Synesthesia and Number Cognition in Children
Jennifer A. K. Green & Usha Goswami
Centre for Neuroscience in Education, University of Cambridge
Correspondence address:
Jennifer Green,
Centre for Neuroscience in Education,
University of Cambridge,
184 Hills Road,
Cambridge,
CB2 2PQ,
UK.
Tel. +44 1223 767600 or +44 1865 794116
E-mail: jakg2@cam.ac.uk
WORD COUNT: 3050 excluding references
1
Abstract
Grapheme-color synesthesia, when achromatic digits evoke an experience of a specific
color (photisms), has been shown to be consistent, involuntary, and linked with number
concept in adults, yet there have been no comparable investigations with children. We
present a systematic study of grapheme-color synesthesia in children aged between 7 –
15 years. Here we show that such children (but not children with phoneme-color
synesthesia) experience involuntary difficulties in numerical tasks when digits are
presented in colors incongruent with their photisms. Synesthesia in children may thus
have important consequences for certain aspects of numerical cognition.
2
Synesthesia, the involuntary multi-modal perception of objects or events that are usually
perceived unimodally, has greatly interested neuroscientists (Rich & Mattingley, 2002).
For example, seeing a digit like 5 may automatically elicit a simultaneous color percept
or “photism” (grapheme-color synesthesia), whereas a taste may evoke a tactile
sensation. Estimates of the prevalence of the condition range from 1 in 25,000
(Cytowic, 1996) to 1 in 20 (Galton, 1883), with grapheme-color synesthesia generally
accepted as the most common form. Scientific investigation of synesthesia is expected
to yield important clues to the neural mechanisms that underlie the integration of
sensory information (Rich & Mattingley, 2002). However the study of synesthesia has
so far focused exclusively on adults. This research strategy can only throw light on the
end state of sensory integration. It cannot show whether synesthesia affects the
development of sensory systems in ways that perturb the end state, or whether
synesthesia has effects on cognitive developments that depend on sensory integration.
Although widely assumed to be present from early childhood (Rich & Mattingley,
2002), studies examining synesthesia in children are limited to case studies from the late
nineteenth and early twentieth centuries (Riggs & Karwoski, 1934). It has been
suggested that synesthetes are simply reporting idiosyncratic childhood associations
between colors and numbers (Calkins, 1895). If it can be established that children
experience grapheme-color synesthesia consistently (Baron-Cohen, Harrison, Goldstein,
& Wyke, 1993; Baron-Cohen, Wyke, & Binnie, 1987) and automatically (Mattingley,
Rich, Yelland, & Bradshaw, 2001; Mills, Boteler, & Oliver, 1999; Odgaard, Flowers, &
3
Bradman, 1999) as adults do, one obvious developmental question concerns potential
effects on the acquisition of culturally-acquired cognitive skills such as numeracy and
literacy. If grapheme-color photisms for numbers are involuntary, this could affect the
development of certain aspects of number cognition. For example, if a young child
automatically experiences the digit 1 as having the color green, will this affect her
ability to learn that 9 is a larger count number if 9 is printed in green in her maths book?
In other words, will color interfere with conceptual understanding of magnitude
relations? Somewhat analogous confusions have been noted in the domain of literacy.
One adult reported ‘I may call someone “Debbie” when she is really “Paula”, because D
and P are more or less the same color green’ (Rich & Mattingley, 2002)
Grapheme-color synesthesia has been associated anecdotally with deficient
mathematical ability (Cytowic, 2003). In a recent large-scale survey, reports of
weakness in the area of mathematics were significantly greater among synesthetes
compared to a control group (Rich, Bradshaw, & Mattingley, 2005). Interestingly,
however, the percentage of synesthetes who reported mathematics as an area of strength
was also significantly greater than that of controls, although the number of synesthetes
reporting an advantage for mathematics was much smaller. It is not clear whether and
how the mathematical difficulties or advantages experienced by grapheme-color
synesthetes might be impacted by the experience of color itself. While it is accepted that
photsims are triggered automatically, it is not yet known how synesthetic color might
affect the way numerical information is processed in the brain. However research with
adult synesthetes suggests that the concept of a number alone can elicit photisms
(Dixon, Smilek, Cudahy, & Merikle, 2000; Jansari, Spiller, & Redfern, 2006). Subjects
4
presented with single digit sums (e.g. 5 + 2) followed by color patches were slower to
name the color of the patch when it was incongruent to the photism elicited by the
solution. Additionally, while synesthesia was at first thought to occur in only one
direction (e.g. numbers evoke colors, but colors do not evoke numbers) recent research
suggests that co-activation occurs bi-directionally (Brugger, Knoch, Mohr, & Gianotti,
2004; Cohen-Kadosh & Henik, 2006a; Knoch, Gianotti, Mohr, & Brugger, 2005). It has
also been demonstrated that color alone can evoke numerical magnitude in adult
synesthetes (Cohen-Kadosh & Henik, 2006a, 2006b; Cohen-Kadosh et al., 2005).
