How to Succeed in Math
A. Nature of Math Classes
1. Math classes trains you on processes: Thinking Process and Writing Process.
Thinking process: To think systematically, logically, step-by-step.
Writing process: To write your idea neatly and clearly. Write what you mean and mean what you write.
2. Sequential learning process: Building blocks on the top of the others.
The lesson on the next day depends on the lesson today. Students are required to understand and apply today’s lesson BEFORE the next lesson. Being weak or incorrect understanding at early stage greatly jeopardize later stage.
We need to be very aware of the difference of the learning process required in Math and in other courses. Learning process required for other class may not fit the learning process required in Math. This is also the reason why some students may do well in other courses but not in Math. Strangely, it does not really go the other way around: Students doing well in Math tend to do better in other courses.
3. Mechanical v. Memorization; Internalization and Intuition: At early stage of math study, at lot of mechanical work and a little memorization. As you progress, more memorization and less mechanical. This is especially clear in Applied Math course (Statistics, for instance). However, when to memorize and when to be mechanical is not clear until internalization process is done and intuition is well-shaped. This is why, besides being correct, the SPEED of solving problems is also a good way to measure the understanding and application of concepts.
4. Lecture à Apply à Internalization à Interconnection.
Lecture is the place you absorb the information. You need to apply the information, concepts, technique right away with in-class practice. At home, you will do more practice for reinforcement and internalization. Interconnection is usually done to sharpen your intuition.
Remember: You don’t know the concepts until you apply them. You don’t remember the concepts until you internalize them. You don’t understand the concepts until you have the intuition.
B. What to do
1. Attend all classes
You don’t know what happens in class unless you are there. Missing a class (especially in the first few weeks) significantly reduce your success rate.
2. Be in class on time, leave the class only after it is dismissed, and stay fully-focused all the time in-between.
Turn-off your cell, no text-messaging, no unnecessary talks. Try to sit at the middle front rows.
3. Be prepared!
You need at least two sharpened pencils (preferably mechanical pencils), eraser, notepad, scratch paper, and a textbook. Bring your calculator is recommended by your instructor.
4. Form a support group ASAP
Get at least two classmates as your “study-buddies”. Exchange phone numbers and/or emails. Let them be your source of “notes and support” if you really need to miss a class.
My study shows that students with study group do significantly better than those without.
5. Schedule yourself.
Set up a priority list of activities. Put it on writing. Create a schedule you can reasonably follow and do your best to follow. Discipline yourself.
At the beginning, it’s hard to fulfill your entire plan. But, as you get used to it, you will know what is “reasonable” for you.
Rule of Thumb: Study at least one hour every day for every one class-hour. (Some senior faculties say 1.5 or even 2 hours). Make sure you are not tired, distracted, nor disengaged during your study.
Remember: No one plans to fail. But, “fail to plan” is just another “plan to fail”.
6. Study often and regularly.
Six-times-1-hour study is always better than one-time-6-hour study. Study for too long is not optimal for you. Your brain may be optimal for as long as 1.5 hour. You need around 20-30 minutes of break after that before going back to study math. Even after break, your brain is usually not 100% anymore.
Another reason behind this advice: A lot of math courses are designed with “multiple-exposure” idea. According to researches done by some community colleges senior faculties, the more you get exposed to a mathematical concept, the better you “feel” it. This has a lot to do with internalization process.
7. Do not procrastinate.
That’s one of the greatest sins in college! Do your homework right away, on the same day if possible. Refer back to your notes and textbook. If you know you can’t finish it right away, at least come up with a plan for progress. Remember that it’s always a good idea to do more than what is required by your Instructor.
The best structure is as the following order:
- Review the notes. Rewrite if possible.
- Review the previous lesson from the textbook.
- Do homework.
- Practice more.
- Preview next lesson.
- Watch lecture video, if available.
8. Know where and when to get help: Note & textbook, your instructor, other instructors, study-buddies, and tutors.
9. Don’t be satisfied with simply getting the correct final answer.
Remember that Math is about Thinking Process and Writing Process. It’s better for you to make some silly mistakes in a well-organized, clear, systematic solution instead of a hap hazardous chaotic work even with the correct final answer.
People do make silly mistakes. But, the learning processes acquired by showing your work properly increase your mathematical maturity and intuition. This will provide you a better foundation for a more advanced lesson.
Hap hazardous, chaotic works give no room for corrections. Students with this habit tend not to be able to pinpoint their mistakes, tend to be immature mathematically.
10. Get to know your instructor.
Find his/her first name, last name, office, office-hour, and email. Believe it or not, there is a mystical, strong relationship between knowing your instructor as a person and understanding what your instructor teaches.
C. What not to do
1. Don’t touch your calculator until you know why you need it!
A calculator is not smarter than you. It won’t give you what you need if you don’t even know what to do with it. A calculator is especially not helpful when you are in a 100-level course. Depending on calculator will dull your mathematical intuition.
2. Don’t get too much visualization.
At times, abstraction forces you to go deeper into the essence of the concepts. After all, the best things in your life are best viewed with closed eyes. (Some people call them “dreams”).
3. Never underestimate your instructor however young, inexperienced, or lousy he/she is.
4. Never overestimate yourself.
Don’t be too happy simply because you solve a problem correctly. Make sure you can solve the problem by showing all the necessary work neatly, clearly, understandably, with proper speed.
5. Don’t give up if you don’t understand a concept right away.
Math is tough! It is normal not to get it right away. Meditate on the concepts. Ask for helps.
D. Before and On the Test.
1. First of all, the test is there to measure your achievement, not to criticize you. That is the chance for you to “show-off” what you have learnt in-class AND off-class. Your teacher is not your enemy, he/she is there to help your improve and go up to the standard required to move on.
2. For the reason we have in #1, then if you have studied and prepare yourself, you should expect to do reasonably OK in the test. Those who don’t prepare themselves are the ones supposed to get anxious.
3. Studying Math should be a DAILY habit. Those who try to study “last minute” will not do well, usually because they get overwhelmed.
4. Try to get some sample test and try to do them with restricted time.
5. Get enough sleep on the night before the test. Make sure you prepare the material of the test before you go to bed: pencils, sharpener, eraser, (calculator and scantron, if required).
6. Make sure you don’t have empty stomach when you take the test. You need some sugar-level to have your brain working well. However, don’t get too full either, that takes too much blood from your brain.
7. Some people like to drink coffee during the test. Even if your instructor allows you to drink in class, be aware that caffeine may increase your anxiety. This includes soda with higher caffeine.
8. Once you receive the test paper, right after you write your name, take 15-20 seconds to read the directions and browse through the whole test. This gives you a feeling on the difficulty level of the test.
9. During the test, mark problems on which you don’t have confidence, even after you solve it. If there is any time left, go back to them.
E. False Myths about Math:
1. All I need is a good tutor.
A good tutor will help you to grow. But, you still need to grow, not the tutor. Also, you are the one taking the class and taking the test, not your tutor.
2. A nice teacher must be a good teacher; a good teacher must be nice.
A nice and good Math teacher is hard to find. A teacher can be nice to the students to compensate the good education and discipline he/she can’t provide. A good teacher pushes you out from your comfort-zone, makes you think, challenge you to a deeper understanding. This may make a good teacher look “not-nice”.
3. I always have a bad teacher.
Yes, there may be a lot of bad teachers out there. Unfortunately, there are a lot more bad students. Make sure you are first a good student before you make a claim that your teacher is bad.