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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

Specialty section: This article was submitted to Educational Psychology, a section of the journal Frontiers in Education

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 is permitted which does not comply with these terms.

Previous research indicates that the use of fingers as representations of ordinal and cardinal 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 for children to connect different external representations of number (including verbal, symbolic, and non-symbolic representations). Therefore, we predicted that an intervention that combined 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 part in an intervention study over the course of 4 weeks. The study tested the impact of five different conditions on participants’ quantitative skills, their finger gnosis, and their ability to compare magnitudes of two non-symbolic representations of number. Relative to a control group, those children receiving a finger training intervention saw gains in finger gnosis skills (the ability to differentiate fingers when touched, without visual cues). Those children who played number games saw an increase in their non-symbolic magnitude comparison skills. However, only those children who experienced both aspects of the intervention saw increases in quantitative skills, which were assessed using an instrument informed by Gelman and Gallistel’s (

Finger gnosis (sometimes referred to alternatively as “finger sense,” or “finger localization”) is the ability to mentally represent and differentiate the fingers (Gerstmann,

This section first sets out the evidence for a relationship between finger gnosis and quantitative skills, together with some discussion of a possible theoretical framework connecting these phenomena. We then describe the intervention tested in this study, designed to support children’s developing understanding of number.

The majority of evidence for an association between finger gnosis and arithmetic fluency is correlational, but this evidence comes from a number of studies. Fayol et al. (

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 of such a link between finger movements and response to number. Of the three parietal circuits described by Dehaene et al. (

Butterworth (

Further evidence for the functional hypothesis comes from the study by Gracia-Bafalluy and Noël (

Moeller et al. (

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 a bridge, 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 and non-symbolic representations of number can support the development of quantitative skills in young children. Siegler and Ramani (

The motivation to research novel interventions to support young children’s numerical understanding derives from research findings showing that a secure foundation of quantitative skills is essential for children to succeed in their later mathematics learning (Jordan et al.,

An intervention study was designed in order to test the hypothesis that a combined finger training and number games intervention would be effective in improving children’s quantitative skills, and more effective than either intervention alone.

The intervention designed for this study was based on those used in studies described above (particularly, Gracia-Bafalluy and Noël,

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

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 right hand. “Match 3 to 7” for example, would require children to touch the middle finger of the right hand (3) to the first finger of 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 a number 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 and mazes with different fingers.

Each session began with the teacher or researcher explaining and demonstrating a different game and the pupils playing in pairs 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 the games were understood and being followed. Different games were used 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 number of 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 face when the total from two dice being thrown is closer to 10, and taken away if closer to 0.

“Shut the box”: 2 dice are thrown and pupils have to turn over any of their 1–9 cards to make the same total.

A between-groups quasi-experimental design was employed in order to compare five different conditions:

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.

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 give teachers some experience of the intervention activities described above. During the intervention, the researcher led the first session of the week for all the groups except the control group. The teacher led the second session of the week, apart from the researcher-led group where both sessions were delivered by the researcher. This additional input from the researcher was designed to remind the teachers of the activities and suitable mathematical language to use during the sessions, as had been practised during the training days.

In line with previous research, we expected the finger training intervention to lead to improvement in finger gnosis scores (Gracia-Bafalluy and Noël,

One hundred and thirty-seven children aged 6–7 years old took part in the study. They were drawn from three primary schools in a 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 all larger 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

School 1 | School 2 | School 3 | ||
---|---|---|---|---|

Class 1, 28 pupils | Class 2, 23 pupils | Class 3, 27 pupils | Class 4, 28 pupils | Class 5, 27 pupils |

Teacher-led finger training and number games | Control | Teacher-led finger training | Teacher-led number games | Researcher-led finger training and number games |

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, and arithmetic fluency.

The finger gnosis test was administered on a one-to-one basis using a task adapted from the study by Gracia-Bafalluy and Noël (

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

Number system knowledge was tested using an instrument based on the study by Gelman and Gallistel’s (

A 1 -min paper-and-pencil test of magnitude comparison was used following a format from the study by Nosworthy et al. (

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 administered individually in a quiet space outside the children’s classroom used for group work. This would reduce distraction from noises within the classroom and yet to be in a space which was familiar to the students and therefore aid confidence. All tests were repeated after the intervention sessions had been completed in March 2014.

The set of five tests used to measure quantitative skills showed a high level of reliability (five items; Cronbach’s α = 0.814). Therefore, subsequent analysis used a composite “quantitative skills” score generated by adding scores from the five components.

There was a significant positive correlation between finger gnosis and quantitative skills at pretest (

A one-way ANOVA was used to compare improvement in quantitative skills between the five experimental conditions. This revealed a significant effect of condition (_{4, 128} = 16.71,

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’

Condition | Mean | SD | SE | |
---|---|---|---|---|

Combined intervention (researcher-led and teacher-led) | 55 | 19.80 | 9.02 | 1.22 |

Other groups combined (control, finger training only, number games only) | 78 | 8.56 | 8.11 | 0.92 |

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 and compared with those that did not. Descriptive statistics can be seen in Table

Condition | Mean | SD | SE | |
---|---|---|---|---|

Groups that received finger training | 82 | 1.90 | 4.26 | 0.47 |

Other groups combined (control, number games only) | 51 | 0.16 | 3.13 | 0.44 |

In order to determine whether the number games aspect of the intervention had an effect on non-symbolic magnitude comparison, groups that received the number games intervention were combined and compared with those that did not. Descriptive statistics can be seen in Table

Condition | Mean | SD | SE | |
---|---|---|---|---|

Groups that received number games | 83 | 3.08 | 4.30 | 0.47 |

Other groups combined (control, finger training only) | 50 | 1.3 | 4.03 | 0.57 |

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 quantitative skills 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 quantitative skills. The two versions of the intervention that combined both the finger training and number games aspects were successful in improving participants’ quantitative skills relative to controls, and with a large effect size.

The findings show that the combined intervention, incorporating both finger training and symbolic number games, gave rise to significant improvements in participants’ numeration scores. Neither intervention alone had an effect on numeration scores. This is an important and original contribution to knowledge in this field, as this combination of interventions has not been tested before, to our knowledge. This finding suggests that children’s developing 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 in the 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.

Prior to the intervention taking place, the pretest data showed a correlation between finger gnosis and number sense. This supports previous findings from the study by Fayol et al. (

The findings of the present study do not fully align with those of the study by Siegler and Ramani (

The findings presented here suggest that for an intervention to be successful in increasing children’s quantitative skills—when the children are starting within the normal range of ability—then the intervention should involve a combination of number representations, rather than one particular set of representations.

Confidence in the above interpretation is added by the fact that 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 that while both aspects of the intervention have a potential role to play in supporting children’s learning, it is only in combination that they 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 quantitative skills (Butterworth,

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.

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

A second possibility is that the combined intervention led to better results as it was more likely to match children’s particular needs. Dowker (

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 quantitative skills. Children generally need explicit exposure to relationships between numerical phenomena or relationships in order to internalize them (Fuson,

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 learning and 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 more convincing evidence for the effectiveness of the intervention.

A second limitation relates to the fact that posttests were carried out soon after the last session of the intervention. It is therefore not possible to know whether the gains in quantitative skills 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 and number games intervention can contribute to young children’s quantitative skills and their developing mathematical understanding. We understand that further research will be needed in order to fully determine the underlying mechanisms by which the interventions leads to gains in skill, and to add confidence in the effectiveness of the intervention, but argue that sufficient evidence has been gained from this study to warrant such further work.

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 and replication, 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.

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 teachers of all children who participated.

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

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.