However, the developmental origins of this 2-way relationship are not known, as there
have been no studies of preschool or school-aged children with synesthesia.
We therefore recruited a group of children with photisms for digits, and explored
whether these photisms were elicited automatically as in adults, and whether they
played a role in memory for digits (for participant details, see Table 1). Children were
asked to recall digits that were colored either congruently or incongruently with their
photisms, or that were neutrally colored. Additionally, we investigated whether
photisms can elicit a sense of numerical magnitude in children. Accurate counting
involves learning the correspondences between Arabic numerals and semantic
representations of set sizes (“numerosity”) (Landerl, Bevan, & Butterworth, 2004). As
Arabic numerals are acquired, they are thought to access these semantic representations
for numbers, leading to modality- independent size and distance effects (Dehaene,
1997). We adapted Besner and Coltheart’s (1979) size congruity paradigm, in which
pairs of digits were presented with one of the digits being physically larger than the
other. Participants were asked to ignore the physical size of the digits and to indicate
5
which was numerically larger. Adults were both slower to select the larger digit when it
was presented as the physically smaller (incongruent), and faster when it was presented
as the physically larger (congruent), than when both digits were of equal size (neutral).
We created an analogous color congruity paradigm, in which pairs of digits of equal
size were presented in colors that were either congruent with or incongruent with the
child’s photisms. We expected participants to be slower to select the larger digit when it
was in the “wrong” color, particularly if the incongruent color matched a numerically
smaller digit than the comparitor. A similar effect has been documented with an adult
synaesthete (Cohen-Kadosh & Henik, 2006a).
Methods
Participants. Six grapheme-color (GC) synesthetes, four girls and two boys, took part in
the study. All of these children reported experiencing color when they saw or thought
about numbers and letters. Five (all but G15) also reported color associations for days
of the week, with three of these (G9a, G9b, and G13) also having color associations
with the months of the year. One participant (G15) experiences color for musical notes.
All volunteers were given a version of Baron-Cohen’s ‘Test of Genuineness’ (hereafter
TOG) (Baron-Cohen, Harrison, Goldstein, & Wyke, 1993; Baron-Cohen, Wyke, &
Binnie, 1987). Children were asked to fill out a color survey which asked them to list
the colors they experienced for digits 0 – 9 and ten selected letters of the alphabet.
They were then retested on their color assignments after a period of at least two weeks.
If the child achieved at least 90% consistency on the TOG, parents were asked for
written consent for participation in the main part of the study. Children were then asked
6
to choose the colors that they experienced for digits 0 – 9 on a color wheel to enable
creation of the experimental stimuli.
Two control groups were studied (see Table 2 for details). Thirty typically-developing
control children of average cognitive ability were recruited from local schools and were
matched to the GC synesthetes for age and gender. Five control children were matched
for each of the six synesthetes in the GC group and received tasks based on that
synesthete’s colors. It was envisaged that children would be matched based on IQ
measures as well, but some of the synesthetes scored extremely highly on these
measures and it was not possible to find absolute matches (see Table 1). A group of
phoneme-color synesthetic children, one boy and three girls, formed a further control
group. Phoneme-color synesthetes also experience color for numbers and letters but
differ from grapheme-color synesthetes in that it is hearing letters or number words
spoken that induces color experience rather than seeing them written or printed (BaronCohen, Harrison, Goldstein, & Wyke, 1993). Given the visual presentation format used,
phoneme-color synesthetes were not expected to show effects of color congruency in
the memory and number comparison tasks. These children were included to control for
any general developmental effects of being a synesthete. These children tended to be
less consistent on the color re-test of the Test of Genuineness, but all were above 80%.
Tasks. Both experimental tasks were designed using EPrime psychological testing
software and were presented on a laptop computer.
7
Memory for digits task. We used an adaptation of a matrix memory paradigm
used with adults (Smilek, Dixon, Cudahy, & Merikle, 2002) simplified for use with
children. Grids of either nine digits (3 x 3) or sixteen digits (4 x 4) were presented on
the computer screen for a period of 60 seconds. After piloting with a separate control
sample, only the 7 year-olds received the nine-digit grid. Children were then given a
blank grid printed on a piece of paper and instructed to fill in as many digits as they
could remember in the correct spatial positions. Children received three critical
conditions, presented in a fixed order: neutral, congruent, incongruent. In the neutral
condition, digits were presented in black on a gray background (or in dark gray on paler
gray if the child had a black photism). In the congruent condition, digits were presented
in the colors corresponding to the child’s photisms. In the incongruent condition, digits
were presented in colors incongruent with the child’s photisms. As in the study by
Smilek et al (2002), incongruent color assignments corresponded to digits one greater
than the digit presented (e.g. 5 appeared in the color the child associated with 6).
Children were scored for the number of correctly recalled digits in the correct locations
out of 16 (scores from the 7 year-olds were prorated; child G7 scored 9/9, 9/9 and 5/9 in
the neutral, congruent and incongruent conditions, respectively).
Magnitude discrimination task. This task required children to decide which was the
numerically larger of two same-sized digits presented on the computer screen, by
pressing designated keys on the keyboard. The keys ‘A’ and ‘L’ were used, with
stickers covering the letters. Children were instructed that ‘A’ should be pressed when
the digit on the left was larger and ‘L’ when the digit on the right was larger. Digits
were presented in 4 different color conditions:
8

‘Neutral’ – digits printed in black (or if child had a black photism, gray)

‘Congruent’ – digits printed in colors congruent to the child’s photisms

‘Incongruent consistent’ – incongruent colors were chosen to correspond to the
child’s photism for either the digit above (d + 1) or the digit below (d – 1) the
target digit. The color assignments for both digits in the pair went in the same
direction, so that if the pair 3 and 7 were presented, and 3 was assigned the color
for 2 (d – 1), then 7 would be assigned the child’s color for 6 (also d – 1). The
colors chosen therefore reflected the same larger-smaller relationship as the
digits presented.

‘Incongruent inconsistent’ – here the inconsistent colors assigned were reversed,
so that the smaller number (e.g. 3) was assigned the ‘larger’ photism (e.g. the
color associated with 6) and the larger number (e.g. 7) was assigned the
‘smaller’ photism (e.g. the color associated with 2). Crucially the larger-smaller
relationship was thereby reversed.
A practice round of ten trials was administered so that children could become
accustomed to pressing buttons and reacting to stimuli. None of the number pairs from
the experimental trials appeared in the practice round. There were 64 experimental
trials in all, sixteen in each condition, presented in pseudo-random order. Trials were
presented in two sets of 32, each with a short rest break after 16.
Results and Discussion
9
The number of digits recalled successfully in the memory for digits task in the neutral,
congruent and incongruent conditions is shown in Figure 1. A clear effect of
congruency was observed for the grapheme-color group only. Phoneme-color
synesthetes and control children showed similar performance across conditions. Effects
were confirmed by a 3 x 3 analysis of variance taking condition (neutral, congruent,
incongruent) as the within-subjects factor and group (grapheme-color synesthesia,
phoneme-color synesthesia, controls) as the between-subjects factor. There was a
significant effect of condition (F (2, 74) = 3.65, p <.031, p2 = .09) and a significant
interaction between condition and group (F (4, 74) = 3.168, p < .018, p2 = .15). Posthoc tests (Newman-Keuls) revealed a significant decrease in memory for digits in the
incongruent condition for the grapheme-color synesthetes only (10.83 v 5.65, p < .01).
Hence child grapheme-color synesthetes experience detrimental effects on memory for
digits when digits appear in the “wrong” colors, just like adults (Smilek, Dixon,
Cudahy, & Merikle, 2002).
This detrimental effect was also reflected in the individual data, as shown in Table 3.
