Home · Insights · Research & Learning Science
Research & Learning Science · For parents & teachers

Feedback that works in maths — and the kind that backfires

Feedback is one of the most powerful influences on learning ever measured. It's also one of the most unreliable: in a major analysis, more than a third of feedback interventions made performance worse. That gap — between feedback that transforms and feedback that harms — is almost entirely about how it's given and whether anyone acts on it. Here's what separates the two.

A maths test comes back covered in red ink. Ticks, crosses, a few scribbled comments, and a grade circled at the top. The student's eyes go straight to the grade — "6 out of 10" — they feel the small sting or shrug of relief, and the page goes into the bag, comments unread. The teacher spent twenty minutes marking it. The student spent twenty seconds with it, and learned nothing they didn't already know. Multiply that by every test, every term, and you have one of education's quietest, most expensive failures: enormous effort producing almost no learning.

It doesn't have to be this way. Feedback, done well, is near the very top of the list of things that improve learning. The problem is that "done well" is surprisingly specific — and most of what passes for feedback misses it. This article is about the difference between feedback that changes what a student can do and feedback that, at best, is ignored and, at worst, makes them worse.

The marked test that taught nothing

The red-ink test is the classic case, but the pattern is everywhere: the parent who marks homework and reads out every correction while the child glazes over; the comment "needs to show more working" written for the fortieth time on the fortieth piece of work; the "well done!" that means nothing because it's on everything. In each case there's plenty of feedback and almost no effect, because feedback only works when it's understood, actionable, and — the part everyone forgets — actually acted upon. Information that no one uses isn't feedback; it's just commentary.

The hidden problem: feedback that's received but never used

Two design flaws sink most feedback. The first is the grade. When a mark and a comment appear together, the mark wins: students read the number, compare it with their neighbour's, and skip the comment entirely. The grade satisfies the question they care about ("how did I do?") and switches off curiosity about the more useful one ("how do I improve?").

In plain English

Imagine a fitness coach who, after every session, just shouts your weight at you and walks off. You'd learn nothing about how to train better — you'd only feel good or bad about the number. A grade on a test does the same: it tells a child where they stand but not what to do. Useful coaching says "your knee was collapsing inward — push it out on the next squat." Useful maths feedback says "you flipped the inequality sign here — what happens to the direction when you divide by a negative?" One ends the thinking; the other starts it.

The second flaw is aim. A lot of feedback is pointed at the person rather than the work: "you're so clever," "careless again," "you're better than this." This feels natural, but as we'll see, person-directed feedback is exactly the kind the research finds most likely to do nothing — or to harm.

What the research says

Finding 1 · Powerful, but wildly variable

Hattie and Timperley's much-cited review (2007) describes feedback as "among the most powerful influences on achievement" — but stresses that its effect can be positive or negative. The most effective feedback, they argue, answers three questions for the learner: Where am I going? (the goal), How am I going? (current progress), and Where to next? (the action). Feedback that names the next step is the kind that moves learning.

Finding 2 · Formative assessment is a big lever

Black and Wiliam's landmark review (1998) of formative assessment — checking understanding during learning to adjust it — found it among the most effective ways to raise achievement, with the largest gains for lower-attaining students. The point isn't more testing; it's using everyday checks to find out what a student doesn't yet understand and doing something about it before moving on.

Finding 3 · Over a third of feedback makes things worse

The sobering counterweight comes from Kluger and DeNisi (1996), whose meta-analysis of 600+ effects found feedback helped on average — but in over a third of cases it actually reduced performance. Their key insight: feedback that directs attention to the self ("you're brilliant / hopeless") tends to backfire, while feedback that directs attention to the task and how to do it better tends to help. Feedback is not automatically good; its aim decides everything.

Why a third of feedback backfires

Pull these together and a clear pattern emerges. Feedback helps when it points a learner's attention at the task and the method and gives them something to do next. It harms — or does nothing — when it points attention at the self, because ego-level feedback triggers self-protection rather than problem-solving. Praise like "you're a natural" can make a child anxious about losing the label (see our piece on maths confidence); criticism like "careless" stings without saying what to change. Either way, the learner's mind goes to themselves instead of the maths.

The other reason feedback fails is simpler: nobody acts on it. The Education Endowment Foundation, which rates feedback as worth several additional months' progress and especially effective in maths, is blunt that the gains come only when feedback changes what the learner does next. Feedback received and filed is feedback wasted. The most important moment isn't the marking — it's the time, afterwards, when the student reworks the problem in light of it.

Feedback that tends to backfire or fizzle

"6/10." · "You're so clever." · "Careless." · "Wrong, the answer is 14." · "See me." Points at the grade or the person; ends the thinking.

Feedback that tends to work

"Your method is right up to line 3 — check what you did to both sides there." · "What should happen to the sign when you divide by a negative?" Points at the task; starts the thinking; names a next step.

How different systems use it

Feedback and formative assessment around the world
Tap a system. Assessment cultures shape whether feedback helps or just sorts.

The "Assessment for Learning" movement grew from Black and Wiliam's UK research, and ideas like comment-only marking and "directed improvement and reflection time" are now widespread in English schools. The EEF's evidence has pushed feedback up the priority list — though workload pressures mean it isn't always done in the high-impact way the research describes.

Finland's low-stakes, formative-leaning culture — few standardised tests in the early years, an emphasis on ongoing teacher assessment and descriptive feedback over grades for younger children — is closer to the research ideal of feedback that informs rather than ranks.

Singapore pairs a high-stakes exam culture with strong, structured teaching, and has been deliberately broadening its assessment to include more formative, feedback-rich practice — a recognition that exam scores alone don't tell a teacher what to do next.

