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Right Approach To Problem Solving

Dear Students, The Tips and strategies given below are very useful and skill developing and will definitely benefit you if you practice them sincerely. Consistent study of 6 to 7 hours daily with proper planning can give success even if you are an average student. And remember there are no shortcuts to success. Success is not something which you will find lying on the road. Success demands lot of sacrifice, discipline and hard work. As Henry Ford has rightly said.

“The Harder You Work The Luckier You Get”

In general most of the students do not have correct approach towards problem solving. Some of the common made mistakes are

• Many students read the question and the solution and then satisfy themselves that they could have attempted the question in a similar manner.

• Many students lay too much emphasis on solving higher number of questions

Step – I : Proper understanding of concept and its application.

Step – II : Mastering skills such as visualization

Step – III : Continuous interaction between theory and problems

Remember that there is no dearth of books and problems available. One has to draw boundaries and concentrate on quality rather than quantity. Doing 100 quality and concept based questions is more important than doing 1000 questions which have not been selected carefully. Remember that the purpose is to sharpen problem-solving skills. It is possible to prepare a topic by doing 30-40 problems only, if you try to solve them completely by yourself. This may also involve devoting half an hour or one hour or may be even more on an occasional problem. On the other hand, your preparation can be very weak and hollow even if you have attempted more than 200 problems on the same topic in the same time, thereby devoting much less time on difficult problems and leaving them as doubts to be cleared by your Teachers. The key to success in sharpening problem solving skills is to practice quality questions without seeing their solutions. In fact, it should be noted that Problem solving is the end result of many other important activities like:

If you have done all these activities properly, only then you would be able to solve problems successfully. Another misconception is collecting problems from all sources and then trying to solve them. Plan beforehand and tell yourself that you will solve a particular number of problems in the topic. Once you have achieved proficiency you need not waste your time in collecting still more problems. Also important here is that you have to solve relevant problems, problems of the level that are asked in the exams. Solving problems from here and there can lead to frustration which can disturb the entire plan. Let us now discuss each of the above key steps involved in problem solving.

Phase - I : Proper understanding of Concept and its Application

It has been seen that normally students move directly to the formulae and start solving problems. The result, after solving few problems they get stuck and ultimately get frustrated. This is basically because of wrong approach towards the subject. It is advised that student should follow following steps in order to have proper understanding of concepts and their applications. Basic steps of learning any concept.

• Understand the background of the concept

• What is the concept all about?

• What does the concept say?

• Focus on significance of the concept

• What are the exceptions to this concept?

• When, where and how to apply this concept?

• Follow the steps of derivation of the concept (very important)

• Try to reproduce concept in your words

• In case of any doubt read and understand the concept again

• Understand the application method of the concept

• Practice questions on the concept (Start from easy and gradually move to difficult ones)

• Diagnose the problems and take corrective measures

While Practicing, try to solve the questions completely

After mastering the concept and application methods, try to solve the question on your own. In the beginning (till you have achieved mastery of the application method and concept), write every step of the application method and solve the question completely. Once you have achieved mastery you may ignore some steps. Remember that trying to miss steps or solving in a brief manner in the beginning itself will lead to serious problems and the student will not be able to gain perfection. If you cannot solve the question, look at its answer briefly and then try truly to solve it again.

Phase – II : Visualization of the Problem

Follow the following steps to convert the problem. Conversion of problem in the form of a diagram helps in better understanding of the concept. Visualization of problem involves following steps.

Step – 1 : Draw the diagram as per the problem. (If possible)

Step – 2 : Once the diagram is drawn, check the problem again to see if what is asked in the question is clearly represented in the diagram.

Step – 3 : Check if the diagram makes sense. If the diagram looks absurd, there is some problem in your understanding of the question.

Step – 4 : Understand the question now by going through the diagram instead of the question. If you find that this is not possible, then your representation is wrong. You should be able to explain what is required by interpreting the diagram.

Step – 5 : Make modifications in the diagram till you are clear that the diagram is exact representation of the problem.

Step – 6 : Do not proceed to the next step till you are confident about the diagram.

Phase – III : Interplay between theory and problem solving

Normally students read the theory, understand the concept and then they keep on solving more and more questions. So the approach followed can be shown by the following diagram.

This is a wrong approach. Ideally, the student should move to and fro between text and questions. Remember, reading the text and solving homework problems is a cycle. Questions lead to answers that lead back to more questions. It is recommended that the students should solve questions in rounds and in multiple sittings.

Also remember that learning always happens in jumps. So rather than trying to complete entire exercise at one go it is recommended that students should attempt exercises in multiple sittings. The aim of sittings should be

First Round Objective : You should be able to solve 60 to 70% questions.

Second Round Objective : You should be able to solve 70 to 80% questions.

Third Round Objective : You should be able to solve 90% and above. Remember, you will learn more in six 1 hour periods spaced through the week than in one 6 hour period.

Four important tips for smart preparation :

• Well thought plan, firm determination and positive attitude.

• Strengthening the basic concepts and fundamentals.

