Note-Taking Strategies

What You’ll Find Here: 3 Videos • Note-Taking Strategies • Self-Check

On This Page: Why Copying Everything Doesn't Work | What to Write Down | Creating Studyable Notes | A Better Note-Taking Routine | Self-Check | When Your Notes Aren't Helping | One Action

Good Math Notes Are More Than a Record of Class

It can be tempting to think that good note-taking means writing down as much as possible. But in a math class, copying every word, equation, or example can actually make learning harder. When you are focused entirely on keeping up with what is being written, you may have less time to think about:

• Why a step was taken

• How one idea connects to another

• What part of a problem is important

• Where you became confused

• What you will need to remember later

Effective math notes are not simply a copy of class. They are a tool that helps you understand, remember, practice, and review mathematics. On this page, you will learn:

• Why trying to copy everything can get in the way of learning

• What information is worth recording during a math lesson

• How to include examples without simply copying solutions

• How to mark questions and confusing points

• How to turn class notes into something you can actually study from later

Your notes do not need to be beautiful or perfectly organized. They need to be useful to you.

Trying to record everything your instructor says or writes may feel productive. After all, if everything is written down, nothing can be missed. But there is a problem. When most of your attention is spent copying, there may not be much attention left for understanding. Math learning requires you to notice patterns, make connections, ask questions, and think about why a method works.

As You Watch

Think about this question: When you take math notes, are you mostly recording information—or are you also thinking about what the information means?

Try It Now

Look at a recent page of notes from one of your classes. Choose one section. Now ask yourself what did I record? Did you mostly write:

• Exactly what the instructor wrote?

• Every line of a worked example?

• Definitions word-for-word?

• Formulas without explanations?

Now look for evidence of your own thinking. Did you include:

• A note about why something works?

• A question?

• A warning about a common mistake?

• A connection to an earlier topic?

• An explanation in your own words?

• A reminder about when to use a strategy?

If your notes contain mostly copied information, that is okay. The goal is not to stop recording information. The goal is to add enough thinking to make the information useful later.

If you should not copy everything, what should you write down? The answer is not the same for every class or every student, but there are several types of information that are especially useful in mathematics.

As You Watch

Think about this question: If you opened today's notes three weeks from now, what information would you need in order to understand them?

Try It Now

During your next math lesson, try to capture these six types of information.

1. The Main Idea

What is the lesson actually about? Instead of recording only “Solving linear equations”, you might add “Goal: isolate the variable while keeping both sides equal.” That short explanation gives the procedure meaning.

2. Important Vocabulary and Notation

Record new:

• Vocabulary

• Symbols

• Formulas

• Rules

• Definitions

But whenever possible, include a short explanation in your own words. For example: “Coefficient: the number multiplying a variable.”

3. Important Steps

If there is a process or procedure, record the major steps. You do not necessarily need every tiny detail. Focus on the decisions you will need to make when solving a problem yourself.

4. Worked Examples

Examples are valuable - but try not to record only the finished calculations. Include notes such as:

• Why did we choose this strategy?

• What told us to use this formula?

• Where is a common place to make an error?

• What would change if the problem were slightly different?

5. Warnings and Common Mistakes

These may become some of the most valuable notes you have. Examples:

• Be careful: distribute the negative sign to every term.

• Remember: you can only add fractions directly when the denominators match.

• Check whether the answer should be positive or negative.

6. Your Questions

If something does not make sense, mark it. You might write “? Why can we cancel these terms?” or “? I understand the formula but don't know how to recognize when to use it.” You do not need to interrupt your entire note-taking process every time you are confused. Mark the question so you know exactly where to return later.

Notes are most useful when they help you do something later. A notebook filled with completed examples may look thorough, but it can still be difficult to study from if the answers are already visible and there is nothing asking you to think. Good study notes should help you:

• Recall information

• Explain ideas

• Solve problems

• Identify mistakes

• Make connections

• Notice what you still need to practice

As You Watch

Think about this question: Can your notes help you practice without simply rereading them?

