What is it with mirror perception of letters and numerals?
When learning to read and write letters and numerals, children mistake some letters and numerals for other similar ones, especially those that appear similar when rotated on an axis. The characters may seem to be seen in a mirror.
These sorts of errors are sometimes called “reversals” or “mirror writing.” Sometimes children will even write entire sentences or passages starting from the right of a page.
Here is an example. It’s a photo of a piece of paper that literally blew into our yard. I am pretty sure that a neighborhood child named “Ethan” created this expression of his world. Obviously, if it is from Ethan, he’s just learning how to write.
Although reversals of some letters will make no difference (for example, the printed letters ‘t’ and ‘x’ look the same written either “frontwards” or “backwards”), reversals of other letters and numerals makes a difference. Here are some common examples of reversals:
A 3 can appear to be a capital E that’s rounded and reversed,
A lower-case b looks like a d or an upside-down p.
In addition to the frontwards-backwards reversal of characters, readers or spellers may transpose the order of letters in a word or a string of numerals. That is, the order of letters or numerals might be mixed so that they differ from a model.
A phone number, 937-3722, might be repeated as 937-7322.
Not only might “saw” be written as “was,” but it’s possible that “causal” might be miswritten as “casual”—There’s a conceptual misrepresentation!
Why does this happen? What’s to be done about it?
Samuel Orton, an MD and a pioneer in learning disabilities (the Orton Dyslexia Society, which was named after him, has morphed into the International Dyslexia Association), promoted a theory that reversals were a result of incompletely established lateral dominance. According to this theory, the dominant hemisphere of the brain, which usually controls language, stores one version of an “engram” such as “was” or “b” while the non-dominant hemisphere stores a mirror image of the engram—”saw” or “d.” If an individual has incompletely establish dominance (that is, might be right handed, left eyed, and right footed), then she or he will sometimes use the engram from the non-dominant hemisphere, and thus read or write the mirror image (Boder, 1973). This theory has been discounted, but the idea persists in popular thinking.
Although nearly all young learners make reversal errors as they learn to read and write, most gradually stop doing so during the primary and elementary grades. Also, if one considers the percentage of total errors that are reversal errors, students with reading problems make no more reversal errors than do their peers who read relatively well; students with reading problems simply make more errors of all types. That is, we see those weaker readers making more reversal errors than their peers who read without problems because they make more mistakes overall (Fischer, Liberman, & Shankweiler, 1978; Holmes & Peper, 1977).
What Can Be Done?
Perhaps more important than mistaken theories or factual explanations of the phenomenon, people would like to know what to do about reversals or mirror writing. Clearly, one thing that teachers and parents can do is simply explain that with letters and numerals, it matters which way they point. When a cup is right-side up or up-side down, it’s still a cup. When a person is lying down or standing up, it’s still the same person. But when a b is rotated, it’s not a b any more.
From my visits in the 1970s with Zig Engelmann, I remember him suggesting printing b on a transparency and getting children to label it correctly as /b/ or “not /b/.” He recommended flipping the transparency horizontally and vertically. The kids just had to label each presentation correctly as the teacher flipped and twisted the transparency in orientation. (Engelmann also recommended exaggerating the differences between b and d in printed materials by using different typefaces for them in early reading materials.) Carnine (1976) showed that introducing similar stimuli—d and b—separately and only after one of them had been learned to a high criterion reduced the chances of learners confusing them.
These recommendations show how what the behaviorists among us call “stimulus control” is really important. We need to help bring students’ behavior under the control of specific stimuli. We don’t want their behavior to be random or mistaken when presented with a stimulus such as b or d.
In cases where the problem persists after the primary grades, it may merit treatment or intervention. A simple teaching technique has repeatedly been shown to correct mirror writing (Fauke, Burnett, Powers, & Sulzer-Azaroff, 1973; Hasazi, & Hasazi, 1972; Lahey, Busemeyer, O’Hara, & Beggs, 1977; Stromer, 1975, 1977). Essentially all one has to do is differentially reinforce correct letter formation in writing. The adult can set up a situation in which the child is to write letters, numerals, and words from dictation—somewhat like an old-time spelling test, but kept light and fun—and provide copious amounts of consistent praise contingent on correctly written repsonses:
“O.K., here we go. Write the letter for the sound /mmm/.”
[If correct] “That’s it. Great!” [Put a smiley face next to it. Go to the next item.]
[If incorrect] “Nope. Here’s how you write /___/.” [Demonstrate.] “Copy it here.”
Check and correct
O.K., next one. Write the letter for the sound /___/.”
[Continue with items, checking and correcting.
[Return to mistaken items after a few new items.]
The adult should use mostly very well known items, those that the child is likely to write correctly. Include difficult items, those on which a child makes mistakes, at a ratio of about 1 for every 7-9 known items. If some letters or numerals are particularly problemsome, the adult might pre-correct by showing a model just before the child is asked to write: “Oh boy, here comes that hard one. I’m going to ask you to write a 3 and you should make it look like this [show model, then remove it]. O.K., write a 3.” Only use the model a few times, gradually using it on fewer and fewer trials. The adult should keep records about the number of correct responses and overall respones; count each trial (correct or error) rather than estimating.
For reading rather than writing, one can use the same system but substitute touching for writing. For example, show the child an array of two (later three or more) items—for example, written m and 3—and say, “Touch the one for the sound /mmm/.” The items should be readily discriminable in the early trials, but gradually the adult can mix in tough items such as n vs. m, b vs. d, or saw vs. was. Parallel this activity with another in which the child points to each letter and says its sound; increase the difficulty in a similar way. Remember that correction and reinforcement are critical for increasing the probability that child will respond correctly.
With either the reading or writing tasks, repeat the practice trials daily for multiple days. Gradually make them more challenging. Don’t expect these problems to be corrected in one or a few trials. This is not something where children develop sudden insight. It’s more like dribbling a ball than grasping a concept. Keep it fun and make sure that the tasks you give the child are selected so that he or she gets ~90-95% correct.
Mirror writing or reading is not a sign of neurological disability. It’s just that the reader or writer hasn’t learned how to form characters or say the right things for characters. We can teach them how to do so using relatively simply instructional processes.
Boder, E. (1973). Developmental dyslexia: Prevailing diagnostic concepts and a new diagnostic approach. Bulletin of the Orton Society, 23, 106-118. https://www.jstor.org/stable/23769543
Carnine, D. W. (1976). Similar sound separation and cumulative introduction in learning letter-sound correspondences. Journal of Educational Research, 69, 368-372.
Fauke, J., Burnett, J., Powers, M. A., & Sulzer-Azaroff, B. (1973). Improvement of handwriting and letter recognition skills: A behavior modification procedure. Journal of Learning Disabilities, 6, 296-300.
Fischer, F. W., Liberman, I. Y., & Shankweiler, D. (1978). Reading reversals and developmental dyslexia: A further study. Cortex, 14, 496-510.
Hasazi, J. E., & Hasazi, S. E. (1972). Effects of teacher attention on digit-reversal behavior in an elementary school child. Journal of Applied Behavior Analysis, 5, 157-162. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1310746/pdf/jaba00068-0061.pdf
Holmes, D. L., & Peper, R. J. (1977). An evaluation of the use of spelling error analysis in the diagnosis of reading disabilities. Child Development, 48, 1708-1711.
Lahey, B. B., Busemeyer, M. K., O’Hara, C., & Beggs, V. E. (1977). Treatment of severe perceptual-motor disorders in children diagnosed a learning disabled. Behavior Modification, 1, 123-140.
Stromer, R. (1975). Modifying letter and number reversals in elementary school children. Journal of Applied Behavior Analysis, 8, 211. https://onlinelibrary.wiley.com/doi/abs/10.1901/jaba.1975.8-211
Stromer, R. (1977). Remediating academic deficiencies in learning disabled children. Exceptional Children, 43, 432-440.
Editor’s note: I first published a version of this post 5 Mar 2007 on LDBlog.com . I revised it 15 Jan 2008. I republished this revised version 20 April 2022. I also edited to correct the link to the International Dyslexia Association.