MAKING MATHS EASY

How to study Maths when the subject feels so difficult?

Many students find it very difficult to solve Maths problems. They keep attempting and somehow either they get stuck in the middle or if they get to the answer, they find that it is not right. How to solve this problem? How to study Maths? Especially when the subject feels so difficult?

Follow the steps below one after the other. Don’t jump any step because these steps are progressive. If you don’t succeed in completing a step, you must not continue. Make sure you finish the earlier step successfully and then come back here.

Pick up one chapter from your Maths textbook that is difficult for you and apply these steps diligently. You will then see that your Maths performance improves a lot.

1. Revise earlier learning

The first job you should do without assuming anything is to make sure that your previous record is thorough. You must pick up 10 problems randomly from the earlier question papers and try to solve them.

If you get eight or more problems right, then you can continue with the next step. Otherwise, do this first exercise until you get at least eight of them right.

You may not be able to score 80% on your earlier syllabus because of the following reasons:

· You may not have understood the concept clearly

· You may not remember the formulas correctly

· You may not have followed the steps suitably

· You may have missed the rationale behind the calculation

· You may have erred while putting the signs properly

Whatever is the reason, check it, correct it, and keep at it until you get 80%. Don’t be in a hurry to finish everything in one go. What you learn now is going to help you throughout your life.

2. Analyze the first problem

Once you have decided on the chapter in the current syllabus, take the first problem and try to analyze it.

· What is the question about?

· What exactly should you get as an answer?

· How do you derive the steps?

· What kind of thinking is involved?

· How many substitutions are there?

· How many deductions are there?

· What formula is being applied and why?

· What rule is being followed and why?

3. Inverted Triangle

Do not be in a hurry to pick up a similar problem from the exercise section and try to copy the solution. This is the greatest mistake done by almost all students.

There are a few more stages of preparation before you do it.

Imagine an inverted triangle. Look at the problem and try to fill in the gaps.

How to study Maths when the subject feels so difficult?

On the working sheet, draw an inverted triangle as shown above, and answer the following questions.

· Find out how many steps are there to arrive at the solution?

· What happens in each step? Write down next to the step.

· Sometimes a value is assumed, a parameter is added, a substitution is done, or a deduction is undertaken.

· Whatever happens, note it down until you reach the solution.

· Once you complete this exercise, compare the problem with the solution.

· How are they different? What insight comes through?

4. Counting Steps

The most important aspect of the whole exercise is to remember the number of steps you need to solve the problem.

Each problem has a fixed number of steps and every time you come across a problem, always remember to count the number of steps.

In the above example, only five steps have been shown for illustrative purposes. In actual cases, it could be more.

Just look at the other problems solved in the textbook within the same chapter and see if the number of steps changes or remains constant.

If they change, then try to analyze why there is a change?

You have chosen the easiest problem in the chapter by taking the first problem. Determine how things are added as the content progresses.

5. Compare the first with the last

Compare the first problem with the last problem and then come down to other problems. This is essential to understand the variation in the concept and the application of the concept.

Each problem in the chapter should be compared with the first problem so that you will have an idea as to what changes happen between them.

6. Follow Rules like BODMAS

Maths is highly systematic in its functioning and adheres to the rules very strictly. Errors creep in when these rules are either ignored or forgotten.

Check what kind of rules are being followed in the chapter.

· Sign

· addition

· subtraction

· division

· indices

· power

· exponential

· simplification

· estimation, etc.

7. Remember Formulas

You must remember the formula at any cost. To achieve this, you have to know the formula by heart. Try to write down the formula without referring to any notes or textbooks. Do this every day until you feel you are thorough. Then, reproduce it after a gap of three days, one week, one fortnight, and one month.

8. Prepare Charts

Make separate charts of rules, formulas, symbols, diagrams, etc. These charts will not only help you to remember things vividly but also minimize your exam preparation.

You can even devise strategies to make separate charts, for example, one chart on Area, another on Volume, etc.

9. Extract Common factors

These charts will also help you in extracting common factors between one problem and the other. Suppose you choose 'Volume', you can see what is common between the volumes of almost all shapes, whether it is a cube, sphere, cuboid, square, circle, pyramid, prism, cone, etc.