• Strengthening application of fundamentals.

• Strengthening speed/strike rate and time management.

Last but not the least keep in mind that “Questions In Competitive Examinations are not difficult. They are just different

51 Basic Tips For Best Preparation For JEE (Main and Advanced)

1. Setting your own goal Let us consider life as a continuous stream of choice or desires. At each point, there is a progression choice, or a regression choice, but over and above there is a growth choice. Every rational human being has natural instinct to rise in what-ever he does. Students are no different, for a growth choice, you naturally set up goals, knowingly or sub- consciously, and why not, because Without them, you lack a sense of purpose in your attempts.

Goals direct. Have you ever noticed that when you take a trip, you become more impatient as you approach your

Goals motivate destination? This experience describes a very natural phenomenon buried in conscience. If you set a goal, you gain greater motivation to succeed, as you approach it. . Achievement of goals strengthens your desire to achieve other goals. As a result, you attain a

Goals reinforce self esteem higher sense of self worth and start climbing to paramount height; of success. The goal of becoming an engineer is very well in context and I hope is applicable to all the students undergoing our teaching programme. However, to achieve this goal, you have to develop certain sub-goals also. Competing JEE (Main and Advanced) is here a sub-goal. But remember that each sub-goal is a complete goal in itself, and deserves whole hearted attention. I hope that you would have realised that if you succeed in the sub-goal (i.e. getting through the competitive exam by finding a place in merit list), the main goal of becoming an Engineer or a Doctor will automatically be achieved in due course. If you select a very distant goal without sub-goals, you fail to see progress and become discouraged. You will be quite logical if you ask me as to how to set up a long term goal followed by a series of sub goals.

2. Start from where you are now As your first exercise, learn or practice something you can reasonably expect yourself to master in a relatively short period of Time. Then go over to the next step. If you have too much trouble in your first lesson, probably you have selected something too difficult for this stage. Look for an easier task in the same or related area. Evaluate your understanding of the fundamental principles behind that problem. Then move to the more difficult ones

3. Practice The only way to develop self confidence in any subject/discipline is to Practice Hard. The more variety of questions you handle, the more confident you become.

4. Read By Text Books Many of us can not afford to drudge through text books, but it is important to do so to get a feel for all the fundamentals and application potential of the subject.

5. Pace Yourself Don't attempt frantically to work out problems that are over your head at the outset, or else you will just end up frustrated. Learning to master the subject can be very enjoyable if you properly pace yourself. Work at a comfortable level and experiment with numericals to learn more. If you make it fun, you will learn more in the long run.

6. Start With Your Favourite Subject Start with your favourite lesson if you find it difficult to start from very beginning.

7. Link The Chapters Make a chain of proceeding and following chapters in your study.

8. Identify Your Weak Subjects Identify those subjects in which you are particularly weak and pay more attention to them.

9. Test Yourself Let your friends test your abilities and grasp on the subject from time to time.

10. Work-Out a Time-Plan Work according to a time table.

11. Don't Waste Time Time is the costliest commodity in the universe that you can afford to waste.

12. Participate In Games and Sports Etc. Spare time for extra curricular activities also, but without letting your studies suffer.

13. Pay Attention to Your Personality Develop your personality as personality, behaviour and professional qualifications go hand-in-hand in life.

14. Repeat What You Have Studied Repetition helps you remember the things with greater effectiveness.

15. Repetition Refreshes Memory Mind is like a Dynamic RAM in a computer, and needs a refreshing pulse to prevent loss of data

16. Work-Out An Attack Plan Golden rule of chess soliciting planned moves is applicable in studies also with equal effectiveness while solving problems. It is better to have a bad plan then not to have any at all.

17. Ask Questions From Yourself Every night, ask from yourself, "Are you satisfied with your work habits!" and "Are you satisfied with your progress?"

18. Don't Be Frustrated Don't get disheartened by your lapses in the past. Redefine your sub-goals and prepare yourself to achieve them with strong determination.

19. Use Free Time Judiciously Use your idle hours (like when going to school, coming back from a friend's place or waiting at barber's shop for your turn) to memorise formulae or relevant information.

20. Connect Common-Life Events With Your Studies Develop a taste for practical problems. Try to analyse the events occurring everyday around you with a scientific attitude.

21. Think Rationally Towards Future Formulate to yourself the very worst that can happen, and then examine the eventuality and its consequences as objectively as possible. Then work-out ways to avoid pitfalls, or to make them the least injurious, if they are unavoidable.

22. Take Benefit of Advice of Superiors Seek advice of your parents, guardians, teachers and friends most freely. They are willing to help you, and your development is their concern also.

23. Act Immediately Act today. Never get into the habit of keeping the things pending.

24. Don't Befool Yourself By Inventing Excuses You can always find fifty one excuses for not doing a work (assigned to you by your ownself in this case), but for God's sake, don't try to deceive yourself by doing so.

25. Don't Skip Difficult Questions Pay a lot of attention to trivial questions. The questions that you tend to dismiss as insignificant can be important from the competitive examination's point of view, or for proper understanding of the subject.

