How to understand Maths when it is so Complicated?

Is Maths difficult? Or is it made difficult?

I have encountered several thousand students, parents, and teachers telling me that “maths is the most difficult subject!” They claim that it is very difficult to understand Maths because it is complicated.

They are quite far from the truth.

Provided we know why we study Maths, it becomes very easy to understand the subject and the topics it deals with. Maths can be understood by following the Sutra FASUP (Pronounce this as Face Up). After completing these projects, you can hold your head high because you can score as much as you want in Maths. And no longer it will be complicated.

Maths is the only subject that is very Flexible, Applicable, Systematic, Unambiguous, and Predictable.

SUTRA to Understand Maths

F – Flexible

A – Applicable

S – Systematic

U – Unambiguous

P – Predictable

The problem is not only in the understanding of the concepts in Maths but also in understanding the necessity of mathematical inquiry.

Let us delineate one by one.

1. Maths is Flexible

It is dynamic and flexible but provides certainty. Almost all subjects can use Maths to make their subject matter strong.

Flexibility comes in the form of converting from one system to another. For instance, weight is represented as pounds versus kilograms, height can be depicted as either inches or centimeters., and so on. Similarly, a graphical representation can be accurately drawn in so many ways.

Another characteristic of flexibility comes from comparison. The power of Maths has shown that almost anything in the universe is measurable. By quantifying a trait or a characteristic, comparison between two or more units, persons, things, ideas, etc., is possible.

The third characteristic is it reduces inaccuracy. As the values can range between the lowest and the highest in their minutest manifestation, the accuracy becomes almost perfect.

Students sometimes find it difficult to switch over from one system of metrics to another, but once they see the rationale behind such a conversion, it becomes so easy to extrapolate between the systems.

SOLUTION

Try different permutations and combinations of measurement. After solving a problem, try changing the value of one parameter or the sign of a parameter, and see the difference. This will provide a great insight into the breadth and depth of the flexibility present in Maths.

Ask creative questions like, suppose you go to a country where there is a right-hand drive instead of a left-hand drive, what all should change in thinking, and how Maths can help you to do so!

2. Maths is Applicable

Each concept in Maths has an application. Unlike other subjects where some theory is propounded, in Maths, everything is laid down as usable in day-to-day affairs.

The moment you come across a concept, find out where it is used, how it is used, what are its limitations, and what are its related concepts. For example, if you are studying a parabola, it makes a lot of difference to know where parabola calculation is used and why the calculation is done.

For instance, once you understand the Pythagoras Theorem, not only geometry but also algebra will become so easy. You have to stop looking at these subdivisions separately. They are quite intertwined in reality. However, we study them separately for our convenience in understanding.

My students felt that the normal probability theory is purely a hypothetical concept until they could find out how almost all the natural phenomena are distributed normally.

SOLUTION

Make a list of all the important concepts in Maths, one below the other in one column, and against each concept write down its application value in the second column. If you don’t know the application of a particular concept, don’t skip it but search for it either in your textbook or on the internet.

Compare and contrast the application of one concept against the other. For example, how are the areas of a circle and a triangle related? What happens when the area of a square is taken out of the area of a circle?

3. Maths is Systematic

Unlike almost all other subjects, where you may jump from one issue to another, Maths is highly organized, systematic, structured, and hierarchical.

One step leads to the other. You can’t skip a step nor can you add any extra steps. If an equation (or sum) has to be solved in seven steps, those seven steps are there for a purpose.

Students rarely count the number of steps necessary to solve the problem. In each step, there is a part of logical reasoning happening, which leads to the solution of the problem.

This logical reasoning can be of two types: deductive and inductive reasoning. Rarely do we find a distinction made between these two. A few assumptions have to be made in inductive reasoning whereas we stick to the given facts in deductive reasoning. Depending upon the logic, a set of rules are applied in both cases, which is once again systematic.

It always amazed me when my students couldn’t calculate square roots! When I reminded them that they have studied it in school and they are supposed to remember it, they used to tell me that they passed those classes and later started using calculators.

SOLUTION

Always count the number of steps necessary to arrive at the solution. Remembering this will make Maths so easy that you will start wondering what is the difficulty, here!

Next, find out whether Deductive or Inductive logical reasoning is used. In deductive reasoning, there is simple substitution and all you need to remember are the rules. Stick to the facts and you will automatically arrive at the solution.

In inductive reasoning, you make generalizations, assumptions, or estimations. Try to remember them and the context in which they are used. You can apply the same principles elsewhere when similar problems are given to you.

In so many cases, both deductive and inductive reasoning are used within a single problem. Identify these separately.

More about this you will find out in the other article: “How does thinking in mathematics differ from other subjects when all thinking appears similar?

4. Maths is Unambiguous

There is absolutely no scope for confusion in Maths, it is quite straightforward.

There is no ambiguity and hence can form the basis of universal laws.

Maths operates on a set of simple rules.

By following the rules in Maths, you can solve all problems.

Why students find it difficult is they tend to forget the rules. Suppose they have studied a rule in arithmetic in their primary school, the same rule applies even when they are studying engineering. However, by the time they complete high school, they would have ignored the rules. They think the rules and principles were important only in the primary class and not now.

What every Maths student should remember is: A rule is a rule all the time. Whatever your level of studies, the rules do not change, nor can be ignored.

I had to remind my students about BODMAS (BIDMAS), every time they were calculating something. If they used it yesterday after my prompting, it doesn’t mean they can skip it today! It is a universal rule that applies always whether the sums are big or small.

SOLUTION

Maintain your rule book. Keep filling in the rules every time you come across a rule for the first time.

Update it every year. Never lose the book. If possible, learn these rules by heart. They are very crucial in deciding your Maths performance. Teachers can’t repeat these rules every year because each year there are a set of new rules added to them. Teachers usually assume that you remember the earlier rules as you have passed the lower classes.

The simpler the rule is, the greater the chances that it may be forgotten. Simple rules form the foundation and ignoring them may prove very costly in the higher exams.

5. Maths is Predictable

What comes next, how it is constructed, how does it look, where do things appear – all these are laid out in an organized way only in the Maths subject.

Once you have the formula with you, you will know what to do, how to apply it, and what results to obtain.

There are no two or more ways. For instance, if you are finding the area of a circle, using the formula you can automatically confirm that the obtained value represents the area only. Unfortunately, students don’t analyze the formula before trying to recall it by heart.

If only they find the rationale behind the formula, why the different parameters are used, what is the connection between one parameter and another, and how is the obtained result a representative of all these parameters, it can never be easier than this.

Once I asked two engineering students to calculate the percentage of a value. I told them both the numerator value and the denominator value. Still, both could not solve the simple problem because they said they have forgotten the formula. When I asked, why they need a formula for such a simple thing, they said because they learned in school, they have not used the formula for a very long time.

SOLUTION

Always analyze the formula by taking into consideration the relationship between the numerator and the denominator as well as the left-hand side versus the right-hand side of the equation. For example, while calculating a percentage the obtained or given value divided by the total gives you the value in decimals for a total of one. To convert this proportion into a percentage, you multiply it by 100. The word percent should give meaning to you. Once you know this relationship, you can recreate the formula whenever you need it.

How to understand Maths when it is so Complicated?

Understanding Maths

In conclusion, Maths can be made meaningful by analyzing and understanding it qualitatively. It can be easily understood and no longer it is complicated. Rather than simply doing calculations, and keep spending our valuable time practicing the same type of problems, it becomes more worthwhile and interesting to know the why and the how of all these efforts.

Find everything about learning maths in the following ebook: