Pre-Algebra Study and Test-Taking Techniques Help (page 3)
Study and Test-Taking Techniques
Having an understanding of math anxiety and being able to reduce stress are not enough to be successful in mathematics. You need to learn the basic skills of how to study mathematics. These skills include how to use the classroom, how to use the textbook, how to do your homework, how to review for exams, and how to take an exam.
In order to learn mathematics, it is absolutely necessary to attend class . You should never miss class unless extreme circumstances require it. If you know ahead of time that you will be absent, ask your instructor for the assignment in advance, then read the book, and try to do the homework before the next class. If you have an emergency or are ill and miss class, call your instructor or a friend in the class to get the assignment. Again, read the material and try the problems before the next class, if possible. Be sure to tell your instructor why you were absent.
Finally, if you are going to be absent for an extended period of time, let your instructor know why and get the assignments. If you cannot call him or her, have a friend or parent do it for you.
Come to each class prepared. This means to have all the necessary materials, including homework, notebook, textbook, calculators, pencil, computer disk, and any other supplies you may need.
Always select a seat in front of the classroom and near the center. This assures that you will be able to see the board and hear the instructor.
Pay attention at all times and take good notes. Write down anything your instructor writes on the board. If necessary, bring a tape recorder to class and record the sessions. Be sure to ask your instructor for permission first, though.
You can also ask you instructor to repeat what he or she has said or to slow down if he or she is going too fast. But remember, don't become a pest. You must be reasonable.
Be sure to ask intelligent questions when you don't understand something. Now I know some of you are thinking, "How can I ask intelligent questions when I don't understand?" or, "I don't want to sound stupid."
If you really understand the previous material and you are paying attention, then you can ask intelligent questions.
You must also remember that many times the instructor will leave out steps in solving problems. This is not to make it difficult for you, but you should be able to fill them in. You must be alert, active, and pay complete attention to what's going on in class.
Another important aspect you should realize is that in a class with ten or more students, you cannot expect private tutoring. You cannot expect to understand everything that is taught. But what you must do is copy down everything you can. Later, when you get home, apply the information presented in the chapters of this book.
Be alert, active, and knowledgeable in class.
The textbook is an important tool in learning, and you must know how to use it.
It is important to study your book. Note that I did not say "read" your book, but I purposely said study .
How do you study a mathematics book? It is different from studying a psychology book. First, look at the chapter title. It will tell you what you will be studying in the chapter. For example, if Chapter 5 is entitled "Solving Equations," this means that you will be doing something (solving) to what are called "equations." Next, read the chapter's introduction: it will tell you what topics are contained in the chapter.
Now look at the section headings. Let's say Section 5.3 is entitled "Solving Equations by Using the Multiplication Principle." This tells you that you will be using multiplication to solve a certain type of equation.
Take a pencil and paper and underline in the book all definitions, symbols, and rules. Also, write them down in your notebook.
Now, actually work out each problem that is worked out in the textbook. Do not just copy the problems, but actually try to solve them, following the author's solutions. Fill in any steps the author may have left out. If you do not understand why the author did something, write a note in the book and ask your instructor or a friend to explain it to you. Also, notice how each problem is different from the previous one and what techniques are needed to find the answer. After you have finished this, write the same problems on a separate sheet of paper and try to solve them without looking in your book. Check the results against the author's solutions.
Don't be discouraged if you cannot understand something the first time you read it. Read the selection at least three times. Also, look at your classroom notes. You may find that your instructor has explained the material better than your book. If you still cannot understand the material, do not say, "This book is bad. I can't learn it." What you can do is go to the library and get another book and look up the topic in the table of contents or appendix. Study this author's approach and try to do the problems again.
There is no excuse. If the book is bad, get another one.
Remember that I didn't ever say that learning mathematics was easy. It is not, but it can be done if you put forth the effort!
After you have studied your notes and read the material in the textbook, try to do the homework exercises.
Probably the single most important factor which determines success in mathematics is doing the homework. There's an old saying that "Mathematics is not a spectator sport." What this means is that in order to learn mathematics, you must do the homework. As stated previously, it is like learning to play an instrument. If you went to music class but never practiced, you could never learn how to play your instrument. Also, you must practice regularly or you will forget or be unable to play your instrument. Likewise, with mathematics, you must do the homework every day it is assigned. Here are my suggestions for doing your homework:
- First and most important: DO YOUR HOMEWORK AS SOON AS POSSIBLE AFTER CLASS . The reason is that the material will still be fresh in your mind.
- Make a habit of studying your mathematics regularly – say, three times a week, five times a week, etc.
