Wesleyan University
The Honors College
The Role of Language in the Development of Number
Concepts: Evidence From and Towards an
Understanding of Oral Deaf Cognition
by
Rebecca Lange
Class of 2013
A thesis submitted to the
faculty of Wesleyan University
in partial fulfillment of the requirements for the
Degree of Bachelor of Arts
with Departmental Honors in Psychology
Middletown, Connecticut
April, 2013
The Role of Language in the Development of Number Concepts:
Evidence From and Towards an Understanding of Oral Deaf Cognition
Table of Contents
Acknowledgements
2
Abstract
3
Introduction
I.
Why study number development in oral deaf children?
a. Informing the choice to implant
b. Informing our explanation for the deaf achievement gap
c. Informing our understanding of the role of language in cognition
II.
How does oral deafness impact number development?
a. Impact of hearing ability on language, number word knowledge
b. Impact of language on nonverbal number knowledge
i. Cross-cultural number cognition
ii. Prelinguistic number cognition
1. Analog-magnitude system
2. Object-file system
iii. Proposals for the cognitive role of language in core systems
III.
The present study
a. Prediction: Aural input drives language development
b. Prediction: Language development drives number development
4
4
5
8
10
11
11
14
15
17
17
19
20
24
25
26
Methods
I.
II.
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29
37
Tasks
Participants
Results and Discussion
I.
Aural input and language development
II.
Oral deaf and typically hearing performance on each task
III.
Age-controlled and hearing-controlled comparisons
39
39
39
51
Implications and Future Directions
I.
Deaf community
II.
Psychology
III.
Philosophy
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66
Works Cited
69
Language in Number Development: Oral Deaf Cognition
2
Acknowledgements
First and foremost, I would like to thank Anna Shusterman, for her constant
support and wisdom both intellectually and otherwise, and for introducing me to the
value and fun of translational research. I hope to carry her philosophy towards
research with me well beyond my time on this project! I am so grateful to have been
given the opportunity to work on the Oral Deaf Project as my senior thesis; having
these ideas rolling around in my head for two and a half years has been a joy.
Huge thanks to all of the members of Cognitive Development Lab; I cannot
imagine my academic experience at Wesleyan without this community. Thanks to my
lab manager, Jess, for her helpful edits and support, and huge thanks to past lab
manager, Tali, who did much of the early data collection on this project. Special
thanks my fellow thesis students Sim and Sam for all the late night commiserating,
singing, and data epiphanies, some of which turned out to be correct. I would also like
to thank labmates Taylor, Andy, Angela, Sydney, and Ariel, whose love and baked
goods literally sustained my work these past few semesters.
Thanks also to my family, my housemates Eliza and Alahna, and Ono for
providing balance and love to my life throughout this process.
Thanks to the National Science Foundation and the Howard Hughes Research
Fellowship program for funding this project and my involvement in it, and to Prof.
Stemler for serving as my second thesis reader!
Finally, thanks so much to all of the families and preschools who took the
time to participate in this research, generously contributing to a greater understanding
of these important questions. This project would not exist without them.
Language in Number Development: Oral Deaf Cognition
3
Abstract
Past research has suggested that language may play an important role in
shaping the development of our fundamental concepts, such as number. Oral deaf
children, by receiving less aural linguistic input than do typically hearing children of
the same age, serve as an experimentally useful population for isolating the effects of
language on number development. Because these children are otherwise cognitively
typical, they allow for the role of language to be separated from other domain-general
developmental factors. 98 typically hearing and 42 oral deaf children were tested both
on a variety of number tasks measuring both verbally and nonverbally the two
different cognitive systems at work in the development of number concepts, the
analog-magnitude and the object-file system. These evolutionarily primitive systems
theoretically develop independently of language. It was found that, as expected,
differences in aural input and language development drove differences in verbal
number development. Furthermore, language also drove differences in nonverbal
development of the analog-magnitude system. Nonverbal object-file system
development was unaffected by language delays. These findings indicate that
language plays an important role in even nonverbal number development, suggesting
that our fundamental concepts may be shaped, not just expressed, by language. These
findings also have important implications for deaf educators and parents of deaf
children, who may be unaware of the depth of cognitive repercussions of delaying
aural language input. The language-independent development of the object-file
system, though, is potentially useful for this community in understanding and
addressing achievement gaps in deaf education.
Language in Number Development: Oral Deaf Cognition
4
Introduction
I.
Why study number development in oral deaf children?
When typically hearing parents learn that their child is born hard of hearing or
profoundly deaf, they are confronted with a choice: To teach their child sign language
and immerse them in signing culture, or to give their child a cochlear implant and
teach them spoken English in “mainstream” culture. In considering raising a Deaf,
signing child, hearing parents may see this option as limiting their child’s
opportunities, and may fear being unable to communicate with their own child if they
do not know sign language. In considering a cochlear implant, parents may be
informed by doctors and early interventionists of the difficulties a child with an
implant (heretofore referred to as an oral deaf child) may encounter, such as years of
therapy to learn to effectively use the cochlear implant to hear, the chance that the
cochlear implant may fail, and the likely possibility that the child may have difficulty
with articulation and speech.
While not of interest to speech therapists and early interventionists who focus
on the effective use of a cochlear implant for hearing and speaking, research on the
educational achievement of oral deaf children suggests that they may encounter
cognitive difficulties that transcend superficial difficulties in articulation patterns. For
example, deaf high school seniors’ median performance on the Stanford Achievement
Test was a fourth-grade reading comprehension level and a sixth-grade math
achievement level, and these gaps have been stable over the last three decades (Qi &
Mitchell, 2011). Despite the knowledge that these disparities exist, and the existence
of psychological and philosophical research tools with the power to explain why, very
Language in Number Development: Oral Deaf Cognition
5
little research has been done to directly measure the cognitive development of this
population and the precise cognitive cause of this achievement gap. Such research on
the psychological processes at work will not only be of crucial relevance to parents
aiming to make an informed decision about their deaf child, but will also be
immensely valuable to basic research in cognitive development and philosophical
work on the processes involved in language and conceptual thought.
The present study seeks to compare number development in typically hearing
and oral deaf preschool-aged children. It explores relationships between the aural
input a child receives, the development of her language skills, and the development of
the conceptual systems that underlie an understanding of number. In so doing, we
hope to tease apart the cognitive mechanisms behind number development, exploring
the extent to which the pace of this development is set by language ability. Because of
the potential for delayed aural input to inhibit this development, this project is of
crucial relevance to early interventionists and parents of deaf children, as well as to
their educators. Because it seeks to understand the cognitive mechanisms at work
behind language and thought, it is also of relevance to basic psychologists.
I will now separately explore the translational utility of this project to parents
and early interventionists, the potential applications to deaf education, and the
academic utility to psychologists.
a. Informing the choice to implant
Without much experience with Deaf culture, parents may see teaching a child
to sign and live in signing communities as limiting for her future. Such a decision also
Language in Number Development: Oral Deaf Cognition
6
requires enormous parental investment, because it involves a parent finding a way to
quickly learn an advanced level of sign language, or to somehow find a signing
caregiver who will help raise the child. In addition to solving to these massive
logistical difficulties, the possibility of a cochlear implant may also appeal to hearing
parents for its apparent power to enable a deaf child to be mainstreamed and fulfill
her potential as a member of hearing society. For example, the resource website
www.OralDeaf.org advises the following in its introductory paragraph:
Take a deep breath; we’re here to help. When you find out your child
is deaf, don’t panic – start with the following: Talk to the doctor – you
may be surprised to learn that many forms of deafness are at least
partially curable.
Thus, at first, parents may be eager for a “cure” which will allow their child to
live a mainstream life. Intuitively, it may make sense that giving a deaf child as close
as possible to typical hearing abilities would allow her to live as close as possible to a
typical life, allowing her to succeed academically and not be limited by deafness. The
downsides to a cochlear implant which are commonly presented to parents by early
interventionists, primarily speech and articulation issues, may seem trivial, and thus a
choice to raise a child who speaks spoken English may at first glance make sense.
Advocates of Deaf culture might respond that deafness is something to take
pride in, rather than something to cure, and that Deaf children who are raised with
their own natural language, American Sign Language, do in fact lead successful lives
with all of the richness and achievements of typically hearing individuals.
Whether one prioritizes inclusion in mainstream society and concedes to the
enormous logistical difficulties of raising a child in a foreign language, or prioritizes
raising a child with her natural language, is to some extent a personal choice. What is
Language in Number Development: Oral Deaf Cognition
7
important to realize is that regardless of one’s opinion on this contentious issue, the
fact remains that research on the deeper cognitive impact of oral deafness is often not
considered one way or another when making this decision. Cognitive research is
mostly absent from conversations about cochlear interventions, despite the wealth of
research suggesting the importance of language to cognition.
By empirically evaluating the claim that language is cognitively crucial for
developing conceptual thought, rather simply for expression of pre-existing thoughts,
this research may shift the conversation around cochlear implantation to emphasize
the importance of language input and the potential negative ramifications of delaying
such input. Research on the deeper cognitive effects of cochlear implantation will
thus help to inform parents’ difficult decisions about cochlear implantation.
