Study Tips


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The following is a collection of tips for studying mathematics. These have been gathered from a number of sources (texts, websites, personal experience) over a number of years.

General:

Keys to success include desire and discipline. You must want success and you must discipline yourself to do what it takes to get success.
Keys to success include motivation and time management (rewording of the above).
Everything that you learn increases your value.
If you need help, get it! Find out what resources are available to you.
Math is cummulative - what you learn today will be used tomorrow.
Take responsibility for your education.
No two students will learn in the same way. Discover what it takes for you to learn math.
Don't expect to understand every new topic the first time you see it. Learning mathematics takes time, patience and repetition. "All mathematics is easy, once you understand it."
You must practice speaking a foreign language regularly in order to become fluent in it. Mathematics is like a language - you must practice it regularly and become fluent.
If you memorize procedures without understanding, you will soon forget the procedures.
Being a full time student is a full time job. For each in class hour of instruction, two to four hours of studying (including doing homework) should be completed.
Account for how you spend every half hour of your time for one entire week. Add up your totals for sleep, study, work, recreation, and social activities. Does the amount of time allocated to each seem appropriate?
The ability to concentrate depends on adequate sleep, decent nutrition and the physical well-being that comes with exercise.
Lectures:

Read the related sections of your text before it is discussed in the lecture. Even if you do not totally understand what you've read, hearing it in class will now be the second time you've seen the material.
When taking notes, leave space. Later you can go back, adding details, extra notes from text, examples, etc.
If lecture notes are provided (such as via a course website), make use of them. Read them before the class and then you'll actually have a chance to listen to your instructor during the lecture.
Attending a lecture is more than just showing up and taking notes. Be attentive. Each is an hour of your time - why not make proper use of it?
Ask questions in class. This will keep the lecture more active and interesting, and will also ease your comfort in approaching your instructor outside of class.
If you miss a class, it is your responsibility to find out what was discussed.
After each class, rewrite - or at least reread - your notes, filling in details and/or making corrections as you do so.

Homework/Studying:

Don't simply work problems to get answers. Try to understand the big picture - how does this relate to what we did last? where would we go next?
Research shows that we remember only 10% of what we read, 20% of what we see, but a full 90% of what we say and do. So, whenever possible say and do.
Find a group of students (3-5) to work with outside of class. Explaining concepts out loud will deepen your understanding. But remember that working a problem with help is not the same as working a problem on your own.
Mathematics is personal - make sure that you can do it.
Check your answers with those provided in the back of the text or solution manual only after having worked through the problem yourself. But do get in the habit of checking your work to gain confidence in your abilities.
You work a problem and get the wrong answer. You rework the problem and you get the right answer. Be sure to go over your first solution and find out where you went wrong. This is a great learning tool and will help you avoid making the same mistakes again.
Working one hour per day every day is better than working 7 hours in one day.
Keep reviewing. After doing the current work, go back a section or two and try to rework a few problems. You will be amazed at how much your knowledge will improve with regular review (and you'll be able to avoid those all night cram sessions!).
At the end of each week, take note of the progress that's been made. What do you now know that you didn't know on Monday?
Don't use excuses to avoid studying. Use them to take half hour breaks from studying, about every hour or two.
Eliminate obvious visual distractions when you study. This includes magazines and texts from another class.
Tests:

Cramming for a test only creates text anxiety. Keep up with homework and there's no need to cram. Start studying several days before the exam and get a good sleep the night before.
Scan the test and pick out the problems that are the easiest for you. Do these first to gain confidence and jump start your thinking.
Use the marks allocation to judge the amount of time that should be spent on each question.
When you've completed a question you are confident about, place a check mark beside it. Place a question mark beside problems that you want to go back and have another look at if time permits.
When a test is returned, rework all problems checking to see what you did correct, what you did wrong. Consult model solutions and get help on anything you still don't understand.