RESEARCH REPORT
Does finger sense predict addition performance?
Sharlene D. Newman1
Received: 25 November 2015 / Accepted: 1 March 2016
� Marta Olivetti Belardinelli and Springer-Verlag Berlin Heidelberg 2016
Abstract The impact of fingers on numerical and math-
ematical cognition has received a great deal of attention
recently. However, the precise role that fingers play in
numerical cognition is unknown. The current study
explores the relationship between finger sense, arithmetic
and general cognitive ability. Seventy-six children between
the ages of 5 and 12 participated in the study. The results of
stepwise multiple regression analyses demonstrated that
while general cognitive ability including language pro-
cessing was a predictor of addition performance, finger
sense was not. The impact of age on the relationship
between finger sense, and addition was further examined.
The participants were separated into two groups based on
age. The results showed that finger gnosia score impacted
addition performance in the older group but not the
younger group. These results appear to support the
hypothesis that fingers provide a scaffold for calculation
and that if that scaffold is not properly built, it has con-
tinued differential consequences to mathematical
cognition.
Keywords Finger gnosia � Cognition � Number �Arithmetic
Introduction
Mathematical competence, like all of cognition, begins
early and has a neurological basis that is itself linked to the
active experiences of children. It is a general and well
accepted fact that the activities that we engage in have a
direct impact on brain development and future cognitive
processing (Greenough et al. 1987). This is particularly
true of children due to the rapid neural development that
takes place. Here, we focus on finger processing and its
relationship to mathematical competence. Because finger
use as well as finger sense has been shown to positively
predict mathematical achievement in children (Fayol et al.
1998; Noel 2005; Chinello et al. 2013; Penner-Wilger et al.
2007, 2008), it is important to understand its precise role in
mathematical cognition. This is especially important
because several studies (Penner-Wilger et al. 2007, 2008;
Fuson et al. 1982; Fuson 1988; Butterworth 1999a, b,
2005) suggest that finger processing may play a role in
setting up the neural networks on which more advanced
mathematical computations are built.
The relationship between fingers and number has
received a great deal of attention recently. It has been
assumed that fingers play a significant role in the devel-
opment of a mature counting system (Fuson et al. 1982;
Fuson 1988; Butterworth 1999a, b, 2005). There are a
number of hypotheses to account for the role of fingers in
number processing: they are a memory aid during counting
(Fuson et al. 1982); they aid in understanding cardinality
(Fayol and Seron 2005); in the development of the one-to-
one correspondence principle (Alibali and DiRusso 1999),
among others. Additionally, it has been suggested that
finger counting habits may influence the way numbers are
represented and processed (Pesenti et al. 2000; Zago et al.
2001; Fias and Fischer 2005; Di Luca et al. 2006; Fischer
Handling editor: Martin H. Fischer, University of Potsdam, Germany.
Reviewers: Marco Fabbri, Second University of Naples, Italy; Ilaria
Berteletti, University of Illinois at Urbana-Champaign, USA.
& Sharlene D. Newman
1 Department of Psychological and Brain Sciences, Indiana
University, Bloomington, IN 47405, USA
123
Cogn Process
DOI 10.1007/s10339-016-0756-7
2006; Domahs et al. 2010; Newman and Soylu 2014; Sato
et al. 2007).
Furthermore, there has been some suggestion that finger
sense may play a role in arithmetic as well as number
processing. A number of studies have confirmed Gerst-
mann’s (1940) findings of an association between finger
agnosia and arithmetic. For example, Reeves and Hum-
berstone (2011) demonstrated that finger sense changed
between the ages of 5 and 7 and that those changes were
related to finger use in arithmetic computation, suggesting
an important role for finger sense in arithmetic. Addition-
ally, Fischer and Brugger (2011) hypothesize that fingers
are important for setting up the space number associations
which have been shown to be extremely important in
mathematical cognition from magnitude processing to
calculation. These studies along with others demonstrate
the importance of fingers in mathematical cognition.
However, the underlying mechanism that supports this
relationship is unclear.
There is a growing body of research that suggests the use
of concrete materials aids classroom learning, particularly in
math (Suh 2007; Thompson 1994; Fuson 1990; Fuson and
Briars 1990). The use of manipulatives is thought to help
students ‘‘think, reason, and solve problems’’ (Burns 1996,
p. 48). They are an additional resource for helping students
construct ideas, giving meaning to mathematical concepts
and subsequently facilitating performance (Sternberg and
Grigorenko 2004). Fingers are, in essence, a manipulative
that is always present and that has a well-connected internal
representation. Fingers are a part of the body, always pre-
sent; they do the manipulating (with other manipulatives
such as counting counters or pieces of fraction pies). They
allow for physical interaction with number (e.g., they can be
moved) which has been shown to enhance memory and
understanding (Glenberg et al. 2004) and because of their
constant availability, experiences with fingers in number
contexts are likely to far exceed other concrete aids. For
example, in a recent study using the iCub child-like robot, it
was found that number knowledge was more efficiently
learned when number words are learned with finger count-
ing as opposed to without finger counting (De La Cruz et al.
2014). If a similar mechanism is at play for children, fingers
may be a good tool to aid number learning.
In order to examine the impact of finger processing on
mathematical competency the current study examined the
relationship between finger sense, arithmetic performance
and general cognitive ability in a group of children between
the ages of five and twelve. The first goal of the current
study was to assess how cognitive ability interacts with
addition performance and finger sense. The general cog-
nitive abilities examined included phonological processing,
short-term and working memory as well as verbal and non-
verbal IQ. These measures were chosen because they have
previously been shown to be correlated with mathematical
performance (De Smedt et al. 2009; Jordan et al. 2010;
Passolunghi and Lanfranchi 2012; Passolunghi and Siegel
2004; Passolunghi et al. 2007; Robinson et al. 2002; Imbo
and Vandierendonck 2007). However, few studies have
explored how all of these factors—age, finger sense, gen-
eral cognitive ability and mathematical ability—interact.
Based on previous work, it was expected that age would
correlate with all factors, but that finger sense and cogni-
tive ability would have independent relationships with
arithmetic performance.
The second aim explored here was to test the hypothesis
that fingers provide a ‘‘natural scaffold for calculation’’
(Jordan et al. 2008). In other words, fingers may provide the
support necessary to build calculation skills; it is founda-
tional to mathematical competency. To explore this
hypothesis, the relationship between age, finger sense and
addition performance was further explored. As Reeves and
Humberstone (2011) reported, finger sense is still develop-
ing during the early elementary school years; however, it
may be expected to be somewhat stable at older ages. Along
with the development of finger sense, addition skill is also
being developed in younger children. A recent study by
Berteletti et al. (2015) found a relationship between sub-
traction performance and finger related activation in
somatosensory cortex. They argued that children with lower
performance engaged finger processing areas more than
children with higher performance. Because age was corre-
lated with subtraction accuracy, this differential involve-
ment of finger processingmay be a function of development.
Therefore, studying both a younger (5–8 years old) and
older group (9–12 years old) will allow for the examination
of the importance of the finger scaffold in both the early
learning of addition as well as the later instantiated addition
skill of older children. Based on previous findings, it was
expected that younger children would show a stronger
relationship between finger sense and arithmetic processing
performance than older children who may be expected to
have developed more mature retrieval strategies.
Methods
Participants
Seventy-six children (5–12 years of age, M = 8.67 ± 2,
36 males) participated in the study for pay. Participants all
attended local schools and had no history of neurological or
psychiatric disorders or diagnosed dyslexia or dyscalculia
as reported by parents. Written informed consent was
obtained from parents and assent from each participant, as
approved by the Institutional Review Board of Indiana
University, Bloomington.
Cogn Process
123
Measures
Finger gnosia
The finger gnosia test is a standard assessment that dates
back to Benton (1955). During the test, participants sat
with both hands palm down on the table in front of them.
They were instructed to close their eyes and to keep them
closed during the entire procedure (eyes were checked
regularly). There were two phases of the test. During the
first phase, the experimenter, with a pointer, touched a
single finger of the left hand in a pre-determined order,
touching each finger (5 trials). After each finger touch the
subject was instructed to indicate by moving the corre-
sponding finger of the other hand (1 point per trial). During
the second phase, the experimenter touched a combination
of two fingers in succession (5 trials) and the participant
was instructed to indicate which two fingers were touched
and the order that they were touched by moving the cor-
responding fingers of the other hand (2 points per trial; 1
point for the correct fingers and 1 point for the correct
order). The score was the total number of points earned
divided by the total possible points. There were 15 possible
points.
Handedness
The Edinburgh Handedness Inventory (Oldfield 1971) was
administered to each participant. Each question was read to
the participant, and they demonstrated how they would
perform the task. For example, for the question which hand
do you use to throw a ball? The participant would be
encouraged to simulate throwing. All subjects were right-
handed.
Digit span
The forward (FDS) and backward digit span (BDS) tasks
were administered to assess short-term and working
memory, respectively. For both, a series of digits were read
to the participant at a constant pace starting with two digits
and increasing by a single digit until failure to recall occurs
twice. For the FDS, participants were told to repeat the
digits in the order read. For the BDS, they were told to
repeat the digits in the reverse order read. The score was
the percent correct.
Word attack
The word attack (Woodcock et al. 2001) task was admin-
istered to assess phonological skills. The initial items
require participants to produce the sounds for single letters.
Afterward, difficulty increases. For the remaining items
they were required to read aloud letter combinations that
are phonically consistent patterns in English but are non-
words or low frequency words. The score was the percent
correct.
Vocabulary
The vocabulary subtest of the Wechsler Intelligence Scale
for Children was administered as a test of verbal IQ. This
test measures verbal fluency, concept formation, word
knowledge and usage. It is an untimed test in which par-
ticipants are read a word and are asked to define it. The
score was the percent correct.
Matrix reasoning
The matrix reasoning subtest of the Wechsler Intelligence
Scale for Children was administered as a test of non-verbal
IQ. This test measures visual processing and abstraction
and spatial perception. Children are shown colored matri-
ces or visual patterns with something missing. The child is
then asked to select the missing piece from a range of
options. The score was the percent correct.
Timed addition test
Participants were presented with 40 single-digit addition
problems and given 1 min to complete as many as they
can. The problems were organized with easy problems
presented first with problems becoming more difficult, with
difficulty being defined by the size of the operands (all 9 or
less). Therefore, the largest magnitude of the answers was
18. No tie problems were presented (e.g., 2 ? 2). The total
percent correct (out of 40) and the number of problems
attempted were examined.
Results
No significant relationship was found between any of the
factors and gender or handedness. As a result, neither was
further considered.
Multiple regression analysis
A stepwise multiple regression analysis using the PHREG
procedure in SAS was performed. The independent vari-
ables examined—age, word attack, finger gnosia, FDS,
BDS, vocabulary and matrix reasoning—were entered into
the analysis to determine which predicted performance on
the timed addition task. The stepwise selection process
resulted in a model with four explanatory variables—age,
word attack, FDS and BDS. The model with these four
Cogn Process
123
variables explained 61 % of the variance [F(4,71) =
28.31, p\ 0.0001, MSE = 0.561, R2 = 0.6147].
Effect of age
Because age is expected to be responsible for a large
portion of the variance in addition performance, a second
analysis designed to explore the impact of age on the
relationship between finger gnosia and addition perfor-
mance examined older and younger children separately.
The subjects were divided into two groups based on age:
older group (N = 42; M = 10.2 ± 1.01), younger group
(N = 34; M = 6.7 ± 1.1). A stepwise multiple regression
analysis was performed on each group separately. For the
older group vocabulary, matrix reasoning and forward digit
span significantly predicted addition performance
[F(1,40) = 5.09, p\ 0.005; accounted for 29 % of the
variance]. For the younger group, age and word attack
predicted addition performance [F(1,32) = 17.29,
p\ 0.001; accounted for 54 % of the variance].
Finally, because one of the primary aims of the study
was to explore the relationship between finger sense and
arithmetic, this relationship was further explored. First, a
correlation analysis was performed with age partialled out
(see Fig. 1). In the full dataset the correlation between
finger gnosia and addition performance was significant
before controlling for age (r = 0.36), after controlling for
age the correlation was only trending (r = 0.2; Table 1).
However, the two factors were correlated in the older group
(r = 0.32, p = 0.04) but not the younger group (r = 0.17,
p = 0.35). Second, to further explore the interaction
between age and addition performance, a regression anal-
ysis was performed with only finger gnosia entered as a
predictor. While this is an atypical analysis, it was
performed to simply explore the data further. Finger gnosia
was found to significantly predict addition performance for
the older group [F(1,40) = 4.41, p\ 0.05; accounted for
10 % of the variance] but not the younger group [F\ 1;
accounted for 3 % of the variance].
Discussion
The primary aim of the current study was to explore
whether finger sense as measured by the finger gnosia test
contributes to arithmetic computation performance in
children. The impact of finger sense on addition perfor-
mance is currently not well understood. Studies have
shown that it predicts later mathematical competency in
children; also imaging studies have found evidence of
finger processing in adults and children during calculation
and when viewing numbers (Berteletti et al. 2015;
Tschentscher et al. 2012). Additionally, a number of
studies have shown a relationship between arithmetic per-
formance and general cognitive ability including working
memory and phonological processing. The findings pre-
sented here provide further insight into the relationship
between these factors and how they impact arithmetic
performance in young children. First, addition performance
was found to be predicted by general cognitive ability,
particularly language processes and short-term memory.
Second, the predictors of addition performance varied as a
function of age group. Finally, the impact of finger sense
varied as a function of age group with it having no pre-
dictive power in the younger group and a modest impact in
the older group.
Previous studies have attempted to link finger process-
ing during arithmetic to finger counting strategies (Imbo
Table 1 Correlation matrix
controlling for age (the top
number is the r value bottom
number p value)
Pearson correlation coefficients, N = 76
Prob[ |r| under H0: q = 0
WA FDS BDS GNOSIA ADD VOCAB MATRIX
WA 1 0.389
0.0006
0.4162
0.0002
0.056
0.63
0.252
0.03
0.179
0.13
0.214
0.066
FDS 1 0.244
0.035
-0.018
0.88
-0.121
0.30
0.083
0.48
0.078
0.51
BDS 1 0.066
0.58
0.312
0.0064
0.225
0.053
0.396
0.0004
GNOSIA 1 0.192
0.0992
0.106
0.37
0.238
0.039
ADD 1 0.244
0.035
0.23
0.041
VOCAB 1 0.295
0.01
MATRIX 1
Cogn Process
123
and Vandierendonck 2008; Reeves and Humberstone
2011). Here the older children (ages 9–12) were not
expected to use finger counting during simple, single-digit
addition. It is actually thought that finger use during
addition is an indication of mathematical deficits in older
children while finger use in younger children is helpful. For
example, Jordan et al. (1992, 1994) found that finger use
was linked to higher accuracy on number combinations in
kindergarten and first-grade students. Those students who
rarely spontaneously used finger counting had poorer per-
formance and typically came from low-income households.
However, by second grade there was a shift in that better
mathematical performance was associated with less finger
use (Jordan et al. 2008) and a greater reliance on retrieval
strategies. These findings may reflect a developmental
trajectory in which finger counting sets the stage for more
advanced skills, but once those skills are acquired finger
counting is no longer needed, so that children who are still
finger counting are the children who have not acquired
those more advanced grade level skills. By analogy, in a
kindergartener, invented spelling (writing ‘‘kitten’’ as
KTTN) is a sign of precocity and readiness to learn to read;
the same behavior in a 4th grader is a negative indicator of
age-appropriate literacy (Treiman and Zukowski 1991).
Again, finger counting during addition performance was
not assessed here. However, it was found that finger sense
better predicted performance in the older children than the
younger children. This suggests that poorer finger gnosia
scores in older children is a better indicator of mathemat-
ical computation deficits than in younger children. Because
both addition skills and finger sense are still developing in
the younger group, finger sense may not be a good pre-
dictor of addition performance at younger ages. However,
both skills should be developed within the older group
(9–12 years old), making the relationship between these
two factors more evident. As mentioned in the introduc-
tion, there is a growing body of research focused on the
association between finger sense and numerical and
mathematical competency, perhaps through the discrimi-
nation of numerical quantities (Halberda and Feigenson
2008; Mazzocco et al. 2011). This previous research along
with the previous studies that demonstrate that finger sense
at younger grades predict math performance later (Fayol
et al. 1998; Noel 2005; Penner-Wilger and Anderson 2013)
support the hypothesis that poorer finger sense in older
children is an indication of significant mathematical
deficits.
The relationship between finger sense and finger
counting has not been well studied. Finger sense has been
found to be correlated with number knowledge which in
turn is essential to mathematical performance and finger
counting appears to be an important and possibly necessary
part of early mathematical calculation skill development.
But how finger sense and finger counting relate to each
other has not been clearly articulated. One possibility is
that finger counting depends on finger sense. Reeves and
Humberstone (2011) suggest that finger counting and finger
sense, and their relations to numerical and mathematical
processing, co-develop but give no information regarding
the causal direction. Finger sense may positively impact
the use of finger counting in young children via two
mechanisms. The first possible route is via motoric pro-
cessing. For example, better finger sense allows for better
fine motor skills which may be necessary for both finger
counting and for counting small entities (like rows of
counters). Finger sense and/or these activities of counting
fingers and things may also foster an increased ability to
individuate the fingers which in turn leads to better finger
counting. In any case it appears that if finger sense is not
developed by a particular age, it can have detrimental
effects on arithmetic performance later. Together this
suggests that finger sense is an important factor in the
development of arithmetic skills. However, the mechanism
that links finger sense to arithmetic is still not understood.
Another, none contradictory, explanation for the dif-
ferential effect of finger sense on the two age groups is that
the younger and older groups are using different strategies
to solve the addition problems. The younger children are
likely using costly counting procedures that heavily rely on
working memory and phonological processing. The use of
such strategies may be related to their under developed
finger processing skills as discussed above. As such, for
younger children general cognitive ability would be
expected to play a larger role. Conversely, older children
may rely more heavily on more automatic procedures
whether they are retrieval from long-term memory or
automated counting procedures (Barrouillet and Thevenot
2013). It should be noted that there is some controversy as
to whether finger processing is involved in these automatic
Fig. 1 Correlation between finger gnosia score and addition
performance
Cogn Process
123
procedures. Barrouillet and Thevenot (2013) argued that
counting strategies cannot be ruled out as a mechanism for
processing small operand, single-digit arithmetic problems,
even in adults. Additionally, studies have demonstrated
automatic recruitment of finger representations when pro-
cessing numerical information (Di Luca et al. 2006; Di
Luca and Pesenti 2008; Badets and Pesenti 2010; Badets
et al. 2010). Therefore, it may be that finger sense plays an
even larger role in addition for older children than younger
children due to the underdeveloped finger sense/use in
younger children; and this is what the results presented
here demonstrate. These differences in strategy use may be
expected to have differing relationships with finger sense.
Interestingly, language factors predicted addition per-
formance here as it has been found to do in previous
studies. Language has been found to be an important pre-
dictor of arithmetic performance, particularly phonology
(De Smedt et al. 2010; Simmons and Singleton 2008), and
meaning-related skills (Aunola et al. 2004). For example,
Geary (1993) hypothesized that developmental dyscalculia
is due to a difficulty in representing and retrieving
phonological information. Also, Krajewski and Schneider
(2009) suggest that phonological awareness allows for the
differentiation of individual words in a number sequence
which supports arithmetic problem-solving. Here, different
aspects of language was found to predict addition perfor-
mance in the younger and older groups with phonological
processing predicting performance in the younger group
and vocabulary in the older group. These differences may
be related to differences in strategy use with phonological
processing being more related to short-term memory pro-
cessing and vocabulary to long-term memory processing.
Limitations
There are some limitations of the current study that should
be noted. Even though the test is a standard assessment
(Benton 1955), the finger gnosia task used may not be
sensitive enough to adequately assess finger sense in young
children. In order to correctly respond during the task not
only does the participant have to ‘‘sense’’ the touch but she
also must generate an internal representation of her
hand(s) and fingers and then map this internal representa-
tion of the hand and fingers onto another representation,
either their opposite hand or a picture of a hand. Thus,
finger sense tasks like the one used here are measuring
more than just the ability to discriminate the finger tou-
ched, they also measure the ability to create an internal
representation and then map it onto another representation
which requires a host of processes including working
memory and spatial processes. In fact, there is a strong
correlation between finger sense and matrix reasoning (a
test of non-verbal reasoning) scores—children with high
finger sense also have higher matrix reasoning scores.
Because these mapping processes may not be developed
fully in the young group, the test may not be appropriate
for younger children. A second limitation is the age range
used. Although there was an older and younger group of
children, having a narrower age range and larger N’s would
provide a clearer picture of the relationship between age,
finger sense and addition.
Conclusions
The current study demonstrates that finger sense does
indeed contribute to arithmetic performance; however, its
direct impact varies with age. Finger sense impacted the
performance in the older group but not the younger group.
It may be that their well-developed finger sense has laid the
foundation for mathematical skills, possibly by facilitating
mapping processes that now allow for fact retrieval to be a
more efficient strategy than the laborious finger counting
strategy. It may also be that variance in finger sense in the
older group is more meaningful because it may differen-
tiate individuals who have finger sense deficits as well as
arithmetic processing deficits. One hypothesis that deserves
greater consideration in future studies is that fingers pro-
vide a ‘‘natural scaffold for calculation’’ (Jordan et al.
2008) such that it may lay the foundation for future
mathematical as well as spatial skills. Support for this
hypothesis comes from studies showing that calculation
skills may actually derive from finger sequencing and from
neuroimaging studies that show that finger and calculation
skills have overlapping neural bases (Ardila 1993; Berte-
letti et al. 2015). The results here also seem to support this
hypothesis. Additionally, the results presented here
demonstrate that low finger gnosia scores in older children
may indicate significant arithmetic deficits, suggesting that
if this ‘‘natural scaffold’’ is not properly developed early
that it can have important consequences later. Further
research exploring those older children with low finger
sense as well as the younger children with high finger sense
may be important to understanding the necessity of finger
processing to mathematical cognition.
Acknowledgments This research was funded by a Grant from
Indiana University (FRSP). I would like to thank Roy Seo, Jessica
Denton, Galen Hartman, Priyanka Ghosh and Taylor Hurst for the
assistance with data collection.
Compliance with ethical standards
Conflict of interest The authors declare that they have no conflict
of interest.
Informed consent Informed consent was obtained from all indi-
vidual participants included in the study.
Cogn Process
123
Ethical approval All procedures performed in studies involving
human participants were in accordance with the ethical standards of
the institutional and/or national research committee and with the 1964
Helsinki declaration and its later amendments or comparable ethical
standards.
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