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With two simple experiments we investigate the overlooked influence of handshape similarity for processing numerical information conveyed on the hands. In most finger-counting sequences there is a tight relationship between the number of fingers raised and the numerical value represented. This creates a possible confound where numbers closer to each other are also represented by handshapes that are more similar. By using the American Sign Language (ASL) number signs we are able to dissociate between the two variables orthogonally. First, we test the effect of handshape similarity in a same/different judgment task in a group of hearing non-signers and then test the interference of handshape in a number judgment task in a group of native ASL signers. Our results show an effect of handshape similarity and its interaction with numerical value even in the group of native signers for whom these handshapes are linguistic symbols and not a learning tool for acquiring numerical concepts. Because prior studies have never considered handshape similarity, these results open new directions for understanding the relationship between finger-based counting, internal hand representations and numerical proficiency.

Numerous studies appear to show that fingers might be related to numerical and arithmetical proficiency in more than one way, both in children and in adults (

More recently, different studies have investigated how finger-based strategies and internalized finger representations may relate to arithmetic proficiency but also more broadly to numerical and quantity processing. The relationship between finger gnosia and proficiency in arithmetic in children appears to show mixed results where some have found that finger gnosis correlates and selectively predicts later numerical and arithmetic ability in children (

Although some studies have questioned whether the use of fingers counting and finger-based strategies is necessary or simply a useful tool (

Interestingly, on the one hand, studies have debated on whether the somatosensory representation of one’s fingers is related to arithmetic performance in children; on the other, studies have shown that processing numerical information presented as Arabic digits is influenced by personal representations of finger configurations. However, no study has directly investigated whether the hand configuration

The overall aim of this study is to test the hypothesis that recognizing hand configurations might present its own, distinct processing effects and that it might interfere when processing numerical information presented on the fingers. In two experiments, we test the impact of hand configuration properties and whether hand configuration properties can interfere with numerical processing even in high levels of expertise. Here, we postulate that handshapes representing closer numbers also share greater representational overlap, either visual or somatosensorial, and hence might interfere with processing the numerical information. To test this hypothesis, we use the handshape sequence for numbers in American Sign Language (ASL) to measure the influence of handshape similarity. The first advantage to using the ASL number signs is that all numbers are represented on one hand only (

This means that there is a dissociation between the numerical meaning and the number of fingers raised for at least part of the sequence. In ASL, numbers 1 through 5 have a transparent representation of the numerical value: the number of fingers raised corresponds to the numerical value conveyed (i.e., iconic symbols). For ASL numbers 6 through 9, this correspondence does not hold as all are represented with only three fingers raised (i.e., abstract symbols). For example, 6 is represented with the thumb touching the little finger, 7 with the thumb touching the ring finger and so on (see

For the first time, in this study we will be able to test the impact of handshape by dissociating the physical properties of the stimuli from their numerical meaning, test whether handshape configurations interfere with the processing of the numerical information, and if expertise can eliminate the interference due to the similarity of the hand configurations. Last but not least, we test for the first time if the classical numerical distance effect can be observed in ASL number signs 1 through 9 as it has been observed for other number formats (e.g.,

In a group of hearing non-signers, we test the hypothesis that the handshape similarity can influence reaction time (RT) when asked to process the physical property regardless of whether numerical information is relevant. We specifically selected a group of participants unfamiliar with the ASL number signs as our aim was to test if processing handshapes carries its own pattern of responses. Therefore, participants were asked to make a same-different judgment on the physical properties of ASL handshapes. Participants were presented with pictures of pairs of ASL handshapes for number signs 1 through 9 and were asked to judge if these were the same or different. We first predicted the typical numerical distance effect for numbers up to five as observed with other formats for numbers (

We predicted that comparing handshapes would be increasingly hard with increasing shared properties which we operationalized by counting the number of common fingers. We also predicted an interaction where both variables, numerical value and the handshape similarity, would interfere with the same-different judgment. That is, trials where the handshapes share more common features as well as being numerically closer in the number of fingers raised, would be the ones showing the greatest interference. Additionally, to further test the influence of handshape similarity independently of numerical value, using the ASL handshapes for 3, and 6 through 9, all presenting three fingers raised (

