- Email: [email protected]
Mirror writing of digits and (capital) letters in the typically developing child
c o r t e x 4 7 ( 2 0 1 1 ) 7 5 9 e7 6 2
available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/cortex
Note
Mirror writing of digits and (capital) letters in the typically developing child Jean-Paul Fischer Developmental Psychology, InterPsy Laboratory, EA 4432, Nancy, France
article info
abstract
Article history:
Typically developing 5- to 6-year-old children often reverse some digits (e.g., 3 for 3) or
Received 14 July 2010
single (capital) letters (e.g., 6 for R) when they are required to write them under dictation.
Reviewed 14 September 2010
A theoretical approach to this phenomenon, based on an implicit right writing rule and
Revised 9 October 2010
that postulates an influence of the preceding writing, was tested in an experimental study
Accepted 1 February 2011
of 300 children aged 5e6 years. The data support the implicit right writing rule and show
Action editor Roberto Cubelli
the considerable influence of the preceding writing. For example, 73% of the children who
Published online 9 February 2011
correctly wrote the letter C mirror wrote an immediately following digit 3, whereas only 10% of the children who mirror wrote the letter C also mirror wrote an immediately
Keywords:
following digit 3. ª 2011 Elsevier Srl. All rights reserved.
Mirror writing Directional apraxia Mirror generalization Implicit rule Visuomotor priming
1.
Introduction
Teachers and parents know that almost all children have a tendency to reverse the writing of some single letters (e.g., 6 for R) or digits (e.g., 3 for 3) when they begin learning to write between 4 and 6 years of age. Because this spontaneous behavior seems lost in normal adults, it is intriguing to ask which process is responsible for such mirror writings. The motor-based “directional apraxia” hypothesis (Della Sala and Cubelli, 2007) and the visual-based “neuronal recycling” hypothesis (Dehaene, 2007) share the assumption that there is a period in development when children know how to compose the letters and digits but they do not know whether an individual letter or digit, for example, the digit 3, should face left (3) or right (3). Two recent empirical results (Fischer,
2010a, 2010b) offer some clues on how 5- to 6-year-old children choose one of the two directions (left or right). Fischer (2010a) showed that frequencies of mirror writing were different for different digits. For example, the digit 3 was reversed in 45.60% of cases, whereas the digit 4 was only reversed in 16.22% of cases. Fischer’s research also suggests that the preceding digit may trigger a form of motor priming (or a visuomotor priming when the digits are written adjacently) which influences the direction of the subsequent digit. Further, Fischer (2010b) reported that children mostly reversed two capital letters e J and Z e and that these reversals were frequent. Fischer interpreted these findings as the result of children developing an implicit rule for writing capitals according to which capitals have distinctive features on the right or face right. Children may learn such an “implicit right
E-mail address: [email protected]. 0010-9452/$ e see front matter ª 2011 Elsevier Srl. All rights reserved. doi:10.1016/j.cortex.2011.01.010
760
c o r t e x 4 7 ( 2 0 1 1 ) 7 5 9 e7 6 2
writing rule” because the great majority of the asymmetrical letters have a vertical line on the left side and their distinctive feature on the right (B, D, E, F, K, L N, P, and R), face right1 (C and G), or have a tail on the right (Q). The implicit right writing rule indicates the correct direction for the capitals listed above, but it does not do so for the letter J. For the letter S, which does not clearly face right or left, and the letter Z, which has a diagonal line and not a vertical line, the rule is not relevant. These two hypothesized mechanisms for bootstrapping2 the direction of writing e an implicit right writing rule for capitals and visuomotor priming from the preceding writing for digits e generated two different hypotheses. According to the global hypothesis, since the implicit right writing rule gives the correct writing direction for 12 of the 15 asymmetrical capitals, the 12 capitals B, C, D, E, F, G, K, L, N, P, Q, and R should benefit from activation of the rule. Moreover, also the correct writing of 6 should be induced by the activated rule. While the effect on the digits 4 and 5 is unclear, then no mirror writing was hypothesized for these digits, the activated rule should promote mirror writing for 1, 2, 3, 7, 9, and J. Because the rule is not relevant for S and Z, the choice of direction for these two letters should be made by chance. Hence, the global hypothesis states that, as a group, the capital letters B, C, D, E, F, G, K, L, N, P, Q, R and the digits 6, 4, and 5, should be mirror written less frequently than the group of remaining asymmetrical characters. The local hypothesis, combining the implicit right writing rule and visuomotor priming from the preceding writing, predicts that digit 3 will be mirror written more frequently after a correct writing of C or E, than after a mirror writing of C or E, respectively. For the letter J, it predicts more mirror writings after a mirror writing of 7 than after a correct writing of 7, and more mirror writings after a correct writing of 6 than after a mirror writing of 6. Therefore, mirror writing of J (1) should occur least frequently after a correct writing of 7 or after a mirror writing of 6, (2) should be at an intermediate level when J is at the beginning of a series, and (3) should occur most frequently after a mirror writing of 7 or after a correct writing of 6. Analyses of the writing of 3 after B were exploratory because of the hidden 3 in B.
