WHY DO WE FEAR IN MATHEMATICS?
Mathematics is
considered as a dreadful subject by more than 90% of the people. A survey
conducted by NCERT few years back showed that more than 50% of class V students
are not able to do simple arithmetical calculation. The Annual Status of
Education Report (ASER) 2011 pointed the situation something more alarming. The
ASER report produced by a coalition of non- governmental organization has found
that less than a third of class III students in rural Indian schools can solve
two digits subtraction problems. The same trend was seen in the ASER 2012
report with almost citing the same problem and the surprising part of this
report was that the performance of students in 2012 was not better even by 0.5
% as that of 2011. Now the big question is - - Why do we fear in mathematics?
Let
me begin with a simple question---
How many of you would
feel comfortable in declaring that you are not capable of reading?
II
am sure none of you.
But if I ask how many
of you are not good at mathematics, some of you will answer in affirmative. It
is quite acceptable in our society to say that – I can’t do mathematics. It is
all because Mathematics has a tarnished reputation in our society. It is a
commonly accepted facts that mathematics is difficult, obscure and of interest
to certain people.
Why do People Hate Mathematics?
People hate
mathematics because it requires them to think and forces them to give the
correct and exact values. Math has a clear distinction of right and wrong. Most
people love to speak about any issues but hate to accept the fact that they are
wrong. Lack of good books, tarnished image in society, wrong teaching style and
lack of confidence are some of the cause responsible for hatred of mathematics.
Let’s begin with some
common examples:-
a) When
I look at math problem my mind goes completely blank. I fail to remember even
the simplest things.
b) I
am not good at calculation so mathematics is not for me.
c) Maths
exam terrify me. My palms get sweaty. I breathe too fast and I can’t focus on
my paper. When I see people around me working I feel myself stupid.
d) Mathematics
requires a special brain. I am not blessed with the special one so I can’t do
mathematics. I can’t learn the formula as it is tough to understand.
e) Mathematics
is not for girls.
These are the common
feeling among students. A feeling of intense frustration or helplessness about
one’s ability to do math is known as MATHS ANXIETY.
Have you ever delivered a speech?
If your answer is
yes, then go back in your old memory and recall your own situation when you
went to the stage for the first time. I am sure you would say that you were
nervous a lot. But if you are a regular speaker then certainly the fear factor
or nervousness would have taken a back seat. The same is true for mathematics.
One factor that affects math performance more than any other is confidence.
Studies do show that positive thinking can improve math performance. Always
believe in your own abilities and make it a habit of saying ---
I CAN DO MATH.
I AM GOOD AT MATH.
Such sentences will
boost your confidence level.
Do you know -- when
does the most powerful leaning usually occur?
When one makes a mistake
the learning process occurs most.
Never feel badly
about making mistakes in math. Positive attitude towards math is the first step
of success.
Let’s
now try to find out the reason of Maths Anxiety.
a) Social Acceptance:
- People hate mathematics because it is acceptable in our societies. People are
filled up with the notion that mathematics is a tough subject, it is for extra-
ordinary people and it requires the inborn blessing to be good at maths. If you
are terrible grammar you are made fun and looked down upon by your peers.
However, if you have difficulty even doing simple maths, people make a joke of
it. For example you will hear your peer or teacher saying- Ha-ha, do you need
my calculator to figure out this problem. Not one person will come to support
you that there is something wrong with that.
b) Wrong Impression:
- Mathematics is not tough but it is due to the prejudice eye that makes the
impression that mathematics is tough. If your father was good at mathematics
during his school days then he would expect you to be equally good in the
subject. Consider the situation when a child does not perform well in a unit
test and fails miserably then he is sure to be welcomed at home with the famous
dialogue--- YOU ARE NOT SMART ENOUGH. MATHEMATICS IS NOT FOR YOU. This feeling of inferiority and outright fear
puts a heavy burden on the tender mind of a child and he begins to think
himself not genius enough to cope up with mathematics. Let me
tell you the story of Albert Einstein. Albert Einstein failed in Algebra in his
sixth grade and was expelled from the school. His father scolded him much for
his inability to perform in Algebra. His maternal uncle was sure that Einstein
would do well and decided to teach him Algebra. He took Einstein to the nearby
jungle and politely asked --- Can you identify the bird flying in the sky?
Einstein replied in negative. His maternal uncle laughingly said—Let the birds
flying be x and took out a gun and fired a bullet. A bird fell dawn in the
bushes. Einstein and his maternal uncle went to search the bird and found the
dead bird was a CROW. Einstein said x = CROW. This was a simple story with a
deep message hidden in it. Algebra is nothing but a process to reach the
unknown. A simple story changed the life of Einstein that can happen with you.
