SUMMER 2010 COLLEGE ALGEBRA ONLINE

MATH STUDY SKILLS TIPS

How To Read Your Math Textbook

The way you read a math textbook is different from the traditional way students are taught to read textbooks in other courses. There are several appropriate steps in reading a math textbook, as outlined below.

1. Skim the assigned reading material.
   Skim the material to get a general idea about the major topics. Read the section objectives and the introductory paragraphs for each section. Also read the prerequisites listed at the beginning of each section so you know what prior knowledge is assumed. You do not want to learn the material at this time; you simply want to get an overview of the section.
2. As you skim the section, circle (using pencil) the new words you do not understand.
   If you do not understand these new words after reading the section, look up the word in the index and read the relevant pages. You can also look up the word in a dictionary and check the Chapter Review at the end of the chapter to see if the word is defined there. You can also contact your instructor or seek tutoring help.
3. Put all your concentration into reading.
   While reading the section, highlight the material that is important to you. Be careful not to highlight more than 50 percent of a page because the material will not be narrowed down enough for future study. Reading a math textbook is difficult. It might take you half an hour to read and understand just one page.
4. When you get to the examples, go through each step.
   If the example skips any steps, make sure you write down each one of those skipped steps in the textbook for better understanding. You may also want to rework the example in your notebook and write down all the steps as well as make notations on what was done. This will also help when studying for a test.
5. Mark the concepts and words that you do not know.
   You may have marked them the first time while skimming through the section. If you understand them now, erase the marks. If you do not understand the words or concepts, then reread the page, look them up in the index or Chapter Review, or ask your instructor or tutor for help. Try not to read further until you understand all the words and concepts.
6. If you do not clearly understand some words or concepts, add these words to a note-taking glossary in the back of your notebook.
   Your glossary will contain all the words and concepts you do not currently understand. Make sure you know these words and concepts before taking the test.
7. If you do not understand the material, follow these points until you do understand the material.
   
   • Go back to the previous page and reread the information to maintain a train of thought.
   • Read ahead to the next page to discover if any additional information better explains the misunderstood material.
   • Locate and review any diagrams, examples or rules that explain the misunderstood material.
   • Read the misunderstood paragraph(s) several times aloud to better understand their meaning.
   • Refer to another math textbook, computer software program, or video tape that expands the explanation of the misunderstood material.
   • Define exactly what you do not understand and contact your math tutor or instructor for help in understanding the material.
8. Reflect on what you have read.
   Combine what you already know with the new information you have just read. Think about how this new information enhances your math knowledge. Prepare questions for your instructor or tutor about the confusing information. Ask these questions at your earliest convenience.

How To Do Your Math Homework

Doing your homework can be frustrating or rewarding. Most students jump right into their homework, become frustrated and stop studying. These students usually go directly to the math problems and start working them without any preparation. When they get stuck on one problem, they flip to the back of the text for the answer. Then, they either try to work the problem backward to understand the problem steps, or they just copy down the answer. To improve your homework success and learning, refer to the following steps.

1. Review the textbook material that relates to the homework.
   A proper review will increase the chances of successfully completing your homework. If you read your section following the steps given above in "How to Read Your Math Textbook", you should already have a good understanding of the material in that section.
2. Do your homework as neatly as possible.
   Doing your homework neatly has several benefits. When asking questions from a tutor or your instructor, he or she can more easily understand your attempts to solve the problem, locate the mistake and show you how to correct the steps. Another benefit is that, when you review for a test or exam, you can quickly relearn the homework material without having to decipher your own writing.
3. When doing your homework, write down every step of the solution.
   Even if you can do the step in your head, write it down anyway. This will increase the amount of homework time, but you are overlearning how to solve problems, which improves your memory. Another advantage is that, when you rework the problems you did wrong, it is easy to review each step to find the mistake.
4. Understand the reasons for each problem step and check your answers.
   Do not get into the bad habit of memorizing how to do problems without knowing the reasons for each step. Many students are smart enough to memorize procedures required to complete a set of homework problems. However, when similar problems are presented on a test, the student cannot solve the problem. To avoid this dilemma, keep reminding yourself about the rules, laws, or properties used to solve the problem. Once you know the correct reason for going from one step to another in working a math problem, you can answer any problem requiring that property.
   
