Teaching and learning resources of Mathematics

RESOURCES OF TEACHING MATHEMATICS

Introduction:

A fact that to keep teaching interesting and make it effective we have to make use of certain material aids. The use of these materials aids makes the teaching effective, simple and interesting. The use of sensory aids in teaching of Mathematics is of recent origin. The maths teacher we have been using text-books, writing materials Geometric instruments and the black-board since long as in used the equipment for mathematics classes. For many years resourceful teachers have been using models, instruments, drawings and other devices for stimulating interest and to facilitate learning of Mathematics. Since Mathematics is considered as a dry subject so to create interest in learning mathematics has been a constant problem for teacher. In mathematics teaching we require one or the other aid at every step.

Place of Projected and Non-Projected teaching aids in Mathematics:

There are so many abstractions in Mathematics which cannot be easily followed by the students. To make such abstract or complex ideas less abstract, rather concrete, teacher takes helps of various teaching aids. Thus teaching aids are aids to imagination of pupils. The importance of teaching aids in teaching mathematics in justifies on the following considerations.

i)  They help in clear understanding of the subject and clarifying the abstract ideas.

    ii) They appeal the senses of the pupils and so they satisfy their innate tendencies and interests.

   iii).They stimulate pupil participation. They are based on the maxim, “Learning by doing”.

    iv).They make the teaching-learning process interesting.

    v).They help in saving time and energy because it takes a long time in clarifies an abstract idea

       Verbally but the point can be made clear at once by using some appropriate teaching aid.

   vi).The needs of individual students are met. Some pupils learn by listening but a majority of

        they learn by doing.

   vii).They help in creating a lasting impression on the mind of the learner. Things are well retained

          in the mind since the sensory impression is more permanent.

Criteria for selection of Appropriate Teaching aids

             The planning and preparation of teaching aids require the teacher to:

Ø  Select the concepts to be concretised.

Ø  Translate the ideas into a visual form.

Ø  Select the most appropriate medium of presentation.

Ø  Design the layout and choose effective colour combination.

Ø  Prepare the aid

Ø  Evaluate its effectiveness for future revision.

Principles for the selection of Teaching Aids

1.       The selection of the audiovisual aids should be based on the age, the intelligence and experience of the students.

2.       The selected aids should help in providing the required multi-sensory experience to the students.

3.       The teaching aid should serve some purpose i.e. it should help in achieving the desirable outcome.

4.       The teacher should be able to make an effective use of the aid.

5.       The cost of the aid should be reasonable and within limits. The teaching aid should be appropriate and accurate in contents, measurements, clarity of concepts etc.

When to Use Teaching Aids

The audiovisual aids can be used for a variety of purpose such as:

Ø  Arousing curiosity.

Ø  Maintain interest.

Ø  Motivating the students.

Ø  Introducing lesson.

Ø  Development of a lesson.

Ø  Interpreting mathematical ideas and principles.

Ø  Correlating mathematical ideas with life and other fields.

Ø  Summary and review.

Ø  Follow up of a lesson.

Suggestion for effective use of teaching Aids:

The teaching aids serve their purpose best only when these are highly used.

Following suggestions be kept in mind while making use of these aids

 1. The aids should serve some useful purpose. Aid should not be used just for the sake of     using     

      an aid. Rather it should help in teaching a particular lesson. The teacher should be clear about   

      the purpose for which he is using the aids.

  2. The aid should be selected according to the general interest, abilities at the pupils.

  3. The size of the aid should be neither too large nor too small. It should be clearly visible to the   

      student. In mathematics, the diagrams, concepts, figures formulae etc. depicted through the    

      aids must be accurate. Accurate is very important.

  4. Aid should be used only at the right moment. If it is meant for introduction of the lesson it   

         should be shown at the proper time. Aid used at the wrong time may prove harmful.

   5. If the number of aids is to be used, then every aid must be used at the proper time and not  

    6. in a haphazard manner. The systematic display gives good results.

     7. The aid should be kept before the students as long as it serves some purpose. It should be    

         removed when it has served its purpose.

      8. While using teaching aids, encourage pupils’ participation.

      9. The aid used should be clearly visible (if it is a visual aid) and audible (in case of audio     

          materials.) to the entire class.

   10. The aids must be systematically displayed at the appropriate time. It is not advisable to  

           exhibit all the teaching aids to the class before they are used.

    11. Sufficient time should be given to the students to see the aid so as to observe and draw   

           inferences.

  Various teaching aids in teaching Mathematics:

   (i)  Non Projected aids:-

a)      Real objects

b)      Charts

c)      Models

d)      Black-Board

e)      Flannel-Board

f)       Bulletin-Board.

  (ii)  Projected aids:-

a)      Magic lanters

b)     Filmstrip

c)      Projector

d)     Epidiascope

e)      Motion pictures etc.

  (iii)   Excursions etc.