Always understand one thing that
Mathematics does not inherently
come with an intimidating force field, it is not inherently owned by someone
like your father, teachers etc, it is not inherently a means for separating
winners from losers, it is simply a collection of discoveries inviting your
interest.
c) Wrong teaching style: -
I am sure many of you will not agree my view point but it
is the ultimate truth. People who are good at math are treated as if they are
super hero. Even the school teachers who are assigned the job to teach
mathematics do hardly make any efforts to make mathematics learning a fun. They
show no sympathy to the students who are poor at math on the contrary he/she
tries to put the impression directly or indirectly that poor students should
not do math. The result of this is an anti math bias at an impressionable age. H J S Smiths writes: - Poor teaching leads to
the inevitable idea that the subject (mathematics) is only adapted to peculiar
minds, when it is the one universal science, and the one whose ground rules are
taught us almost in infancy and reappear in the motions of the universe. Let’s
take some examples to understand the role of teachers in one’s life. Srinivas Ramanujan was a child prodigy but
many of you know that when he was in third standard he asked his teacher why
don’t we get quotient one when we divide zero by zero? His teacher rebuked him
for asking such silly questions and disturbing the class. Most of the students
face this situation in class. When he/she fails to understand a step and
inquires the question related to that the teacher in most of the cases make him
/ her feel a second graded student. This result to his/ her frustration and
distraction in mathematics in long run.
Here I would like to request all teachers to welcome the students who
ask questions in the class. Answering questions with proper reasoning will make
understanding of mathematics easier. Now
let me take one example of another child prodigy Carl Fredrick Gauss. His
teacher Butner accepted the facts that there was nothing left to him that could
be taught to Gauss. With the help of King,
Butner ensured that Gauss get scholarship for his study throughout his life.
d) Men are Naturally Better than Woman at
mathematical thinking: - There is not a 0.1% truth in this concept
that mathematics is for men and women can’t do fairly well in mathematics.
History tells the other version of story. Take the example of Hypatia of
Alexandria. She was the first woman to make a substantial contribution to the
development of mathematics. The list goes continuously. Thousands of woman
mathematician have made their contribution in popularizing mathematics with
their research and innovative ideas. Girls
are generally discouraged by the parents, peers and teachers with the
admonition that math “just is not something girls do”. The approach of teacher
towards girls taking mathematics is not favorable. The subtle messages sent by
teachers throughout the primary and secondary school years – perhaps without conscious
intention that technical subjects are too hard for girls. This attitude
practiced long is the reason of psychological fear among girls for taking a
back foot when it comes to taking mathematics in higher education. There
has been research examining gender difference in performance on standardized
tests across various countries. But you will be astonished to know that
Margaret Murray in her book – Women Becoming Mathematicians : Creating a
Professional Identity in Post World War II America has shown that since 1980,
women have earned over 17 percent of the mathematics doctorates in the United
States. We have seen that viewing
intellectual or mathematical abilities as a gift can create vulnerability in
females. It makes them susceptible to a lowered sense of belonging, to a loss
of confidence, and to decrements in performance in the face of difficulty and
in the presence of stereotypes. However, most important, we have also seen that
sending a message that these abilities can be developed can alleviate the
vulnerability. Females who heard this message- whether through an intervention
or through a lesson that portrayed mathematical ability in this way- remained
on a par with males in terms of their math grades, their achievement test
score, and their performance on a very challenging maths exam. Another research has shown that the female
brains is more decentralized and have a greater ability to multitask because
their cerebrum is more active. Women use a variety of parts of their brains
when they do a single task. The female brain is more integrated with more
complex connections between both hemispheres. Women can think logically and
emotionally at the same time. Other
tests have claimed that females are superior in language, verbal fluency, speed
of articulation and grammar, also arithmetic calculation. In year 2005, Psychological
scientist Stephen Ceci and Wendy Williams of Comell University set out to
understand the difference between men and women in maths- intensive fields such
as physics, electrical engineering, computer science, economics and chemistry
and found that women’s choices not abilities keep them out of maths intensive
fields.
