Math

How to use a math textbook

Math textbooks are a bit different from textbooks for other subjects; they cover a lot of information very concisely, so you have to read them carefully. Here are some strategies to help you use your math textbooks effectively:

• Identify the key concept of the section you are working on. In math textbooks, each section covers a specific key concept.

• Read each sentence carefully and don’t move on until you understand. If you do not understand a term, look it up in the glossary. You may have to re-read a section a few times to fully understand.

• When you encounter an example, write it down. Copy down each step into your notes and try to understand each step before writing the next. Make note of any steps you do not understand, so that you can ask for help.

• Take note of theorems, equations and key terms. Important information is often highlighted by appearing in a box, italics, bold, or different colours. Be sure to write down this information in your notes.

• Do lots of practice problems. Each section in a math textbook will have associated practice problems that help you to master the material in that section.

• When working through practice problems, use the textbook examples as your guide. Complete the practice problems step by step and take your time. Go slow, so that you fully understand the material.

• Work through practice problems in order. Practice problems generally start out simple and get more challenging as you progress through them. The first few questions will help you practice the key fundamental concepts of a chapter, while the later questions often incorporate previous knowledge.

• Do not be alarmed by large numbers, decimals, or fractions in practice problems. Remember the key concepts and how you would apply them to whole numbers. It is no different with these numbers.

• Do chapter reviews to prepare for tests or exams. Reviews cover material on all sections covered in a chapter.

Additional Resources

• Reading a Mathematics Text

• Mathematics Study Skills: Using a Mathematics Textbook - Douglas College

How to take class notes

Math involves a lot of specific procedures and details. It would be difficult to remember everything you learn in class, which is why it’s important to have good notes. Here are some strategies for taking notes and organizing them to be the most useful.

Taking Notes

• Only write down the important information.You can develop a shorthand so that you can take down the information quickly. Write down formulas, new topics, examples, and anything the professor puts a lot of emphasis on.

• If you don’t understand something, circle it for later.If there is a concept or procedure you don’t understand, it’s important to get clarification. If something comes up in class that you don’t understand, circle it or highlight in your notes. As soon as you have the opportunity to ask questions, you can ask your professor.

• Record the class if needed. If you have a hard time keeping up with your notes while listening to your professor, ask if you can record the class. If they agree, you can listen to/watch the class again later to fill in anything you missed the first time.

• Capture all the details. Write all of the steps for solving a problem, even if you understand it. You may not remember everything later. Write down the solutions for problems using the symbols, and add an explanation of what you’re doing in each step.

• Use different colours to highlight/emphasize information. You can use highlighters or different coloured pens to divide sections, write titles, or highlight important information.

• Review your notes. After class, look over your notes and make sure you’re clear on all the concepts. Reviewing your notes after class and periodically before the exam helps reinforce the information in your memory.

Organizing your notes

• Label your notes. At the top of each page of notes, write the course name, the topic of the lesson, the date, and any corresponding textbook section. This will make it easier for you to find information to review later.
• Divide your notes into sections. Instead of having a page full of notes with formulas, explanations and topics altogether, many people find it useful to divide the notes into different sections. The Three-Column method and the Cornell method are two ways you can divide your notes. See which method is right for you.

Organizing: Three-Column Method

Watch the video and read the instructions below.

Instructions:

1. Draw two vertical lines on the page to divide it into three equal columns.

2. Label each column:

   • Left column: Topic

   • Middle column: Problem

   • Right column: Notes/Explanation.

3. During class, write your notes into the relevant columns:

   • Topics: The topic, key words, formulas or procedure being explained. This is also where you would write an example word problem.

   • Problem: The solution for problems using symbols.

   • Notes/Explanation: Write an explanation of each step of the process.

Organizing: Cornell Method

Instructions:

1. Set up your page: Divide your page into three sections by drawing an upside down T: a Cue column on the left, a Notes column on the right, and a Summary area at the bottom of the page. You can also use the Word Template or the PDF template.

2. Start with the Notes Column: Take notes as you normally would in the Notes column.

3. Fill in your Cue Column: Fill in your Cue column based on the notes you took in step 2. Add questions, key terms, and headings to help you quickly understand what the notes you took relate to.

4. Fill in your Summary section: Summarize the notes from this page into one or two key learning outcomes.

Homework Tips

Homework is an important task for learning math concepts. It is an opportunity for you to apply and practice techniques that you learned in class to make sure that you really understand them. Here are some tips for your math homework:

• Do your homework right away. Do all the assigned problems immediately after the section has been discussed in class, so it’s still fresh in your mind. Work on a group of problems at a time before checking your answers with those in the back of the text.

• Don’t check the answer until you’ve finished the problem. Complete each problem the way you would on a test, and only check the answer to see if you got it right. Some students are good at working backwards from the answer, but you won’t have the answers available on a test.

• When working through problems, use the textbook examples as your guide. Go through the example problems step-by-step to make sure you understand the process.

• Work on it every day. Spending a little bit of time each day will be more productive than trying to do it all on the weekend or the week before the exam.

• After you've finished the problems, examine the results. Problems tend to be grouped together. Ask yourself why they are grouped that way. What was similar about the problems in one group? What was different about the problems in other groups? What clues would tell you which type you were solving on an exam? Learning to analyze problems this way will help you see how to approach problems in the future.

• Try using spiral review. Each time you finish a homework assignment, go back and do a few problems from previous assignments. This technique, known as spiral review, helps you keep older material fresh in your mind, and can help you see connections between different topics. Repeatedly returning to a topic over an extended period of time is one of the best ways to fully assimilate knowledge.

• Review concepts that you had trouble with. After you have finished the homework, it is a good idea to review anything that is still giving you trouble. When you complete the reading, you should be able to answer every problem in the homework and the lecture.

• Learn the concepts and not just the answers. Concentrate on learning the concepts behind the solutions to the problems rather than the solutions to individual problems. The point of the homework is to help you master these concepts, not to obtain answers to every problem in the text. Make sure that you understand not only how to apply a certain procedure to a given problem but also why the procedure can be applied and why it works.

Attribution: Homework tips were adapted by The Learning Portal from Doing Your Homework by Saddleback College, used under CC BY SA. They are available on The Learning Portal under CC BY SA.

How to learn from mistakes

Mistakes are inevitable. The trick is to view mistakes as steps on the road to getting it right. Approach mistakes in the following ways:

• Treat mistakes as part of your growth. They are part of the natural process of learning.

• Remember that mistakes are necessary for learning. You will make mistakes as you learn math concepts. Learning from these mistakes helps you understand the concepts better.

• Look at the thought process that led to the wrong answer. What led you to that answer? What did you get wrong in that process?

• Don’t dismiss all mistakes as silly. Some mistakes can be silly errors caused by the slip of your pencil, but don’t give yourself a pass on all mistakes. Look at whether the mistake was silly, or a genuine misunderstanding of the concept. Recognizing these misunderstandings lets you go back and review the relevant concepts.

Attribution: How to learn from mistakes from The Learning Portal was adapted from The Serious Truth About Silly Mistakes and Wrong But Not Stupid by Ben Orlin on Math with Bad Drawings, used under CC BY NC. It is available on The Learning Portal under CC BY NC.