2.
Method
2.1.
Participants
The participants were 300 children (144 girls and 156 boys) from 18 preschool classes of the French “Ecole Maternelle”.
%Mirror Writings 70 60 50 40 30 20 10 0 1 2 3 4 5 6 7 9 B C D E F G J K L N P Q R S Z
Character
Fig. 1 e Percentage of mirror writings as a function of the character being written.
Thirty-nine other children were excluded because they did not produce any (horizontal) mirror writings or did not produce at least 50% relevant writings. The mean age was 5.715 years (SD ¼ .35; range: 5.00e6.35). Thirty-three children wrote with their left hand and 267 wrote with their right hand. Participants were tested in groups of three or four, and the groups were randomly allocated to one of six experimental conditions (50 children in each condition): the children in the six experimental conditions did not differ in their mean age [F(5,294) ¼ .24, p > .94] or in the ratio of girls to boys [c2(5) ¼ .32, p > .99]. All standard administrative authorizations and ethical rules for such experiments in schools were respected.
2.2.
Material
The children had to write, under dictation and from memory, the 11 digits or letters of a series, in 11 aligned squares (one character per square). The sides of the squares measured 2.2 cm. Three series were used: s1: P, 4, C, 3, 1, 7, J, L, 9, Z, G; s2: J, 0, Z, 5, K, F, 9, B, 3, N, Q; s3: R, E, 3, D, 8, 6, J, S, 2, 9, Z.
2.3.
Procedure
The experimenter encouraged the children to write the digits and capital letters on the strip of paper, moving from left to
1
A character with no vertical line faces right when its main concavity is turned towards the right. Under this definition, the digit 6 faces right, and the digits 2, 3, and 9 face left. In France, the digit 1 is written with a short, left-facing downward stroke at the top of the vertical line that forms the body of the digit; therefore, it also contradicts the implicit right writing rule. 2 To “bootstrap” means “to help oneself, often through improvised means”. Direct observation suggests that children choose the direction of writing on their own, with no outside help, and that they use a self-initiating process. Therefore, it could be said that children bootstrap the direction of their writing (see http:// www.thefreedictionary.com/bootstrap).
Table 1 e Mirror writings of the digit 3 as a function of the preceding writing. Writing of 3
Following A writing of C A writing of E A writing of B Correct Mirror Correct Mirror Correct Mirror
Correct Mirror
67 181
18 2
83 190
14 1
80 152
10 1
761
c o r t e x 4 7 ( 2 0 1 1 ) 7 5 9 e7 6 2
Table 2 e Mirror writings of the letter J as a function of the preceding writing. Writing of J
Following A writing of 7
Correct Mirror
A writing of 6
Correct
Mirror
Correct
Mirror
103 33
31 77
93 108
25 10
right and writing one digit or letter in each square. After writing each series, the children were instructed to write their first name in a specific place on the back of the strip of paper, using either upper-case or lower-case letters. The strips of paper were then collected, in order to prevent the children copying characters from a preceding series. The systematic permutation of the three series yielded the six experimental conditions.
2.4.
Coding
Two judges independently coded the children’s writings. After resolution of conflicts (less than 1%), the writings were classified into three main categories: correct writings, horizontal mirror writings (hereafter designated mirror writings) and non-relevant writings (including non-horizontal mirror writings). Because a child who has no idea how to write a character cannot mirror write it, the percentage of mirror writings was calculated with respect to the number of relevant writings (number of correct writings plus mirror writings). The symmetrical digits 0 and 8 were excluded from this calculation.
3.
Results
3.1.
Preliminary analyses
Out of the 9300 asymmetrical character writings, 1068 (i.e., 11.48%) were classified as non-relevant, 2452 (i.e., 26.37%) were classified as horizontal mirror writings, and 55 were classified as other (vertical or double) mirror writings. The mean percentages of mirror writings in the six experimental conditions did not differ significantly: F(5,294) ¼ .08, p > .99. Neither gender [t(298) ¼ .68, p > .49], nor hand of writing [t(298) ¼ .12, p > .90] had a significant effect on the percentage of mirror writings. The “class” factor (i.e., belonging to the same class at school) had a significant effect on the number of mirror writings: F(17,282) ¼ 1.78, p < .05. Nevertheless, it is important to note that children in all of the 18 classes produced mirror writings, with the mean percentage for each class ranging from 23.94% to 40.87%. Moreover, the significance of the “class factor” disappeared when age was introduced as a covariate: age differed significantly between the classes and was significantly and negatively correlated with the percentage of mirror writings (r ¼ .20, p < .001).
3.2.
No writing (at the beginning of series s2) 141 118
Global hypothesis
The frequency of mirror writings varied considerably according to the character being written (Fig. 1). In particular, the high percentage of mirror writings of the digit 3 (more than 65%) contrasts with the low percentage of mirror writings of some of the letters (less than 5% for K and N). The mean frequency of mirror errors (45.1%; SD ¼ 12.3) for the group of characters that do not conform to the implicit right writing rule (1, 2, 3, 7, 9, J, S, and Z)3 was considerably higher than the mean (8.4%; SD ¼ 4.0) for the group of other characters (4, 5, 6, B, C, D, E, F, G, K, L, N, P, Q, and R). A ManneWhitney test clearly supports the global hypothesis: U ¼ 0, p < .0001, one-tailed test.
3.3. Local hypotheses about the frequency of mirror writings of 3 and J Mirror writing of 3. Table 1 shows that: (1) When 3 was written after C, 72.98% of the children who correctly wrote C mirror wrote 3, whereas 10% of the children who mirror wrote C mirror wrote 3. The difference between these two groups of children was highly significant: c2(1) ¼ 31.06 (corrected), p < .0001. (2) When 3 was written after E, 69.60% of the children who correctly wrote E mirror wrote 3, whereas only 6.67% of the children who mirror wrote E mirror wrote 3. The difference between these two groups of children was highly significant: c2(1) ¼ 22.47 (corrected), p < .0001. (3) When 3 was written after B, 65.52% of the children who correctly wrote B mirror wrote 3, whereas only 9.09% of the children who mirror wrote B mirror wrote 3. The difference between these two groups of children was highly significant: p < .0005, Fisher’s exact probability test (two tailed). Mirror writing of J. Table 2 shows that: (1) When J was written after 7, only 24.26% of the children who correctly wrote 7 mirror wrote J. However, when J was written after a mirror writing of 7, 71.30% of the children who mirror wrote 7 mirror wrote J. The difference between 3
Because the letter S may not have been properly enclosed between characters not respecting the implicit right writing rule (since, when the letter S is written from the top, the first part of it faces right), we also computed the mean for these characters without S. This mean was almost 50% (48.9%), thereby increasing its difference with the mean of the other characters.
762
c o r t e x 4 7 ( 2 0 1 1 ) 7 5 9 e7 6 2
these two groups of children was highly significant: c2(1) ¼ 53.78, p < .0001. (2) When J was written after 6, 53.73% of the children who correctly wrote 6 mirror wrote J. However, when J was written after a mirror writing of 6, only 28.57% of the children who mirror wrote 6 mirror wrote J. The difference between the two groups of children was significant: c2(1) ¼ 7.55, p < .01. (3) When J was written at the beginning of a series (series s2), J was mirror written by 45.56% of the children who produced a relevant writing.
4.
Discussion and conclusion
Children at the age of “directional apraxia” (Della Sala and Cubelli, 2007) or in the period of “unlearning mirror generalization” (Dehaene, 2007) do not explicitly know in which direction the digits and capitals face. However, at this age (5e6½ years) and under the cultural conditions of the present study (almost all French children go to Ecoles Maternelles), they generally know the shape of these characters. Hence, it was hypothesized that children improvise the direction characters face. In the serial writing of characters, this improvisation, or bootstrapping, may be governed by an implicit right writing rule, which is implicitly learned and automatically activated by the writing of almost all the asymmetrical capitals. The implicit right writing rule is also favored by the cultural norm (for the children in the present study) of writing from left to right. Consequently, the immediately preceding writing of a character may influence the present writing both indirectly, by activating or not activating the rule, and directly, by visuomotor priming. This influence on the direction of writing can induce either a correct writing or a mirror writing. More distant preceding writings can also influence the present writing, both indirectly (by activating the implicit right writing rule) and directly (by repetition priming). This hypothesis was supported by the experimental observation of 300 children. First, the characters that contradict the implicit right writing rule (1, 2, 3, 7, 9, J) or that cannot be influenced by it (S, Z), were the most frequently mirror written (see Fig. 1). Second, the frequency with which 3 was mirror written varied considerably as a function of the preceding writing. After correct writings of C, E, and B, 3 was mirror written by 72.9%, 69.6%, and 65.5% of the children, respectively, but after mirror writings of C, E, and B, it was correctly written by 90%, 93.3%, and 90.9% of the children, respectively. Furthermore, the results for 3 suggest that the loop of C is not decisive for explaining mirror writing of the following 3, and that the hidden 3 in B (if recognized) did not substantially reduce mirror writing of the following 3, suggesting the primacy of the implicit right writing rule activated by the letter B. Third, J was mirror written (1) by 24.26% of the children who correctly wrote 7; (2) by 28.57% of the children who mirror wrote 6; (3) by 45.56% of the children when it was at the beginning of series s2; (4) by 53.73% of the children who
correctly wrote 6; and (5) by 71.30% of the children who mirror wrote 7. However, because the present study only thoroughly examined selected characters (3 and J) and included only a small number of all the possible preceding characters, the results must be interpreted with caution. For example, the percentage of mirror writings of S may have been reduced by the fact that the only writing preceding S, namely the digit 2, was often mirror written, thereby priming a correct writing of S. Nevertheless, the results clearly show that some preceding writings (e.g., the writing of C) can statistically explain the mirror writing of a following writing (e.g., the writing of 3) in typically developing 5- to 6-year-olds. Although limited, this is an original finding that should be taken into account in future research and in the re-analysis of older data. This finding indirectly suggests that some other classical factors of mirror writing are of less importance. Correspondingly, the present experiment showed no effect of writing hand, thereby contradicting previous claims suggesting that mirror writing is essentially confined to left-handers (e.g., Schiller, 1932). Della Sala and Cubelli (2007, p. 16) offered several possible explanations that could resolve this contradiction, including the argument that left-handers are better able to deliberately mirror write. In the present study mirror writing was spontaneous, not deliberate. In addition, in contrast with our study where the participants were preschool children, most studies on deliberate mirror writing involve older (and higher school grade) participants, because typical school students hardly ever (1st grade), or almost never (2nd or higher grade), spontaneously mirror write. For example, Schiller (1932), who concluded that mirror writing appears as a “classic symptom of left-handedness” (p. 514), based her conclusion on the deliberate mirror writings of 400 older (than the 5- to 6-year-olds in the present study) students, including 9th graders.
Acknowledgements The author thanks the participating children, teachers, directors, educational advisers, and education inspectors for their cooperation.
references
Dehaene S. Les neurones de la lecture. Paris: Odile Jacob, 2007. Della Sala S and Cubelli R. Directional apraxia: A unitary account of mirror writing following brain injury or as found in normal young children. Journal of Neuropsychology, 1(1): 3e26, 2007. Fischer JP. Vers une leve´e du myste`re des e´critures en miroir (des chiffres) chez l’enfant. L’anne´e psychologique, 110(2): 227e251, 2010a. Fischer JP. Vers une leve´e du myste`re des e´critures en miroir (des lettres majuscules) chez l’enfant: une hypothe`se nouvelle. Enfance, 62(4): 371e386, 2010b. Schiller M. Probleme um die Linksha¨ndigkeit mit Untersuchungen an Stuttgarter Schulkindern. Zeitschrift fu¨r die gesamte Neurologie und Psychiatrie, 140(1): 496e516, 1932.
available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/cortex
Note
Mirror writing of digits and (capital) letters in the typically developing child Jean-Paul Fischer Developmental Psychology, InterPsy Laboratory, EA 4432, Nancy, France
article info
abstract
Article history:
Typically developing 5- to 6-year-old children often reverse some digits (e.g., 3 for 3) or
Received 14 July 2010
single (capital) letters (e.g., 6 for R) when they are required to write them under dictation.
Reviewed 14 September 2010
A theoretical approach to this phenomenon, based on an implicit right writing rule and
Revised 9 October 2010
that postulates an influence of the preceding writing, was tested in an experimental study
Accepted 1 February 2011
of 300 children aged 5e6 years. The data support the implicit right writing rule and show
Action editor Roberto Cubelli
the considerable influence of the preceding writing. For example, 73% of the children who
Published online 9 February 2011
correctly wrote the letter C mirror wrote an immediately following digit 3, whereas only 10% of the children who mirror wrote the letter C also mirror wrote an immediately
Keywords:
following digit 3. ª 2011 Elsevier Srl. All rights reserved.
Mirror writing Directional apraxia Mirror generalization Implicit rule Visuomotor priming
1.
Introduction
Teachers and parents know that almost all children have a tendency to reverse the writing of some single letters (e.g., 6 for R) or digits (e.g., 3 for 3) when they begin learning to write between 4 and 6 years of age. Because this spontaneous behavior seems lost in normal adults, it is intriguing to ask which process is responsible for such mirror writings. The motor-based “directional apraxia” hypothesis (Della Sala and Cubelli, 2007) and the visual-based “neuronal recycling” hypothesis (Dehaene, 2007) share the assumption that there is a period in development when children know how to compose the letters and digits but they do not know whether an individual letter or digit, for example, the digit 3, should face left (3) or right (3). Two recent empirical results (Fischer,
2010a, 2010b) offer some clues on how 5- to 6-year-old children choose one of the two directions (left or right). Fischer (2010a) showed that frequencies of mirror writing were different for different digits. For example, the digit 3 was reversed in 45.60% of cases, whereas the digit 4 was only reversed in 16.22% of cases. Fischer’s research also suggests that the preceding digit may trigger a form of motor priming (or a visuomotor priming when the digits are written adjacently) which influences the direction of the subsequent digit. Further, Fischer (2010b) reported that children mostly reversed two capital letters e J and Z e and that these reversals were frequent. Fischer interpreted these findings as the result of children developing an implicit rule for writing capitals according to which capitals have distinctive features on the right or face right. Children may learn such an “implicit right
E-mail address: [email protected]. 0010-9452/$ e see front matter ª 2011 Elsevier Srl. All rights reserved. doi:10.1016/j.cortex.2011.01.010
760
c o r t e x 4 7 ( 2 0 1 1 ) 7 5 9 e7 6 2
writing rule” because the great majority of the asymmetrical letters have a vertical line on the left side and their distinctive feature on the right (B, D, E, F, K, L N, P, and R), face right1 (C and G), or have a tail on the right (Q). The implicit right writing rule indicates the correct direction for the capitals listed above, but it does not do so for the letter J. For the letter S, which does not clearly face right or left, and the letter Z, which has a diagonal line and not a vertical line, the rule is not relevant. These two hypothesized mechanisms for bootstrapping2 the direction of writing e an implicit right writing rule for capitals and visuomotor priming from the preceding writing for digits e generated two different hypotheses. According to the global hypothesis, since