Mathematics at your fingertips: Testing a finger-training
intervention to improve quantitative skills
JAY, Tim <http://orcid.org/0000-0003-4759-9543> and BETENSON, Julie
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JAY, Tim and BETENSON, Julie (2017). Mathematics at your fingertips: Testing afinger-training intervention to improve quantitative skills. Frontiers in Education, 2, p.
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Original Research
published: 07 June 2017
doi: 10.3389/feduc.2017.00022

Mathematics at Your Fingertips:
Testing a Finger Training intervention
to improve Quantitative skills
Tim Jay1* and Julie Betenson2
1

Edited by:
Ana Lucia Pereira,Ponta Grossa State University, Brazil
Reviewed by:
Ann Dowker,
University of Oxford, United Kingdom
Craig Speelman,
Edith Cowan University, Australia*Correspondence:
Tim Jayt.jay@shu.ac.uk
Specialty section:
This article was submitted to
Educational Psychology,
a section of the journal
Frontiers in Education
Received: 13 February 2017
Accepted: 04 May 2017
Published: 07 June 2017
Citation:
Jay T and Betenson J (2017)
Mathematics at Your Fingertips:
Testing a Finger Training Intervention
to Improve Quantitative Skills.
Front. Educ. 2:22.
doi: 10.3389/feduc.2017.00022

Frontiers in Education | www.frontiersin.org

Sheffield Hallam University, Sheffield, United Kingdom, 2 University of Bristol, Bristol, United Kingdom

Previous research indicates that the use of fingers as representations of ordinal andcardinal number is an important part of young children’s mathematics learning. Further
to this, some studies have shown that a finger training intervention can improve young
children’s quantitative skills. In this article, we argue that fingers represent a means forchildren to connect different external representations of number (including verbal, symbolic, and non-symbolic representations). Therefore, we predicted that an intervention thatcombined finger training with experience playing games involving multiple representations
would lead to greater increases in quantitative skills than either aspect of the intervention
alone. One hundred and thirty-seven children aged between 6 and 7 years old took partin an intervention study over the course of 4 weeks. The study tested the impact of fivedifferent conditions on participants’ quantitative skills, their finger gnosis, and their ability
to compare magnitudes of two non-symbolic representations of number. Relative to acontrol group, those children receiving a finger training intervention saw gains in finger
gnosis skills (the ability to differentiate fingers when touched, without visual cues). Thosechildren who played number games saw an increase in their non-symbolic magnitude
comparison skills. However, only those children who experienced both aspects of theintervention saw increases in quantitative skills, which were assessed using an instrument
informed by Gelman and Gallistel’s (1978) five principles of counting. The findings showthat a finger training intervention, when combined with intensive exposure to multiple
representations of number can support young children’s development of quantitativeskills. This adds to evidence in the literature regarding the role of fingers in children’smathematics learning and may have implications for pedagogical approaches.
Keywords: numeracy, quantitative skills, finger gnosis, intervention studies, counting

INTRODUCTION
Finger gnosis (sometimes referred to alternatively as “finger sense,” or “finger localization”) is theability to mentally represent and differentiate the fingers (Gerstmann, 1940). It is generally indexed
by children’s ability to tell without looking which fingers have been touched. Studies have shown that
there is a relationship between finger gnosis and quantitative skills in young children. However, themechanism through which fingers and arithmetic connect to one another is not yet fully understood,
and there have been only a small number of studies that have demonstrated a causal relationship.
In this article, we make the case that fingers are used by children as a means to connect other1

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representations of number to one another, thus playing a partin children’s developing quantitative skills. This article reports a
study designed to test a two-part intervention, bringing together
work to improve children’s coordination and sensing of their fingers with work to improve children’s ability to translate between
different representations of number through games. We predictthat the combined intervention will be more effective in promoting arithmetic fluency than either aspect carried out in isolation,
as the benefit of finger training is to give children a more efficientmeans to bridge among multiple representations of number.
This section first sets out the evidence for a relationship between
finger gnosis and quantitative skills, together with some discussionof a possible theoretical framework connecting these phenomena.
We then describe the intervention tested in this study, designed tosupport children’s developing understanding of number.

