This math teacher highlights students' mistakes:

grading math homework
  • High School
trisha flassing

All teachers are familiar with this moment: the handing back tests moment. The students are on edge, waiting to receive the final verdict. They reach out to take the form, their eyes immediately looking for the number marked in red at the top of the page. They react with joy, disappointment or indifference and after a quick review of the test at best, they stuff it into the schoolbag.

Have you ever thought about what the students learn from this number? Do two students who received the same grade need to improve in exactly the same things? What if one had difficulty understanding the question and the other actually understood perfectly, but made a mistake in the answer they wrote?

Many teachers invest a great deal of work in marking the students' mistakes and explaining these mistakes, but many students do not come to read the explanations at all, and even if they do, it is not certain that they understand the mistake they made or know how to avoid it in the future.

Teacher Leah Alcala from California, developed an innovative method for checking math tests. Leah's strategy advocates emphasizing mistakes rather than giving grades, in a way that encourages an atmosphere of risk-taking and making mistakes in the classroom.

Leah, a middle school teacher, does not grade the actual tests. Instead, she emphasizes what is really important and what allows students to learn and understand better. Each test that Leah returns is full of marker colors - highlighting the mistakes made in the test. For those who really care about the grade, they can get it later through the school's computerized system.

She says she found that in the past, when she returned graded tests, students would take one look at the test, decide if they were good at math or not, and never look at it again.

Leah wanted her every interaction with the students to become an experience of learning and progress, so she developed the error mirroring method, which she talks about in an interview with the American 'Education Channel' website.



The mirror strategy in three simple steps:

Leah's strategy is simple but effective.

The goal: to make the students think first about the math they are dealing with and only then about the grade.

The method: Marking the mistakes throughout the test.


In the first step, she marks all the mistakes and writes down the grade for herself on the side, which the students will learn only later through the computerized system.


In the second step and before she gives the tests back, she projects some of the exercises in which the students made a mistake on the board, with the mistake highlighted. Of course, she does not say which tests the mistakes are from and emphasizes that they can be from any of the classes she teaches.

The emphasis is only on the part of the answer that was wrong and not on the whole exercise. She shows the class the answer and the marked part but does not explain why she marked it. She then asks the students, sitting in groups, to explain to each other what the mistake was and why.

Leah guides the discussion, each time she projects answers on the board and asks questions such as: "Why did I emphasize the X?” "What should the student have written instead?" and more. Then she sends them to discuss the answers to her questions in groups and later chooses representatives to explain it to the whole class.


In the third step, Leah gives the tests back to the students and asks them to go over the highlighted mistakes and check if they understand them. "If you don't understand the mistake, talk about it with the student next to you and get help from them" she says "If you need help you can also use me"

At this stage the students explain the problem and the solution to each other, so that an atmosphere of mutual help is also created, the message gets through that It's okay to make a mistake. In addition, every student who helps their friends, strengthens their own mathematical knowledge.

After a student has realized his mistake, she asks them to correct it.

"I see that when I return tests, they continue to learn," Leah explains in an interview. At first, Leah encountered resistance from the students who immediately wanted to know how much each question was worth, what their score actually was and whether they passed the test. She patiently reminded them that their grade in the division was not as important as the amount of math they were able to acquire.

Today, she testifies, she almost no longer hears questions about the grade, but mostly about the math itself and the exercises in the test.


Several important highlights:

Leah explains that there are several important points to pay attention to:

1. The amount of underlining is not relevant to the grade. There can be two tests with the same amount of highlighting but with different scores, and this is because the markers will emphasize both minor mistakes and heavier mistakes. As well as the fact that sometimes she will highlight an error in the way of the solution even though the final answer turned out to be correct.

2. How to mark the tests. The marking is done in two rounds.

In the first round, Leah goes through the tests and looks for the exact moment when the mistake was made. She explains that there are three types of mistakes - sometimes a student makes a small mistake and continues to solve the exercise correctly without making any more mistakes, only that the answer he gets is obviously wrong because of that single mistake. In such a case, a number of points will be deducted from the grade for the specific mistake but not for the entire exercise.

In another case, where a student made a mistake along the way and also made a mistake in the final answer (based on the same mistake), points will be deducted both in account ot the mistake along the way and the final answer.

A third type of mistake she emphasizes are mistakes that should be noticed but do not deduct points from the student, for example: an answer to a verbal question in which the student did not understand or did not write what the number he reached represents, such as the number of kilometers a train traveled or the number of cookies mom baked in an exercise. She does this so that the students pay attention to the details and learn to be precise, even if they solved the exercise itself correctly.

In the second round, Leah goes through the tests and tries to identify the type of mistakes that each student makes. She examines whether there is one particular mistake that repeats itself over and over again or whether there are many mistakes of different types.

If there is one mistake that repeats itself, it does not lower a grade for each and every time the student made the mistake. She explains that this is a mistake that is relatively easy to correct, because after one conversation with the student they learn where they are wrong and can correct it throughout the whole problem. On the other hand, a test in which there are many mistakes of different types indicates a fundamental lack of understanding in mathematics and the work with the student will be deeper and longer. "In both types of tests there will be a lot of marks" she explains "but the first test will receive a much higher score than the second test"

3. The time devoted to the test. Leah emphasizes that the amount of time devoted to checking the tests in this way is not longer than the time it takes to check a test using the normal method. "It takes the same amount of time to check the tests, but I enjoy it much more this way," she testifies.

4. Possibility of correction. Leah allows students to retake a test whenever they are ready. She testifies that most of the time they will have to sit with her during private hours before they are ready to take the test again.

The main message that passes through this method to the students, in Leah's opinion, is that recognizing mistakes, analyzing and understanding them, is the meaning of learning. "It's important to me to normalize the fact that they make mistakes" she concludes "It allows them to take more risks and experiment"

What do you think? Want to try? (Read about Growth Mindset and the importance of teaching to make mistakes - here) Wait! This is more than just "cute" middle school stuff - Understanding mistakes can help student master knowlage in a powerful way - see how:

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