch of the subject.

Ø  The nature of work experience or projects undertaken by the students.

4)     4.  Concentric approach:  

          This is a system of organizing a course rather than a method of teaching. It is therefore better to call it concentric system or approach. It implies widening of knowledge just as concentric circles go on extending and widening. It is a system of arrangement of subject-matter. In this method the study of the topic is spread over a number of years. It is based on the principle that subject cannot be given an exhaustive treatment at the first stage. To begin with, a simple presentation of the subject is given and further knowledge is imparted in following years. Thus beginning from a nucleus the circles of knowledge go on widening year after year and hence the name concentric approach. 

 Procedure:

     A topic is divided into a number of portions which are then allotted to different classes. The criterion for allotment of a particular portion of the course to a particular class is the difficulty of portion and power of comprehension of students in that age group. Thus it is mainly concerned with year to year teaching but it its influence can also be exercised in day-to-day teaching. Knowledge given yesterday and should lead to teaching on following day.

Merits of Concentric approach:

Ø  This method of organization of subject-matter is decidedly superior to that in which one topic is taken up in particular class and an effort is made to deal with all aspects of the topic in that particular class.

Ø  It provides a frame work from science course which is of real value to students.

Ø  The system is most successful when the teaching is in hands of one teacher because then he can preserve continuity in the teaching and keeps the expanding circle concentric.

Ø  It provides opportunity for revision of work already covered in a previous class and carrying out new work.

Ø  Since the same topic is learnt over many years so its impressions are more lasting.

Ø  It does not allow teaching to become dull because every year a new interest can be given to the topic. Every year there are new problems to solve and new difficulties to overcome.

Drawbacks:

·         For the success of this approach we require really capable teacher. If a teacher becomes over4 ambitions and exhausts all the possible interesting illustrations in the introductory year then the subject loses its power of freshness and appeal and nothing is left to create interest in the topic in subsequent years.

·         In case the topic is too short or too long then also the method is not found to be useful. A too long portion makes the topic dull and a too short portion fails to leave any permanent and lasting impression on the mind of the pupil.