1. Mr. Dori Lal Chaudhary
(Asstt. Professor)
Department - TT&NFE (IASE)
Faculty of Education,
Jamia Millia Islamia, New Delhi-25
Effective Teaching & Learning in
Mathematics

2. MYTHS ABOUT MATHEMATICS
Many of us used to say that students ignore mathematics
because they feared from it and hence don’t take mathematics
after 10th class, but one important fact, that is very critical,
is that if it is so; then why they used to take admission in ‘commerce stream’,
while course of both the commerce and science stream is same!
Moreover, the number of admissions in science stream, B.Tech, B.Sc.,
B.Sc.Math (H); in last few years, shows an ascending graphical picture. They
are taking interest and are aware about it.
So, conditions are not so fearful or negative, as we are narrating or trying to
prove to be! However, some students (especially girls) feel some hesitation/fear
regarding, studying mathematics; but it is also due to our low-quality teaching-
learning processes and also due to neutralized and inattentive nature of primary
and secondary school teachers!
I hope that there will be an enormous increment in the number of
mathematicians, if we would modify, justifiably, our classroom
environment………

3. WHY?
 Why the children, even having 85-90% marks, are not selected or
failed to pass competitive exams! They know, very well, that
(A+B)2 = A2 + B2 +2AB; (A-B) (A+B)=A2 –B2; AREA OF
TRIANGLE = 1/2 (BASE)(HEIGHT); but they don’t know that
why, or how is it so?
 Teachers used to teach mathematics by a common old-fashioned
method. This leads to a condition, where most of the children are
unable to understand the respective topics or concepts.
 When we, our selves have a keen desire to eat different types of
delicious food for each day; then why do we expect from such
small children that they will take interest or enjoy the ‘same’
teaching-learning method for each topic? Since, they do not enjoy
the classroom environment; we fail to have any positive and
successful learning by them.
 We should encourage children to take part as well as interest in
teaching-learning process so that they learn mathematics with
enjoyment and can implement it in their daily life.
Then, only we can bring out a MATHEMATICIAN from a child.

4. EXAMPLE-1: AREA OF TRIANGLE = ½ BASE HEIGHT
A D
B C
Area of this rectangle = 32 sqs.
= (8 4) sqs.
= (length breadth) sqs.
On halving the rectangle:
Its area = 32/2 sqs. = 16 sqs.
So, area of Triangle ABC = 16 sqs.
= ½ (8 4) sqs.
= ½ (base height) sqs.
Or area of Triangle DAB = 16 sqs.
= ½ (4 8) sqs.
= ½ (base height) sqs.

5. EXAMPLE-2: AREA OF PARALELLOGRAM
A D A D A D
B C B B’ C C’ B C
Therefore,
AREA OF PARALELLOGRAM = AREA OF RECTANGLE
= length breadth
= l b

6. EXAMPLE-3:ADDING OF FRACTION
Children find themselves unable to digest the statement “in like
fractions, only numerator will sum up, not denominator”. We can
clarify this by an activity:
[1/4] [2/4] [3/4]
Hence, we have only to sum up water (numerator), not glass
(denominator) because denominator is only a referencing object or
number, which is describing the value or quality of our expected part
(numerator/water).
So, it is not important for us that students memorize every formula in a
few seconds, but it is important that every student must be able to
derive any formula in few seconds in the condition when he or she
forgets it.

7.  Learning is a verbal and behavioral change or modification,
whose source is our experience.
 Positive and successful use of learned skills, knowledge or
training, completes the process of learning.
 Successful and positive learning will be done only when we
create such condition in which children will learn naturally, even
after knowing its importance and also when they will use it in
their daily life.
 Develop such technologies that can lead to a better classroom
environment so, that students can enjoy their education period’.
Although, caltoonz and use of ICT in education.