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Course Resources

How to Read a Math Textbook

from Math Study Skills by Alan Bass, Addison-Wesley-Pearson Education, Inc. 2008. pg. 48-?

These five steps should be followed for every section. An entire chapter is simply too large for these steps to be effective. You should, instead, approach each section individually in this manner.

Five Steps to Understanding a Section in Your Math Textbook

1. Survey the material. Begin the section by taking 5 to 10 minutes to glance through the material. For this step, you will not do much actual reading at all, but here are a few things you definitely should read:

• Paragraph or section titles

• Boldfaced words (although not necessarily their definitions)

• Instructions for examples (but not the solutions)

• Information that appears in boxes

The idea behind this step is that you will begin to get an overall idea of what the material is about. You will know whether graphing is involved. You will know whether fractions are involved. Certain words will sound familiar, others will not. If you survey the material and everything you see looks totally confusing, that's okay. You have still done your job.

2. Survey the homework. Next, turn to the page that contains the sec­tion homework and see what kind of problems you will be doing in this section. This should only take about five minutes. In particular, read the instructions for the different problem types. If this seems overwhelming, you may want to try reading every fifth problem (1, 5, 10, 15, 20,...). This will give you a good overview of the whole homework set. Or, if your instructor has already given you homework for that section, you could read those problems. In these first two steps, you will be accomplishing several important things:

  • Looking at key words
  • Getting an idea of the big picture
  • Getting to know expectations
  • Again, if you read through these problems and say to yourself, "Well, I just have no idea whatsoever how to do any of this stuff" that's okay! The fact that you have surveyed the material and its corresponding homework is going to help when you actually read the section.

    3. Read the section. Now you're ready to actually read the material. But don't just read it. Your mind needs to be engaged with the material beyond the voice you hear in your head when you read. As you read it is important that you actively keep your mind focused on the topic. There are several ways to do this. Here are a few suggestions: • Write boldfaced words in your glossary as you go. If you don't completely understand the term yet, leave some space below the entry so you can write in more later.

    • Copy down the examples in the book. You don't have to write down every word of the instructions or every word of explana­tion in the solution. But if you at least write down all the math steps that are done it will help avoid that "Why did they do that?" feeling. Many times our eyes just move too fast to see math steps that should be simple. If you write down the math steps in the examples, it will be easier to see why they were per­formed. Think about it; it will also be like training wheels for the homework in that section.

    • Write down anything that appears in a box, particularly formu­las and equations. If it looks familiar and you know it will be important, you could write it on a note card or in a corner of the page where you know you will do homework. If you are a kinesthetic learner, take the time to doodle a formula into your notebook somewhere you know you'll see it again later (but be careful not to waste too much time with that).

    • Read out loud to yourself. This is a great idea if you're an audito­ry learner. Make sure you are not disturbing anyone around you when you do this. But as long as you are not, go for it!

    • Writing in your book is a great way to make friends with it. If you don't mind keeping your book after the course is over and not selling it back, there are several things you can do: = Use a highlighter to make important information stand out.

     Put a question mark (in pencil) beside ideas or examples you have a hard time understanding.

    Circle key terms.

    Using a highlighter is okay, but DO NOT use an ink pen to write in your book. Use a pencil so you can edit your comments later.

    Remember: If you just sit there and read to yourself and that's all, you are not likely to be successful. Your brain needs to be stimulated in other ways to keep it active and interested.

    College Course Structure

    A big part of what makes college math different is. . . well. . . college. That is, many of the difficulties facing students who are entering a college level math class for the first time are a result of the huge difference between a high school class and a college class. With the help of my students, I have com­piled a list of the most important differences.

    Differences Between a High School Class and a College Course

    High School


    Attendance is required. Attendance is optional and may not even be taken.
    Teachers monitor progress and performance closely. Students receive, grades, but are often not informed by the professor when they are in trouble.

    Beginning algebra is covered over the course of 10 months for 6 or 7 hours a week.

    Beginning algebra is covered over the course of 4 months for 4 or 5 hours a week
    The students have contact with the instructor every day. The students often meet with the instructor only twice a week.
    Teachers cover all material for tests in class through lectures and/or activities. Students are responsible for information whether it is covered in class or not.
    Teachers give frequent tests and allow make-ups or retests if the grades are poor There are often only 2-3 tests per semester and no make-ups or retests are allowed
    Grades are often based heavily on level of participation and effort. Grades are usually based exclusively on quality of work and demonstration of college level thinking.
    A grade of "D" is interpreted as "barely passing" and the student is moved to the next-level course. A grade of "D" is interpreted as "barely  not passing" and the student is required to retake the class
    Teachers often offer extra credit for struggling students. Professors almost never offer extra credit.




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    last updated: 2008 February 1