   Checking the answers should be part of your homework duties. Odd-numbered problems have answers in the back of the textbook. It is very important to check the answers, otherwise you might be repeating the same mistake with several problems.
5. If you do not understand how to do a problem, follow the points below.
   
   • Review the textbook material that relates to the problem.
   • Review any similar problems, diagrams, examples or rules that explain the material.
   • Refer to another math textbook, solutions manual, math computer software or video tape to obtain a better understanding of the material.
   • Skip the problem and contact your tutor or instructor as soon as possible for help.
6. Always finish your homework by successfully completing problems.
   Even if you get stuck, go back and successfully complete previous problems before quitting. You want to end your homework assignment with feelings of success.
7. After finishing your homework assignment, recall to yourself or write down the most important learned concepts.
   Recalling this information will increase your ability to learn these new concepts. In addition, there will be a concepts quiz at the end of each chapter and you will be better prepared to answer the questions on this quiz.
8. Make up note cards containing hard-to-remember problems or concepts.
   Note cards are an excellent way to review materials for a test or exam. Some students use 3x5 index cards for this purpose, while others prefer to set aside a section of their notebook to write down important concepts.
9. Getting behind in math homework is the faster way to fail the course.
   Math is a sequential learning process. If you get behind, it is difficult to catch up because each topic builds on the next. To keep up with your homework, it is necessary to complete homework every day, including weekends. Doing your homework for 2 hours each day is better cramming 4 hours every other day. Remember that this is an 12-week course, and you should budget about 12 hours a week to study for this class.

How To Study for a Math Test

Taking a math test is different from taking tests in other subjects. Math tests not only require you to recall the information, you must apply the information as well. Math test preparation is different as well, as you need to practice doing problems in addition to reviewing the concepts. The points below will help you develop better test preparation skills.

• Be sure to read all the material to be covered, and have your notebook organized before you begin your review.
• Plan what you will study and when you will study it.
• Each review session should be limited to one hour. Take short breaks between hourly sessions.
• Review your homework and any notes you took while doing your homework.
• Try to predict test and exam questions. Use the review sheets for each test to help you with this.
• Work all the problems on the review sheet and check your answers.
• Prepare a summary of the important concepts, and make sure you know how to work at least one problem in each concept category.
• Make a mental cheat sheet with important concepts, formulas, and some problems worked out.
• Get a good night's sleep before taking any test or exam. Cramming the night before seldom helps you when you take the test.

The 10 Steps to Better Test-Taking (for tests done in the Testing Center)

1. Use a memory data dump.
   Upon receiving your test, sit down at a desk, turn over the test and write down any information you memorized in your mental cheat sheet. Write down the facts, figures, and formulas that you might not remember later on in the test.
2. Preview the test.
   Put your name on the test and start previewing. Look through the entire test to find different types of problems. Put a mark by the questions you can do easily. These are the questions you will solve first.
3. Do a second memory data dump.
   This is for writing down material that was jarred from your memory while previewing the test.
4. Develop a test progress schedule.
   In the Testing Center, there is no time limit for taking the test. However, you should not plan to be in there for more than two hours, since your mind will probably be too tired after that long to be effective. Decide how many problems should be completed halfway through the test. Work steadily through the test to stay on schedule.
5. Answer the easiest problems first.
   Solve, in order, the problems you marked while previewing the test. Then, review the answers to make sure they make sense. Check your answers if you have time. Clearly write down each step so that you can earn partial credit.
6. Skip difficult problems.
   If you find a problem that you do not know how to do, read it twice, then automatically skip it. Reading it twice will help you understand the problem and put it in your working memory. While you are solving other problems, you mind is still working on that problem.
7. Review the skipped problems.
   Now go back to the skipped problems and think how you have solved other similar problems. If, at any time during the test, you get a brainstorm on how to solve the skipped problem, immediately go to that problem and work it. Do not wait till you finish the current problem, or your brainstorm may vanish.
8. Guess at the remaining problems.
   Do as much work as you can on each problem, even if it is just writing down the first step. You should also rewrite the problem on your lined paper; sometimes doing this jars your memory enough to do the first step or the entire problem.
9. Review the test.
   Look for careless errors or other errors you may have made. Check your answers carefully by reworking the problem or working backwards from the solution.
10. Use all the allowed test time.
    Even though you have no time limit for tests taken in the Testing Center, resist the temptation to leave immediately after you have finished doing all the problems. You have budgeted two hours to do the test, and don't leave until you have checked all your answers and reviewed the test.