the implicit right writing rule gives the correct writing direction for 12 of the 15 asymmetrical capitals, the 12 capitals B, C, D, E, F, G, K, L, N, P, Q, and R should benefit from activation of the rule. Moreover, also the correct writing of 6 should be induced by the activated rule. While the effect on the digits 4 and 5 is unclear, then no mirror writing was hypothesized for these digits, the activated rule should promote mirror writing for 1, 2, 3, 7, 9, and J. Because the rule is not relevant for S and Z, the choice of direction for these two letters should be made by chance. Hence, the global hypothesis states that, as a group, the capital letters B, C, D, E, F, G, K, L, N, P, Q, R and the digits 6, 4, and 5, should be mirror written less frequently than the group of remaining asymmetrical characters. The local hypothesis, combining the implicit right writing rule and visuomotor priming from the preceding writing, predicts that digit 3 will be mirror written more frequently after a correct writing of C or E, than after a mirror writing of C or E, respectively. For the letter J, it predicts more mirror writings after a mirror writing of 7 than after a correct writing of 7, and more mirror writings after a correct writing of 6 than after a mirror writing of 6. Therefore, mirror writing of J (1) should occur least frequently after a correct writing of 7 or after a mirror writing of 6, (2) should be at an intermediate level when J is at the beginning of a series, and (3) should occur most frequently after a mirror writing of 7 or after a correct writing of 6. Analyses of the writing of 3 after B were exploratory because of the hidden 3 in B.
2.
Method
2.1.
Participants
The participants were 300 children (144 girls and 156 boys) from 18 preschool classes of the French “Ecole Maternelle”.
%Mirror Writings 70 60 50 40 30 20 10 0 1 2 3 4 5 6 7 9 B C D E F G J K L N P Q R S Z
Character
Fig. 1 e Percentage of mirror writings as a function of the character being written.
Thirty-nine other children were excluded because they did not produce any (horizontal) mirror writings or did not produce at least 50% relevant writings. The mean age was 5.715 years (SD ¼ .35; range: 5.00e6.35). Thirty-three children wrote with their left hand and 267 wrote with their right hand. Participants were tested in groups of three or four, and the groups were randomly allocated to one of six experimental conditions (50 children in each condition): the children in the six experimental conditions did not differ in their mean age [F(5,294) ¼ .24, p > .94] or in the ratio of girls to boys [c2(5) ¼ .32, p > .99]. All standard administrative authorizations and ethical rules for such experiments in schools were respected.
2.2.
Material
The children had to write, under dictation and from memory, the 11 digits or letters of a series, in 11 aligned squares (one character per square). The sides of the squares measured 2.2 cm. Three series were used: s1: P, 4, C, 3, 1, 7, J, L, 9, Z, G; s2: J, 0, Z, 5, K, F, 9, B, 3, N, Q; s3: R, E, 3, D, 8, 6, J, S, 2, 9, Z.
2.3.
Procedure
The experimenter encouraged the children to write the digits and capital letters on the strip of paper, moving from left to
1
A character with no vertical line faces right when its main concavity is turned towards the right. Under this definition, the digit 6 faces right, and the digits 2, 3, and 9 face left. In France, the digit 1 is written with a short, left-facing downward stroke at the top of the vertical line that forms the body of the digit; therefore, it also contradicts the implicit right writing rule. 2 To “bootstrap” means “to help oneself, often through improvised means”. Direct observation suggests that children choose the direction of writing on their own, with no outside help, and that they use a self-initiating process. Therefore, it could be said that children bootstrap the direction of their writing (see http:// www.thefreedictionary.com/bootstrap).
Table 1 e Mirror writings of the digit 3 as a function of the preceding writing. Writing of 3
Following A writing of C A writing of E A writing of B Correct Mirror Correct Mirror Correct Mirror
Correct Mirror
67 181
18 2
83 190
14 1
80 152
10 1
761
c o r t e x 4 7 ( 2 0 1 1 ) 7 5 9 e7 6 2
Table 2 e Mirror writings of the letter J as a function of the preceding writing. Writing of J
Following A writing of 7
Correct Mirror
A writing of 6
Correct
Mirror
Correct
Mirror
103 33
31 77
93 108
25 10
right and writing one digit or letter in each square. After writing each series, the children were instructed to write their first name in a specific place on the back of the strip of paper, using either upper-case or lower-case letters. The strips of paper were then collected, in order to prevent the children copying characters from a preceding series. The systematic permutation of the three series yielded the six experimental conditions.
2.4.
Coding
Two judges independently coded the children’s writings. After resolution of conflicts (less than 1%), the writings were classified into three main categories: correct writings, horizontal mirror writings (hereafter designated mirror writings) and non-relevant writings (including non-horizontal mirror writings). Because a child who has no idea how to write a character cannot mirror write it, the percentage of mirror writings was calculated with respect to the number of relevant writings (number of correct writings plus mirror writings). The symmetrical digits 0 and 8 were excluded from this calculation.
3.
Results
3.1.
Preliminary analyses
Out of the 9300 asymmetrical character writings, 1068 (i.e., 11.48%) were classified as non-relevant, 2452 (i.e., 26.37%) were classified as horizontal mirror writings, and 55 were classified as other (vertical or double) mirror writings. The mean percentages of mirror writings in the six experimental conditions did not differ significantly: F(5,294) ¼ .08, p > .99. Neither gender [t(298) ¼ .68, p > .49], nor hand of writing [t(298) ¼ .12, p > .90] had a significant effect on the percentage of mirror writings. The “class” factor (i.e., belonging to the same class at school) had a significant effect on the number of mirror writings: F(17,282) ¼ 1.78, p < .05. Nevertheless, it is important to note that children in all of the 18 classes produced mirror writings, with the mean percentage for each class ranging from 23.94% to 40.87%. Moreover, the significance of the “class factor” disappeared when age was introduced as a covariate: age differed significantly between the classes and was significantly and negatively correlated with the percentage of mirror writings (r ¼ .20, p < .001).
3.2.
No writing (at the beginning of series s2) 141 118
Global hypothesis
The frequency of mirror writings varied considerably according to the character being written (Fig. 1). In particular, the high percentage of mirror writings of the digit 3 (more than 65%) contrasts with the low percentage of mirror writings of some of the letters (less than 5% for K and N). The mean frequency of mirror errors (45.1%; SD ¼ 12.3) for the group of characters that do not conform to the implicit right writing rule (1, 2, 3, 7, 9, J, S, and Z)3 was considerably higher than the mean (8.4%; SD ¼ 4.0) for the group of other characters (4, 5, 6, B, C, D, E, F, G, K, L, N, P, Q, and R). A ManneWhitney test clearly supports the global hypothesis: U ¼ 0, p < .0001, one-tailed test.
3.3. Local hypotheses about the frequency of mirror writings of 3 and J Mirror writing of 3. Table 1 shows that: (1) When 3 was written after C, 72.98% of the children who correctly wrote C mirror wrote 3, whereas 10% of the children who mirror wrote C mirror wrote 3. The difference between these two groups of children was highly significant: c2(1) ¼ 31.06 (corrected), p < .0001. (2) When 3 was written after E, 69.60% of the children who correctly wrote E mirror wrote 3, whereas only 6.67% of the children who mirror wrote E mirror wrote 3. The difference between these two groups of children was highly significant: c2(1) ¼ 22.47 (corrected), p < .0001. (3) When 3 was written after B, 65.52% of the children who correctly wrote B mirror wrote 3, whereas only 9.09% of the children who mirror wrote B mirror wrote 3. The difference between these two groups of children was highly significant: p < .0005, Fisher’s exact probability test (two tailed). Mirror writing of J. Table 2 shows that: (1) When J was written after 7, only 24.26% of the children who correctly wrote 7 mirror wrote J. However, when J was written after a mirror writing of 7, 71.30% of the children who mirror wrote 7 mirror wrote J. The difference between 3
Because the letter S may not have been properly enclosed between characters not respecting the implicit right writing rule (since, when the letter S is written from the top, the first part of it faces right), we also computed the mean for these characters without S. This mean was almost 50% (48.9%), thereby increasing its difference with the mean of the other characters.