The US has a heavy summative-testing tradition, where high-stakes scores can crowd out the low-stakes, formative feedback that actually moves learning. Where teachers protect time for formative checks and feedback that's acted on, the gains follow the research.

One finding crosses every border: put a grade and a comment together and the comment is ignored. Studies show students given comments only improve more than those given grades, or grades plus comments. The grade isn't neutral — it actively suppresses engagement with the feedback. This is the single most actionable idea in the whole field.

What parents can do

  1. Resist giving the answer. When your child is wrong, the instinct is to correct: "no, it's 14." That ends the learning. Instead, locate the slip and hand the thinking back: "everything's right until this line — have another look at what you did here." Keep them doing the work.
  2. Talk about the task, not the child. Swap "you're so clever" and "careless" for comments about the maths: "that's a neat method," or "this step is where it went sideways." Person-feedback (good or bad) aims attention at the ego; task-feedback aims it at the problem.
  3. Insist on the redo. Feedback only works when acted on. After any correction, have your child rework the problem — and a similar one — there and then. The five minutes of reworking matters more than the marking that preceded it.
  4. Cover the grade. When a marked test comes home, fold over the score and read the comments first, together: "what's the one thing to fix next time?" The grade will still be there afterward — but the learning happens before they see it.

What teachers and tutors can do

Try comment-only marking, with time to act. Where feasible, give feedback without a grade attached, and build in "reflection and redrafting" time so students actually use it. A shorter comment that gets acted on beats a page of annotations that don't.

Make feedback name the next step. Frame it around "where to next" — a specific, doable action — rather than a verdict. "Re-check line 3" or "try this with a negative value" gives the student a move to make. Keep it about the task and the method, never the person.

Use cheap, frequent formative checks. Mini-whiteboards, exit questions, "show me" tasks, a quick diagnostic — anything that reveals misunderstanding during learning so you can adjust before moving on. Formative assessment isn't extra testing; it's how you find out what to teach next.

Knowledge check
A teacher returns marked tests with a grade and detailed written comments, but students' next tests show no improvement on the same errors. The most likely fix, based on this article, is —
The grade is crowding out the comments, and even read comments do nothing unless acted on. Comment-only feedback plus protected time to rework the errors targets both flaws at once. More detail or a bigger grade won't help — the issue isn't the volume of feedback, it's whether it's read and used.
Is feedback being wasted in your child's learning?
Tick what's true. More ticks means more of the effort is going to waste.

Instant, task-focused feedback — free

The practice portal gives immediate feedback on each question, focused on the method and the next step rather than a grade — and lets students retry, so the feedback actually gets used.

Open the practice portal →

Common myths, corrected

Myth

"More feedback is always better."

What research suggests

Over a third of feedback interventions reduce performance. Aim and action matter far more than volume — a short, task-focused, acted-upon comment beats a page of annotations.

Myth

"Praising ability builds confidence."

What research suggests

Person-directed feedback, even praise, tends to backfire — it aims attention at the ego, not the task. Praise the method and the effort instead.

Myth

"A grade tells the student what they need to know."

What research suggests

A grade says where they stand, not what to do — and it suppresses engagement with the comments that would help. Comment-only feedback is used more.

If you remember five things

  • Feedback is among the most powerful influences on learning — and one of the most variable: over a third of feedback makes performance worse.
  • Feedback that aims at the task and names a next step helps; feedback that aims at the person ("clever", "careless") tends to backfire.
  • Grades crowd out comments. Comment-only feedback, with time to act on it, is used and useful far more often.
  • Feedback only works when acted on — the redo matters more than the marking.
  • Formative assessment (checking understanding during learning) is one of the highest-impact things a teacher or tutor can do, especially for strugglers.

Frequently asked questions

Is feedback always good?

No. On average it helps, but a major meta-analysis found over a third of feedback interventions reduced performance. The harmful kind aims at the person; the helpful kind aims at the task and what to do next.

Why does my child ignore the comments on returned work?

Because there's usually a grade on it. The number answers the question they care about and switches off interest in the comments. Comment-only feedback, with time set aside to act on it, gets read and used far more.

What is formative assessment?

Checking understanding during learning so you can adjust — as opposed to summative assessment, which measures at the end. Used well, it's one of the most effective ways to raise achievement, with the biggest gains for those who are struggling.

What kind of feedback actually helps in maths?

Feedback that answers three questions — where am I going, how am I doing, what's my next step — focused on the method rather than the person, specific, and acted upon. "Re-check line 3" beats "careless" every time.

Should I just tell my child the right answer?

Try not to — giving the answer ends the thinking. Point to where it went wrong and let them find the fix, or offer a hint rather than the solution. The goal is to keep your child doing the cognitive work, because that's where learning happens.

References

  1. Black, P. & Wiliam, D. (1998) 'Assessment and classroom learning', Assessment in Education: Principles, Policy & Practice, 5(1), pp. 7–74.
  2. Hattie, J. & Timperley, H. (2007) 'The power of feedback', Review of Educational Research, 77(1), pp. 81–112.
  3. Kluger, A. N. & DeNisi, A. (1996) 'The effects of feedback interventions on performance: A historical review, a meta-analysis, and a preliminary feedback intervention theory', Psychological Bulletin, 119(2), pp. 254–284.
  4. Education Endowment Foundation (2021) Teaching and Learning Toolkit: Feedback. London: EEF.

Founder, Insight Bay

Aerospace engineer (MSc Astronautics & Space Engineering) turned mathematics tutor. The single biggest change I make to a struggling student's week is rarely new teaching — it's turning feedback from something done to them into something they act on.

About Insight Bay →

Feedback your child will actually use

One-to-one means feedback in the moment, focused on the method, followed immediately by a redo. It's how progress compounds. See it in the free assessment.

Book the free assessment