Here is a question submitted from a Rocket Math user, who would like to know if kids who write their numbers backwards or reversed, should be corrected.

“My school is using the Rocket Math program. We are wondering if you would accept reversals on Rocket Math papers? By the way, I love your program.”

Becky, thanks for your question. Many teachers wonder whether they should accept reversals or backwards numbers, when children are writing out answers to math problems. The answer depends upon the type of reversed numbers. Bet you didn’t know there were two distinct types of reversals, did you?

The benign reversals are single digits written backwards. A backwards 7 or 2 or 4 or 6 should not alarm you greatly. Up until the school years children have learned that a thing has the same name regardless of its orientation. A chair turned upside down or turned left to right is still a chair. Upside down toys are still the same and you learn to recognize things as being the same regardless of how it is facing. Then suddenly in school some things, particular symbols, have to be facing a certain direction. Learning which way the seven has to face, is best accomplished by a patient teacher who points out which way sevens have to face. Extra practice making 7s the right way would be a good idea.

Pre-correcting for the error by writing a model at the top of the paper for students who are persistently getting it wrong can be quite effective. And of course, the quickest learning results from lots of praise for “making these sevens face the right way.” But refusing to accept a 7 as the correct answer because it is facing the wrong way is at best unnecessarily discouraging and at worst, may be confusing. Some students may think they got the wrong answer and conclude that 3 plus 4 is not seven!

On the other hand, there is another kind of reversal that must be treated as an error. The unacceptable reversal is when the digits are written in the wrong order, as when fourteen is written as a four and a one (41) and nineteen is written as 91. This kind of reversal represents a misunderstanding about place value. In addition the student has actually written the wrong number, so he/she must learn that is a different number. “No, that’s not right. You wrote twenty-one and three times four is twelve. Twelve is written like this, 1-2.” Again, it would be smart to give some practice writing numbers from dictation–especially those pesky teen numbers. Modeling on the board or overhead first, followed by practice of a small set of numbers would be most effective.

So, single digits facing the wrong way can be accepted as the right answer, even though you work on correcting the way the numeral faces. But two digit numbers must be written with the tens digit on the left ALL the time.

I can’t leave this topic without pointing out that your students may also be reversing their zeros, ones and eights–but you just can’t tell!