Reading Time
3 min read
Written By
Alyx JordanFounder, Ivy MathsIn this article
Plenty of students have folders of maths notes that took hours to write and never get used. The pages are neat, the headings are coloured in, and reading them back before a test doesn't seem to help.
Notes copied during a lesson usually record what the teacher said. Revising maths needs a record of what you have to be able to do.
1. What makes maths notes different
In history or English, notes are often a summary of ideas you'll later write about. In maths, the exam asks you to carry out a method. A written definition of highest common factor is far less use on the day than having found one five times.
A good maths note is short, then. It holds one method and enough to rebuild it from scratch.
2. The one-page format
Give each method its own page or index card, in four parts.
| Part | What goes in it |
|---|---|
| Method in your own words | Two or three lines, written as instructions to yourself |
| Worked example | One full example with every line shown |
| The usual mistake | The wrong answer people tend to give, and why it's wrong |
| Test question | A fresh question, with the answer folded under or on the back |
3. A sample note: adding fractions
Method. Make the denominators the same by finding a common multiple. Change each fraction to match. Add the numerators and keep the denominator.
Worked example. 23 + 14 A common multiple of 3 and 4 is 12. 23 = 812 and 14 = 312 812 + 312 = 1112
Usual mistake. Adding the tops and the bottoms: 23 + 14 = 37. A quick check shows it can't be right, because 37 is less than 12, and 23 on its own is already more than 12.
Test question. 35 + 16 (answer: 2330)
The mistake section is the part most notes leave out, and it's the part that saves marks. Once you know what the wrong answer looks like, you're far more likely to spot it in your own working.
4. Write the note once you've practised the topic
Taking notes while you're still learning a method means writing down something you don't understand yet. Try a few questions first, then write the note. The method line comes out in your own words, and you'll already know which mistake you're prone to.
5. Revise by covering the page up
Reading a note back feels like revision because everything on the page looks familiar. Recognising a method and being able to do it are different things. Cover the worked example and redo it on scrap paper, then check. Do the test question without looking at the method.
Testing yourself like this is called retrieval practice. In a well-known study, Roediger and Karpicke (2006) found that students who practised recalling a passage remembered much more of it a week later than students who spent the same time rereading it. The material was prose, but the principle carries over to maths methods: pulling something out of memory strengthens it more than looking at it again.
6. Keep a page of your own mistakes
Alongside your topic notes, keep one running page of mistakes from homework and tests. Write the question, your wrong line and the corrected line. Before a test this is the most useful page you own, because it lists the exact things you're likely to get wrong.
7. Get the worked example right first
A note is only as good as its worked example, and copying a half-understood example from the board can fix a mistake into your notes. Each Ivy Maths Quick Lesson works through its topic with a step-by-step example you can copy into the worked example box, and Skill Practice on the same topic gives you the test questions. Pick the topic you're least sure of, open its Quick Lesson and write your first one-page note tonight.