- Get your book, notes, and all previous homework problems, calculator, pencil, paper (everything you will need) before you start.
- Do not dally around. Get started at once and do not let yourself be interrupted after you start.
- Concentrate on mathematics only!
- Write the assignment at the top of your paper.
- Read the directions for the problems carefully.
- Copy each problem on your homework paper and number it.
- Do not use scratch paper. Show all of your work on your homework paper.
- Write neatly and large enough. Don't do sloppy work.
- Check your answers with the ones in the back of the book. If no answers are provided, check your work itself.
- See if your answers sound reasonable.
- Write out any questions you have about the homework problems and ask your instructor or another student when you can.
- Draw pictures when possible. This is especially important in courses such as geometry and trigonometry.
- If you have made a mistake, try to locate it. Do not depend on the teacher to find all your mistakes. Make sure that you have copied the problem correctly.
- Don't give up. Doing a problem wrong is better than not doing it at all. (Note: don't spend an exorbitant amount of time on any one problem though.)
- Use any of the special study aids such as summaries, lists of formulas, and symbols that you have made.
- Don't skip steps.
- Finally, if you cannot get the correct answer to a problem, don't stop. Try the next step.
In order to learn mathematics, it is necessary to review before the tests. It is very important to realize one fact. You cannot cram in mathematics. You cannot let your studying go until the night before the exam. If you do, forget it. I have had students who have told me that they spent 3 hours studying before the exam, and then failed it. If those were the only 3 hours they spent studying, there is no way they could learn the material.
Some teachers provide written reviews. Make sure you do them. If this is the case, you can use the review as a practice test. If not, you can make up your own review. Many books have practice tests at the beginning and the end of chapters. If so, you can use these exams as reviews. Some books have extra problems at the end of each chapter. By doing these problems, you have another way to review.
Finally, if there is no review in the book, you can make up your own review by selecting one or two problems from each section in the chapter. Use these problems to make up your own practice test. Be sure not to select the first or second problem in each unit because most mathematics books are arranged so that the easy problems are first.
When you review, it is important to memorize symbols, rules, procedures, definitions, and formulas. In order to memorize, it is best to make a set of cards as shown here:
On the front of the card, write the name of the property, and on the back, write the property. Then when you are studying, run the cards through the front side and then on the other side. This way you can learn both the property and also the name of the property.
Finally, you must be aware that a review session is not a study session. If you have been doing your work all along, then your review should be short.
There are three types of exams that mathematics instructors give. They are closed book exams, open book exams, and take home exams.
First, let's talk about closed book exams given in the classroom. Make sure that you show up 5–10 minutes before the class begins. Bring all the necessary materials such as a pencil with an eraser, your calculator, paper, and anything else that you may need. Look over and study materials before class. After you receive your exam paper, look over the entire test before getting started. Read the directions carefully. Do all of the problems that you know how to do first, and then go back and try the others. Don't spend too much time on any one problem. Write down any formulas that you may need. Show all necessary steps if a problem requires it.
If there is any time left after you finish the exam, go back and check it for mistakes.
If you don't understand something, ask your instructor. Remember you cannot expect your instructor to tell you whether or not your answer is correct or how to do the problem.
In open book exams, you should remember that the book is your tool. Do not plan to study the book while you are taking the test. Study it before class. Make sure you know where all the tables, formulas, and rules are in the book. If you are permitted, have the formulas, rules, and summaries written down. Also, have sample problems and their solutions written down.
Don't be elated when your instructor gives you a take home exam. These exams are usually the hardest. You may have to go to the library and get other books on the subject to help you do the problems, or you may have to ask other students for help. The important thing is to get the correct solution. Show all of your work.
When your instructor returns the exam, make a note of the types of problems you missed and go back and review them when you get home.
See your instructor for anything that you are not sure of.
A Final Note
There is still one problem left to discuss: What happens if you are in over your head – i.e., the material you are studying is still too difficult for you?
First, try getting a math tutor. Many schools provide tutors through the learning center or math lab. Usually the tutoring is free. If your school does not provide free tutors, then seek out one on your own and pay him or her to help you learn.
There are other things you can do to help yourself if tutoring doesn't work. You can drop the course you are in and sign up for a lower-level course next semester. You can also audit the course, i.e., you can take the course but do not receive a grade. This way you can learn as much as you can but without the pressure. Of course, you will have to enroll in the course again next semester for a grade.
Many colleges and some high schools offer non-credit brush-up courses such as algebra review or arithmetic review. If you need to learn the basic skills, check your school for one of these courses. Usually no tests or grades are given in these courses.
I hope that you have found the suggestions in this program helpful, and I wish you success in your mathematical endeavor.
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