We first analyzed performance on the overall same-different judgment task to ensure participants complied with the task. Then analyzed only the pairs in the different condition for numbers 1 through 5 to test for the presence of what could be interpreted as the numerical distance effect even if no numerical judgement was required. To test for the influence of handshape, we analyzed the pairs based on the number of common fingers (four levels) and then the subset that varies on both numerical distance and number of fingers in common (

Thirty hearing participants who had never been exposed to ASL or had only very minimal exposure to ASL were recruited from the Washington DC metro area. The majority of participants were right-handed (28 out of 30); one participant identified as being ambidextrous and one as left-handed. No participants reported any history of specific learning disability nor suffered any major neurological disorder. Age range was between 19 and 37, with a mean of 27 years and 6 months. Ten participants identified as male. Participants were compensated for their time and the study was approved by the Institutional Review Board.

This experiment was part of a larger study including several numerical tasks. As the other tasks relate to separate questions and hypotheses, those results will not be discussed here. Hearing participants were greeted and instructed to the tasks by an English-speaking research assistant. All tasks were presented on a laptop running Windows 10 using E-Prime 3 software. The background questionnaire on language and demographic information was administered through RedCap.

Stimuli were black line drawings of ASL handshapes for numbers 1 through 9 with hand orientation showing the palm (

The experiment started with an instruction screen explaining the task and response key mapping for ‘same’ and ‘different’ responses. A block started with a 200 ms fixation and then the pair of handshapes remained on the screen until a response was given. During breaks, participants could rest for as long as they needed.

Of the 30 participants, two were administered the wrong task and six performed below 75% accuracy either because they forgot the response key mapping or because they disengaged from the task. Therefore, only 22 hearing non-signers were retained for the analyses. All trials beyond 2.5

Same and different judgments were made equally fast,

For ASL handshapes between 1 and 5, we found a numerical distance effect for RTs,

All pairs, except those including ASL handshapes for 7 and 8, were coded based on the number of common fingers in each pair. The analysis on the number of common fingers (4 levels) returned a significant effect for accuracies and RTs,

Further, in a subsequent analysis, we included number of fingers in common (3 levels) and numerical distance (2 levels). For both accuracy and RT, we found both main effects and the interaction to be significant (

It is important to remember that for ASL handshapes 6 through 9 used in the analysis, hearing non-signers could only extract the information provided by the number of fingers raised, in this case always three. Any difference observed in the next analysis cannot be attributed to numerical meaning or number of fingers in common as it is always the same for all pairs. Differences can only be attributed to the difficulty in processing handshapes based on the distance between fingers bent.

We found a finger distance effect for RT and accuracies, where pairs with adjacent fingers bent (e.g., pair of ASL handshapes 8-9, see

Finally, we tested the pairs of handshapes that provide opposite predictions based on whether numerical or handshape similarity influence performance. In this analysis, we compared performance for the pair of handshapes for 6 and 9, acceptable handshapes for three, with the ASL handshapes for 7 and 8, that are atypical handshapes for three. Results indicate that comparing ASL handshapes for 7 and 8 was harder,

In experiment 1, we asked non-signers to make a same-different judgment on pairs of handshapes used in ASL to represent numbers. We found a numerical distance effect although participants were not required to process numerical information. This result is in line with studies showing automatic processing of numerical information with different numerical formats (

Interestingly, numerical distance appears to modulate the same-different judgment most when the numerical values are closer. Indeed, accuracy was lowest and RTs longest when the pairs shared three common fingers and had a numerical distance of one. Because the two dimensions appear to be processed with some level of dependence, the interaction could occur at different levels in the processing stream: representational or decisional level (see

Another interesting observation is a possible “full-hand” effect. Considering the analysis on shared number of fingers, performance appears to rebound for a distance of 4. Similarly, for the interaction between shared fingers and numerical distance, RTs appear to decrease for three shared fingers and a numerical distance of two. In both these situations, one of the handshapes being compared is always the ASL handshape for 5 (i.e., the full hand;

The following question is whether extensive practice and the explicit request to process the numerical information can counter the handshape similarity effect as the attention is now shifted from the handshape properties to the numerical information conveyed. Can the processing of handshapes become detached from their superficial perceptual features when these are symbols used as part of a language system and not merely as a tool to acquire numerical understandings?

