There is no substitute for learning the subject well for getting better grades. But I have seen many students struggling with math in spite of learning the subject. Here are 10 tips for those students for improving their grade in mathematics. They are based on my experience in tutoring many kids struggling in mathematics.
1. Avoid careless mistakes
Examples are reading question incorrectly, interpreting it incorrectly, mistakes in copying the data from problem, and not using parenthesis correctly during calculations.
2. Avoid performing calculations in your mind
In early years, the calculations are easy and can be done in mind to improve speed. But as the calculations get complex in middle school and high school, if you do not use pencil and paper and calculator, the chances are that you will make mistakes in calculations and get the answer wrong. So whenever allowed, use the calculator.
3. Do not skip writing steps
With some children, there is high chance that they will make mistake when they try to skip writing the steps on answer sheet and perform the intermediate calculations in their head. So it is important to write each step and complete calculation for the same.
4. Check your answer
If you are not sure and if time permits, substitute your answer in the problem and verify that it meets all the conditions specified in the question.
For integration problems in calculus, you can differentiate your answer and see if you get the equation inside integral and vice versa.
5. Slow down
It is better to answer fewer questions (more time per question) and get them right than waste time in answering more questions (less time per question and more mistakes) and get many of them wrong.
6. Concepts from prerequisite courses are not learned well
The only way to fix this issue is to go back and spend time in learning the prerequisite concepts well enough. Simple examples would be to learn to multiply and divide by fractions, factor polynomials, learn what each trigonometric function means etc.
7. Learn your calculator
Most of the graphing calculators that can be used on the test have many tricks built-in to avoid mistakes in performing manual calculations.
There are many shortcuts available in your calculator like not needing to enter answer from previous step again for next calculation, storing and recalling variables from memory etc.
8. Practice, Practice, Practice
Practice makes you perfect. This is an age old saying. There are always some tricks involved in solving different types of problems. These tricks can be learned by first trying all sorts of problems. This is specially true for SAT, ACT, and AP tests.
9. Know the rules of the test
Most tests do not have penalty for wrong answers (e.g. SAT/ACT/ASVAB/AFOQT Tests). Many tests have problems that are arranged in the order of difficulty which allows you to take a better guess at the answer. Knowing the rules of the test will allow you to maximize your score by guessing wisely.
In SAT/ACT tests, first 1/3rd of the questions are easy and last 1/3rd of the questions are tough. This knowledge can help you choose your answer wisely e.g. the most obvious answer may be correct for first 1/3rd of the questions but it may be incorrect for the last 1/3rd of the questions.
Some of the tests would give formulae at the beginning of the test that can be used in solving problems.
10. Get help
If you are facing difficulty in math or any other subject, ask for help. Ask a friend, ask a teacher for after school help, search online or ask at home. Parents should be actively engaged with their children and provide help when needed. It is better to provide help at earliest signs of struggling child than to wait until your child’s grade gets severely affected. Sometimes a tutor may be necessary. A student will learn subject well from an experienced tutor. Also an experienced tutor can pin point and help overcome student's weaknesses and improve student's confidence and grades.