Why do kids mistake letters and numerals for others characters in "reversed" or "mirrored" form? What can be done about this?
Although reversals of some letters will make no difference (for example, the block-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 a lot like a “d” or an upside-down “p”;
The word “saw” might be read as “was”';
The order of letters or numerals might be mixed so that “and” might be written “adn” or “973-3722” might be read as “nine-seven-three, three-seven-two-two.
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 Society; his name is the first part of “Orton-Gillingham”), 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, then she or he will sometimes use the engram from the non-dominant hemisphere, and thus read or write the mirror image. Orton even created a name for this problem: “strephosymbolia,” twisted symbols. This theory has been discounted, but the idea persists in popular thinking.
It should come as no surprise that learners make such mistakes. After all, in a child’s world, it oreintation in space barely matters. Big sister “Isabella” has the same name whether she is standing up right, lying on the couch, or standing on her head in a yoga pose. A cup is a cup, whether it’s sitting on the counter, upside down in the dishwasher, or held tilted toward a mouth.
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 and, thus, we see them make more reversal errors than their peers who read without problems (Fischer et al., 1978; Holmes & Peper, 1977).
So, first take-away: Reversals and mirror writing are not an indicator of neurological problems. They are not a marker of dyslexia. They are developmentally normal.
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—what Barb Bateman called “the pointy rule.” When a person is lying down or standing up, it's still the same person; when a cup is right-side up or up-side down, it's still a cup. But when a “b” is turned around, it's not a /b/ any longer. It’s got a different sound (or name).
In the 1970s I remember Zig Engelmann suggesting printing “b” on a transparency and getting children to label it correctly as "b" or "not b" 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.)
As a preventative, Carnine (1976) showed that introducing similar stimuli—“d” and “b”—separately and only after one of them has been learned to a high criterion reduced the chances of learners confusing them. That’s a programming note for those designing early literacy curricula, and it shows one of the problems with confronting learners with all 44 sounds and 200+ spellings of those sounds at the beginning of their acquisition of reading and writing—i.e., throwing children into a “rich” (i.e., wide-open, uncontrolled) literacy environment
In cases where the problem persists after the primary grades, it merits treatment or intervention. A simple teaching technique has repeatedly been shown to correct mirror writing (Fauke et al., 1973; Hasazi & Hasazi, 1972; Lahey et al., 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/."
[Check and reinforce or correct.]
[If correct] "That's it. Great!" [Put a smiley face next to it. Go to 4.]
[If incorrect] "Not quite. Here's how you should write /___/." [Demonstrate.] "Copy it here."
O.K., next one. Write the letter for the sound /___/."
Check and reinforce or correct. Repeat presentation and check-or-correct steps with 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 hardy-dardy one. I'm going to ask you to write a ‘3!’ 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 percentage of correct responses; count each trial 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, four, and so on) 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 or
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 chances that child will respond accurately in the future. (Importantly, one should also gradually increase the criterion for reinforcement; initially, praising almost every correct response, then every second or third correct response, and then every fifth…but once the learner continues to make accurate responses, mix up the reinforcement, every now and again praising every response and then dropping back to every eighth or ninth correct response.)
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 she or he gets ~90-95% correct.
Second take-away: Reversals can be addressed with systematic instruction.
Although I have focused here on visually confusing stimuli, one should remember that there are also auditorily confusing stimuli, such as “/e/” (as in “pen”) and “/i/” (as in “pin”).
As with virtually any intervention procedure, it’s important to know whether the learner’s performance is improving. Assessing change in performance requires monitoring how the learner is doing over time. Curriculum-based measurement is an excellent way to monitor progress. In this case one may also want to collect some more-focused data. Behavior analysts, for example, keep trial-by-trail records of what stimulus is presented, whether the student responded accurately, and whether reinforcement was delivered. For students with substantial problems with “reversals,” it probably would be beneficial to (a) collect the trial-by-trial data (also helps one analyze the sequence of instruction and the ratios of reinforcement) as well (b) analyze the proportion of reversed letters in “free writing” activities (i.e., those when explicit instruction is not being employed).
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 teaching attention on digit-reversal behavior in an elementary school child. Journal of Applied Behavior Analysis, 5, 157-162. [Available here for free.]
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. [Available here for free.]
Stromer, R. (1977). Remediating academic deficiencies in learning disabled children. Exceptional Children, 43, 432-440.
Note: I published an earlier version of this content on LDBlog.com. The 1st draft appeared 5 Mar 2007; I revised it 15 Jan 2008.