e) Mathematics
requires an inborn attitude: - There is a general
misconception that Mathematics requires an inborn attitude. Gauss, Pascal,
Ramanujan etc. were the child prodigy who showed their early skill in
mathematics at the very early age but there are numbers of mathematicians who
were not good in mathematics in primary stage. Plato, Pythagoras, Newton,
Einstein have had mathematical anxiety at their early age but later they overpowered
mathematics with their mental strength. Researchers do believe the idea that
there is no genius, no great contribution, without great efforts- not for
Edison, Darwin, Mozart or virtually anyone you can name. despite the ‘legends’
, most geniuses put in years of intensive, even obsessive, labor before their
potential reached fruition and they made the contributions we know them for. Mathematics is indeed inborn, but
it is inborn in all of us. It is the confidence level that matters the most. If
you practice mathematics regularly and understand the fundamentals you are the
ultimate winner. People who are good at math have an ability to see a problem
in different ways. This is because they understand it. They apply varieties of
mathematical rules to arrive at the result. On the other hand people who are
bad a t maths stick to one procedure, the one they fell sure about and use it.
Suppose you are to multiply 99 x 25. You can both do a long multiplication
technique and arrive at the answer 2475 after a couple of minutes or break 99 =
100 – 1 using Distributive property you can break and then 99 x 25 = 25 x 100 –
25 x 1 = 2475.
f) Teaching Style is to be blamed:
- In many countries would be math teachers are required only to obtain a
passing grade or more than 50 % marks in mathematics. What does it indicates?
If a person joins a school as a mathematics teacher after obtaining just 51%
marks in mathematics, it means he/she has failed to understand 49% of the math
syllabus throughout his or her carrier. Now you can think about the alarming
situation. In addition to this the teaching methodology is not student
friendly. A method of solving a particular type of problem repeatedly before
moving to next type is being followed for centuries. Such techniques make math
learning a dull experience as no new ideas are generated in the monotonous
environment.
Plutarch
says – The mind is not a vessel to be filled. It is a fire to be kindled. There is a general concept that if you are
good at cramming tables, fast at
calculation, you are certainly having a mathematical mind. During childhood
we all use our fingers for simple arithmetical operations like – addition,
subtraction and multiplication. But when we grow older we stop using fingers
and calculate in mind as our education system put greater emphasize on mental
calculation. There are many who can’t do calculation without using fingers but
feel ashamed in using it because teachers in class discourage such practice
even in upper primary level. It
is ridiculous. What is the harm in counting on fingers? The ABACUS which is popular now a days and
parents seem to be crazy in sending their children to coaching to make their
sons/ daughters equipped with the Chinese technique of fast calculation is
nothing but a sophisticated way of
counting on fingers. Our educational
system is responsible for all this mess. A calculator can perform faster than
most of us do. Does it mean calculator has a large brain? Such misconception is
due to our education systems which emphasize finding solution by rote. This
make the other who has not learnt large number of table to think that maths is
not made for him because he/ she can’t perform fast calculation. There is one
more problem that we emphasize more on getting correct answer rather than
checking the correct process. Now the big question – is maths all about getting right answer? The answer is a BIG NO. It is important that you do
maths correctly answer will come out naturally. Many a times it happens that
you do 90% of your calculation right and gets a single line written wrong or
apply a wrong formula at the end and you are awarded zero marks. This should be
seen in other ways that you are 90% correct and you will be given marks up to
that stage. Here I am advocating the breaking up of the marks into several
segments so that for every correct stage students gets rewarded. I am sure this
practice at the very early stage will put a confidence in students. Always mind
one thing that mathematics is not all about calculation. It is true that
calculation is necessary in math, but it is not the largest part let alone the
true goal of subject.
Now let’s try to find
out the simplest way to overcome the
Mathematical Anxiety.
Let me give you my
own example. I still remember the day when I was in class 9. To deliver a
speech on 15th August, my teacher called me on stage and in a fear I
jumped the school boundary and flee away. Someone informed the principal and
within few minutes 5 students came to my home and overpowered me and took me to
school auditorium. My plan to skip the embarrassing situation failed. Though I
delivered a 5 minutes long speech but the very next day I was suffering from a
high fever. This episode had brought me in a very terrible situation. I skipped
all functions of my school and college. 10 years later, I spoke publically and
addressed the audience. Now it has become a routine job to address the audience
in different seminars, symposium, convention etc and I face the situation
boldly.
What I want to tell
you with my story that once you get the confidence to face the situation
boldly, you enjoy the thing. Mathematics can be done if you practice it
regularly. Regularity brings the confidence and the success gets birth from
confidence.
