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# TEACHING MATHEMATICS IN A FRIENDLY WAY

## practical teaching of mathematics

Teaching mathematics in a student friendly way

Mathematics is a subject which is interesting for some students but disliked by many of them. One of the main reasons for this is the primary school teaching method of mathematics. There itself most of the students start finding it difficult and hence gradually starts disliking the subject. Some teachers are also are having the habit of asking questions in the class to students and when they answer wrongly, the whole class will laugh at them. Due to this, they will purposely miss some classes. This creates missing of continuity and hence poor performance.

Many teachers will make the students to mug up all the formulas, without making the students to understand the actual meaning of it. If we change the methodology of teaching, then we can create more interest for students in mathematics subject. We have to teach mathematics in the context of application of the subject in our daily life and should give pictorial representations for mathematical expressions.

**For example, we can teach (a+b) ^{2} pictorially in this way.**

## pictorial display

## similar thing for a-b

From the figure, (a+b)^{2} = a^{2}+b^{2}+ab+ab

= a^{2}+b^{2} +2ab

**Similarly we can explain (a-b) ^{2} also. It requires little more logic than the above example**

## (a-b)^2

## colours indicate areas

(a-b)^{2} = a^{2}-ab-b(a-b)

=a^{2}-ab-ba-(-b)

= a^{2}-ab-ab+b^{2}

=a^{2}-2ab+b^{2}

In the same way, while comparing volumes of some simple solids, one should have solid models and use water or suitable liquid to fill them and pour them to corresponding containers.

**As an example, volume of a cone and a cylinder of same height and diameter are compared like this.**

## volume examples

## the equations

Volume of the cylinder = pxr^{2}xh.

When on full cone volume of water is poured into the cylinder, only 1/3^{rd} height will be filled. This can be measured by a scale. OR, pour three times and the cylinder is completely filled. So, the volume of the cone of same height of the cylinder and same base diameter muse be 1/3 x volume of the cylinder

So, the volume of the cone = 1/3xpxr^{2}xh.

**Similarly, volume of a cone and a hemisphere of same size are compared like this.**

Let the base diameter of the cone be equal to that of the sphere and the height of the cone be equal to the diameter of the sphere =2r

## cone and hemisphere

## experiment

Volume of a sphere = 4/3xpx r^{3}

So, volume of a hemisphere =1/2 of that of the sphere

= ½(4/3xpxr^{3})

= 2/3xpxr^{3}

Now, the volume of the cone = 1/3xpxr^{2}xh. But here, h=2r

So, volume = (1/3xpxr^{2})x2r

= 2/3xpxr^{3}

So, pour the water from cone to hemisphere and show that they are equal!

## final word

Many teachers think that laboratory and experiments are required for teaching physics, chemistry and biology only. But I feel that it is more essential for teaching mathematics. Experts should set the syllabus in such a way as to teach mathematics in this way. Teachers are to be trained , if required , for this new method of teaching.

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