REAL OBJECTS

These are most useful and most effective means of providing direct experiences to the pupil Example to teach the area of four walls of a room we can make use of the four walls of class-room. Similarly black-board can be used to teach the area of a rectangle.

CHARTS

     Charts are one of the most commonly used teaching aids. The chart is a systematic arrangement of key facts or ideas in a logical sequence or representing ideas and facts in a pictorial or graphic form.

      Charts are defined as a combination of graphic and pictorial media for the orderly and logical visualizing of relationship b/w important facts, ideas or concepts. “Edgar Dale defines a chart as a systematic arrangement of facts in a graphic (or) pictorial form, presenting for convenient reference comparisons of quantity, distribution, trends, and summaries. 

The charts can be used for a variety of purposes such as.

1.       Motivating the students.

2.       Introducing a lesson.

3.       Deriving principles and formulae.

4.       Depicting various geometrical figures and their properties.

5.       Comparison of properties of different geometrical properties.

6.       Showing the steps in proving theorems.

7.       Relating mathematical ideas to day-to-day life situations.

8.       Showing the sequence of steps in geometrical constructions and problem solving.

9.       Highlighting key points in a lesson.

10.   Concretizing abstract mathematical concepts into visual forms.

11.   Summarizing lesson.

12.   Showing applications of mathematical principles and ideas.

13.   Tracing the historical development of certain mathematical concepts.

14.   Depicting interrelationship among mathematical concepts.

                     15. Presenting abstract ideas in a visual from showing continuity in teaching –     

                      learning process and summarizing information presented.

                            16. Motivating and arousing students’ interest.

     The use of charts save the teacher’s time and labour, otherwise wasted in drawing figures and diagrams on the blackboard. The charts help the teacher in presenting the matter in an illustrative manner with precision and accuracy and to capture the attention of the students.

Hints for Preparation and Use of Chart

1.       There should be caption or a title for the chart relating to the main theme presented in the chart.

2.       The chart should depict a single and definite aspect of the subject matter. It should not be clustered with too many facts or ideas.

3.       Charts should be colourful, pleasing a attractive.

4.       The figures, diagrams or sequence of steps presented in the chart should be appropriate, relevant and accurate.

5.       The diagram, figures and lettering should be of proper size. It should not be too big or too small. It should be visible to the whole class.

MODELS:

            Of all the audiovisual aids, models are nearest to live or real experiences. Models are three dimensional representation of an idea and therefore they are replicas of the original thing. For example ’a³’ is the volume of a cube of side ‘a’ units and can be represented by the model of a cube. ‘a²’ is the area of a square of side ‘a’ units and so on. Models provide contrived experiences where reality is altered or simplified for teaching purpose. Thus models simplify the reality and enable the teacher to reduce or enlarge objects to any desirable size.

                 In order to clarify and explain the abstract things, some things concrete like models have to be presented to explain those abstract things. Models are the three dimensional representations of the real objects E.g.

1. Models of geometrical solids such as cone, sphere cylinder etc. These models may be made out of card board (or) chart paper and may be used to teach topics such as area of a cone, are of a sphere, area of a cylinder etc.

2. The concept of angles can be explained easily if two strips are hinged at one end.

3. To prove that the sum of three angles of a triangle is 180o we can take a chart paper model of a triangle and fold it as under.

4. To find the area of a circle can be obtained by cutting a piece of cardboard. This      is then cut into 8 equal parts are these parts are then assembled.

Hints for Preparing Models for Teaching Mathematics

1.       The model should represent real objects and should give a notion of reality.

2.       The mathematical concepts represented by the model should be clear and accurate.

3.       The model should provide opportunities for the students to manipulate, explore and investigate.

4.       The model should provide the necessary motivate for the students to learn mathematical concepts and principles represented by the model.

Some examples for the use of models for teaching mathematics

1.       For teaching the properties and areas of plane figures such as circles, triangles, quadrilaterals, the teacher can make use of these shapes cutouts from chart papers or thin cardboard sheets.

2.       While teaching surface areas and volumes of solids such as cubes, cuboids, cylinder, cone and sphere, it is advisable to use models of such solids prepared out of paper folding or real objects of the same shapes. The use of such models provide opportunities for the students to explore, investigate and understand the various properties, similarities and dissimilarities.

3.       While deriving the expansion of algebraic identities such as (a+ b)², (a+ b+ c)², (a- b)²,

(x+ a)(x+ b), and so on the teacher can make use oif squares and rectangles of appropriate dimensions and rearranging them to get the required terms in the expansion. Similarly for expanding (a+ b)³, the use of cubes and cuboids of the right dimensions would be very effective. This helps the students to relate algebra with geometry and to appreciate their interrelationship.

4.       For teaching the topic ‘Mensuration’ in arithmetic, models will be of great help.

5.       For most of the theorems related to circle and triangles, the teacher can make use of a variety of models.