VIDEO COMMING SOON!!

Try It Now

Choose one page of your existing notes. Now improve it by adding at least three of the following:

• A question you should be able to answer

• A problem to solve again without looking

• A definition covered up so you can recall it

• A note explaining why a step works

• A warning about a common mistake

• A connection to an earlier topic

• A short summary in your own words

• A star beside something especially important

• A question mark beside something you still need to review

Your original notes do not need to be perfect. You can make them more useful after class.

You do not need a complicated note-taking system. Try this six-step routine.

1. Capture

Record the information you are likely to need later. Focus on:

• Main ideas

• Important vocabulary

• Formulas

• Procedures

• Examples

• Instructor emphasis

• Warnings and common mistakes

You do not have to write every word.

2. Organize

Make the structure of the lesson visible. You might use:

• Headings

• Short labels

• Boxes

• Arrows

• Indentation

• Numbered steps

• Space between examples

Organization does not need to be decorative. Its purpose is to help you see how ideas fit together.

3. Process

Add evidence of your own thinking. Write things like:

• This works because...

• This is similar to...

• Use this when...

• The important difference is...

• I need to remember...

Even one short comment can make copied information much more meaningful.

4. Mark

Give yourself an easy way to find important information later. For example:

• ★ Important

• ? Question

• ! Common mistake

• ↺ Review again

You can create your own system. The best system is one simple enough that you will actually use it.

5. Review

Do not wait until the night before an exam to look at your notes again. After class - or later that day - spend a few minutes looking through them. Fill in missing information. Clarify anything that is hard to read. Mark questions. Add explanations while the lesson is still fresh. Even a short review can make your notes much easier to understand later.

6. Use

Do something with your notes. Do not only reread them. Try:

• Covering a definition and recalling it

• Hiding an example and solving it yourself

• Explaining a concept without looking

• Turning headings into questions

• Reworking problems

• Finding examples of common mistakes

• Making a short practice quiz

Your notes become much more powerful when they are a starting point for practice, rather than the end product of class.

Capture → Organize → Process → Mark → Review → Use

Choose a recent page of notes and ask:

• Can I tell what the main topic was?

• Can I identify the most important ideas?

• Are important formulas, vocabulary, and rules easy to find?

• Did I record why or when a method is used?

• Are my examples understandable without being in class again?

• Did I mark anything that confused me?

• Did I record common mistakes or warnings?

• Could I use these notes to quiz myself?

• Could I solve a problem using these notes as a reference?

• Do my notes contain some of my own explanations—not only copied information?

You do not need to answer “yes” to everything. Choose one thing you could improve on your next page of notes.

Sometimes you can take pages of notes and still feel as though you have nothing useful to study from. That does not necessarily mean you took “bad notes.” Your notes may simply need another step. If your notes are mostly copied examples, try covering the solutions and solving the problems again. If your notes contain formulas without explanations, add:

• What does each variable mean?

• When would I use this formula?

If your notes seem disorganized, add headings and labels. If something does not make sense, mark the exact point where you become confused. If your notes are incomplete, compare them with:

• Your textbook

• Posted class materials

• Course videos

• A classmate's notes

• Your instructor's examples

And remember that note-taking is only one part of learning mathematics. Your notes do not have to contain everything you will ever need. Their job is to help you remember the lesson, locate important ideas, and begin practicing.

You do not need to redesign your entire note-taking system. Choose one small change to try:

• Write the lesson's main idea at the top of your next page of notes.

• Add one sentence explaining why a procedure works.

• Mark questions with a ? as you take notes.

• Mark common mistakes with a !.

• Leave a little extra space around worked examples.

• Add a note explaining when to use each formula.

• Cover one completed example and solve it again.

• Spend five minutes reviewing today's notes after class.

• Turn one heading from your notes into a question.

• Add a short summary at the bottom of one page.

Good notes are not measured by how much you write. They are measured by how well they help you understand, remember, and practice the mathematics.