Repetition builds fluency in a method that is already right. Targeted feedback fixes a method that contains a slip. If you repeat a slip, you get better at the slip.
Knowing which you need is a two-minute test, shown below. This page continues from bringing evidence of a recurring difficulty to the trial.
When is repetition the right tool?
Repetition helps when your errors are scattered: a sign here, an arithmetic slip there, nothing twice. It also helps when you are right but slow, such as recalling times tables or formulae under time pressure.
The signal is that your wrong answers have different causes. More practice will reduce random slips by building familiarity.
When is targeted feedback the right tool?
Feedback helps when the same error returns. The signal is a repeating cause: the same step fails on different questions, or the same wrong answer appears again after a correction.
Targeted feedback means someone or something tells you which step is wrong and why, so you change the method, not just the number of attempts.
Worked example: expanding a squared bracket
A student practises expanding brackets. She completes 20 questions; 4 are of the form (x − a)². She gets all four wrong, and the other sixteen right.
Her working on one of them: (x − 3)² = x² − 9.
The test: 4 of 20 wrong is 20%. Are the four wrong answers scattered or repeating? All four show the same pattern: she squares each term and drops the middle term. That is a repeating cause.
If she repeats another 20 similar questions, she will likely lose marks on those same four types again. The fix is one targeted check.
Feedback by substitution: choose x = 5. The left side is (5 − 3)² = 2² = 4. Her answer gives 5² − 9 = 16. The two routes disagree, so the expansion is wrong.
The corrected method: (x − 3)² means (x − 3)(x − 3).
x² − 3x − 3x + 9 = x² − 6x + 9
Check with x = 5: 25 − 30 + 9 = 4 ✓.
Now repetition is worth doing: five more squared brackets, each checked by substitution, to make the corrected method automatic.
The mistake to watch for
The common slip is treating a lot of practice as proof of effort, and effort as proof of progress. Forty questions feel productive, but if the last twenty repeat the error of the first twenty, the extra time changed nothing.
The correction is to stop after any error you have met three times. Pause, choose one of those questions and check it by another route. You have then replaced repetition with feedback.
A two-minute test
- Pick the last five questions you got wrong on the topic.
- Write the cause of each in a few words.
- If three or more share a cause, you need feedback. If all five differ, keep practising.
- If you cannot name the cause at all, that is also a reason for feedback.
Check yourself
1. A student expands (x + 4)² and writes x² + 16. Use x = 1 to show the answer is wrong and give the correct expansion.
Show answer
Left side: (1 + 4)² = 25. Student’s answer: 1 + 16 = 17, so it fails. Correct: (x + 4)(x + 4) = x² + 4x + 4x + 16 = x² + 8x + 16. Check: 1 + 8 + 16 = 25 ✓.
2. A student completes 30 questions and gets 6 wrong, all for different reasons. What share was wrong, and should they repeat or seek feedback?
Show answer
6 ÷ 30 = 20%. The causes differ, so the errors look scattered. More practice with checking is sensible. Feedback is useful if a cause starts repeating.
3. Why can repeating a question after a mistake, without changing anything, make the mistake stronger?
Show answer
Each repeat is another rehearsal of the same steps. Without a change to the method, the wrong route becomes more familiar and more automatic.
Where this leads next
The post-trial reflection guide can help you decide what you learned from feedback in a lesson, and planning further tuition after the paid trial looks at how to think about the next step.
Self-study may be enough when you can find repeating errors by substitution and fix them yourself. If you cannot tell why an error keeps returning, one-to-one Mathematics tuition can focus on one of your own questions, and how the trial works is explained on its own page.