Fingers are used as indicators of cardinal numbers (Brissiaud,2003) and to point at objects when counting a set (Gallistel andGelman, 1992). Alibali and DiRusso (1999) investigated the roleof the fingers in counting a set of objects in more detail. They
found that when children were prevented from using their fingers
when counting a set of objects, they were more likely to makeerrors involving a loss of coordination between number words
and items counted. Thus, it appears that fingers may function as abridge between different mental representations of number.
Further evidence for the functional hypothesis comes from thestudy by Gracia-Bafalluy and Noël (2008), who carried out anintervention study to test the effect of finger training on young
children’s numeracy abilities. In their study, children were trained
to differentiate between their fingers in four activities: following acolored pathway with a particular finger with a similarly colored
sticker on it; pointing at particular colored circles with particularfingers; following a sequence of colors on a keyboard with thesame color-coded fingers; and the final task included performingstrong grips between the thumb and each other finger on the hand.
Gracia-Bafalluy and Noël showed that children who had received
the finger training intervention scored more highly on measuresof finger gnosis. Their results also demonstrated improvements inordinality judgments, counting fingers, and subitizing skills thatwere greater than their peers who did not receive finger training.
Moeller et al. (2011) discussed two accounts of the role offinger counting; from a neurocognitive perspective, and from amathematics education perspective. Both perspectives adhere to
the functional hypothesis of finger gnosis and quantitative skills
described here. However, from the neurocognitive perspective,
finger-based numerical representations are integral to numericaldevelopment, while from the mathematics education perspective
finger counting is often a starting point in representing number
but should be replaced with mental representations over time. The
development of an intervention that encourages finger gnosis toincrease quantitative skills makes sense from either perspective.
However, from the neurocognitive perspective, such an intervention would work by developing lasting connections between
finger representations and other symbolic and/or non-symbolic
representations of number, while from a mathematics education
perspective, the intervention would use finger representations totemporarily bridge between other representations so that a directconnection could be made more easily.

Evidence for an Association between
Finger Gnosis and Arithmetic Fluency

The majority of evidence for an association between finger gnosis
and arithmetic fluency is correlational, but this evidence comesfrom a number of studies. Fayol et al. (1998) and Marinthe et al.
(2001) report that measures of finger gnosis taken at the age of
5 years are excellent predictors of numerical ability 3 years later.
Noël (2005) reports that measures of finger gnosis taken whenchildren were 6 years old predicted scores on numeracy ability,
but not reading ability tests, 15 months later. The predictive powerof finger gnosis for later numerical ability is generally explainedwith reference to the localization hypothesis or to the functional
hypothesis.

Localization Hypothesis

The relationship between finger gnosis and numerical ability
may simply be a result of the fact that the part of the brain that
responds to number lies in close proximity to the area that is
activated whenever subjects perform pointing and grasping
activities. fMRI studies have provided compelling evidence ofsuch a link between finger movements and response to number.
Of the three parietal circuits described by Dehaene et al. (2003)
that relate to number sense, two are in close proximity to the area
responsible for finger activity. Simon et al. (2002) note that thehorizontal segment of the intraparietal sulcus area was activatedboth when subjects were performing mathematical tasks, andwhen carrying out pointing and grasping tasks. A later study byAndres et al. (2012) analyzed fMRI scans of adult brains and also
found evidence to suggest that the circuits in the brain which
involve finger representation were an intrinsic component ofarithmetic operations in adults.

Development of an Intervention to
Improve Quantitative Skills

The literature reviewed above provides support for a functional
relationship between finger movements and quantitative skills.
More specifically, it appears that children’s fingers may function as abridge, or mediator, between other verbal and symbolic representations of number. This leads us to posit the idea that an intervention
to improve quantitative skills may be more effective if it combines
finger training with other activities that involve other (verbal,
symbolic, and non-symbolic) representations of number.
There is some evidence that games involving symbolic andnon-symbolic representations of number can support thedevelopment of quantitative skills in young children. Siegler andRamani (2008), for example, found that when children played

Functional Hypothesis

Butterworth (1999) argues for a functional relationship between
finger gnosis and numerical ability. Evidence for this comes froma number of sources. Butterworth (1999) refers to evolutionary
evidence to suggest that our use of the base 10 system is due to thefact that we have 10 fingers. Fingers are typically used by children
to support the learning and recitation of the count sequence—thefingers on the right hand used to represent the numbers one tofive, and the left to represent six to ten (Sato and Lalain, 2008).

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a simple numerical board game for four 15-min sessions, theirnumerical estimation abilities improved. Skwarchuk et al. (2014)
found that parental reports of children’s exposure to games athome that involve number predicted children’s performance ina non-symbolic arithmetic test. Studies such as these have notexplicitly promoted finger training, although fingers are certainly
used in many games. However, given that games like thesegenerally involve children making connections between multiple
representations of number (matching the number of dots on a diewith a number of moves on a board, for example), they represent
a promising source of activity to combine with a finger training
intervention.
The motivation to research novel interventions to support
young children’s numerical understanding derives from researchfindings showing that a secure foundation of quantitative skills
is essential for children to succeed in their later mathematics
learning (Jordan et al., 2003). In turn, achievement in mathematics is associated with broader academic and economic successin later life (Butterworth et al., 2011). Successful interventions
to support young children’s quantitative skills must account forthe complexity of the thinking and learning required. Dowker(2008) has shown that individual difference in arithmetic ability
is best explained with a componential model of expertise and thatan intervention that addresses the particular components that achild is experiencing difficulty which has the best chance of success. However, there has, to date, been little research of potential
interventions that account for possible interactions between suchcomponents. This is a potentially rich seam, as previous research
has shown that such interactions are an important aspect of children’s mathematics learning (Mundy and Gilmore, 2009; LeFevre
et al., 2010).

touch the middle finger of the right hand (3) to the first fingerof the left hand (7).
• Pressing on fingers 1, 2, 3…., 10 for the same number of seconds.
• A group of counters is put in front of each pupil and they must
guess how many. Then, they count using the matching finger(third finger for a set of three, for example).
• Hold up fingers to represent a calculation—show 6 + 2 = 8, or
7 – 3 = 4, for example, by raising or lowering fingers to add or
subtract from an initial set.
• Matching finger representations to a number pointed to on anumber line—e.g., 34 would be 10, 10, 10, and 4 fingers.
• Draw numbers 1, 2, 3, 4, 5 large, or draw maze lines from top
left to bottom right of page. Children follow numbers andmazes with different fingers.

Number Games Activities

Each session began with the teacher or researcher explaining
and demonstrating a different game and the pupils playing inpairs wherever possible. The teacher and other adults in the class
moved around the groups to encourage the pupils to verbalize
the numbers they were seeing and to ensure that the rules of thegames were understood and being followed. Different games wereused during each session:• Dominoes: Used for matching equal sets of dots; or for finding
combinations that add to a given number.
• Playing cards: Used for “snap” game—matching same numberof symbols; or for a memory game finding pairs when the cards
are face-down.
• Snakes and ladders board game.
• “Smiley face” game: A counter is placed on a template of a facewhen the total from two dice being thrown is closer to 10, andtaken away if closer to 0.
• “Shut the box”: 2 dice are thrown and pupils have to turn overany of their 1–9 cards to make the same total.

The Present Study

An intervention study was designed in order to test the hypothesisthat a combined finger training and number games intervention
would be effective in improving children’s quantitative skills, andmore effective than either intervention alone.
The intervention designed for this study was based on thoseused in studies described above (particularly, Gracia-Bafalluy andNoël, 2008; Siegler and Ramani, 2008; Skwarchuk et al., 2014) andcomprised the following activities.

MATERIALS AND METHODS
DesignA between-groups quasi-experimental design was employed inorder to compare five different conditions:Finger Gnosis Activities• Teacher-led finger training intervention.
• Teacher-led symbolic number games intervention.
• Teacher-led finger training and symbolic number games combined intervention.
• Researcher-led (Julie Betenson) finger training and symbolic
number games combined intervention.
• Control condition; teacher-led business-as-usual.

Each session began with the teacher demonstrating, and thepupils joining in with, various finger movement activities.
The content varied across sessions but included a combinationof the following activities designed to improve children’s recognition of the cardinal and ordinal properties of number andstrengthening links between these and the visual and physicalrepresentations given by the fingers:

All conditions, except for the control condition, involved eight
30-min sessions; two sessions per week for 4 weeks. Two days of
training was given to teachers in participating schools prior to
the study to explain the rationale for the experiment and to giveteachers some experience of the intervention activities describedabove. During the intervention, the researcher led the first sessionof the week for all the groups except the control group. The teacher
led the second session of the week, apart from the researcher-led• Counting 1, 2, 3…, 10 and 10, 9, 8……., 1 verbally together
with representations using fingers.
• Counting in 2s, 5s, and 10s with fingers.
• “Show me” activity. The teacher says “show me 7” (for example), and children show 7 fingers (using numbers 1–10).
• Matching fingers from the left hand with fingers on the righthand. “Match 3 to 7” for example, would require children to

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group where both sessions were delivered by the researcher. Thisadditional input from the researcher was designed to remind theteachers of the activities and suitable mathematical language touse during the sessions, as had been practised during the trainingdays.
In line with previous research, we expected the finger training intervention to lead to improvement in finger gnosis scores(Gracia-Bafalluy and Noël, 2008), and the number games intervention to give rise to improvements in non-symbolic arithmetic
scores (Skwarchuk et al., 2014). We expected all groups bar thecontrol group to show improvements in quantitative skills, withthe highest level of improvement expected for those in the combined finger training and number games groups.

A further set of measures were combined so that they could
be administered to children in groups, as a series of pencil-andpaper tests, as follows:

Quantitative Skills Tests

Number system knowledge was tested using an instrument
based on the study by Gelman and Gallistel’s (1978) five implicit
principles of counting. The first page (count) required the pupil
to count numbers of objects which involved the one-to-one correspondence principle where “one” and “two” are assigned to eachcounted object, the abstraction principle which allows objects ofany kind to be collected together and counted and the cardinality
principle where the final word tag defines the number of items
counted. The second page (dice) involved the recognition andthe adding together of regular dot arrays displayed as dice. This
activity also involved the one-to one correspondence, abstraction,and cardinality principles. The third page (number) included theidentification of the larger number of two, the ordering numbers
up to 102 and the placing of different numbers in the correct order
on a number line. This was based on the stable order principle
where the order of the word tags does not vary between sets ofnumbers. The fourth page (sequencing) involved the completionof number sequences going forwards and backwards in ones,
twos, fives, and tens. This also used the stable order principle. The
final page (manipulation) involved splitting numbers into theircomposite parts and creating a larger number from a combination of two or three smaller numbers. This incorporated the orderirrelevance principle where numbers can be put together in any
sequence to make a given tagged number. The test pages usedboth symbolic and non-symbolic representations of number andwere arranged on five different sheets of paper. One minute wasallowed for completion of each page. A maximum score of 126
was possible on these five pages. Although the pages tested different aspects of counting, it was expected that there would be astrong correlation between the scores for each of the five pages, aseach incorporated the five principles of counting. The tasks were
all piloted and refined with children of the same age as the sampleof this study, and in collaboration with experienced teachers.

Participants

One hundred and thirty-seven children aged 6–7 years old took
part in the study. They were drawn from three primary schools ina city in the South of England. Other than the age of the children,no specific criteria were used during recruitment other than an
enthusiasm to take part in the research. The three schools are alllarger than average sized primary schools, with pupils of similar,
diverse, ethnic backgrounds. The use of three schools allowed
for five different classes to be randomly allocated different elements of the intervention program in order to reduce selection
bias (see Table 1).

Instruments and Measures

A set of measures were taken from all participants both before
and after the intervention sessions took place, in order to assess
different aspects of finger gnosis, symbolic number sense, andarithmetic fluency.

Finger Gnosis Testing

The finger gnosis test was administered on a one-to-one basis
using a task adapted from the study by Gracia-Bafalluy andNoël (2008). Each participant was asked to put their hand flat on
the table inside a box so that the participant could not see theirfingers. The researcher then lightly pressed the pupil’s fingers in apredetermined non-sequential order so that the pupil could say
the number corresponding to the finger which had been touched.
Thirty trials were completed in the same manner. The same set oftrials was used for each pupil in order to ensure consistency andto ensure no advantage was gained from a particular finger beingpressed more often than others. Participants’ responses werevoice recorded so that they could be checked and collated after
the testing had taken place. A correct answer was scored as 1 andtherefore a maximum total of 30 could be achieved on this test.

Magnitude Comparison Test

A 1 -min paper-and-pencil test of magnitude comparison wasused following a format from the study by Nosworthy et al.
(2013). Pupils were given 1 min to compare 20 pairs of dot arrays
and to tick the larger set of dots each pair. The differences between
the numbers of dots in each pair varied between one and six dots.
The test was designed as a simple accuracy measure giving amaximum total of 20 marks.

Procedure

All pupils completed the group-administered mathematics
achievement tests, which consisted of numeration and calculation
tests, and the magnitude comparison tests, prior to intervention
in January 2014. These were delivered in their usual classroom
space with their teacher present to reduce any possible effects on
performance for children who found change in personnel or surroundings distracting. The finger gnosis testing was administeredindividually in a quiet space outside the children’s classroom used

TABLE 1 | Five experimental groups.
School 1

School 2

School 3

Class 1, 28
pupilsClass 2, Class 3, 27
23 pupils pupils

Class 4, 28
pupilsClass 5, 27
pupilsTeacher-led finger
training andnumber games

Control

Teacher-led
numbergames

Researcher-led
finger training andnumber games

Teacher-led
finger training

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revealed a significant effect of condition (F4, 128 = 16.71, p < 0.0005).
Post hoc tests showed that both versions of the combinedintervention (teacher-led and researcher-led) led to greater
improvements in quantitative skills than the other three conditions, which did not differ from one another (see Figure 1).
The two versions of the combined intervention did not differ
significantly from one another in terms of improvement inquantitative skills.
In order to calculate an effect size for improvement in quantitative skills, the two combined intervention groups were combined,
and compared with the three other groups combined; Hedges’
g = 1.32, a very large effect. See Table 2 for descriptive statistics
for the combined groups.
In order to determine whether the finger training aspect of
the intervention had been effective in improving finger gnosis
scores, groups that received finger training were combined andcompared with those that did not. Descriptive statistics can beseen in Table 3, and an independent t-test revealed a significant
difference in improvement in finger gnosis scores (t = 2.53,
df = 131, p = 0.013).
In order to determine whether the number games aspect of theintervention had an effect on non-symbolic magnitude comparison, groups that received the number games intervention werecombined and compared with those that did not. Descriptive statistics can be seen in Table 4, and an independent t-test revealed afor group work. This would reduce distraction from noises within
the classroom and yet to be in a space which was familiar to thestudents and therefore aid confidence. All tests were repeated after
the intervention sessions had been completed in March 2014.

RESULTS
Analysis of Pretest Data

The set of five tests used to measure quantitative skills showeda high level of reliability (five items; Cronbach’s α = 0.814).
Therefore, subsequent analysis used a composite “quantitativeskills” score generated by adding scores from the five components.
There was a significant positive correlation between finger gnosis and quantitative skills at pretest (r = 0.33, n = 133, p < 0.0005),
in line with previous research. There were also significant
positive correlations between quantitative skills and magnitude
comparison (r = 0.37, n = 133, p < 0.0005), and between finger
gnosis and magnitude comparison (r = 0.171, n = 133, p = 0.05).
However, the correlation between finger gnosis and magnitude
comparison disappeared when quantitative skills were partialedout (r = 0.058, n = 133, p = 0.511).

Analysis of Posttest Data

A one-way ANOVA was used to compare improvement in quantitative skills between the five experimental conditions. This

FIGURE 1 | Improvement in numeracy score by experimental group.

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Prior to the intervention taking place, the pretest data showeda correlation between finger gnosis and number sense. This supports previous findings from the study by Fayol et al. (1998) andAndres et al. (2012). The findings do not fully corroborate thefindings of Gracia-Bafalluy and Noël (2008), who found that an
8-week finger training intervention alone improved quantification skills in a sample of 6–7-year-old children (approximately thesame duration and age-range as in the current study). A possible
explanation for this difference is that Gracia-Bafalluy and Noëlselected participants who had poor finger gnosis at the outset of
their study, while the present study included participants with afull range of initial levels of finger gnosis. However, the findingspresented here do agree with the main findings of Gracia-Bafalluy
and Noël, in that a finger training intervention—when combinedwith the number gains intervention—did lead to gain in finger
gnosis, and that these gains were accompanied by gains in quantitative skills.
The findings of the present study do not fully align withthose of the study by Siegler and Ramani (2008), Skwarchuk
et al. (2014), and others who have found that playing games
involving symbolic representations of numbers can improvechildren’s numerical knowledge. However, Siegler and Ramani(2008) worked with a sample of low-income children with lowlevels of numerical knowledge at the outset of their experiment,
which again differed from the range of participants included in
the present study. Again, though, in combination with the finger
training, the number games intervention did lead to gains inquantitative skills.
The findings presented here suggest that for an intervention to be successful in increasing children’s quantitativeskills—when the children are starting within the normal rangeof ability—then the intervention should involve a combinationof number representations, rather than one particular set ofrepresentations.
Confidence in the above interpretation is added by the factthat the finger training intervention (but not the number games
intervention) was shown to improve participants’ finger gnosis
scores, and the number games intervention (but not the finger
training intervention) was shown to improve non-symbolic
magnitude comparison scores. This supports the argument thatwhile both aspects of the intervention have a potential role to playin supporting children’s learning, it is only in combination thatthey can be shown to improve children’s quantitative skills. We
argue that this provides evidence for the functional hypothesis,
regarding the relationship between finger gnosis and quantitativeskills (Butterworth, 1999), whereby fingers act as a bridge, ormediator, between other representations of number.

TABLE 2 | Improvement in quantitative skills—combined intervention
compared with other groups.
Condition

N

Mean

SD

SE

Combined intervention (researcher-led andteacher-led)
Other groups combined (control, finger training
only, number games only)

55

19.80

9.02

1.22

78

8.56

8.11

0.92

TABLE 3 | Improvement in finger gnosis score—those that received finger
training compared with other groups.
Condition

N

Mean

SD

SE

Groups that received finger training
Other groups combined (control, number
games only)

82
51

1.90
0.16

4.26
3.13

0.47
0.44

TABLE 4 | Improvement in magnitude comparison score—those thatreceived the number games intervention compared with other groups.
Condition

N

Mean

SD

SE

Groups that received number games
Other groups combined (control, finger training only)

83
50

3.08
1.3

4.30
4.03

0.47
0.57

significant difference in improvement in magnitude comparison
scores (t = 2.38, df = 131, p = 0.019).

Summary

The results show that the finger training aspect of the intervention
was effective in improving participants’ finger gnosis scores, but on
its own was not effective in improving scores on the quantitativeskills test. Similarly, the number games aspect of the intervention
was effective in improving non-symbolic magnitude comparison
scores, but on its own was not sufficient to improve quantitativeskills. The two versions of the intervention that combined boththe finger training and number games aspects were successful inimproving participants’ quantitative skills relative to controls, andwith a large effect size.

DISCUSSION AND CONCLUSION
The findings show that the combined intervention, incorporating
both finger training and symbolic number games, gave rise tosignificant improvements in participants’ numeration scores.
Neither intervention alone had an effect on numeration scores.
This is an important and original contribution to knowledge inthis field, as this combination of interventions has not been tested
before, to our knowledge. This finding suggests that children’sdeveloping number sense is best supported by experience of a
combination of representations of number—in this case including fingers plus verbal, symbolic and non-symbolic representations—rather than by a particular set in isolation. Confidence inthe finding is added by the fact that the intervention led by a class’s
usual teacher showed a similar increase in number sense as did
the group led by the researcher.

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Multiple Components of Numerical
Understanding

Further consideration is needed here, of possible mechanisms
to explain the fact that the finger training and number games
interventions led to significant increases in quantitative skills
when combined, but not in isolation. It will be useful to draw
on previous research relating to the complexity of numerical
understanding, and its componential nature.

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One possibility is that the effects were additive, and only
reached significance in combination. This is somewhat unlikely
as each intervention in isolation led to levels of quantitative skills
that were very close to those of the control group (Figure 1).
However, although differences were not significant, the meanscores of the finger training-only group and the number gamesonly group were higher than that of the control group, and so it
is not possible to discount this possibility without replication of
the current study.
A second possibility is that the combined intervention led tobetter results as it was more likely to match children’s particularneeds. Dowker (2005, 2008) has shown that there are several
components involved in children’s developing understandingof number and arithmetic and that intervention is most effective when it addresses the particular component that child is
experiencing difficulty with. In the case of the current study, it ispossible that some children may have needed more intervention
in finger gnosis and others in symbolic number manipulation or
magnitude comparison.
A third possibility is that the combined intervention helped
children to make connections between representations of
number. This possibility follows from the functional hypothesis
regarding the relationship between finger gnosis and quantitativeskills. Children generally need explicit exposure to relationships
between numerical phenomena or relationships in order tointernalize them (Fuson, 1986). It may be that the combination ofactivities in the intervention helped make relationships between
different representations of number for participating children.
This hypothesis would place the current study within a growing
body of work showing that children often find it difficult to makeconnections between different aspects of number. Goffin andAnsari (2016), for example, show that children’s judgments ofcardinality and ordinality of number independently predict individual differences in arithmetic fluency, and that there is a lackof relationship between them. Similarly, De Smedt et al. (2013)
noted a lack of relationship between skills in processing symbolicand non-symbolic representations of number. Further work isneeded in order to determine which relationships are necessary
for the development of expertise with number, and how children
experience barriers and enablers for these in their learning.

therefore not possible to know whether the gains in quantitativeskills demonstrated by the two groups participating in the combined intervention would have persisted long enough to show
an effect on a delayed test. If an intervention such as this is to
be useful in a school context then it will be important to show
both that gains persist and that they contribute to a more flexible
foundation for further learning.
Despite the limitations of the study, we argue that it has provided promising evidence that a combined finger training andnumber games intervention can contribute to young children’squantitative skills and their developing mathematical understanding. We understand that further research will be needed inorder to fully determine the underlying mechanisms by which theinterventions leads to gains in skill, and to add confidence in theeffectiveness of the intervention, but argue that sufficient evidence
has been gained from this study to warrant such further work.

Conclusion

This study has shown that an intervention that combines finger
training with number games can improve quantitative skills
among 6–7-year-old children. It supports the findings of previous
research arguing for a functional relationship between finger gnosis and numeracy. We argue that this study provides evidence that
fingers represent a means for children to bridge between other(verbal, symbolic, and non-symbolic) representations of number
and that this contributes to children’s developing understanding.
The large effect size suggests that with further refinement andreplication, the combined finger training and number games
intervention could be a useful tool for teachers to use to support
children’s developing understanding of number.

ETHICS STATEMENT
The study was approved by the ethics committee of the Graduate
School of Education, University of Bristol. Opt-out consent was
gained from all parents of children who participated. Informed
consent was gained from head teachers and classroom teachersof all children who participated.

AUTHOR CONTRIBUTIONSLimitations

The study reported in this article was carried out as part ofDr. Betenson’s doctoral studies at the University of Bristol,supervised by Dr. Jay. Dr. Jay adapted the article from­Dr. Betenson’s thesis, carrying out a reanalysis of data and­additional literature review.

Each of the five experimental groups comprised children who
normally worked together as a class. This means that there may
have been unobserved intra-cluster factors that affected learningand performance. For example, children in one class could conceivably respond more positively or more flexibly to an intervention than those in another class, with another teacher. A future
fully randomized study could address this issue and provide moreconvincing evidence for the effectiveness of the intervention.
A second limitation relates to the fact that posttests werecarried out soon after the last session of the intervention. It is

FUNDINGThe research reported in this article was carried out as part of thesecond author’s doctoral study, funded by the UK Economic andSocial Research Council at the University of Bristol.

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Conflict of Interest Statement: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could beconstrued as a potential conflict of interest.
Copyright © 2017 Jay and Betenson. This is an open-access article distributed under
the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s)or licensor are credited and that the original publication in this journal is cited, in
accordance with accepted academic practice. No use, distribution or reproduction ispermitted which does not comply with these terms.

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