Redo Incorrect Math Problems After Reading the Solution?

A review of 40 computer-based studies compared several kinds of feedback. Explanations produced better learning than simply marking an answer right or wrong. They also did better than showing only the correct answer^[1]. The advantage was especially clear on questions requiring more than basic recall^[1].

A larger review covered 435 studies and more than 61,000 learners. Feedback generally improved learning, but its value depended heavily on the information it contained^[2]. Feedback was more helpful for thinking and physical skills than for motivation or behaviour^[2].

That difference matters when an algebra paper comes back. A red cross tells you that something failed. A correct final answer tells you where the work should end. Neither one necessarily identifies the broken step.

Compare these two comments:

• “Incorrect. The answer is 11.”
• “When distributing 3, multiply both terms inside the brackets by 3.”

The second comment tells you what to change. A broad review recommends feedback that is specific, timely, supportive, and focused on improving the learner’s next action^[3]. It also reports that the usefulness of feedback changes with the learner and the task^[3].

So read the written correction before redoing the problem. Do not treat the solution as something to copy. Use it to identify the rule, decision, or calculation that went wrong.

The sources here do not directly compare two high-school algebra groups, with one only reading corrections and the other re-solving every problem. That exact advantage remains unsettled.

Still, re-solving is a sensible test of whether the correction changed what you can do. The page is no longer guiding each step once you cover it. You must choose the method and carry it through.

Revision has some indirect support. In one middle-school poster-design game, seeking critical feedback and revising went with greater learning during the game^[4]. Because this was not an algebra experiment, it cannot prove that redoing equations causes better mathematics learning^[4].

The practical point is narrower. Reading gives you information. Re-solving checks whether you can act on that information.

Consider this equation:

Suppose your original work began like this:

You then found $x=7$. The first line already reveals the misconception. You multiplied $3$ by $x$, but not by $-2$.

The correction should explain the distribution rule:

Now finish the corrected solution:

Subtract $2x$ from both sides:

Add 6 to both sides:

Check it in the original equation:

Both sides equal 27. The check confirms that 11 solves the original equation.

At this point, cover every corrected line. Start with the original equation on blank paper. As you distribute, say the reason in words: “The 3 multiplies every term inside the brackets.”

If you write $3x-6$, the original misconception may be fixed. One correct repeat is not a perfect guarantee, so use a nearby problem:

Distribute 4 across both terms:

Subtract $2x$:

Subtract 4:

Divide by 2:

Substitution gives $4(3+1)=16$ and $2(3)+10=16$. If you had written $4x+1$, the same misconception would still be active. You would need another explanation before more practice.

You do not need to redo the entire assignment blindly. Focus first on questions where your reasoning failed, not those with an isolated copied number.

1. Locate the first wrong line. Later lines may follow correctly from an earlier mistake. Mark where the work first stops being valid.
2. Name the reason. Write a short note such as “distributed to only one term” or “changed the sign incorrectly.” Specific feedback is more useful than knowing only that an answer is wrong^[1][3].
3. Cover and re-solve. Use blank paper. If you need to uncover the correction, read only enough to restart. Then cover it again.
4. Change the numbers and test the idea. Solve one similar problem. This separates remembering that page from applying the corrected rule.

A Learn4Less session can use this routine to trace a repeated error to its first incorrect step.

Do this soon after receiving the assignment, while the teacher’s marks still make sense. A review of digital mathematics feedback identified timing, personalization, interaction, and teacher support as recurring design principles across 33 papers^[5]. That review covered secondary and university mathematics from 2012 to 2024^[5].

Redo the full problem when you chose the wrong method, misunderstood a rule, or cannot explain the correction. These errors can return in a new-looking question.

A shorter check may be enough when the only issue was copying $8$ as $3$. Correct the number, finish from that point, and verify the final answer. If copying mistakes keep repeating, however, they deserve a checking routine of their own.

When you cannot identify the first wrong line, ask for a more specific explanation. A correct answer without reasoning gives less guidance than feedback explaining the mistake^[1]. Your question can be precise: “Why can’t I distribute the 3 this way?” That is easier to answer than “What did I do wrong?”

None of the sources here directly tested the exact routine of reading a corrected high-school algebra solution, covering it, and solving again. One revision study used a middle-school poster game rather than mathematics^[4]. One review covered corrective feedback for children around ages 3 to 11, not high-school students^[6]. The large feedback reviews combined many tasks and feedback formats, so they do not establish how many repeated problems any one student needs^[1][2].

For your next returned assignment, choose one mistake that involved reasoning. Read the explanation and circle the first wrong line. Write the missing rule in one sentence. Then cover everything and solve the original problem again.

Finish with one similar problem using different numbers. If both attempts are correct and you can explain the key step, move on. If the same mistake returns, stop repeating and get a clearer explanation first.