In a group of Deaf ASL native signers, we first tested and predicted a numerical distance effect for all ASL numbers signs 1 through 9 since these signs are numerical symbols equivalent to any other number format. Bull and colleagues (

Deaf native signers were asked to judge which of two ASL number signs was numerically larger to ensure that they were retrieving numerical information and stack the deck against a more cognitively superficial perceptual processing strategy. Importantly, the aim was to evaluate how handshape interferes with numerical processing and not the reverse. We first analyzed the numerical distance effect to test the prediction that ASL number signs, regardless of whether they are transparent (1 through 5) or not (6 and above), are comparable to other number formats by showing the classical numerical distance effect (

Thirty-six Deaf native signers were recruited for this study. All declared having been exposed to ASL prior to age two and have received the majority of their instruction in ASL. All reported using ASL on a daily basis and were recruited from the DC metro area where a sizeable Deaf-ASL signing community thrives. Four participants declared being left-handed and two ambidextrous, whereas all others reported being right-handed. Five participants were excluded due to their report of prior Attention Deficit and Hyperactivity Disorder or other learning disability. Age range for the 31 participants retained for the analyses was between 18 and 32, with a mean of 23 years and 6 months. Eleven participants identified as male and 20 as female. Participants were compensated for their time and the study was approved by the Institutional Review Board.

This experiment was part of a larger battery of numerical tasks administered to both the hearing non-signer group and the Deaf native signers. For optimal communication with our Deaf signing group, the research assistant leading this study was also a Deaf native ASL signer. All tasks were presented on a laptop running Windows 10 using E-Prime 3 software. Stimuli were black line drawings of ASL number signs 1 through 9 (

The experiment started with an instruction screen explaining the task and the keys for responding. A block started with a fixation for 200ms and then the pair of ASL number signs remained on the screen until a response was given. Participants could rest as long as they wanted between blocks.

All 31 participants were retained for the analyses as overall accuracy was over 88%. All trials beyond 2.5

Performance for determining the larger of two ASL numbers signs showed the expected numerical distance effect for both accuracy and RTs,

We also analyzed the data for ASL numbers signs 6 through 9 as these ASL numbers do not represent the numerical quantity through a corresponding number of fingers raised but are non-transparent symbols. Again, performance showed a numerical distance effect for both accuracy,

In this analysis we entered numerical distance (5 levels) and number of common fingers (3 levels) as variables. For accuracies and RTs, both main effects and the interaction were significant (

Crucially, the interaction showed that the impact of common fingers was greater for numerically closer pairs than numerically more distant pairs,

The first relevant result from Experiment 2, is that ASL numbers signs induce the classical numerical distance effect, as widely documented in all other number formats. Even when only considering the subset of ASL signs for numbers 6 through 9, which are abstract symbols. This is the first time it has been tested with handshape configurations representing all numbers on one single hand. The second result is that handshape similarity has a significant influence on the processing of the ASL number signs where signs that share more common hand features, that is share more common fingers raised, are harder to process than those that share less features. Therefore, even in a group of individuals with extensive training, who communicates primarily through the use of hands, the superficial features of the handshape interfere with the processing of the numerical information.

Again, we see that the processing for the two dimensions occur with a certain level of dependence. Because these handshapes constitute linguistic symbols for ASL native signers, an interesting question is whether the interference occurs at a different level compared to the one observed in hearing participants.

