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

sdnewman@indiana.edu

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.

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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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