762
c o r t e x 4 7 ( 2 0 1 1 ) 7 5 9 e7 6 2
these two groups of children was highly significant: c2(1) ¼ 53.78, p < .0001. (2) When J was written after 6, 53.73% of the children who correctly wrote 6 mirror wrote J. However, when J was written after a mirror writing of 6, only 28.57% of the children who mirror wrote 6 mirror wrote J. The difference between the two groups of children was significant: c2(1) ¼ 7.55, p < .01. (3) When J was written at the beginning of a series (series s2), J was mirror written by 45.56% of the children who produced a relevant writing.
4.
Discussion and conclusion
Children at the age of “directional apraxia” (Della Sala and Cubelli, 2007) or in the period of “unlearning mirror generalization” (Dehaene, 2007) do not explicitly know in which direction the digits and capitals face. However, at this age (5e6½ years) and under the cultural conditions of the present study (almost all French children go to Ecoles Maternelles), they generally know the shape of these characters. Hence, it was hypothesized that children improvise the direction characters face. In the serial writing of characters, this improvisation, or bootstrapping, may be governed by an implicit right writing rule, which is implicitly learned and automatically activated by the writing of almost all the asymmetrical capitals. The implicit right writing rule is also favored by the cultural norm (for the children in the present study) of writing from left to right. Consequently, the immediately preceding writing of a character may influence the present writing both indirectly, by activating or not activating the rule, and directly, by visuomotor priming. This influence on the direction of writing can induce either a correct writing or a mirror writing. More distant preceding writings can also influence the present writing, both indirectly (by activating the implicit right writing rule) and directly (by repetition priming). This hypothesis was supported by the experimental observation of 300 children. First, the characters that contradict the implicit right writing rule (1, 2, 3, 7, 9, J) or that cannot be influenced by it (S, Z), were the most frequently mirror written (see Fig. 1). Second, the frequency with which 3 was mirror written varied considerably as a function of the preceding writing. After correct writings of C, E, and B, 3 was mirror written by 72.9%, 69.6%, and 65.5% of the children, respectively, but after mirror writings of C, E, and B, it was correctly written by 90%, 93.3%, and 90.9% of the children, respectively. Furthermore, the results for 3 suggest that the loop of C is not decisive for explaining mirror writing of the following 3, and that the hidden 3 in B (if recognized) did not substantially reduce mirror writing of the following 3, suggesting the primacy of the implicit right writing rule activated by the letter B. Third, J was mirror written (1) by 24.26% of the children who correctly wrote 7; (2) by 28.57% of the children who mirror wrote 6; (3) by 45.56% of the children when it was at the beginning of series s2; (4) by 53.73% of the children who
correctly wrote 6; and (5) by 71.30% of the children who mirror wrote 7. However, because the present study only thoroughly examined selected characters (3 and J) and included only a small number of all the possible preceding characters, the results must be interpreted with caution. For example, the percentage of mirror writings of S may have been reduced by the fact that the only writing preceding S, namely the digit 2, was often mirror written, thereby priming a correct writing of S. Nevertheless, the results clearly show that some preceding writings (e.g., the writing of C) can statistically explain the mirror writing of a following writing (e.g., the writing of 3) in typically developing 5- to 6-year-olds. Although limited, this is an original finding that should be taken into account in future research and in the re-analysis of older data. This finding indirectly suggests that some other classical factors of mirror writing are of less importance. Correspondingly, the present experiment showed no effect of writing hand, thereby contradicting previous claims suggesting that mirror writing is essentially confined to left-handers (e.g., Schiller, 1932). Della Sala and Cubelli (2007, p. 16) offered several possible explanations that could resolve this contradiction, including the argument that left-handers are better able to deliberately mirror write. In the present study mirror writing was spontaneous, not deliberate. In addition, in contrast with our study where the participants were preschool children, most studies on deliberate mirror writing involve older (and higher school grade) participants, because typical school students hardly ever (1st grade), or almost never (2nd or higher grade), spontaneously mirror write. For example, Schiller (1932), who concluded that mirror writing appears as a “classic symptom of left-handedness” (p. 514), based her conclusion on the deliberate mirror writings of 400 older (than the 5- to 6-year-olds in the present study) students, including 9th graders.
Acknowledgements The author thanks the participating children, teachers, directors, educational advisers, and education inspectors for their cooperation.
references
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