All grapheme-color synesthetes except one (child G9b) showed poorest retrieval in the
incongruent condition. Child G9b has particularly poor memory in all conditions. Child
P11, a phoneme-color synesthete, also appears to show an effect of color incongruency
for digit memory. This child may have performed the task by orally rehearsing the
digits that were seen, thereby activating her synesthetic photisms. It may also be of
note that this child was the only ‘projector’ – the only synesthete who reported
10
experiencing photisms as projected externally in space1, as opposed to experiencing
them internally, or in ‘the mind’s eye’ (Dixon, Smilek, & Merikle, 2004)(Dixon,
Smilek, & Merikle, 2004)(Dixon, Smilek, & Merikle, 2004)(Dixon, Smilek, & Merikle,
2004)(Dixon, Smilek, & Merikle, 2004)(Dixon, Smilek, & Merikle, 2004)(Dixon,
Smilek, & Merikle, 2004)(Dixon, Smilek, & Merikle, 2004)(Dixon, Smilek, & Merikle,
2004)(Dixon, Smilek, & Merikle, 2004)(Dixon, Smilek, & Merikle, 2004)(Dixon,
Smilek, & Merikle, 2004).
Performance in the number comparison task was measured in terms of mean reaction
time for the correct trials only. However, whereas most children made only 1 or 2 errors
in the number comparison task, two children (G9a and G9b) made 29 and 14 errors
respectively and were also very slow in their responses. When these two children were
excluded from the data set, a Kruskal-Wallis test revealed no significant effect of group
or condition. However, inspection of the data from the correct trials completed by G9a
and G9b showed a clear incongruency effect. This is illustrated in Figure 4. Both
children were around 400 ms slower in the incongruent inconsistent condition. This
pattern suggests that for these children, magnitude relations were still being established:
color incongruency interfered with the magnitude judgements required.
The effect of color incongruency on judgments of numerical magnitude may thus be
characteristic of a certain stage of mathematical development. According to some
researchers, the automatic activation of magnitude information from Arabic digits
develops around the third grade, when children are 8 or 9 years old (Girelli, Lucangeli,
1
She reports experiencing colour as ‘mists’ before her eyes when she hears letters or
numbers.
11
& Butterworth, 2000). Hence the difficulties experienced by the 9-year-olds in this
study may reflect their point on a developmental trajectory. This may also explain why
the 7-year-old did not show an incongruency effect. Alternatively, given her extremely
high score on the non-verbal IQ measure (see Table 1) and her excellent performance in
the magnitude judgment task (errors and RTs comparable to the much older children)
she may have advanced beyond the 9-year-olds in terms of the developmental trajectory
for numerical skills. As will be recalled, G7 also showed excellent memory for
numbers, in contrast to G9a and G9b.
Note also that whereas in our study the three GC children aged from 11 – 15 did not
show a color incongruency effect, Cohen-Kadosh et al. did find a color incongruency
effect with an adult in an analogous (although not identical) magnitude judgement task.
Clearly, it is not possible to draw firm conclusions regarding possible developmental
effects from this small sample. Without testing more synesthetes, it is unclear whether
this adult or our teenagers are atypical. Furthermore, studies with synesthetic adults
suggest there is a high level of individual variability among synesthetes, even among
those with the same form of synesthesia (Dixon, Smilek, & Merikle, 2004; Hubbard,
Arman, Ramachandran, & Boynton, 2005). Hubbard and Ramachandran (2005;
Ramachandran & Hubbard, 2001) suggest that differences observed in behavioural
performance on cognitive tasks may reflect differences in the neural mechanisms
underlying the individual synesthesiae. Further, they propose that these difference might
serve to categorise synaesthetes into two groups: ‘higher’ and ‘lower’, based on when
during processing, and perhaps where in the brain, synaesthetic co-activations occur
12
(Ramachandran & Hubbard, 2001). Further group studies of both children and adults
are needed in order to explore possible reasons for individual variability.
This is the first study of which we are aware to report on grapheme-color and phonemecolor synesthesia in children. As in adults, synesthetic photisms appear to be consistent
and involuntary. Most children with grapheme-color synesthesia showed a significant
deterioration in memory for digits when the digits were presented in colors incongruent
with their photisms, and children with less mathematical expertise (the 9-year-olds
studied here) were also significantly slower to make judgments about the relative
magnitude of numbers when colors were incongruent with their photisms. In fact, child
G9b remarked, “In my head, some colors are bigger than other colors. I just get the
feeling that blue is bigger than red, and green is bigger than orange”.
