TL;DR:
After a quiz or problem set, record each mistake with the wrong step, the right step and the cause.
Sort causes into concept, careless or misread, because each cause has a different fix.
Review the log weekly, and redo the problems you got wrong a few days later.
You get a quiz back with a number of red marks and a score. You look at the score, nod, and put it in your bag. Two weeks later, on the test, you make three of the same mistakes, and you cannot say why, because the quiz is in a folder you never opened.
An error log is a short notebook of what you got wrong and why. It is dull to keep and one of the most direct ways to stop paying for the same mistake twice. Here is how to run it, using five mistakes from one algebra quiz.
Why a mistake is worth more than a right answer
A right answer tells you that something works. A mistake tells you exactly where your understanding or your habits break. That makes it the best study material you will ever get: it is personal, specific and already sorted by what you need.
The trouble is that a red mark by itself is easy to forget. Writing down what happened turns it into something you can look at again, and sorting it by cause tells you what to do about it.
What the log looks like
One row per mistake, in a notebook or spreadsheet.
Columns: the problem, what you did, what was right, the cause, and the fix.
Three cause labels only: concept (you did not understand the idea), careless (you knew it and slipped), misread (you answered a different question).
How to log a quiz, step by step
Redo each missed problem without looking: Do it fresh before you look at the correction. Whatever happens tells you more about the cause.
Write the wrong step and the right step: Be specific: the exact line, not "algebra".
Pick one cause label: If you could explain the idea to a friend, it was careless or misread. If you could not, it was concept.
Write a fix you can act on: "Be careful" is not a fix. "Underline the question word" or "re-learn FOIL" is.
Worked example: logging five algebra mistakes from one quiz
Problem | What I wrote | Right answer | Cause | Fix |
|---|---|---|---|---|
Expand (x + 3)² | x² + 9 | x² + 6x + 9 (the middle term is 2 × x × 3) | Concept | Practise the square of a binomial, five examples |
Solve 2x − 5 = 11 | x = 3 | x = 8, because 16 ÷ 2 = 8 | Careless | I subtracted 5 instead of adding it. Always undo with the opposite, and substitute to check |
Find the perimeter of a 4 by 7 rectangle | 28 | 22, because 2 × (4 + 7) = 22 | Misread | I found 4 × 7, the area. Circle the word "perimeter" before starting |
Evaluate −3² | 9 | −9, because the square applies to 3 first | Concept | Review order of operations and where negatives sit |
Simplify 4(x − 2) | 4x − 2 | 4x − 8 | Careless | Draw arrows from the 4 to each term |
Rechecking the corrections
(x + 3)² = x² + 6x + 9. Test with x = 1: left side is 16, right side is 1 + 6 + 9 = 16.
2x − 5 = 11: x = 8 gives 16 − 5 = 11.
Perimeter of a 4 by 7 rectangle: 4 + 7 + 4 + 7 = 22, and 28 is the area.
−3² means −(3²) = −9, while (−3)² = 9.
4(x − 2) = 4x − 8. With x = 3, left side is 4, right side is 12 − 8 = 4.
What the tally shows
Count the causes: concept 2, careless 2, misread 1, which is 2 + 2 + 1 = 5 mistakes. The two concept errors need real study time. The careless and misread ones need a habit, not more studying, which is a different use of your evening. Without the labels, all five would have looked like "I should study algebra more".
The weekly review
Once a week, spend ten minutes reading the log from the top. Redo three problems that you got wrong at least a few days ago, with the answers hidden. Cross out a row only when you have done it correctly on two separate days.
Look for patterns across weeks: if "careless" dominates, practise checking steps. If "misread" shows up, slow down on question words. If "concept" repeats on the same topic, go back to teaching yourself that topic.
Turning the log into practice
The log also gives you a ready-made practice set. Each Friday, pick one concept row and write two fresh problems of that type, with your own numbers, such as (x + 5)² and (2x + 1)². Solve them cold, expand them again by multiplying out the brackets as a check, and compare. If the middle term is right both ways, the idea has probably settled. If not, the row stays on the list.
Mistakes about error logs
Logging every typo. Keep the log for errors you could learn from.
Skipping the cause. A log without causes is a list of shame.
Never reading it. The weekly review is the point.
Writing "I need to be more careful". Replace it with an action you can actually do.
Your plan for this week
Take your latest returned quiz or homework and log each mistake using the five columns.
Tally the three causes.
Pick one fix and apply it to tomorrow's homework.
On Sunday, redo three logged problems from a blank page.
Frequently asked questions
Paper or spreadsheet?
Whichever you will actually open. A spreadsheet is easy to filter by cause; paper is easy to carry.
What if I cannot tell the cause?
Redo the problem with no hints. If you get it right, it was careless or misread. If you cannot, it is concept.
Get started