- Confidence is the key of Mathematics: - Mathematics is the backbone of life. The Kothari Commission says: - Mathematics should be taught on Compulsory basis to all pupils as a part of general education during the first ten years of schooling. It means you can’t think to get rid of mathematics at least for the first ten years of your schooling. It means you have to give due importance to this subject. There is a wrong impression in the mind of people that mathematics is an insipid subject and it is designed for the talented people. If you think so, then first change your mind because mathematics is not the ancestral property of any white collared people. It is not for any caste or race. It is for all. First bring confidence in you and assure yourself that YOU CAN DO IT. The confidence comes with regular practice and understanding the subjects. Hey, then what are you waiting for? Be ready, take your pen and copy and be ready for practice. The more you practice with proper reasoning and understanding the more confidence you gain and that brings a positive change in your attitude towards mathematics and you begin to love it.
- Develop a good rapport with
your teacher: - In class, develop a good rapport with your
teacher and let him/ her know when you are feeling lost. Don’t wait for the class to over.
Raise your hand the minute you feel uneasy. Mind one thing that your
silence can bring a pressure on your mind resulting your distraction from
the subject. So it is better to have the doubt clear. Always remember-
your success is your teacher’s success. Teaching mathematics is an art
which every teacher does not have. Those students who fall in right hands
love mathematics.
- Always try to know WHY AND HOW
in mathematics: - We focus too much on the HOW of arithmetic and
calculation instead of WHY. A lot of the historical questions that caused
people to pioneer new solutions or even develop new areas of mathematics
is all due to their generalization of question WHY. The birth of Non-
Euclidean Geometry is due to the questioning of Euclidean Geometry. Let me
tell you a story. I was in 6th standard when Algebra was first introduced in
our class. The teacher came and taught us some fundamental concept of
algebra and wrote: - 7
– 5 = 2 5 – 7 =
- 2 I raised my hand to inquire
why is 5 – 7 = - 2 but the teacher rebuked me for not being attentive in
class. In the very next class he
wrote -
(+) x (+) = + ( - ) x ( - ) = + on the black board.
Like
others, I too noted down the mathematical formulas form the blackboard but
could not understand the reasoning behind it. I raised my hand once again and
the result was same. I was made to stand on the bench for asking such silly and
childish question. I then went to a friend of my teacher Mr. Dheeran Ram and
asked him why 5 – 7 = - 2? He gave a simple reasoning. Plus (+) means you are
having that thing and minus (-) means that you are borrowing certain thing from
your neighbor. Suppose you got 7 apples borrowed from your neighbor (i.e. – 7 )
and returned 5 apples (+5) so you are still in debt of 2 apples, hence 5 – 7 =
-2. Many a times, a simple reasoning can
make your doubt clear and that happened with me. I, therefore advise you to ask
your teachers, parents, elders, neighbors
etc. when you face any
doubt however simple it may look to other. Even though all of us suffer from
maths anxiety to some degrees but is a serious problem for some of us. If is
like a burden that interfere with our lives, preventing in form achieving
goals. I
would like to put one another example from my college days. I used to take
tuitions in group with my batch mates. Many of my friends keep saying – yes
sir, yes sir for every step my tutor used to write on paper despite the facts
that they didn’t understand it properly. I was a problematic child for my
teacher. Whenever I used to enquire the reason behind writing the certain step,
my teacher used to scold me saying why did you take Mathematics Honors when you
could not understand the basic thing? I later found my friends coming to my
room to get the doubt clear. This is somewhat called suppression. This is a
very common practice by students. Students don’t want their weakness to be
known publically and in later phase it becomes the cause of their frustration. Understand one thing that feeling of maths
anxiety is common and that it doesn’t mean that there is anything wrong with
you or inferior about your ability to learn maths. Find a friend or relative who are good at maths and whom
you trust to respect your feelings. Share your negative thought about
mathematics. Ask him to guide you to handle any odd situation that comes in the
learning process.
- Build Missing Blocks: -Maths
is cumulative. In simple words, most math classes build on knowledge you
have got in previous classes. If you avoided mathematics in lower grade
then you will suffer in middle level. The same is true for other level.
You may be feeling stressed out because your background is weak. You can
overcome this situation easily by skimming through a text book that was
written for a level slightly lower than your current class. The foundation
of buildings is constructed with heavy iron rods, good quality cement etc.
if the foundation is weak the building is sure to collapse in a year or
two. The same theory applies here. If you were good at class 3 maths then
surely you will do well in class 4th maths. The courses are
designed by the expert committee in such a way that there is some inter
relation between previous class and current class. So if you want to excel
in mathematics you need to solid your knowledge of previous class. If you
put off your math requirement, you will be faced with the unpleasant
situation of having to learn new material and relearn all the forgotten
material at the same time. Remember one thing –MATHS IS NOT A SPECTATOR
SPORT! You must be actively involved in the learning process if you want
to do well in maths.