Further developmental studies of synesthesia are required to understand potential effects
on the development of different aspects of number cognition. Although synesthetes are
frequently believed to have difficulties with mathematics (Cytowic, 2003; Rich et al.,
2005), the number of participants in our study was too small to enable strong
conclusions. Here, for all synesthetes except one (G9a, male), performance on a
standardised test of mathematical reasoning was above the population mean, and
sometimes remarkably so (see G13, G15, P11). This does not suggest impaired
acquisition of mathematical concepts in these synesthetic children. Similarly, the
synesthetes in this sample had good spatial reasoning, with scaled scores on the Block
Design test as high as 17 and 19 (such scores are over 4 SD above the population
mean). This is interesting with respect to the connections between spatial and
13
mathematical cognition now being documented (Hubbard, Piazza, Pinel, & Dehaene,
2005). However, the only synesthetes affected by color incongruency in the magnitude
task were the two male participants, and they showed above-average spatial reasoning
(scoring 1 – 2 S.D. above the population mean on the WISC block design subscale).
Given that children as young as 7 years show consistent and involuntary graphemecolor synesthesia, studies with larger groups are clearly required to document fully the
potential effects of synesthesia on the development of number cognition.
14
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16
Table 1 – Characteristics of the grapheme-color (G) and phoneme-color (P)
synesthetes.
Synesthete
Age
Gender
(years)
BPVS
WISC
Blocks
WISC
Arithmetic
G7
7.33
female 92a
19
11
G9a
9.83
male
104
14
8
G9b
9.33
male
125
12
G11
11.66 female 100
10
10
G13
13.58 female 160+
10
18
G15
15.33 female 160+
17
17
P9
9.33
male
101
14
P11
11.08 female 119
12
16
b
P14a
14.16 female 131
10
10
P14b b
14.16 female 119
11
12
Note. Numerals represent age in years, dashes represent unavailable data. British
Picture Vocabulary Scale (BPVS) scores are standardised (population mean = 100, SD
= 15) and Wechsler Intelligence Scales for Children (WISC) subtest scores are scaled
(population mean = 10, SD = 1.5).
a
note that English is not this child’s first language
b
these two participants are twins
Table 2 – Characteristics of the control groups (matched to grapheme-color
synesthetes only).
Control Group
Age
Gender BPVS
WISC
WISC
(years)
Blocks Arithmetic
7 year olds
7.50
female 116
14
(0.33)
(16.01) (1.15)
9 year-olds (a) 9.45
male
114
12
(0.17)
(10.37) (1.58)
9 year-olds (b) 9.18
male
118
10
(0.21)
(15.94) (3.90)
11 year-olds
11.80
female 106
12
(0.08)
(4.60)
(2.59)
13 year-olds
13.29
female 114
10
(0.16)
(6.19)
(2.30)
15 year-olds
15.13
female 122
13
(0.25)
(19.40) (2.95)
Note. Ages and scores are presented as means with standard deviations in parentheses.
N = 5 for each group.
17
Figure 1 – Mean number correct (out of 16) in the memory for digits task.
16
number correct out of 16
14
12
GC
PC
Controls
10
8
6
4
2
0
neutral
congruent
incongruent
Figure 2 – Mean reaction times in ms for each group in each of the 4 color
conditions in the Magnitude Discrimination task.
1200
mean reaction time
1000
GC
PC
Controls
800
600
400
Neutral
Congruent
Incongrent
Consistent
18
Incongruent
Inconsistent
Table 3 – Individual scores for each synesthetic child on the Memory for Digits
task out of 16.
Neutral
Congruent
Incongruent
16
16
8.88
G7*
5
8
5
G9a
5
3
5
G9b
9
14
5
G11
14
12
4
G13
16
12
6
G15
12
12
10
P9
16
14
10
P11
11
10
15
P14a
10
9
10
P14b
* scores for the 7 year old were prorated from the 9-digit grid
19
Figure 4 – Mean reaction times (in ms) of individual grapheme-color synesthetes in the
magnitude discrimination task. Bars represent each of the four color congruency
condition.
G9a
G7
G9b
2000
2000
2000
1800
1800
1800
1600
1600
1600
1400
1400
1400
1200
1200
1200
1000
1000
1000
800
800
800
600
600
600
400
400
400
200
200
200
0
0
0
G13
G11
G15
2000
2000
2000
1800
1800
1800
1600
1600
1600
1400
1400
1400
1200
1200
1200
1000
1000
1000
800
800
800
600
600
600
400
400
400
200
200
200
0
0
0
Neutral
Congruent
Incongruent Consistent
20
Incongruent Inconsistent