10. Remember unique factors

Similarly, identify unique factors. There are certain things you consider in some calculations, which you will never consider in other calculations. Extracting these unique factors will help you to understand the special characteristics. For example, if you choose Area, you can now see what is unique between the Areas of a triangle, circle, square, rectangle, trapezium, rhombus, equilateral triangle, sphere, semicircle, etc.

11. Go to basics when stuck and apply your knowledge

If you are stuck somewhere in the middle while trying to solve the problem, don’t refer to the textbook or notes, and immediately correct your mistake. This is the gravest mistake almost everyone will do. The correction will happen on paper because you have copied it. But correction will not happen in your brain, where the information is stored. Chances are the same thing is bound to happen later, too. Let’s not carry this mistake to our exams, too.

So, try to reason out why you are stuck. Sometimes, we may have forgotten some basic principles. So, go back to basics and verify where you have gone wrong. Only then, come back to this problem, apply what you have learned, and try to solve the problem without any help.

12. Variation due to change in plus to minus

Once you successfully solve a problem, do not stop there. Change the sign from plus to minus once and see how the calculation varies from one problem to another. Now you will know the importance of plus and minus. The majority of the students make the mistake of writing plus for minus and vice versa. This is what leads them to miscalculations.

In addition, change the value of just one parameter, and see how the calculation differs from the original.

This kind of manipulation during practice is necessary for us to find the nuances in Maths.

13. Try to come from the Answer to the Problem

Another manipulation you can do is to see how things add up when you proceed from the answer to the question. If you can see the differences that occur in each step and how important it is, you will be able to master Maths.

14. Choose randomly and apply formulae

Pick up problems randomly from different sections of the book when you practice. Don’t stick to one chapter only. Remember that in the examination, questions come randomly. They don’t mention that the first problem is from the first chapter, and so on. When you do this during practice, you will have control over judging the questions correctly.

Doing this will also let you know which formula to use, and when. Many times, students get confused when they see the problem. They don’t know if they have to use linear equations or quadratic equations when they encounter the problem. If you have understood the nature of the problem and the use of the formulas, then Maths will become your favorite subject.

15. Clarify when the problem is given in words

Read the problem, convert it into a chart or a graph, or a diagram, and note down the numbers, values, and symbols used in the question.

Read the problem once again but start from the end and proceed to the beginning of the problem. In case you have missed something during the first reading, you will get it in the second reading.

Before you attempt to answer, convert the given problem into a diagram, especially in geometry.

16. Recreate Formula

The best way to remember the formula is to recreate it. When you recreate, you will know why exactly addition or subtraction happens? Why there is a division in most of the formulas? What is the importance of multiplication? What role do the notations play?

17. Don’t keep practicing day and night; learn how to practice

Identify mistakes done in the past and don’t repeat a mistake. Make new mistakes and try to correct them. You can afford to make mistakes during practice but not during the examination. If you know what mistakes you make now, you will not repeat them later.

There is a method to practice and it has to be systematic. Go through my article on “How to practice?” Maths is a skill and it must be practiced using the trial and error method only.

18. Don’t keep the textbook or notes open when you solve the problem

As much as possible the textbook or notes should be kept closed. The less you depend upon them, the more your learning will be. They should be used as a frame of reference and not as a crutch.

19. Warm up for mathematics before the exam

Don’t sit and practice till late at night just before the exam. I have seen plenty of students who prepare the night before only to come and sleep during the exam. Even when we wake them up and ask them to wash their faces, they continue their slumber.

Lack of sleep hampers our performance. Instead, go through the charts you have prepared and think about the problems you may get during the examination. It doesn’t cost to guess! Just before the exam, do some simple calculations so that the brain warms up for more complicated problem-solving. In addition, mentally go through the formulas and ensure you get them right.

20. Remove fear, anxiety, and stress

What most of the students have picked up is an unnatural fear of Maths. It almost becomes a phobia in a few students. As you practice associating fear with Maths, you start being anxious about your performance. Then there is a stress to please your parents and teachers.

Instead of yielding to these emotions, make sure that you have nothing to worry about as you have mastered Maths.

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Studying Maths

So, try to follow these steps one after another. There are no shortcuts in life. You may think why to struggle so hard. The advantage of a scientific method is, you need to train only once. Afterward, it is just practice. There is no need to keep learning the same thing over and again. We can invest the same time to learn something new.

Comment about how you were able to use these strategies so that others can also benefit from them.

All the best for you in your next Maths exam.