After so many years of studying, teaching and tutoring math and physics (approximately 30 years) I have some ideas on how to study these subjects more efficiently which I would like to share with whom they might be interested. By more efficiently I mean how to optimize your effort in your attempt to increase your marks in these subjects. My analysis and ideas might be of a particular benefit for students from elementary school up to first year university because that is the group with whom I am more experience.
I would like to start with a note of optimism and assure you that the overwhelming majority in the above group approximately 95% can do reasonably well in these subjects.
First of all try to ignore any negative experience you might have studying these subjects. You will need some combination of a good teacher, tutor and book.
Let's start from the beginning of the learning process which is your classroom. Try to concentrate as much as possible and make every effort to understand your teacher. Do not hesitate to ask questions whenever necessary.
Once at home, the best advice I can give you is to take your time. When studying, study by time and not by the number of chapters or pages you supposed to cover. Make every effort to capture every detail. It may take you one hour to understand one page. Trust me is worth it. You will see that gradually you will be able to learn faster.
Start from theory of the topic you have to study. Whatever you can't completely understand make a note. Then proceed to the exercises and problems that your teacher assigned. A reasonable teacher would base his/her evaluation plan (assignments, quizzes, tests, exams) on the material he/she asks the students to prepare. Again make a note of each problem you can't answer. Take these notes to your teacher or a tutor and make sure you resolve them completely. Please don't ignore them. Trust me you will find them in front of you sooner or later.
Regarding the problems you have to solve approximately 90% of them are based on a certain methodology that any efficient teacher should be able to give you. You might also find these methodologies in some books. The rest 10% are a matter of practice and luck.
Try as much as you can to work in time intervals that your actual exam or test will be. What do I mean? The majority of final exams in college is 3 hours long. So try to study for 3 hours straight. That will help you develop the right mental stamina for the real exam.
Finally few days before an exam or test, a week before will be ideal, have the best simulation of the actual exam. Find a past exam, the more recent the better (is usually easy to get one with a bit of search on internet), create conditions as close as possible to the ones that the real exam will be and do it. Check your answers with a professor or a credible tutor. If you do well that means you are on the right track, and that will again boost your psychology. If not don't get disappointed. You still have a week to work on the areas that you experience weaknesses.
PREPARING FOR A MATH OR PHYSICS EXAM
Even the most well prepared and self confident student will have some stress before a major exam; that's natural. The following tips will help you minimize that stress:
a) Never study at least an hour before your exam. The risk of finding something you don't know which will result in increasing your anxiety is much greater than the benefit of resolving something which will be on that exam.
b) Always get a good night sleep the night before the exam. It will give you the correct energy level you need during the exam. You will be alert but not anxious.
c) Keep your daily routine. For example, if you have never had a coffee in your life don't tried the day before your exam. This is not a time for exploring new things.
d) Keep things in prospective. You did what you suppose to do. In life in general you have to learn to care about things that you can control. To worry about factors beyond your control is a waist of time and energy.
e) Finally in the worst case scenario that you fail badly in this exam (which I don't think so if you follow my advice above) is not the end of the world. You will have another change to prove yourself. Keep in mind like life academic achievement is a marathon not sprint.
WRITING THE MATH OR PHYSICS EXAM
Once started writing the exam:
a) If among the problems or questions on the exam are proofs, start from these. The reason is that if you will be able to do them it means that 99% you did it correct (unless you are so unlucky that you reach the right conclusion by accident). This is very good because while you didn't waste any time you answered a question correctly. This will boost your psychology for the rest of the exam. And psychology is very important specifically in the beginning of the exam.
b) Don't look at the problem. Write. Very few times in very easy exercises you might have the answer from the top of your head. In the majority of cases you have to write down your thoughts mostly in the form of formulas that you will have to combine together in order to get your answer. Is very difficult and stressful to keep all these thoughts at your mind.
c) When applying step (b) try to locate the section(s) the problem refers to. Write down all the formulas that involve what is given and what you are trying to find. Make sure you use all the data given. In the overwhelming majority of problems is useful. In very few cases is there only to confuse you. Try the rule first, if it doesn't work use the exception.
d) Do not spent more than 15 minutes in a problem that you can't solve. Move to the next one. Spending too much of your time unproductively will increase your stress and frustration. Stay positive through the whole exam time.
e) Unsolved problems from (d) try them again the 2nd third of the total exam time. What do I mean is let's say the total exam time is 3 hours. Try again problems you weren't able to solve after an hour from the start of the exam. Studies on the topic have shown that it is the best time to tackle difficult problems. And of course it makes a perfect sense; you are warmed up but not exhausted, hence is your best chance to do these challenging problems.
e) Make sure you leave some time (15-20 minutes) for review. The worst thing is to loose marks from questions you know but you didn't answer them correctly because you were not fully concentrated when you were working on them. Going through your exam one last time it might give you the opportunity to detect and correct them.
f) Finally never leave the exam before the end of the exam period unless you are 100% certain that you have done it right.
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Thank you