Furthermore, while parents may be informed that cochlear implants
sometimes fail in ways that are impossible to predict or diagnose ahead of time, they
may not realize the cognitive implications of such an “oral failure”: Importantly, once
it is clear that an implantation has failed, a critical window of opportunity for learning
language has already passed. Thus, including cognitive research in the conversation
about cochlear implantation may provide crucial information both about the choice to
delay aural input by a year, if a cochlear device is implanted, and also about the
potential cognitive risks involved in the case of such an implant failing.
Importantly, such research on the cognitive mechanisms behind language and
thought will continue to be of relevance even as the technological landscape changes.
Because the FDA has required since the year 2000 that individuals must be at least 12
months old in order to be eligible for cochlear implantation, this delay in aural input
Language in Number Development: Oral Deaf Cognition
8
may be the driving force behind delayed language development, and in turn, other
cognitive delays. The risk that a cochlear implantation may fail is currently estimated
to be between 3% and 10%, as reported by large implant centers (Kuhn et. al., 2012).
However, both of these factors may change with changing technologies. Thus,
research on the cognitive mechanisms affected by this delayed exposure to language
input will not only help explain deaf cognition and educational achievement as it
currently exists, but will also allow our understanding to shift along with inevitable
changes in cochlear technology and the changes to things like the earliest allowed
ages of implantation or the potential for a cochlear implant to fail.
b. Informing our explanation for the deaf achievement gap
Research on the educational achievement of deaf students shows a staggering
achievement gap: A recent study found that less than one-half of 18 year old students
who are deaf/hard-of-hearing leaving high school reach a 5th grade level of reading
and writing (Traxler, 2000). The age at which a cochlear implant is received has been
shown to be related to speech and literacy outcomes (Connor, Hieber, Arts, et al.,
2000; Connor & Zwolan, 2004; Lederberg & Spencer, 2005; Tomblin, Barker,
Spencer, et al., 2005; Zwolan, Ashbaugh, Alarfaj, et al., 2004), and this advantage to
early implanation is greater than what can be attributed to simply longer device use
(Connor, Craig, Raudenbush, Heavner, & Zwolan, 2006). and also about the potential
cognitive risks involved in the case of such an implant failing.
However, while deaf children’s delays in more obviously language-based
skills like literacy, reading, writing, and speech may be intuitive, research also
Language in Number Development: Oral Deaf Cognition
9
crucially shows achievement delays in other academic areas: A 1986 study found that
deaf children were 2 standard deviations below matched nonhearing impaired peers in
general conceptual development (Bracken & Cato, 1986). The limited pool of
research on deaf mathematical achievement has also robustly shown that deaf
students demonstrate low levels of achievement in various areas of mathematics
involving computation and problem solving (Ansell & Pagliaro, 2006; Marschark &
Everhart, 1999; Traxler, 2000; Kritzer, 2009).
Thus, while educators may be aware of the difficulties that deaf students may
face in more obviously speech- and language-related skills (reading, writing,
speaking), it seems less obvious that deafness may impact math ability, which does
not on its face seem like it is a fundamentally verbal or aural skill. Studies show that,
indeed, many early educators are unaware of the implications of deafness on math
achievement (Kritzer & Pagliaro, 2005). Thus, research on cognitive mechanisms at
work behind learning basic number concepts, and the relevance of language to these
processes, may prove useful to deaf educators in closing the gap in mathematical
achievement.
This project’s focus on early childhood is particularly vital to closing this gap,
because investing in early education yields dramatic returns: Research shows that
early academic ability predicts later school achievement (Duncan et al., 2007;
Jimerson, Egeland, & Teo, 1999; Stevenson & Newman, 1986). With regard to math
achievement specifically, the importance of early mathematical knowledge, even
before formal schooling, appears crucial. Research has found that early number sense
correlates with school math ability and predicts later school math performance
Language in Number Development: Oral Deaf Cognition
10
(Kritzer, 2009; Libertus, Feigenson, & Halberda, 2011; Mazzocco, Feigenson, &
Halberda, 2011). Thus, researching the development of these very basic cognitive
abilities may have implications beyond the scope of preschool; their development
plays a crucial role in later school achievement and academic success. Understanding
which linguistic factors may cause delays in this area, and how, can help educators
and parents to equalize the landscape of educational opportunity.
c. Informing our understanding of the role of language in cognition
While this project may be understood as using psychology to better
understand oral deaf children and explain the academic challenges they may face, it
may also be conceptualized as using oral deaf children to understand psychology:
Because oral deaf children are linguistically delayed, due to delayed aural input, but
are otherwise oftentimes cognitively typical, they provide psychologists with a unique
opportunity to isolate language factors from other maturational effects and domaingeneral learning skills. Thus, by utilizing diversity in hearing ability and experience
to study the role of language in learning, we can better understand the basic
psychological processes that underlie not just deaf cognition, but all cognition.
Thus, researching number development in oral deaf preschoolers has wideranging and interdisciplinary relevance: Understanding the relation between language
and thought may have important applications for parents of deaf children, for whom
the choice of whether to delay language input may have greater cognitive
ramifications than difficulties in articulation. It may also help deaf educators aiming
to close an achievement gap, by providing cognitive evidence for unexpectedly wide-
Language in Number Development: Oral Deaf Cognition
11
ranging academic consequences of language delays, and providing support for
addressing this gap in early education. Finally, it may serve to answer important basic
psychological questions about the cognitive effects of language in conceptual
development.
II.
How does deafness impact number development?
a. Impact of hearing ability on language and number word knowledge
The rapidly developing technology of hearing aids and cochlear implants has
given hearing to many children born with profound hearing loss. Due to the impact of
newborn hearing screening programs, increasing numbers of infants and young
children are now presenting to implantation centers and early intervention programs
(Nott, Cowan, Brown, & Wigglesworth, 2009). Research finds that the age at which a
child receives a cochlear implant is an important predictor of her speech and language
outcomes, (Connor, Hieber, Arts, et al., 2000; Connor & Zwolan, 2004; Lederberg &
Spencer, 2005; Tomblin, Barker, Spencer, et al., 2005; Zwolan, Ashbaugh, Alarfaj, et
al., 2004), and that the advantage of earlier implantation is even greater than what can
be attributed simply to longer device use at any given age (Connor, Craig,
Raudenbush, Heavner, & Zwolan, 2006). As technology improves, children are able
to hear at younger and younger ages; however, even those fitted with the device at a
very young age still exhibit delays. Research finds that even deaf children who were
fitted with a cochlear implant before 30 months of age (and many much younger)
took significantly longer to learn 100 words and produce word combinations than
typically hearing peers (Nott, Cowan, Brown, & Wigglesworth, 2009). Thus, it is
Language in Number Development: Oral Deaf Cognition
12
clear that aural experience and exposure to language, particularly at a young age, is
incredibly important to language development, and that the lack of such input that
oral deaf children receive prior to being fitted with a hearing aid may impede such
development.
In addition to the role of limited aural input in delaying oral deaf children’s
language development directly, social factors may also play an important role in oral
deaf children’s limited early exposure to language, and number words in particular.
For example, parenting behavior may differ between parents of oral deaf and
typically hearing children. Even deaf and typically hearing infants receive different
kinds of language input from their mothers, who use different language and talk about
different things to deaf children and typically hearing children (Morgan and Woll,
2012). Beyond infancy into childhood, even once a hearing device has been
implanted, parental interactions with oral deaf children may differ in cognitive and
linguistic stimulation from the interactions that typically hearing children experience
(Quittner et al., 2012). Parents of children with cochlear implants may fine-tune their
own vocabulary and sentence complexity to that of their child (Schenker, 2012). With
regard to number language specifically, studies show that parents of deaf children are
less likely to use incidental number language and engage in number-related play
(counting, number games, etc.) than parents of hearing children (Kritzer, 2009).
This differential social and incidental exposure to words (and number words
in particular) is especially concerning considering the importance of such informal
learning: In a variety of studies documenting the informal use of mathematically
based terms and concepts in the home, mothers of young hearing children were found
Language in Number Development: Oral Deaf Cognition
13
to incorporate such terms through activities such as counting snacks, playing number
games, and reading numbers off of license plates while traveling. Research has found
a strong correlation between these informal parenting behaviors and children’s
number development (Aubrey, Bottle, & Godfrey, 2003; Gunderson & Levine, 2012;
Saxe, Guberman, & Gearhart, 1987). Qualitative research shows the importance of
naturalistic exposure of mathematically based terms and concepts (such as
number/counting, quantity, time/sequence, and categorization) to the acquisition of
those terms and concepts (Kritzer, 2009). The importance of number-based parenting
behavior to learning number concepts suggests that the differential parenting
behaviors of parents of oral deaf and typically hearing children may exacerbate
existing differences in language exposure and ability, thus further hindering oral deaf
children’s number development.
In addition to the lack of exposure to number words itself that may impact
number concept acquisition, the general limited exposure to language and syntactic
structure that oral deaf children receive may inhibit number concept acquisition, due
to the role that both a greater vocabulary and an understanding of syntactic structure
may play in learning number words. Recent research shows that there is a strong
correlation between number-word knowledge and general vocabulary, suggesting that
having a larger nominal vocabulary helps children learn number words (Negen &
Sarnecka, 2012). Additionally, understanding the rule that words have precise, rather
than rough or overlapping, meanings may be useful for number development.