- Make a habit of doing homework
regularly: - Consider a situation after a particular class is
over; teachers generally give homework base on the class work. One night
you are sitting on your chain with class notes, text book to do home work.
After writing few lines your pen stops. You begin to turn the exercises,
class notes, and sometime in a puzzling mode call your friend over phone
to check whether you have a clue. May
I ask you a simple question? Have you read the class notes and
text books before attempting to solve the problem? Probably not. Hey, what
are you waiting for? Do it first. Maths is not a novel so take a pen and
paper. Maths is a dense written book. Every line contains a deep idea that
requires a novel way of thinking. It may take you half an hour to
understand a single page. Work through the example until you understand
the concept properly. Write each step on copy. It is better to write
things down rather than highlighting. Once you have gone through the book,
you are ready to work at the exercise. Sir Isaac Newton wrote: - I keep the
subject constantly before me and wait till the first dawning is open
little by little into the full length.
- Punctuality - Practice – Persistent: - My teacher used to
say - Mathematics is made of 3 P’s- Punctuality- Practice – Persistent.
Mathematics requires daily drilling. Make a habit of studying mathematics
2 hours – 3 hours a day. Choose time of your choice. The school text book
has a limited number of sums so I would advise you to buy some reference
book so that you may get varieties of problem.
- A good/ bad first exam score
doesn’t mean you are good/ bad at maths: - If you
get good marks in the first exam, don’t decide that you are brilliant
enough and you need not work hard for the rest of exam. The good result or
grade simply means you are doing justice with your maths subject. So don’t
get cocky and be consistent in reading. On the other hand if you get bad
score in exam, don’t jump on the conclusion that mathematics is not for
you. All the bad score means is that you need to do a little more work for
the next exam. I have seen many students getting A grade in first semester
and ending with C grade in the exam whereas there are many who scored C
grade in the first exam and finished with A grade in the final exam. Your
score simply doesn’t translate into a course grade. There is a whole
semester in front of you and lots of opportunities to improve your grade
so don’t despair if you didn’t do as well as you wanted to on the first
exam.
Let us sum up this chapter with some
list of DO and DON’T.
LIST OF DO’S
·
Do use your reasoning ability to study mathematics.
·
Make a list of your strengths and weakness. Workout
the area where you are weak. Take help from your teacher, parents and friends.
·
Attend class regularly and be attentive in the class.
·
Keep all the things on your study table neat and
organized. You should not have to waste time searching for stuff each time you
go for study.
·
Study 2-3 hours of mathematics with 1-2 break in
between. An hour of concentrated uninterrupted study of maths with no break is
sufficient to gain your confidence.
·
Find a quieter place in your house. If your table
faces the window, move it against the wall so that you can’t see the child
playing.
·
Make notes. Notes should consist primarily of
concepts, explanation, reasoning etc.
·
Memorize definition, properties and important rules.
·
Use definition, concepts and deductive reasoning for
every step in every exercise.
·
Answer questions/ ask questions. If you don’t
understand the concept ask your teacher for its explanation. For every right
answer pat yourself on the back. For every wrong answer take a vow that you
will not repeat the same mistake.
·
Find a friend who is poor at mathematics. Teach
him/her the chapter you have mastered well.
·
Make a list of formulas on a sheet of paper and paste
it on the wall.
·
Read good quality reference book.
·
Make mathematics a fun. Convince yourself that
mathematics is not all about calculation but it has fun side too. Read
mathematical puzzle, game and quiz book in free time.
·
Review old test paper to become friendly of the
question style.
DON’T
·
Read Mathematics book as a novel. Always take a pen
and paper and write important steps.
·
Don’t cram the test.
·
Don’t assume getting right answer is the ultimate goal. Don’t try to study by only working problems. Solve some problem that has no solution and of different style.
Don’t assume getting right answer is the ultimate goal. Don’t try to study by only working problems. Solve some problem that has no solution and of different style.
·
Don’t hesitate to ask a question. Be assured that if
you have a question more than one of your fellow students have the same
questions and virtually all in the class can benefit from a discussion of your
question.
·
Before moving to next chapter, get proper reading,
problem solving of the previous chapter. Complete 1st then move 2nd.
It is well said- It is better to
learn everything of something
rather than something of everything.
This is a chapter of one of my book Enrich your Maths Skill published by Prabhat Prakashan.
Please buy this book and read.
Send your comments at
Rajesh Kumar Thakur
rkthakur1974@gmail.com
