Preschoolers prior formal mathematics education engage numerical magnitude representation rather than counting principles in symbolic ±1 arithmetic: Evidence from the operational momentum effect.

In numerical cognition research, the operational momentum (OM) phenomenon (tendency to overestimate the results of addition and/or binding addition to the right side and underestimating subtraction and/or binding it to the left side) can help illuminate the most basic representations and processes of mental arithmetic and their development. This study is the first to demonstrate OM in symbolic arithmetic in preschoolers. It was modeled on Haman and Lipowska's (2021) non-symbolic arithmetic task, using Arabic numerals instead of visual sets. Seventy-seven children (4-7 years old) who know Arabic numerals and counting principles (CP), but without prior school math education, solved addition and subtraction problems presented as videos with one as the second operand. In principle, such problems may be difficult when involving a non-symbolic approximate number processing system, whereas in symbolic format they can be solved based solely on the successor/predecessor functions and knowledge of numerical orders, without reference to representation of numerical magnitudes. Nevertheless, participants made systematic errors, in particular, overestimating results of addition in line with the typical OM tendency. Moreover, subtraction and addition induced longer response times when primed with left- and right-directed movement, respectively, which corresponds to the reversed spatial form of OM. These results largely replicate those of non-symbolic task and show that children at early stages of mastering symbolic arithmetic may rely on numerical magnitude processing and spatial-numerical associations rather than newly-mastered CP and the concept of an exact number.

Theory of Mind and Parental Mental-State Talk in Children with CIs.

Previous studies have suggested that parents may support the development of theory of mind (ToM) in their child by talking about mental states (mental state talk; MST). However, MST has not been sufficiently explored in deaf children with cochlear implants (CIs). This study investigated ToM and availability of parental MST in deaf children with CIs (n = 39, Mage = 62.92, SD = 15.23) in comparison with their peers with typical hearing (TH; n = 52, Mage = 52.48, SD = 1.07). MST was measured during shared storybook reading. Parents' narratives were coded for cognitive, emotional, literal, and non-mental references. ToM was measured with a parental questionnaire. Children with CIs had lower ToM scores than their peers with TH, and their parents used more literal references during shared storybook reading. There were no significant differences in the frequencies of cognitive and emotional references between groups. Parental emotional references contributed positively to children's ToM scores when controlling for the child's age and receptive grammar only in the CI group. These results indicated some distinctive features in parents of deaf children with CIs' MST and highlighted the role of MST in the development of ToM abilities in this group.

Moving attention along the mental number line in preschool age: Study of the operational momentum in 3- to 5-year-old children's non-symbolic arithmetic.

People tend to underestimate subtraction and overestimate addition outcomes and to associate subtraction with the left side and addition with the right side. These two phenomena are collectively labeled 'operational momentum' (OM) and thought to have their origins in the same mechanism of 'moving attention along the mental number line'. OM in arithmetic has never been tested in children at the preschool age, which is critical for numerical development. In this study, 3-5 years old were tested with non-symbolic addition and subtraction tasks. Their level of understanding of counting principles (CP) was assessed using the give-a-number task. When the second operand's cardinality was 5 or 6 (Experiment 1), the child's reaction time was shorter in addition/subtraction tasks after cuing attention appropriately to the right/left. Adding/subtracting one element (Experiment 2) revealed a more complex developmental pattern. Before acquiring CP, the children showed generalized overestimation bias. Underestimation in addition and overestimation in subtraction emerged only after mastering CP. No clear spatial-directional OM pattern was found, however, the response time to rightward/leftward cues in addition/subtraction again depended on stage of mastering CP. Although the results support the hypothesis about engagement of spatial attention in early numerical processing, they point to at least partial independence of the spatial-directional and magnitude OM. This undermines the canonical version of the number line-based hypothesis. Mapping numerical magnitudes to space may be a complex process that undergoes reorganization during the period of acquisition of symbolic representations of numbers. Some hypotheses concerning the role of spatial-numerical associations in numerical development are proposed.

False Belief Understanding in Deaf Children With Cochlear Implants.

Theory of mind (ToM) is crucial for social interactions. Previous research has indicated that deaf and hard-of-hearing children born into hearing families (DoH) are at risk of delayed ToM development. However, it is unclear whether this is the case for DoH children who receive cochlear implants (CIs) before and around the second year of life. The present study aimed to investigate false belief understanding (FBU) in DoH children with CIs. The relationships between false belief task (FBT) performance, sentence comprehension, age at implantation, duration of CI use, and Speech Recognition Threshold were explored. A total of 94 children with typical levels of hearing (TH) and 45 DoH children (age range: 3-8), who received their first CI between 6 and 27 months of age, were tested on the FBT and a sentence comprehension test. Results showed that 4- and 5-year-old children with CIs performed significantly worse than their peers with TH on the FBT; 6- to 8-year-old children with CIs performed similarly to age-matched children with TH. Age at implantation and duration of CI use were correlated with sentence comprehension but not with the FBT. The results indicated that FBU was delayed until the age of 6 years in most of children with CIs.

The plural counts: Inconsistent grammatical number hinders numerical development in preschoolers - A cross-linguistic study.

The role of grammar in numerical development, and particularly the role of grammatical number inflection, has already been well-documented in toddlerhood. It is unclear, however, whether the influence of grammatical language structure further extends to more complex later stages of numerical development. Here, we addressed this question by exploiting differences between Polish, which has a complex grammatical number paradigm, leading to a partially inconsistent mapping between numerical quantities and grammatical number, and German, which has a comparatively easy verbal paradigm: 151 Polish-speaking and 123 German-speaking kindergarten children were tested using a symbolic numerical comparison task. Additionally, counting skills (Give-a-Number and count-list), and mapping between non-symbolic (dot sets) and symbolic representations of numbers, as well as working memory (Corsi blocks and Digit span) were assessed. Based on the Give-a-Number and mapping tasks, the children were divided into subset-knowers, CP-knowers-non-mappers, and CP-knowers-mappers. Linguistic background was related to performance in several ways: Polish-speaking children expectedly progressed to the CP-knowers stage later than German children, despite comparable non-numerical capabilities, and even after this stage was achieved, they fared worse in the numerical comparison task. There were also meaningful differences in spatial-numerical mapping between the Polish and German groups. Our findings are in line with the theory that grammatical number paradigms influence. the development of representations and processing of numbers, not only at the stage of acquiring the meaning of the first number-words but at later stages as well, when dealing with symbolic numbers.

The spatial-numerical congruity effect in preschoolers.

Number-to-space mapping and its directionality are compelling topics in the study of numerical cognition. Usually, literacy and math education are thought to shape a left-to-right number line. We challenged this claim by analyzing performance of preliterate precounting preschoolers in a spatial-numerical task. In our experiment, children exhibited a spatial-numerical congruity (SNC) effect during a nonsymbolic numerosity comparison (quicker reaction times to smaller sets presented on the left side of the screen and to larger ones presented on the right side). These findings suggest that left-to-right number ordering may also have some sources that are independent of reading and math education. We argue that the current explanations of the spatial-numerical link need to be reconsidered.

More linear than log? Non-symbolic number-line estimation in 3- to 5-year-old children.

The number-line estimation task has become one of the most important methods in numerical cognition research. Originally applied as a direct measure of spatial number representation, it became also informative regarding various other aspects of number processing and associated strategies. However, most of this work and associated conclusions concerns processing numbers in a symbolic format, by school children and older subjects. Symbolic number system is formally taught and trained at school, and its basic mathematical properties (e.g., equidistance, ordinality) can easily be transferred into a spatial format of an oriented number line. This triggers the question on basic characteristics of number line estimation before children get fully familiar with the symbolic number system, i.e., when they mostly rely on approximate system for non-symbolic quantities. In our three studies, we examine therefore how preschool children (3-5-years old) estimate position of non-symbolic quantities on a line, and how this estimation is related to the developing symbolic number knowledge and cultural (left-to-right) directionality. The children were tested with the Give-a-number task, then they performed a computerized number-line task. In Experiment 1, lines bounded with sets of 1 and 20 elements going left-to-right or right-to-left were used. Even in the least numerically competent group, the linear model better fit the estimates than the logarithmic or cyclic power models. The line direction was irrelevant. In Experiment 2, a 1-9 left-to-right oriented line was used. Advantage of linear model was found at group level, and variance of estimates correlated with tested numerosities. In Experiment 3, a position-to-number procedure again revealed the advantage of the linear model, although the strategy of selecting an option more similar to the closer end of the line was prevalent. The precision of estimation increased with the mastery of counting principles in all three experiments. These results contradict the hypothesis of the log-to-linear shift in development of basic numerical representation, rather supporting the linear model with scalar variance. However, the important question remains whether the number-line task captures the nature of the basic numerical representation, or rather the strategies of mapping that representation to an external space.

Does the TPJ fit it all? Representational similarity analysis of different forms of mentalizing.

Mentalizing is the key socio-cognitive ability. Its heterogeneous structure may result from a variety of forms of mental state inference, which may be based on lower-level processing of cues encoded in the observable behavior of others, or rather involve higher-level computations aimed at understanding another person's perspective. Here we aimed to investigate the representational content of the brain regions engaged in mentalizing. To this end, 61 healthy adults took part in an fMRI study. We explored ROI activity patterns associated with five well-recognized ToM tasks that induce either decoding of mental states from motion kinematics or belief-reasoning. By using multivariate representational similarity analysis, we examined whether these examples of lower- and higher-level forms of social inference induced common or distinct patterns of brain activity. Distinct patterns of brain activity related to decoding of mental states from motion kinematics and belief-reasoning were found in lTPJp and the left IFG, but not the rTPJp. This may indicate that rTPJp supports a general mechanism for the representation of mental states. The divergent patterns of activation in lTPJp and frontal areas likely reflect differences in the degree of involvement of cognitive functions which support the basic mentalizing processes engaged by the two task groups.

Perceived Motion and Operational Momentum: How Speed, Distance, and Time Influence Two-Digit Arithmetic.

Operational momentum was originally defined as a bias toward underestimating outcomes of subtraction and overestimating outcomes of addition. It was suggested that these estimation biases are due to leftward attentional shift along the mental number-line (spatially organized internal representation of number) in subtraction and rightward shift in addition. This assumes the use of "recycled" mechanisms of spatial attention, including "representational momentum" - a tendency to overestimate future position of a moving object, which compensates for the moving object's shift during preparation of a reaction. We tested a strong version of this assumption directly, priming two-digit addition and subtraction problems with leftward and rightward motion of varied velocity, as velocity of the tracked object was found to be a factor in determining representational momentum effect size. Operands were subsequently moving across the computer screen, and the participants' task was to validate an outcome proposed at the end of the event, which was either too low, correct, or too high. We found improved accuracy in detecting too-high outcomes of addition, as well as complex patterns of interactions involving arithmetic operation, outcome option, speed, and direction of motion, in the analysis of reaction times. These results significantly extend previous evidence for the involvement of spatial attention in mental arithmetic, showing movement of the external attention focus as a factor directing internal attention in processing numerical information. As a whole, however, the results are incompatible with expectations derived from the strong analogy between operational and representational momenta. We suggest that the full model may be more complex than simply "moving attention along the mental number-line" as a direct counterpart of attention directed at a moving object.

The Development of Understanding Opacity in Preschoolers: A Transition From a Coarse- to Fine-Grained Understanding of Beliefs.

Intensionality (or opacity) is a core property of mental representations and sometimes understanding opacity is claimed to be a part of children's theory of mind (evidenced with the false belief task). Children, however, pass the false belief task and the intensionality tasks at different ages (typically 4 vs. 5;1-6;11 years). According to two dominant interpretations, the two tests either require different conceptual resources or vary only in their executive or linguistic load. In two experiments, involving 120 children aged 3-6 (Experiment 1) and 75 children aged 4-6 (Experiment 2), we tested two variants of the executive load hypothesis: The differential linguistic complexity of the two tests, and the dual-name problem of the intensionality task. The former was addressed by standardizing and minimizing the linguistic demands of both tasks (contrasted with the typical narrative intensionality task), and the latter by introducing the dual-name problem into the false belief task as well, so that it was present in both tasks. We found that (1) two structurally different intensionality tasks shared more variance with each other than with the structurally similar false belief task, and that (2) introducing a dual label problem into the false belief task did not reduce the developmental gap. Our results speak against interpreting the difference between the time children pass the two tests entirely in terms of performative issues, and support the conceptual enrichment hypothesis. We discuss the theoretical relevance of these results, suggesting that they are best explained by fine-grained increments within the concept of belief, rather than a radical conceptual change. We conclude that understanding opacity of minds - which emerges between age 5 and 6 - is an important step toward a more advanced form of ToM.

Processing False Beliefs in Preschool Children and Adults: Developing a Set of Custom Tasks to Test the Theory of Mind in Neuroimaging and Behavioral Research.

The theory of mind (ToM) is the ability to attribute mental states to others and is extremely important for social functioning. It has been widely examined in both behavioral and neuroimaging research, usually with the use of the many versions of the false-belief (FB) task. However, there is still not enough evidence from studies on the neurodevelopmental mechanisms of ToM mostly because of methodological limitations: lack of selectivity, mismatch of experimental and control tasks, and focusing on participants older than 6 years old. In the current study, we attempted to develop a computerized tool for ToM assessment suitable for both behavioral and neuriomaging testing in preschoolers. We designed a version of the classic change-of-location task with custom visuals and three fine-tuned conditions: FB, true-belief, and no-belief (NB). The usability of the task for further application in neurodevelopmental research was tested with three methods: first, behaviorally, with the use of a touch screen on a group of 75 children, followed by a functional MRI (fMRI) study on 13 adults, and a functional near-infrared spectroscopy (fNIRS) study on 19 preschool children. In line with our expectations, on the behavioral level, our task elicited the all-or-none performance in preschoolers. There was also a progression of performance with age in the FB condition. On the neural level, we observed the activation of structures involved in the ToM brain network in response to our task in both adults and children. The results therefore suggest that our task can be a useful tool for studying ToM development and its neural underpinnings.

Working together to orient faster: The combined effects of alerting and orienting networks on pupillary responses at 8 months of age.

Multiple visual attention mechanisms are active already in infancy, most notably one supporting orienting towards stimuli and another, maintaining appropriate levels of alertness, when exploring the environment. They are thought to depend on separate brain networks, but their effects are difficult to isolate in existing behavioural paradigms. Better understanding of the contribution of each network to individual differences in visual orienting may help to explain their role in attention development. Here, we tested whether alerting and spatial cues differentially modulate pupil dilation in 8-month-old infants in a visual orienting paradigm. We found differential effects in the time course of these responses depending on the cue type. Moreover, using Principal Component Analysis (PCA) we identified two main components of pupillary response, which may reflect the alerting and orienting network activity. In a regression analysis, these components together explained nearly 40 % of variance in saccadic latencies in the spatial cueing condition of the task. These results likely demonstrate that both networks work together in 8-month-old infants and that their activity can be indexed with pupil dilation combined with PCA, but not with raw changes in pupil diameter.

Corrigendum: A Mental Odd-Even Continuum Account: Some Numbers May Be "More Odd" Than Others and Some Numbers May Be "More Even" Than Others.

[This corrects the article DOI: 10.3389/fpsyg.2018.01081.].

A Mental Odd-Even Continuum Account: Some Numbers May Be "More Odd" