How to Take Math Notes: A Two-Column Method With a Calculus Example

The best way to take math notes is to split each page into two columns: the steps of every worked example on the left, and the rule or reason for each step on the right. Copy every step, including the ones your teacher does in their head, and put a question mark on the line where you got lost. After class, cover the solutions and rework the examples as practice problems instead of rereading them. The method is the same for high school algebra and college calculus, and statistics needs only a small change.

We make Ophaya smart pens and an LCD tablet that works with them. They come up in the tools section, and everything before it needs only a notebook and a pencil.

How to set up a math notes page

Draw a vertical line about two thirds of the way across the page. The wide left side holds the math: the problem at the top, then one numbered step per line. The narrow right side holds the reason each step is allowed, in a few words ("chain rule," "divide both sides by 2"). Put the date and the textbook section at the top to match the page to the homework.

Leave more room than feels necessary for the steps you'll add later. The University of Redlands' note-taking tips for science and math classes suggest pencil or erasable pen. If you write in ink, cross out mistakes with one line so you can still see what went wrong.

Our note taking methods guide puts the reasons in a left margin instead, like a Cornell notes page. Either side works if you keep it the same all term.

A worked example: calculus notes in two columns

Here is a made-up page from a chain rule lesson in first-semester calculus. The teacher went straight from line 2 to line 4, so the student put a "?" next to the jump and worked out line 3 that evening. Line 3 is also an easy step to drop on a test.

Algebra works the same way. Once x² - 5x + 6 = 0 is factored to (x - 2)(x - 3) = 0, the next line, x = 2 or x = 3, gets "zero product property" on the right.

How to take notes in math class

Copy every worked example in full. Redlands' handout says to write down "all worked problems and examples, step by step," and we'd go one further: when your teacher says "and this simplifies to," write the simplification down too, because you'll have to do it yourself on the homework.

The question mark goes on the exact line that lost you. A "?" beside step 3 tells you which move to ask about in office hours, while "didn't get this" at the bottom of the page doesn't. If the board moves on while you're still writing, leave a gap, write "missed" and keep listening. The textbook or a classmate can fill it in that day.

Definitions and theorems go in a box, copied word for word, so you can find them in the middle of a problem set. Paraphrasing is fine for a history lecture, but math statements hang on their conditions. The Mean Value Theorem applies only when f is continuous on [a, b] and differentiable on (a, b), and a paraphrase that drops them will cost you points when a test asks you to check them.

After class: turn examples into practice problems

Later that day, cover the left column of each example and rework it on scrap paper from the problem line. When you stall, uncover one step, then cover it again. Once you can get through it clean, change the numbers. The chain rule example becomes f(x) = (2x³ - 5)³, and the answer to check against is f'(x) = 18x²(2x³ - 5)².

This is the student's version of advice given to teachers. A 2007 practice guide from the Institute of Education Sciences, written by a panel chaired by Harold Pashler, recommends that math and science teachers alternate worked examples with problems students solve on their own. The panel rated the evidence as moderate.

Keep a running list of mistakes on the last page of the notebook. Write each one as the rule you broke, like "dropped the derivative of the inside" or "divided both sides of x² = 3x by x and lost x = 0." Before a test, work one fresh problem for each line.

Review by reworking problems instead of rereading

Rereading math notes feels productive, because every step makes sense once someone has written it out. In a 2013 review of ten study techniques, John Dunlosky and colleagues rated practice testing as high utility and rereading as low. In math, a practice test is just a problem worked with the solution out of sight. Our guide to taking better notes covers other subjects.

Mix problem types when you review. In a 2013 American Educator article, Dunlosky describes a study in which college students learned to find the volumes of four kinds of geometric solids. Those who practiced one kind at a time scored higher in the practice sessions, but on the exam a week later, the students who had mixed them did three times better. Tests don't label which rule a problem needs, so shuffle reworked examples from several sections and name the rule before you start each one.

Tools for math notes: paper, LCD board, iPad or smart pen

A spiral notebook and a pencil are enough for everything above. Do homework attempts on a scratch pad so the notebook stays clean enough to rework from.

An LCD board for scratch work

A basic LCD writing board is fine for attempts you plan to throw away: work the factoring, and clear the screen once it checks out. It saves nothing, so copy out anything you want to keep (our study gadgets guide compares cheap options).

An iPad

An iPad with Apple Pencil suits courses that post PDF worksheets. In Apple's Notes app, math expressions are solved inline when you write or type an equal sign, which is handy for checking arithmetic and tempting during homework. At our October 1, 2026 check, the iPad (A16) started at $449 and the Apple Pencil (USB-C) cost $79.

The Ophaya pen, notebook and LCD tablet

The Ophaya pen writes in ink and has an infrared camera that reads a printed dot pattern, so it captures handwriting on Ophaya dot-code notebooks and the Ophaya LCD writing tablet. Ordinary paper gets the ink but no digital copy. We'd take class notes in the notebook, and the pen syncs what you write over Bluetooth to the free Ophaya Pro+ app on iPhone, iPad or Android. Homework goes on the 10-inch LCD tablet with the same pen: strokes stream to the app as you write, and when a problem is worth keeping, you tap save before you press erase.

The app's OCR turns handwriting into editable text, but it's built for words. We wouldn't expect equations or symbols to convert cleanly, so we keep math pages as PDF or PNG exports. The app can also record audio on your phone or tablet (the pen has no microphone) and link it to what you wrote, so a "?" line becomes a spot to replay, if your teacher allows recording. The 3-in-1 set (pen, dot-code notebook and LCD tablet) is $99.95. Our guide to writing tablets with a pen compares it with E Ink tablets and the iPad.

Frequently asked questions

What is the best way to take math notes?

Use two columns, with steps on the left and reasons on the right, and copy every step with a "?" where you got lost. Within a day, rework the examples from a blank page.

What if my teacher goes too fast to copy every step?

Write only the left column in class and add the reasons that evening, with the matching textbook example open. If you want to record the class, ask first. Our guide on how to record lectures covers permission and setup.

How should I take notes in a statistics class?

Use the same two columns, with the right column saying why you chose a method: "comparing the means of two independent groups, so a two-sample t-test." Write each conclusion as a full sentence about the data, since "reject H0" on its own doesn't say what you found.

Should I rewrite my math notes after class?

No. Fill in missing steps and reasons on the original page, then put the time you'd have spent recopying into reworking problems from it.