In these two experiments, we tested whether the handshapes for representing numbers can carry its own processing effects and if it can interfere with the numerical processing when part of a symbolic system. Answering this question is relevant given that often finger-based strategies are used to teach children how to count and given the observation that processing numerical information appears to rely on or recall these internalized hand configurations and finger-based strategies (

In these two studies, we show several effects. In our first experiment with hearing non-signing participants, we replicate a numerical distance effect for pairs of iconic handshapes (where the number of fingers raised represents the numerical value) as observed in a Stroop-like paradigm by

Further, implicit numerical information also interfered with handshape processing. When the pairs of handshapes shared more common features, and thus were harder to discriminate, the influence of numerical distance was greater. This suggests that the two dimensions are not completely independent. An interesting question relates to the locus of the interference. Some studies have identified common brain areas responsible for processing both dimensions (

In our second experiment, we also find another set of novel findings with our group of Deaf ASL native signers. First, we show for the first time that handshapes for numbers presented on one hand, ASL number signs 1 through 9, elicit the classical numerical distance effect even when the handshapes used have no transparent correspondence between the number of fingers raised and the numerical meaning conveyed. The previous study by

The second relevant result observed in the experiment with Deaf native signers is that expertise in using ASL number signs as part of one’s language system does not prevent the interference caused by handshape similarity. Indeed, there was an effect of handshape similarity and it was stronger with decreasing numerical distance. It is relevant to highlight that our stimuli used here are far from what a Deaf signer experiences during everyday linguistic interactions. Hence, it remains to be determined if this influence is related to the format in which the stimuli were presented in this experiment; Deaf signers usually process handshapes while in movement and in a linguistic context, not fixed hand drawings.

The results from the two experiments both agree in showing how handshape similarity has its own effect and that it can interfere with numerical information processing as well as being subject to numerical interference. This brings new insights to the possible relationship observed between finger gnosis and arithmetic proficiency in children (

These results also provide new directions for reinterpreting the findings showing a relationship between internal representations of hand configurations and numerical processing. Maybe some of the differences observed in behavioral studies using canonical patterns and non-canonical patterns could also be explained by the observation that canonical patterns are usually sequences of consecutive fingers being raised for each successive numerical value whereas non-canonical patters are often hand configurations that deviate from this succession (e.g.,

Studies with hearing participants have subdivided canonical hand configurations into montring and counting sub categories. Montring refers to the handshapes used to show a cardinal amount whereas the counting handshapes refer to the sequence used when counting items (^{rd}, palm orientation would go from outward to inward. Our current stimuli, showing inward palm orientation, are consistent with an egocentric view of a cardinality representation. It would be interesting to test whether stimuli showing the back of the hand, static or in movement, also produce the same effects^{1}

In a personal communication with a teacher from a local Elementary School for the Deaf, it appears that children are encouraged to use the same ASL number signs for both counting, calculating and montring. The teacher reported that this was done to reduce the amount of possible confusion, especially for ASL numbers above 5.

.If we know that these handshapes are the canonical representation for our Deaf signing group, we unfortunately don’t have such information for our hearing participants. Our results are only based on the assumption that this group of English-speaking participants were exposed to the culturally-canonical counting sequence. The lack of this information does not however necessarily weaken the findings. Our results show a numerical distance effect regardless of whether the handshapes were part of the canonical pattern and we see an interference effect of numerical information on the handshape similarity suggesting that numerical information was automatically processed. We can conclude that the handshapes were either familiar enough to our group of participants or, if they were not part of their canonical configurations, these still provided automatic access to numerical information for an interference to occur.

The other interesting question that is raised here is whether these stimuli presented as handshapes automatically activated an internal representation of the body and if the interference observed occurs at a visual-perceptual level or at a somatosensory level. If processing numbers and calculation have shown activations in somatosensory areas for the fingers in the brain (

In conclusion, in this study we show an impact of handshape similarity for processing handshape configurations used for counting. Even in a group of highly experienced Deaf native signers, handshape similarity interfered with the numerical processing of the ASL number signs. This suggests that handshapes are qualitatively different from other number formats and might carry their own specific difficulties when used as support for learning and teaching numerical concepts as well as linguistic symbols in sign languages.

This project was supported by Gallaudet University and the NSF/Gallaudet University’s Science of Learning Center on Visual Language and Visual Learning (VL2).

The authors also want to express their gratitude to the participants who have joined the study.

The authors have declared that no competing interests exist.