26. Learn By-Heart Learn the lessons by heart. Don't try to cram them.

27. Finish Every Day's Work Everyday Work kept in abeyance keeps on compiling.

28. Manage your time efficiently Like money, time has a way of disappearing-a dribble here, a dash there, until you find yourself asking at the end of the day," Where did it go?"

29. Budget Your Time It is only by budgeting the hours and minutes of the day that you can have lime left over for buying confidence in studies.

30. Try Tricky Problems After Small Time Gaps Some tricky problem has become just inconceivable/ unsolvable for you. Never mind. Relax. Did you ever notice that one of the first things that strike you about a girl in her perfume? After you have been with her a while, the perfume seems to disappear. But if you leave her and come back, the scent is as vivid as ever! May be that is what you should do with this question. Leave it for a while and do something else. Then come back to it.

31. Handle the Problem In different Phases Like stories, all problems have a beginning, a development and an end. When you come across a seemingly difficult problem, at least you can start solving it (beginning) and do something in its development phase also, even if you are not able to bring it to an end. Resist the temptation of surrendering abjactly.

32. Try Alternatives Consider alternative approaches of solving a problem to eventually save time in the examination hall. Otherwise also by knowing different ways of solving a problem, you can enhance your confidence to tackle problems.

33. Plan Your Actions You need a game plan for your day. Otherwise, you will allocate your time according to whatever happens around you. Start each day by making a general schedule, with particular emphasis on two or three major themes you would like to accomplish.

34. Concentrate Of all the principles of time management, none is more basic than concentration. The amount of time spent on a problem/chapter/subject is not what counts: it's the amount of uninterrupted time, and knowledge gained thereof which actually matters.

35. A Golden Rule Yesterday is a cancelled check. Forget it. Tomorrow is a promissory note. Keep it in mind. Today is ready cash. Use it!!!

36. Try Readily Available Audio-Visual Aids One friend of yours records his class notes on cassette tape recorder and plays them back while dressing.

37. Sleep Well But remember, half hour nap can equal three hours of night sleep. However, there is one more factor; how well you rest means more than how long you sleep. Don't over-sleep.

38. Arrange For Some Accomplishment Feedback This is the art of designing tasks so that you succeed bit by bit, reaping a reward and strengthening your desire to achieve more. Promise to yourself small rewards after attaining your goals, and fulfill these promises.

39. Seek Models of Achievement See the movement of successful people around you. It will stimulate your desire to succeed and you can learn a great deal by visualising how they act/react in certain circumstances.

40. Take Benefit From Other's Experience Learn from other's experience, especially from high achievers, by seeing/listening to them.

41. Finish Up Every Job You Take Up In Hand Never get into the habit of leaving the job unfinished.

42. Share Your Experiments If you are a topper, then share your experience with others. No-body can beat your talent, but your thoughts will be further stimulated by doing so, to your own advantage.

43. Learn the Art of Quick Scanning Seasoned readers use little tricks, often quite unconsciously. They go through a shelf of books (as in a library). Pulling out a volume, they glance through its preface, scan the table of contents, run through the index and bibliography, look up a few references/chapters in the text. How do you do it

44. Devise Your Own Study Plan Skimming a book is like prospecting for oil. After you learn the signs, you get fewer dry holes.

45. You Need Not Start Reading From The Very Beginning Most people believe that the way to read a book is to start on page one and read straight through. Sometimes this is the only way to real understanding. But it consumes a prodigious amount of time and energy. I have found that many Scientists and Engineers start reading technical books with the summary at the end and then they turn back to check the findings. However, this method is not advisable for text-book level maiden studies.

46. Mark Key Points In the hands of a seasoned reader, a pencil is a probe that digs the meaning out of a book. You can underline key points, number them in the margin and index them on the flyleaf, or on a piece of paper for future reference (provided the book belongs to you!).

47. Use More Than One Text Books Dr. Eugene Ehrlich, Professor, In-charge of Reading Improvement at Columbia University's School of General Studies, recommends getting several books on the same subject and switching from one to another. "Three or four difficult texts are easier than one", he says," for one book illuminates another".

48. Control Your Sentiments Control your mood viz. feeling of getting hurt (when losing a friendship, a loved one, self esteem etc.), anxiety {worried, frightened, uptight), anger or guilt, as they all interfere negatively with your learning process.

49. Have Faith In Your Caliber There isn't much difference in the native intelligence of students. The one thing that distinguishes the 'A class students is that 1 whereas normal students, after hitting die book as hard as they can, say" Well, that's that", the 'A's say "Let's give it one more reading for good measure".

50. Criticise Yourself Be a critic of your own doings, with all your fairness

51. Stop Short-Circuiting Yourself With Alibis Unfocussed students do this constantly. They say, "The timing is wrong" or" my teachers arc not really good". They play the if only games:" IF only I had more money to hire tutors.........if only, I weren't so tied down......". The alibis go on and on, and just reinforce the three deadly characteristics-inertia, self doubt, and aimlessness.