Children’s understanding, for example, that the word “three” refers only to sets of
three and not to sets of two or four comes not only from an understanding of number
Language in Number Development: Oral Deaf Cognition
14
but also from an understanding of the specificity of language, in this way. Thus,
language and vocabulary development may be important not only in exposing
children to number words themselves, but also in how they contribute to the
development of an understanding of language and other nominal vocabulary that may
aid in the number word acquisition process.
Thus, for reasons of limited perceptual input as well as indirect social and
parenting factors, oral deaf children received limited exposure to number words,
general vocabulary that may help scaffold the meaning of number words, and general
syntactic principles. Given the documented importance of such language input to
language development, particularly in the case of number words, it is unsurprising
that deaf children perform worse in studies measuring children’s performance on
number word tasks (Leybaert and Van Cutsem, 2002). So, hearing ability and aural
input have important effects on number development, in terms of verbal number word
knowledge. Importantly though, this verbal number knowledge is not the only factor
involved in number development, as I will show in the next section.
b. Impact of language on nonverbal number knowledge
In addition to knowledge of number words, another crucial factor in the
development of number concepts is nonverbal number knowledge. If the role of
language in learning number concepts were purely verbal expression of alreadyunderstood prelinguistic number concepts, then the difference in performance would
be limited to tests that measure verbal expression of these concepts. Differences in
performance would not extend to tests that measure nonverbal number understanding;
Language in Number Development: Oral Deaf Cognition
15
deaf children would perform similarly to hearing children on these tasks.
Interestingly, research is mixed on whether this is the case. Some research indicates
that deaf children perform similarly to hearing peers on nonverbal number concept
assessments (Leybaert and Van Cutsem, 2007), while other research have found that
whether number ability is measured verbally or nonverbally, deaf and hard-of-hearing
students perform consistently worse than their hearing peers (Kritzer, 2009). The
mixed results of deaf nonverbal number development indicate that more research is
needed to understand precisely what cognitive factors in number development are
inhibited by deaf children’s delayed language abilities, and which faculties are
unaffected by language ability.
While little research exists on deaf number cognition specifically, existing
research from cross-cultural, infant, and nonhuman animal studies can shed important
light on the nature of nonverbal number knowledge. I will now explore this research
and its relevance to this project:
i. Cross-cultural number cognition
Some researchers have studied this verbal impact on nonverbal number
knowledge through studying cultures whose language involves limited vocabulary for
number concepts, such as the Pirahã, Mundurukú, and Anindilyakwa tribes. These
tribes’ languages do not have words for specific numerosities or natural integers;
instead, they have a small number of words that refer roughly to approximate
numerosities. Research with these communities can yield information about which
Language in Number Development: Oral Deaf Cognition
16
components of number development are influenced by language differences and
which are universal or independent of linguistic factors.
Depending on the nature of the number task used in research with these
communities, tribal individuals’ performance varied widely: For example, Pirahã
perform well on tasks that allow for the use of a visual matching strategy, such as
when shown a row of objects and asked to create a row alongside it or orthogonal to it
that contained the same number of objects. Evidence for similar performance of these
tribal members on nonverbal tasks extends outside visual tasks, though:
Anindilyakwa children perform as accurately as English-speaking children on tasks
that required matching the number of sounds with a previously shown number of
objects (Butterworth & Reeve, 2012; Butterworth & Reeve, 2008; Butterworth,
Reeve, Reynolds, & Lloyd, 2008). Thus, by some measures, number knowledge
appears to develop similarly even in tribes without a verbal integer system like ours.
However, by other measures, these tribes’ performance on nonverbal number
tasks is dramatically inhibited by their lack of number language: For example, on a
task in which participants saw a number of nuts put in a can, and then a number of
nuts removed from the can, and had to make a judgment about whether there were
still nuts left in the can, Pirahã participants struggled considerably (Butterworth &
Reeve, 2012; Frank, Everett, Fedorenko, & Gibson, 2008). Anindilyakwa children
also performed very poorly on a nonverbal matching task involving addition;
interestingly, older children who used an enumeration strategy (possibly reflecting
schooling) often did even more poorly than younger children who often used a
visuospatial pattern strategy to solve the task (Butterworth & Reeve, 2012). Thus, in
Language in Number Development: Oral Deaf Cognition
17
some instances, the use of enumeration strategies in place of other cognitive faculties
inhibited performance!
The varied performance on these nonverbal number tasks suggests that
research must be done to tease apart the different cognitive faculties involved in order
to investigate which processes are inhibited by lack of number language, and which
processes develop independently from language.
ii. Prelinguistic number cognition in infants and nonhuman
animals
In addition to cross-cultural studies, infant and animal studies are another way
of investigating nonverbal numerical development, and exactly which parts of this
development are influenced by language. Importantly, this research has robustly
found that we, and many other animals, are born with two distinct prelinguistic
number concept acquisition systems, referred to as the analog-magnitude system (also
sometimes called the approximate number system or number sense), and the objectfile system (also sometimes referred to as the individual-file system or parallel
individuation). I will describe each system independently, and then explore the
precise cognitive function of putting these prelinguistic, implicit understandings into
linguistic, explicit terms.
1. Analog-magnitude system
The analog-magnitude system is an evolutionarily ancient system that is used
by human adults, human infants, and nonhuman animals. In this system of
Language in Number Development: Oral Deaf Cognition
18
representations, number is represented by “a physical magnitude that is roughly
proportional to the number of individuals in the set being enumerated” (Carey, 2009,
p. 188).
A signature of this system of representations is that sensitivity is in
accordance with Weber’s law; in other words, the discriminability of any two
magnitudes is a function of their ratio. Under this system, therefore, it is easier to
discriminate 1 from 2 than 7 from 8, and it is easier to distinguish 4 from 8 than 24
from 28. As previously stated, evidence for this system has been found in several
nonhuman animal species, indicating its primitive evolutionary origins. Preverbal
infants also form analog-magnitude representations of number, even when controlling
for other possible bases of judgment such as cumulative surface area, element size,
and density (Carey, 2009).
A number of models have been proposed for exactly how these
representations are computed from perceptual input, and these proposals vary in how
they incorporate linguistic representations of numerosities. While initial proposals
suggested iterative mechanisms that mimic counting-like procedures (Curch and
Meck, 1984), current research favors a proposal by Russell Church and Hillary
Broadbent (1990) that does not involve an iterative process. A noniterative
mechanism could compute visible numerosity by “directly representing the average
density of individuals in a set, representing the total spatial extent occupied by the set
of individuals, and dividing the latter by the former” (as cited in Carey, 2009, p. 134).
Importantly, the mechanism involved in creating analog-magnitude representations
does not require each individual in the set to be enumerated and then ticked off one at
Language in Number Development: Oral Deaf Cognition
19
a time (Carey, 2009). That these mechanisms do not implement any iterative or
counting procedure will become important in assessing the role that the verbal
counting practice plays in developing number cognition, which will be explored in
section iii.
Importantly, the format of analog-magnitude representations is iconic, rather
than linguistic, and its numerical content is implicit, rather than explicit. Iconic
representations differ from language-like symbolic in that they are analog. In analog
iconic symbols, such as a realistic picture of a dog representing a dog, parts of the
symbol are analogous to parts of the represented entity: the ears on the picture
represent the ears of the dog, etc. (In contrast, the word “dog,” which is a linguistic
rather than iconic representation, is not analog because parts of this word do not
correspond to parts of a dog). Analog-magnitude number representations are analog
in that "the symbol for 3 ( ------) contains the symbol for 2 ( ---- ), respecting the
actual numerical relations between 2 and 3” (Carey, 2009, p. 135). Thus, the
numerical content of this system of representation is implicit in the operations of the
mechanisms that produce the representations. Language may be crucial in moving us
beyond these implicit kinds of representations.
2. Object-File System
In addition to the analog-magnitude system, humans have one other
prelinguistic system of numerical representations, called the object-file system. This
system involves individuation and numerical identity, allowing infants and even nonhuman animals to distinguish between sets with two numerically distinct objects from
those with three objects or one object. Recent research shows that this system
Language in Number Development: Oral Deaf Cognition
20
operates as part of our working memory (Zosh & Feigenson, 2012). Essentially, a
mental file on each object is temporarily kept track of as objects are tracked through
time and space.
Like the analog-magnitude system, the object-file system is also distinguished
by a signature computational constraint. Instead of Weber’s Law, though, object-file
representations are constrained by a set size limit of 4 object-files (Barner, Wood,
Hauser, & Glynn, 2008; Carey, 2009). Because of this, the object-file system
underlies performance on many small-number studies. Performance on many number
representation tasks involving small sets show the set-size signature of object-file
representations rather than the Weber-fraction signature of analog-magnitude
representations (Carey, 2009; Starkey & Cooper, 1980).
Like the analog-magnitude system, it is important to note that in this system,
number is only implicitly encoded. The representations involved are a symbol for
each individual in the set (requiring implicit use of principles of individuation and
numerical identity) rather than any symbol with the abstract numerical content “two”
(Carey, 2009).
iii. Proposals for the cognitive role of language in core systems
So, with these prelinguistic analog-magnitude and object-file representations
already intact, in what ways does the element of language merely help put into
explicit terms these concepts which are already being understood and utilized at an
implicit level, and in what ways might it play an even more important role of actually
Language in Number Development: Oral Deaf Cognition
21
going back and informing the implicit content that is being represented? There are a
variety of proposed answers to this question:
In 1978, Gelman and Gallistel put forth a theory that children already
understand number concepts as distinct integers, and essentially merely have to solve
a mapping problem of connecting these pre-existing concepts to words. The
constructed, culturally-variable nature of our language’s integer system, as has been
touched upon, would seem to undermine the plausibility of this theory, which rests
upon the assumption that our integer system is natural and universal.
An alternative proposal suggests that number words may serve as a memory
aid for the representations maintained in working memory, allowing for enriched
parallel individuation (Carey, 2009).
Butterworth and Reeve propose that language may also help to narrow, finetune, and solidify the implicit analog-magnitude representations that exist
prelingusitically. Since the child’s analog representation is inexact (an analogmagnitude representation of fiveness overlaps with that of fourness and of sixness),
repeated verbal use may help the child make a representation more precise and more
like our verbal system of natural numbers. In this way, language does more than
express what we already represent, or help us hold these representations in mind, it
also influences and “fine tunes” those representations.
Karen Wynn, in researching how children understand the culturally
constructed process of counting, went one important step further in assessing the
centrality of language to number development: She suggested that language plays a
role in the fundamental shift that occurs between a child understanding number words
Language in Number Development: Oral Deaf Cognition
22
as descriptors of individual objects as they are counted, and understanding the idea
that number words refer to cardinality, or the cumulative total of all objects counted
so far in the set. The exact processes behind the acquisition of this cardinal principle
are not yet understood, but we know through Wynn’s work that various components
must be understood before the cardinal principle can be acquired. These necessary
prerequisite components include the ability to recite the verbal count list, the mutual
exclusivity of number words in corresponding to a precise meaning (so that if a child
sees a set of three objects and does not yet know the word “three,” but she
understands “two,” she will not refer to this unknown set as “two”), the successor
function (the notion that the addition of one more object to a set means that one uses
the subsequent word in the verbal count list), and the mapping of number meanings to
their words. Wynn showed that even children who understand the verbal count list
and the mutual exclusivity of number words have learned the meanings of some
words but not others (Carey, 2009). In fact, children learn these meanings in order:
First understanding “one;” and then both “one” and “two;” and then “one,” “two,”
and “three;” and so forth. With all of these components intact, and some practice,
children at some point acquire the cardinal principle, usually around the time they are
mapping “five” or “six.” In some way, the verbal component at work here plays a role
in helping children make the jump from a collection of understandings (analogmagnitude representations, object-file representations, the verbal count list, the
successor function, the mutual exclusivity of number words meanings, and a growing
collection of word mappings) to understanding number as the representation of
Language in Number Development: Oral Deaf Cognition
23
overall cumulative quantity that it is. The notion that language plays this crucial role
seems highly promising (Carey, 2009).
A variety of proposals exist for how exactly this process of acquiring the
cardinal principle works, but cognitive development expert Susan Carey writes that it
somehow involves using analogical reasoning to bootstrap unknown or partially
understood pieces of information, thus integrating the various components at work
into an understanding (cardinality) that is more than the sum of its parts.1 It is unclear
exactly what analogy or analogies comprise this bootstrapping: The crucial step might
depend on drawing analogies between later in the count list and larger numerosity as
represented by the analog-magnitude system (Carey, 2009). Alternatively, it might
depend drawing analogies between next on the count list and next state after the
addition of one individual to a set (Carey, 2009). Regardless of what exact analogical
or inferential leap might be the crucial step in this process, it inevitably seems to
involve the “bootstrapping” element of “an explicit structure [being] learned initially
without the meaning it will eventually have, and at least some of the relations among
the explicit symbols [being] learned directly in terms of each other. The list of
numeral words and the counting routine are learned as numerically meaningless
structures” (Carey, 2009). Thus, both proposals involve using language to integrate
previously distinct representations (Carey, 2009).
Regardless of exactly how this bootstrapping process works, it seems clear
that the verbal, explicit aspect provided by language does more than make the implicit
1
This kind of cognitive epiphany that is reached when the child makes the analogical inference
connecting these various components is paralleled in other documented conceptual shifts. For example,
the word-mapping process itself involves reaching a certain vocabulary size, suddenly understanding
the notion that words refer to things, and then rapidly ratcheting word knowledge (Patrick, Hurewitz,
and Booth, 2012).
Language in Number Development: Oral Deaf Cognition
24
verbally expressible. It also serves to integrate the analog-magnitude and parallel
individuation systems (and the various other learned principles such as the successor
function and specificity of number words, which are learned through general
vocabulary knowledge and pragmatic inference). In doing so, it enables us to acquire
the crucial principle of cardinality, and understand the construction of natural
number. This understanding, which seems to be only possible through language, also
gives us the power to do things like understand the difference between 1,973,562 and
1,973,563 (a difference which is far outside the bounds of the Weber fraction of the
analog-magnitude system or the set-size limit of parallel individuation) and
communicate and manipulate mathematical concepts even more abstract than these
natural integers, such as zero, negative numbers, or irrational numbers.
III.
The present study
To what extent, and in what ways, does language merely help put into explicit
terms these concepts which are already being understood and utilized at some implicit
level, and in what ways does it actually help to bootstrap, acquire, and solidify these
terms as culturally constructed integers? Is making these concepts explicit merely to
map them to verbal terms, or does making them verbal also go "back" and inform the
implicit content? What is the precise role that language plays in the development of
number concepts?
This study aims to answer these intricate cognitive questions through
measuring the development of language and of these core number systems in both
oral deaf and typically hearing populations. By collecting data on oral deaf children’s
intervention histories, and by using a variety number measures (verbal and nonverbal,
Language in Number Development: Oral Deaf Cognition
25
tapping both ANS and object-file representations), a language measure, and a general
cognitive measure, we hope to be able to tease apart the cognitive mechanisms at
work. In doing so, we aim to discover the causal relations between aural input,
language development, and number development, and the precise cognitive function
of language in number development. We expect:
1) That aural input will set the pace for language development.
2) That language development will, in turn, drive number development.
I will now explore these two hypotheses, discussing alternative conclusions
and the circumstances under which the data would support them.
a. Prediction: Aural input drives language development
While this first component of the hypothesis seems straightforward, it is
possible that the language assessment is also influenced by not merely the amount of
language exposure a child receives, but also by the quality of this exposure. For
example, aural input could vary in terms of the types and number of social
interactions and incidental learning experiences, even beyond the variance in amount
of time with the potential to ability to hear.
Another possibility is that calculating the months since a child’s first device
may not be a perfect a measure of her aural input. This is because many oral deaf
children do not use their cochlear implants or hearing aids full-time. Because children
often turn the devices off outside school settings, the amount that a cochlear implant
or hearing aid is used may be an important factor mediating the effect of the technical
Language in Number Development: Oral Deaf Cognition
26
amount of time spent with the implant on the amount of aural and linguistic input
received, and thus on language development.
b. Prediction: Language development drives number development
The role of language in affecting performance on these tasks will be assessed
in two different ways:
First, I will simply examine the disparity between oral deaf and typically
hearing children’s performance on each task.
Secondly, I will examine these disparities closer by seeing for which tasks
they persist even once aural input is controlled for. In this way, we can focus on the
role of aural input specifically, and can tease apart exactly which core system(s) are
affected by language. If even nonverbal measures of core cognitive systems are
affected by differences in aural input / language ability, this would suggest that deaf
disparities in number development may be traced to fundamental cognitive
differences rather than solely differences in verbal cognitive ability (or cognitive
ability measured verbally), much less superficial differences in speech and
articulation.
As will be shown in the Methods section, these features allow for crosscategorization of each task as either verbal or nonverbal, as well as measuring either
sets smaller than 4 (thus, likely requiring use of the object-file system) or greater than
4 (likely requiring use of the approximate number system). It may be useful to think
about these options as a 2x2 chart into which all tasks fit:
Language in Number Development: Oral Deaf Cognition
27
Small Large
V
Non-V
For each task, and thus for each quadrant of the chart, there are 3 possible
outcomes:
(1) Performance is significantly different between oral deaf and
typically hearing participants, and this disparity can be attributed to
language differences.
(2) Performance is significantly different between oral deaf and
typically hearing participants, and this disparity cannot be attributed to
language differences.
(3) Performance is not significantly different between oral deaf and
typically hearing participants.
The expected outcome consists of global oral deaf delays on all tasks in which
verbal number knowledge is assessed, or in which number knowledge is assessed in a
verbal way, and that this delays would be attributable to oral deaf delays in aural
input, and thus language development.
The expected outcome also consists of mixed findings regarding non-verbal
number development, which might help explain the mixed evidence in the literature
Language in Number Development: Oral Deaf Cognition
28
about such number development. We hope that the pattern of which nonverbal tasks
are driven by or independent on language differences will be meaningful, so that it
may shed light on which cognitive systems are dependent on language. It may be the
case that, when measured nonverbally, only the analog-magnitude system is
language-driven, or only the object-file system is language-driven, for example.
Given that oral deaf children are cognitively typical, no findings of oral deaf
delays which are not attributable to aural input delays / language development delays
were predicted.
An alternative finding in which oral deaf and typically hearing populations
perform differently on all verbal measures but similarly on all nonverbal measures
would indicate that the role of language is merely to put into explicit terms concepts
which are already being understood and utilized at an implicit level, and that the role
of language is no more cognitively fundamental to acquiring these concepts.
Language in Number Development: Oral Deaf Cognition
29
Methods
This study involved seven tasks, five assessing primarily (verbal or nonverbal)
number knowledge, one assessing primarily language development, and one assessing
primarily general cognitive ability, as measured through executive function
performance. In this section, the tasks and assessments will be described in depth.
Diagrams next to each task will indicate its role in the conceptual 2x2 framework of
nonverbal/verbal and small/large measurements.
In order to avoid fatigue effects, the battery of seven tasks was divided into
two separate sessions, each of which lasted roughly 30 minutes to an hour. The
sessions were generally scheduled no more than one week apart. The first session
consisted of Which-Has-X, Fast Cards, Give-a-Number, and an Executive Function
task, in that order. The second session consisted of Which-Has-More, Caterpillar, and
the Pearson Peabody Vocabulary Assessment, in that order. The only deviation from
this order of tasks occurred in oral deaf preschools that had already administered their
own language assessment previously, and in certain rare cases where the participant
became bored of a task and it was returned to after completion of the subsequent task,
after a break, or during the next session.
I.
Tasks
a. Which-Has-X (adapted from Wynn 1990)
In this verbal forced-choice task, children were presented with two pictures
showing sets of contrasting numbers of objects, and asked to point to the picture
Language in Number Development: Oral Deaf Cognition
30
showing a requested number of objects. For example, in the first trial, the participant
was asked, “Which picture has one elephant?”
Children were prompted to point to sets of 1, 2, 3, 4, 5, 7, 10, 15, 25, 30, and
50, each for a total of four times. For set sizes of 10 or fewer, children were required
to discriminate between this set and the next smaller set and next larger set each two
times. Set sizes of 15 or greater, rather than being compared against the next smaller
or larger set, were presented in more easily discriminable comparisons of 15 versus
30, and 25 versus 50.
The order of prompts was counterbalanced, although the randomized smallnumber comparisons were presented as a block before the randomized large-number
comparisons. Additionally, the first two trials were both comparisons of 1 and 2, in
order to help the child understand the task before moving on to more difficult
comparisons. The left-right presentation of each comparison was also
counterbalanced.
In comparing small sets, this task is likely requiring use of the object-file
system, and in measuring large sets (7 vs 10, 15 vs 30, and 25 vs 50), this task is also
requiring likely use of the approximate magnitude system. In each case, it does so
verbally, though the use of verbal number words.
S L
V
Non-V
Language in Number Development: Oral Deaf Cognition
31
b. Give-a-Number (adapted from Wynn 1992)
In this verbal task, children were asked to count a set of 15 small plastic fish,
and then an expanded group of 20 fish. Children were then asked to put a requested
number of them into a bowl (presented to the children as “their swimming pond”).
Sets of 1-8 fish were requested using a titration method developed by Karen Wynn, to
determine the greatest number for which a child was able to produce the requested
set. Requested sets were titrated until a child failed a particular trial three times in a
row, indicating consistent failure to master a given number.
Whether correct or incorrect in their fish selection, children were always
asked to “count and check to make sure it’s [x],” giving children an opportunity to
use the counting process to identify and correct their potential error.
The need for exact encoding of small sets makes this task an object-file
system measure. The need for understanding cumulative verbal cardinality and
applying verbal names to each fish as it is counted make it a verbal measure of this
system.
S L
V
Non-V
c. Fast Cards (adapted from Le Corre & Carey, 2007)
In this verbal fast estimation task, children were quickly shown a slide
displaying a set and asked to generate the corresponding number word. Children were
asked “what did that look like” rather than “how many,” in order to discourage
counting.
Language in Number Development: Oral Deaf Cognition
32
Sets contained either 1,2, 3, 4, 6, 10, or 14 items. The order of set presentation
was randomized. For half of the sets, total surface area was controlled for, and for the
other half, item size was controlled for. In total, each set was presented four times.
In estimating small sets (of 1, 2, and 3), this task is a likely measure of the
object-file system, and in estimating large sets (of 6, 10, and 14), this task is a likely
measure of the approximate number system. In both cases, the task was verbal, in that
knowledge verbal number words was being measured.
S L
V
Non-V
d. Which-Has-More (adapted from Halberda & Feigenson, 2008)
In this nonverbal numerical acuity task, children were presented with slides
displaying two sets of dots, and were asked to select which set had “more.” Set sizes
varied from 5-16 dots, and sets differed by ratios of 1:2, 3:4, 5:6, or 7:8. For half of
the trials, the summed area was anti-correlated with the number of dots. Immediate
nonverbal feedback was given for each trial in the form of a successful or
unsuccessful sound from the computer, as well as an appropriately happy or
disappointed affective and verbal response from the experimenter.
Performance on the task was measured in two ways: Weber fractions
reflecting the smallest ratio discriminated with 75% accuracy were derived for each
child as a quantitative measure of numerical acuity using a psychophysical model
(Pica et. al., 2004, Halberda, J. & Feigenson, L., 2007). In addition, percent of correct
trials was also calculated.
Language in Number Development: Oral Deaf Cognition
33
S L
V
Non-V
e. Caterpillar Task (adapted from M. Hannula)
In this nonverbal numerosity assessment, children were presented with
caterpillars with different numbers of feet, and were told that the caterpillars were a
group of brothers and sisters who were going on a walk and needed socks for their
feet. They were told to bring back “just enough” socks for the caterpillars, because if
they brought back too many socks, it would make a big mess and the caterpillars’
parents would be upset, and if they didn’t bring back enough socks, the caterpillars’
feet would be cold. The 1-footed caterpillar was presented first, and then 3-footed, 7footed, 5-footed, 9-footed, 6-footed, and finally 3-footed. Socks were hidden in a
location from which the caterpillar was not visible, requiring children to hold some
kind of mental representation of the quantity in working memory order to complete
the task well, whether that representation be visual or verbal.
Children were not encouraged to count feet or socks, or to employ the tool of
verbal number at all in completing the task (the script avoided number language,
asking children to bring back “just enough” socks rather than “the right number”).
However, children who spontaneously counted were not discouraged from doing so.
It is also important to note that the verbal script was not necessary to
understand the task or complete it successfully. Because the act of putting on socks
and matching feet to socks is highly visual and a common everyday action that
children are already familiar with, the task is robustly nonverbal.
Language in Number Development: Oral Deaf Cognition
34
Unlike previous iterations of this task, caterpillars’ feet were in one row
instead of two rows, due to concerns in past studies that some children were
completing the task by chunking the feet into groups using these rows. The singlerow presentation was done in an effort to avoid providing children with the
opportunity to chunk feet in this way.
S L
V
Non-V
f. Executive Function Task
In this nonverbal task, children were introduced to two puppets who each had
different rules for playing a game. Children were trained on these puppets
individually, and were then required to task-switch when the two puppets played the
game at the same time.
Two large buttons were placed in front of the child, and the first puppet (an
elephant) played a game in which after the elephant pressed a button, the child was
asked to press the same button. After training on this task, the second puppet (a
crocodile) played a game where after the crocodile pressed a button, the child was
asked to press the other button. Finally, after children received a reminder to ensure
that they remembered both sets of rules, the elephant and the crocodile took turns
pressing buttons, requiring the child to task-switch and keep both animals’ rules in
mind.
While task-switching is only one component of executive function, this task
also utilizes the related component of working memory (keeping the rules in mind
Language in Number Development: Oral Deaf Cognition
35
and using them to guide behavior). The task does not directly measure other
components of executive function, such as self-regulation or inhibition; however,
measuring every component of a construct as heterogeneous and unwieldy as
executive function is virtually impossible. Task-switching and working memory are
components that lend themselves well to a nonverbal measure, which was crucial for
this particular study.
The crucially nonverbal nature of this measure means that it is able to be used
across both typically hearing and oral deaf populations. Linguistic factors play no role
in the understanding of the rules of this task, meaning that it is measuring purely
executive function development without being confounded by language development.
g. Language Assessment
Most children were assessed using the Peabody Picture Vocabulary Test
(PPVT-4); however, some oral deaf preschools used other measures (such as the
CELF-4, ROW-PVT, and others). The PPVT and its substitutes all measure receptive
language ability. In order to standardize the scores and compare across measures, age
equivalencies were computed for each assessment, and thus a “language age” (which
had meaning independent from the assessment used to calculate it) was derived for
each child.
Some language assessment scores provided by the oral deaf preschools were
from tests administered at a date months earlier (or in rare cases, later) than our
battery of number and cognitive tasks (average testing date discrepancy = 6.29
months). In order to estimate how a participant would have scored on the assessment
Language in Number Development: Oral Deaf Cognition
36
on the date that her number knowledge was assessed, (in other words, the degree to
which a child would likely have improved over the span of time between tests),
language scores were plotted against children’s hearing ages on the date of language
assessment, and a slope was calculated, f(x) = .002x3 - .14x2 + 3.81x, r2= .57. The
need for such a slope, rather than linearly adding the number of months between the
language assessment and the number assessment onto the child’s language age’s from
the time of language assessment, is due to the nonlinear nature of language
development: the same disparity of time could lead to varying degrees of language
development disparity depending on the age and language age of the child. This slope
allowed us to estimate the amount by which a participant’s language score would
change over a given period of time, thus allowing us to calculate a rough estimation
of the participant’s language age at the time of number testing.
The PPVT is a semantic measure; in other words, it assesses children’s
knowledge of word meanings. As discussed, both semantic information as well as
syntactic understanding may underlie or influence number word learning; thus, the
PPVT is a slightly imperfect measure for the language constructs that would be most
relevant. However, due to attentional constraints of the child and the likely high
correlation between development of syntactical and semantic understandings, the
PPVT serves as the sole language measure for this study.
Language in Number Development: Oral Deaf Cognition
37
Here is a representation of the tasks showing their placement within the chart:
Verbal
Small sets
(likely object-file
system)
Large sets (likely
approximate number
system)
Which-Has-X (sets <4)
Fast Cards (sets <4)
Give a Number
Which-Has-X (sets >4)
Fast Cards (sets >4)
Caterpillar (sets <4)
Which-Has-More
Caterpillar (sets >4)
Nonverbal
Because four objects is the set size limit of the object-file system, a set size of
four was chosen as the dividing point for whether a task was considered to be
measuring the object-file or the analog-magnitude system. While the finding that four
is the limit of the working memory’s capacity in this regard is relatively robust, it
should be noted that it is not absolute; smaller set sizes may not be exclusively reliant
upon the object-file system.
IV.
Participants
Participants in this study included a total of 137 preschool aged children,
consisting of both an oral deaf population (n = 42) and a typically hearing population
(n = 98). Typically hearing participants were either recruited from around central
Connecticut and tested in a laboratory setting or were tested at local Middletown
preschools or Head Start programs. Oral deaf participants were tested at private oral
deaf preschools in New York, Massachusetts, and Connecticut.
Language in Number Development: Oral Deaf Cognition
38
Oral Deaf
Typically
Hearing
Age range
40 – 74 months
36 – 79 months
Average age
51.02 months
57.54 months
Male
22
46
Female
20
52
Total
42
98
Certain participants did not complete certain tasks, due to becoming bored or
fussy, not wanting to complete the task, or being absent for the second session of
testing. Participants were excluded or included from analyses depending on whether
they completed the relevant tasks.
Did Not
Finish
(Hearing)
Did Not
Finish
(Deaf)
Did Not
Finish
(Total)
WHX
GN
FC
EF
WHM
CAT
PPVT
5
5
10
7
25
11
14
4
2
5
4
14
3
13
9
7
15
11
38
13
13
Language in Number Development: Oral Deaf Cognition
39
Results and Discussion
I.
Aural input and language development
The first hypothesis was that aural input would drive language development.
Results confirm these predictions: Months of aural input was calculated for oral deaf
participants by calculating months since first hearing device. For typically hearing
participants, months of aural input was equivalent to age. A linear regression found
that aural input significantly predicted language assessment scores, b = .462, t(115) =
5.59, p < .001.
Establishing that language differences are attributable to differences in aural
input will provide important explanatory leverage in interpreting number task
performance results: Variance in number task performance based on aural input may
reasonably be attributed to differences in language development produced by aural
input.
II.
Oral deaf and typically hearing performance on each task
Oral deaf and typically hearing performance on each task was compared using
two-way ANOVAs. Performances on each task are illustrated on the following pages,
after which analyses will be reported and discussed.
6.00
5.00
4.00
3.00
2.00
1.00
0.00
36
42
48
54
Age (months)
60
66
72
78
Give-a-Number Task:
Oral Deaf vs. Typically Hearing Performance
Language in Number Development: Oral Deaf Cognition
Knower Level
84
Oral Deaf
40!
Typically Hearing
!
6.00
5.00
4.00
3.00
2.00
1.00
0.00
36
42
48
54
Age (months)
60
66
72
78
Which-Has-X Task (Low Set Sizes):
Oral Deaf vs. Typically Hearing Performance
Language in Number Development: Oral Deaf Cognition
Knower Level
84
Oral Deaf
41!
Typically Hearing
!
90.00
70.00
50.00
30.00
10.00
36
42
48
54
Age (months)
60
66
72
78
Which-Has-X Task (High Set Sizes):
Oral Deaf vs. Typically Hearing Performance
Language in Number Development: Oral Deaf Cognition
Percent correct
84
Oral Deaf
42
Typically Hearing
100%
75%
50%
25%
0%
36
42
48
54
Age (months)
60
66
72
78
Which-Has-More Task:
Oral Deaf vs. Typically Hearing Performance
Language in Number Development: Oral Deaf Cognition
Percent correct
84
Oral Deaf
43
Typically Hearing
10
9
8
7
6
5
4
3
2
1
0
36
42
48
54
Age (months)
60
66
72
78
Fast Cards Task (Low Set Sizes):
Oral Deaf vs. Typically Hearing Performance
Language in Number Development: Oral Deaf Cognition
Summed mean error on sets of 1, 2, 3, and 4
84
Oral Deaf
44!
Typically Hearing
40
35
30
25
20
15
10
5
0
36
42
48
54
Age (months)
60
66
72
78
84
45
Typically Hearing
Oral Deaf
Fast Cards Task (High Set Sizes): Oral Deaf vs. Typically Hearing Performance
Language in Number Development: Oral Deaf Cognition
Summed mean error on sets of 6, 10, and 14
20
18
16
14
12
10
8
6
4
2
0
36
42
48
54
Age (months)
60
66
72
78
84
Caterpillar Task (Low Set Sizes):
Performance of Oral Deaf vs. Typically Hearing Participants
Language in Number Development: Oral Deaf Cognition
Error (sum of mean error on first attempts at 1-, 2-, and 3-footed
caterpillars)
Oral Deaf
Typically Hearing
46
45
40
35
30
25
20
15
10
5
0
36
42
48
54
Age (months)
60
66
72
78
Caterpillar Task (High Set Sizes):
Performance of Oral Deaf vs. Typically Hearing Participants
Language in Number Development: Oral Deaf Cognition
Error (sum of mean error on first attempts at 5-, 6-, 7-, and
9-footed caterpillars)
84
Oral Deaf
Typically Hearing
47
100.00
90.00
80.00
70.00
60.00
50.00
40.00
30.00
36
42
48
54
Age (months)
60
66
72
78
Language Assessment Task:
Oral Deaf vs. Typically Hearing Performance
Language in Number Development: Oral Deaf Cognition
Language assessment age equivalency
84
Oral Deaf
48!
Typically Hearing
!
100
90
80
70
60
50
40
30
20
10
0
36
42
48
54
Age (months)
60
66
72
78
Executive Function Task:
Oral Deaf vs. Typically Hearing Performance
Language in Number Development: Oral Deaf Cognition
!
Percent correct
84
Oral Deaf
Typically Hearing
49!
Language in Number Development: Oral Deaf Cognition
50!
Two-way analysis of variance tests revealed a significant effect of
hearing/deaf status on executive function (F (1, 54) = 7.59, p = .008) and on language
ability, F (1, 52) = 6.16, p = .016; as well as on performance on the Give-N task, F (1,
59) = 6.21, p = .016; low set sizes of the Fast Cards task, F (1, 57) = 4.76, p = .033;
and the Which-Has-More task, F (1, 51) = 4.14, p = .047. For these tasks, oral deaf
children’s development is delayed, but the development progresses at a similar rate to
that of typically hearing children. However, on low set sizes of the Which-Has-X
task, two-way ANOVAs revealed an interaction between age and hearing/deaf status,
F (3, 59) = 3.64, p = .018, indicating that while oral deaf and typically hearing
children may appear similar at a young age, oral deaf children develop at a slower
rate, taking longer to acquire the same skills.
Thus, according to these ANOVAs alone, it may appear as though language
influences only performance on Which-Has-More, Give-N, low set sizes of Fast
Cards, and low set sizes of Which-Has-X. However, it is important to remember that
these ANOVAs are indicating group-level differences between two two groups with
lots of individual variance within each group. Each oral deaf child has an
idiosyncratic personal aural history consisting of different intervention strategies at
different ages; thus, grouping these individuals together under the title “oral deaf” and
using them to detect the role of language may not be the most effective way of
examining the role of language specifically. Rather than comparing group
performance, the next section takes an approach that allows the role of aural input to
be focused on more accurately.
Language in Number Development: Oral Deaf Cognition
III.
51!
Age-controlled and hearing-controlled comparisons
In order to focus more rigorously on the role of aural input specifically, a
different sort of comparison was needed that would go beyond the group-level
differences in aural input that may actually vary widely among oral deaf individuals.
So, for purposes of focusing on the role of aural input specifically, two
comparison groups were created: One group of participants (n = 84) were matched on
age. For each oral deaf child in this group, there was a typically hearing child of the
same age (within one month). This comparison group will be referred to as the “agecontrolled” group. A second group of participants (n = 52) were independently
matched on months of aural input. For typically hearing participants, aural input was
equivalent to age, but for oral deaf participants, it was calculated as months since a
child’s first hearing intervention. This comparison group will be referred to as the
“hearing-controlled” group.
With these two comparison groups established, oral deaf and typically hearing
members of each group were compared using 2-tailed t-tests based on their
performance on each task. Based on the previous set of results, we expect that oral
deaf and typically hearing children of the same age (in the age-controlled group)
might perform differently. However, contrasting this difference with the difference
between oral deaf and typically hearing children’s performance when aural input,
rather than age, is controlled for, provides crucial information about the role of aural
input. A difference between aural-input-matched oral deaf and typically hearing
populations that is not significant can be interpreted to mean that a typically hearing
x-year-old child performs the same as an oral deaf child who has been hearing for x
Language in Number Development: Oral Deaf Cognition
52!
years. Thus, a significant difference on an age-controlled comparison which
disappears on an aural-input-controlled comparison indicates that aural exposure may
explain the former effect.
Aural input was used for matching rather than language ability itself in order
to be able to utilize a greater number of deaf data points. However, because aural
input predicts language ability, as was shown earlier, this substitute was considered
acceptable as a means of measuring the role of language. Thus, while these results
only indicate the role of aural input in driving number cognition, it may reasonably be
inferred that this is due to aural input driving language driving number development.
The earlier finding that aural input does, in fact, drive language, allows this claim to
be made.
* indicates significance at the .05 level (p ! .05)
** indicates marginal significance (p ! .1)
80
70
60
50
40
30
20
10
0
Age
*
Task and Comparison Population
Hearing Age
*
Language age
Age-Controlled Hearing-Controlled Age-Controlled Hearing-Controlled Age-Controlled Hearing-Controlled
*
Language in Number Development: Oral Deaf Cognition
Months
Oral Deaf
53!
Typically Hearing
100
75
50
25
0
*
Age-Controlled
WHX (high)
*
Age-Controlled
Hearing-Controlled
EF
Task and Comparison Population
Hearing-Controlled
Language in Number Development: Oral Deaf Cognition
Percent Correct
*
Age-Controlled
Hearing-Controlled
WHM
Oral Deaf
54!
Typically Hearing
14
12
10
8
6
4
2
0
Fast Cards (low)
"
Oral Deaf
CAT error (low)
Typically Hearing
Task and Comparison Population
Fast Cards (high)
*
CAT error (high)
55!
Age-Controlled Hearing-Controlled Age-Controlled Hearing-Controlled Age-Controlled Hearing-Controlled Age-Controlled Hearing-Controlled
""!
Language in Number Development: Oral Deaf Cognition
Error (lower indicates better performance)
6
5
4
3
2
1
0
*
Age-Controlled
WHX (low)
*
Age-Controlled
Task and Comparison Population
Hearing-Controlled
Language in Number Development: Oral Deaf Cognition
Knower-Level
Hearing-Controlled
Give-N
Oral Deaf
56!
Typically Hearing
Language in Number Development: Oral Deaf Cognition
57
The p-values of oral deaf versus typically hearing performance for each
matched population are presented below, for each task:
Developmental Factor
Age
Aural Input
Population
Age-Match
Hearing-Match
Age-Match
Hearing-Match
p-value
0.91
0.00*
0.00*
0.78
As expected because these were the factors on which participants were
matched, age-matched participants were insignificantly different in age, but were
significantly different in aural input. Inversely, hearing-matched participants were
insignificantly different in aural input, but were significantly different in age. While
somewhat self-evident, these facts validate the age-matched and hearing-matched
comparison groups as approaches to controlling for only age and only aural input.
Task
Which-Has-X (low)
Which-Has-X (high)
Give-N
Fast Cards (low)
Fast Cards (high)
Executive Function
Which-Has-More (% correct)
Which-Has-More w-score
Caterpillar (low)
Caterpillar (high)
Language Assessment
Population
Age-Match
Hearing-Match
Age-Match
Hearing-Match
Age-Match
Hearing-Match
Age-Match
Hearing-Match
Age-Match
Hearing-Match
Age-Match
Hearing-Match
Age-Match
Hearing-Match
Age-Match
Hearing-Match
Age-Match
Hearing-Match
Age-Match
Hearing-Match
Age-Match
Hearing-Match
p-value
0.01*
0.14
0.02*
0.82
0.00*
0.34
0.09**
0.85
0.04*
0.45
0.00*
0.78
0.00*
0.59
0.05*
0.16
0.96
0.57
0.03*
0.97
0.00*
0.72
Language in Number Development: Oral Deaf Cognition
58
In order to contextualize the outcomes in this table, it may be useful to recall
the following rubric from the Introduction, listing the possible outcomes for each
task:
(1) Performance is significantly different between Oral Deaf and Typically
Hearing participants, and this disparity can be attributed to language
differences.
(2) Performance is significantly different between Oral Deaf and Typically
Hearing participants, and this disparity cannot be attributed to language
differences.
(3) Performance is not significantly different between Oral Deaf and Typically
Hearing participants.
According to the table, all outcomes except for performance on low sit-sizes
of the Caterpillar Task fall under Category (1). In other words, performance on these
tasks was significantly different between oral deaf and typically hearing participants,
and it was shown that this difference was driven by differences in aural input (and,
thus, language).
In contrast, performance on low set sizes of the Caterpillar Task does not
appear to be driven by language: Under neither age-matched nor aural-input-matched
comparison groups did oral deaf and typically hearing children perform significantly
differently on this task. Thus, this task falls under Category (3).
To reiterate, it was predicted that performance on all verbal tasks would be
Language in Number Development: Oral Deaf Cognition
59
driven by language (these tasks would produce Category 1 outcomes), and that
performance on nonverbal tasks would be mixed in some meaningful way between
being driven by language and developing independently of language (a pattern of
Category 1 and Category 3 outcomes). We predicted no Category 2 outcomes.
Results confirmed these predictions of outcomes for each task. To illustrate,
the following graphic contextualizes the outcome of each task into the crosscategorization chart explained in the Introduction and Methods:
Small sets
(likely object-file
system)
Which-Has-X (low)
(1)
Verbal
Fast Cards (low)
(1)
Give a Number
(1)
Nonverbal
Caterpillar (low)
(3)
Large sets
(likely approximate
number system)
Which-Has-X (high)
(1)
Fast Cards (high)
(1)
Which-Has-More
(1)
Caterpillar (high)
(1)
As predicted, all verbal tasks, whether measuring the object-file system or
approximate number system, were driven by language. While this fact may seem
obvious in comparison to more controversial potential for nonverbal number to be
language-dependent, the dependence of verbal number knowledge on language is
crucial in its own right as well. It is important to remember that many are simply not
cognizant of the potential for delaying aural input to affect anything cognitively
Language in Number Development: Oral Deaf Cognition
60
deeper than speech and articulation. Learning the meanings of number words is not
commonly considered to be a language-based task, and this information alone could
be of crucial importance to deaf educators and parents of deaf children.
Concerning nonverbal tasks, it was predicted that outcomes would be
meaningfully mixed between Categories (1) and (3); in other words, that some tasks
would be driven by language and some would be independent of language. These
predictions were confirmed: Development on all nonverbal approximate number
system tasks were significantly different between oral deaf and typically hearing
populations, and this difference was be driven by language. In contrast, such a
difference was not found for nonverbal object-file tasks. In these tasks, oral deaf and
typically hearing children performed similarly, indicating that the object-file system
develops independently of language. Finally, results also confirmed predictions that
no significant differences between oral deaf and typically hearing populations would
be found that could not be explained by differences in aural input. The psychological
implications of these findings will now be discussed individually:
First, as predicted, significant differences were found between oral deaf and
typically hearing populations when age-matched, but not when hearing-matched, on
all verbal tasks. Perhaps more importantly, but also as predicted, oral deaf and
typically hearing performance was also significantly different on both nonverbal ANS
tasks when controlling for age (p < .001 for large set sizes of the Caterpillar task, p =
.03 for Which-Has-More), but not when controlling for hearing. Not only was this the
case in terms of percent correct on Which-Has-More, but also in terms of w-scores,
suggesting that the development of a pattern of correct responses and the extent to
Language in Number Development: Oral Deaf Cognition
61!
which this pattern aligns with the weber fraction of each comparison is also driven by
aural input.
The fact that Executive Function task performance was significant among agematches but not among hearing-matches shows that its development, too, may be
driven by aural input. While this task was originally intended as a cognitive control
measure, its apparent dependence on aural input is perhaps even more illustrative of
the role of language in number cognition: Importantly, the Executive Function Task
results show that even if one were to attribute performance on nonverbal tasks to
executive function, one must then ultimately attribute it to aural input, because it is
this input which is driving executive function development.
The only deviation from the prediction of Category (1) results on all verbal
tasks and nonverbal ANS tasks consisted of age-matched performance on low set
sizes of the Fast Cards task, which was only marginally significantly different
between oral deaf and typically hearing populations. A possible explanation for this is
that the Fast Cards trials (among all trials, both high and low) were randomized and
presented in fast succession, thus requiring participants to switch quickly between
using their object-file and approximate number systems to represent the numerosities.
The integration of these systems is complex and children’s ability to switch between
them is not well understood; evidence suggests that precisely where the switch from
one system to another occurs may be context-dependent. Thus, it is possible that
children were using an analog-magnitude representation of small numerosities, due to
these quantities appearing amongst a stream of larger numerosities, thus confusing
their estimations. Requiring children to switch between systems rapidly do so may
Language in Number Development: Oral Deaf Cognition
62!
have impeded a clean measure of their object-file representations.
However, this task was fortunately one of three tasks measuring the verbal
object-file system, and thus the more robust significance found on Give-a-Number (p
< .001) and low Which-Has-More tasks (p = .01) is robust evidence for the
dependence of verbal object-file development on aural input.
Next, also as predicted, no Category 2 outcomes were found. There were no
significant differences among typically hearing and oral deaf populations which could
not be attributed to differences in aural input. While perhaps obvious, the finding that
no differences in oral deaf cognition are due to factors other than this delayed
language exposure (that the oral deaf are innately cognitively typical other than being
oral deaf) is optimistic in the context of quickly-developing cochlear technologies.
Once technology inevitably allows for earlier implantation of hearing devices, it
seems probable that the oral deaf achievement gap will disappear.
Finally, and perhaps most importantly, age-matched oral deaf and typically
hearing population’s performances on low set sizes of the Caterpillar task was
insignificantly different (p = .96), thus confirming predictions that nonverbal objectfile representations develop independently from language development. While the
mixed evidence regarding nonverbal number development’s dependency on language
development, coupled with recent research suggesting that ANS development may be
language-driven, suggested that this may be the case, measuring nonverbal object-file
representations directly (and in the context of language delays) is a relatively novel
approach.
Language in Number Development: Oral Deaf Cognition
63!
Implications and Future Directions
!
I.
Implications for the Deaf Community
The findings that the object-file system develops independently from language
and that the analog-magnitude system is language-driven have important implications
for basic psychologists, as well as for educators and parents of deaf children.
For deaf educators, the fact that the object-file system develops typically
despite differences in aural input means that this system has important potential to be
harnessed in teaching early number skills to the oral deaf, or to any individual who is
delayed in language development. Unlike processes by which we estimate larger
amounts or magnitudes, processes of individuation in small sets develop at a typical
pace regardless of linguistic factors. This suggests that deaf educators should focus on
tasks that harness object-file representations rather than analog-magnitude ones, and
may have more success in conveying number concepts through using set sizes under
four.
The knowledge that delayed aural input can cause delays in early number
development, which is known to persist in affecting math achievement for many
years, should also be of great interest to parents deciding whether to give their child a
cochlear implant. While this technology in and of itself does not hinder number
development, the 12 months that a child is currently required to wait before receiving
this implant does produce important delays. It may surprise parents, early
interventionists, and teachers that the delays produced by this technology will not
merely affect speech and articulation, as is commonly assumed, or even the
Language in Number Development: Oral Deaf Cognition
64!
significant segment of cognition comprised by verbal knowledge, but even more
fundamentally still, the primitive cognitive underpinnings of our ability to estimate
quantities and magnitudes. Even the fundamental cognitive ability to keep track of
and follow multiple rules, an ability that has been robustly shown to be predictive of
all kinds of later life achievement, is inhibited by delayed aural input.
So, while it may be intuitive for teachers of the deaf to assume that oral deaf
students will primarily struggle with verbal and speech skills, this research provides
cognitive evidence that this is not the case, supporting existing findings from oral
deaf math achievement.
Similarly, while it may be intuitive for parents of children born deaf to assume
that giving their child the capacity to hear and learn spoken English will afford them
the greatest chance at development and educational achievement that is most typical
(most similar to that of a typically hearing child), this research suggests that this is
actually not the case. By delaying cognitive stimulation through aural input for a year,
language development, conceptual development, and executive function development
are all delayed as well.
II.
Implications and Future Directions for Psychology
The analog-magnitude system is thought to be a core cognitive system: Being
an evolutionarily primitive, it is thought to be innate (the mind is born with a
statistically disproportionate sensitivity to learning numerical ideas of quantity and
magnitude) and modular (independent of influences from higher cognition, in the
Language in Number Development: Oral Deaf Cognition
65!
same way that our higher cognition cannot interfere with our lower perceptual
capacities, thus sometimes causing things like optical illusions).
The discovery that analog-magnitude systems are in fact influenced by a
cultural factor like language suggests that the role of language is much more
evolutionarily pivotal than mere expression and communication of pre-existing terms.
In playing a role in shaping these terms themselves, concepts that humans develop the
capacity for holding and manipulating are not limited to those that are beneficial to
the individual, but include those that may have benefitted a collective group. The
development of language and ability to convey ideas in a linguistic format, enabled
by our simple physiological capacities for speech and audition as well as our shortterm memory, thus has profound consequences for abstract thought. The coupling of a
sound with its meaning enables us to think about quantities (four) which are not
currently perceptually present, concepts (fourness) which are too abstract to be
perceptually present in and of themselves, concepts (two-trillion-and-five) which we
may never see embodied in reality, and yet other concepts (negative numbers,
irrational numbers) which can only exist abstractly. Language thus allows humans,
both on developmental and evolutionary scales, to go beyond perceptions and engage
in abstract conceptual thought, making available new abstract concepts. These
concepts are available even when we are not communicating them with another
individual, and even when we are not thinking in verbal terms at all; they change our
cognitive capacity at a very fundamental level, thus broadening the scope and
capacity of human thought in deep and profound ways.
Language in Number Development: Oral Deaf Cognition
66!
The discovery that the analog-magnitude system is in fact influenced by
language calls for either a redefining of this system as not a core cognitive system, or
a redefinition of the designation “core cognitive system.” Such a redefinition need not
do away with modularity as a qualifying factor; perhaps language is a special kind of
higher cognition that is able to influence these lower-level perceptual categories in
ways that other kinds of higher cognition (reason, external knowledge) are not. Thus,
perhaps core cognitive systems are modular except for influences by language.
Alternatively, (or an alternative way of thinking about this), perhaps language
occupies a special role as neither higher nor lower cognition, or as a member of both,
making it a kind of cognitive polyglot which is able to communicate in formats that
are understood by both higher and lower cognition. This would enable language to
serve as a conduit between higher and lower cognitive processes, such as reason and
perception, and enable this crucial interaction.
Further research will have to be done on language’s ability to influence basic
cognitive processes; for example, does this ability extend beyond number to other
purportedly modular core cognitive faculties, such as identification of objects or
agents? Does it extend even beyond these core cognitive faculties to domain-general
learning? Additionally, is human language truly unique in this capacity, or are there
other ways in which higher-level cognition may influence these conceptual building
blocks? Answers to these kinds of questions may help us clarify the boundaries of
core cognition and the role of language.
III.
Implications for Philosophy
Language in Number Development: Oral Deaf Cognition
67!
The notion that the human mind is structured to be eager to impose certain
concepts on its interpretation of the external world is not a new one; it has a long
history in philosophical thought. Some philosophers, such as Descartes, believed that
these concepts were the product of innate ideas endowed in us by a benevolent God,
and therefore were reliable sources of knowledge about the true nature of the world.
Others, such as Hume, thought that they were passive byproducts of our innate
cognitive architecture, in ways that may benefit us but may lead us astray from an
accurate understanding of reality.
Our minds’ predisposed tendency to think in quantitative terms, and to be able
to effortlessly induce numerical ideas, was of particular importance to these
philosophers, because it was number and mathematical thinking that was believed to
be knowable by humans despite these cognitive biases. Number was thought to be a
more objective quality that our minds allowed us uniquely clear cognitive access to.
While the way we process light is limited to a certain range of wavelengths and
brightnesses, and the way we process touch is disproportionately sensitive to painful
sensations that may have been evolutionarily harmful, the way we process number
was thought to correspond to actual quantities in the world in a uniquely accurate
way. Numerical ideas, as well as mathematical-style proofs, were thought to be
capable of being known with a greater degree of certainty than scientific claims,
which were always confounded by the limits of our sensory faculties and cognitive
biases. Kant revolutionarily thought that this numerical knowledge was in fact the
only means by which we could have certain knowledge about the outside world; that
mathematical knowledge of the sort “all 3-sided figures have 3 angles” was the only
Language in Number Development: Oral Deaf Cognition
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reliable source of useful knowledge of the world, unlike of trivial analytic tautologies
(“all triangles have 3 angles”) or our unreliable and uselessly narrow perceptual
capacities (“this thing I’m looking at has 3 angles”).
This idea of the specialness of math and numerical ideas generated a sort of
“math envy” that has persisted today in intellectual thought’s quest for objectivity (at
least within the sciences and Modernist social science approaches). The notion that
our number concepts, too, may be dependent upon our cognitive architecture, whose
development may be informed and distorted by non-innate cultural factors like
language, throws a wrench in this ancient notion that numerical ideas are different
from, or more objective than, other kinds of ideas.
It is only through contemporary methods in cognitive science and Bayesian
statistics that these more basic cognitive biases are able to be empirically identified,
and it is only through an evolutionary cognitive developmental perspective (a relative
newcomer to psychological theory) that they are able to be explained. Through
continued use of these tools, the linguistic dependence of even our most fundamental
concepts may continue to be discovered, thus informing both basic research and
aiding communities for whom these theoretical debates are of practical importance.
Language in Number Development: Oral Deaf Cognition
69!
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