# How does thinking in Maths differ from other subjects when all thinking appears Similar?

Studying Mathematics is fascinating for some
whereas it is boring for others. A few love to solve problems, whereas the
majority are afraid of attempting it. Why is this contradiction? Is it because
of their schooling or is it their mental makeup? Why don’t schools teach us
what type of thinking is involved in mathematics? How does thinking in
Mathematics differ from other subjects, when all thinking appears similar?

**Why do we Study Mathematics?**

I have asked thousands of people ‘Why do we study Maths?’

Some glare at me, some ignore my question, some
think I am pulling their legs, and others are lost. So far, I haven’t found a
single person who can answer me convincingly.

This is because of a series of lapses in curricular
development.

People stopped asking ‘Why?’ Everyone assumed
that everyone knows why. Nobody wanted to look foolish asking why. You
shouldn’t ask such questions when everybody has accepted it.

**The Purpose of Education**

The purpose of education is not to acquire knowledge. It is for learning new skills and mastering them. As we need tools
to learn skills, we are provided with subjects, curricula, and syllabi.

After helping children to learn the basic skills in
primary education, they are gradually introduced to higher skills. One major
set of skills is thinking skills. Mathematics as a subject provides us with a
lot of opportunities to develop different thinking skills.

Solving problems is not the objective of Mathematics.
It is to find out what type of thinking is involved while solving problems.

**Rational Thinking**

The difference between an educated and an
uneducated person is that the former can carry on rational thinking as against
the latter’s emotional thinking. However, nowhere education has fulfilled this
objective and educated people are as irrational as anyone because they don’t
put into use what they have learned during schooling.

A majority of them don’t even know that they have
learned different types of thinking to put them into use. They still carry on
with their irrationality despite being “educated”!

**Systematic Thinking**

Another equally important aspect of education is to
inculcate systematic thinking against haphazard thinking. The thought processes
are not allowed to run wild. There is less scope for imagination and fantasy in
mathematics.

Whatever is thought about, has to be specific and
accountable. This systematic thinking brings discipline into our thinking
process.

However, despite introducing mathematics in
schools, people who are educated are also influenced by haphazard thinking. You
just have to look at the influence the movies have on people. Film stars are
more famous than scientists. This is because we ascribe less value to
education.

**A Hypothetical Problem**

A wealthy farmer meets with an accident and is
bedridden. He has four children – three sons and one daughter – and his wife is
deceased.

He summons his lawyer and informs him that he wants
to write a Will before he dies.

“How much am I worth?”, he asks the lawyer.

The farmer has irrigated land, dry land, commercial
buildings, houses given on rent, the large bungalow he is living in right now,
jewelry, and cash.

**Abstract Thinking**

Whatever the lawyer answers, he has to first engage
in Abstract Thinking. What is visible, as listed above, translates to Concrete
Thinking. However, the farmer has asked him how much he is worth. This means
that the lawyer has to translate wealth in terms of money.

As soon as we come into numbers, we engage in
Abstract Thinking. We can’t see the amount of money directly but all the
property should be converted into money, which is intangible right now.

Abstract Thinking is a basic ingredient of
intelligence. Why people who are good at Mathematics are attributed to be
intelligent, is because of this reason.

Whatever value the lawyer comes out with is just a
rough estimation. This is because there are so many factors involved when land
and buildings are converted into cash.

All those things have to be taken into account.
However, none of these factors are observable directly, now. Hence, the whole
exercise is done on the level of Abstract Thinking.

**Deductive Thinking**

The farmer says “I want all my wealth to be equally
divided among my children”. This calls for deductive thinking. The lawyer has
to specifically arrive at a number. And the rule is added by the farmer saying
“equally”. This necessitates logic and hence this becomes Deductive Reasoning.

As there are four children, the wealth has to be
divided into four parts, and each part should be given to a child.

This requires calculation and hence, the lawyer
comes out with the equation:

Total Wealth / 4 = X

X is the portion of wealth each child is getting. X
is derived from total wealth.

Deductive reasoning forms a major part of
mathematics. Most of the problems we encounter and almost all the formulas we
use in science subjects adhere to this type of thinking.

Mathematical propositions, theorems, proofs,
operations, and arguments also involve deductive reasoning.

When it is applied to real life, the rules and
regulations call for Deductive Thinking. Traffic rules, timetables, work
schedules, and the roles and positions we have at work, all call for Deductive
Thinking. Deductive reasoning is used when you plan to catch a train or bus, to
reach a destination, to complete a project, or to purchase anything including
groceries.

Why white-collar jobs are compensated more when
compared to other jobs, is because of the need for Deductive Reasoning. This is
the reason why a qualified person earns more than an unqualified individual.

**Inductive Thinking**

Suppose the farmer in our example says, “I want the
wealth distributed according to the contribution each child has made to the
family”, then the lawyer is stuck with a major problem of Inductive Reasoning.

Unlike in the earlier example where a simple rule
“equally” dictated the division, now there are so many variables introduced
into the divisional process.

How do you decide what is each child’s contribution
to the family? First of all, how do you quantify contribution?

Is the yardstick you are using able to include all
variables?

Whichever way the lawyer divides the wealth, there
is scope for disagreements and disputes. Each child may feel that his/her
contribution to the family is greater than the others. Thus,

Total Wealth = Total Contribution of all children +
Total Property

X = Individual Contribution / Total Contribution of
all children * Total Wealth

In Inductive Reasoning, though logic is involved, all
factors cannot be considered, and the decision is made based on what is
important for the moment.

In real life, allocation of resources, compensation
procedures, application of rules and regulations, societal norms, mores, and
taboos, are some examples.

Buying goods and services because of ‘prestige
suggestion’ is a very good example of Inductive Reasoning. Both mass media and
social media are filled with advertisements that provide us only a part of the
truth. Famous personalities are used for advertisements and we conclude that if
it is good for so and so, then it is good for me, too. In addition, we do not
know whether these celebrities are personally using these goods and services!
But we still accept these suggestions.

Though a lot of people look down upon Inductive
reasoning as unscientific, they need to understand its importance by seeing its
application in mathematics. Assumptions and suppositions are so important in
mathematics that you can solve plenty of problems using them. Conditional
statements like if-then abound in mathematics.

Thus, practically, mathematics includes both these
types of reasoning depending upon the nature of the problem. For problems where
assumptions and suppositions are made, we use Inductive Reasoning. Once an assumption
is made, you start solving the problem using Deductive Reasoning.

You can’t assume or suppose whatever comes to your
mind and to that extent, mathematics is an exact science. Please keep in mind
that there are rules even to make assumptions and suppositions and once you
obtain the unknown, you verify the answer, and only then, do you conclude that
your assumptions were right. This is the essence of logical reasoning.

**Other Types of Thinking**

There are other types of thinking where logic is
not directly involved but are still used in not only mathematics but also in
real life.

For instance, in the example above, estimating wealth involves **Evaluative Thinking**, whereas estimating and quantifying the
contribution to the family, per se, involves **Critical Thinking**. Only
when these tasks are complete can Logical Thinking be used.

** Thinking in Maths**

Overall, we can say that mathematics primarily includes
Logical Reasoning where both Deductive Reasoning and Inductive Reasoning are
used. Logic is the hallmark of systematic thinking and is crucial in not only
solving mathematical problems but also day-to-day problems.

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