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/ Oscar ONeill / feedback

Math test corrections that give you new evidence, not just fixed answers

A five-step routine for returning a marked math quiz: specific comments, class time to respond, a fresh question, and a quick look at what the class does with it.

A marked quiz goes back. Students look at the number, then the paper goes in a binder. If there’s a corrections task, a lot of students copy the right answer from a friend or the board. The paper is now correct. Nobody knows much more than they did before.

Corrections can do more than that. The goal isn’t a fixed paper. It’s fresh evidence that the student can now do the thing they couldn’t do on the quiz.

Here’s a routine that aims for that. I’m not a teacher. This comes from building MarkScanner with direct input from Ontario secondary school teachers, and from published guidance on feedback. Adapt it to your class.

The short version

  1. Return the quiz with one specific comment per lost question.
  2. Give class time to respond to the comments.
  3. Students explain the error in their own words, then redo the step.
  4. Everyone answers a new question with different numbers.
  5. Look at the new question, not the corrections, to decide what to reteach.

Step 1: Comments that point at a line

“Check your signs” is true. It rarely tells a student where to look or what to do. A useful comment names the line and gives one action:

Line 3: (x + 1)(x + 3) expands to x² + 4x + 3, but you need −4x. Find two numbers that multiply to +3 and add to −4, then expand to check.

One comment per lost question is enough. One clear thing is easier to act on than a paragraph of advice. There are more examples in the math feedback comment bank.

Step 2: Class time, not homework

The Education Endowment Foundation’s 2021 guidance report on feedback recommends planning for how students will receive and use feedback, not only how it’s written. In practice that means time in class, while you’re in the room to answer “what does this mean?”

For a short quiz, start with about fifteen minutes and adjust.

Step 3: Explain, then redo

Before a student redoes anything, ask for one sentence: what went wrong, in their own words. “I picked factors that multiply to 3 but add to +4.” That sentence is the part that’s hard to copy from a friend.

Then they redo only the step that went wrong, and everything after it. Not the whole quiz.

Step 4: A new question

This is the step that turns corrections into evidence. Give a question with the same structure and different numbers. For the factoring error above:

Find the x-intercepts of y = 2x² − 10x + 12.

A student who copied the corrected answer can’t copy this one. A student who understood the comment will find two negative numbers again: product +6, sum −5.

Keep it short. One or two questions, done on paper, collected on the way out.

Step 5: Decide what to reteach from the new question

Sort the new questions into three piles: got it, close, and still stuck. It’s quick with one or two questions per student, and it’s better evidence for tomorrow’s plan than the original quiz. The original quiz tells you who struggled. The new question tells you who is still struggling after feedback.

If most of the class is still stuck, the comment wasn’t the problem. It’s a reteach. If it’s three students, it’s a small group.

What this routine doesn’t do

One new question is still one piece of evidence on one day. A student who gets it right may not have it next month, and a student who gets it wrong may have rushed. Use it to decide what to look at next, not as a verdict.

It also doesn’t need every quiz. A routine that runs well on the quizzes that matter beats one that runs badly on all of them.

Where MarkScanner fits

MarkScanner helps with step 1. It drafts marks and per-question comments against a rubric you approve, and you review and edit everything before it’s printed. It also gives you a class summary of which questions cost the most marks. Steps 2 to 5 happen in your classroom.

You can see this pattern on full papers in the worked examples, including the quadratic x-intercepts example this post borrows from.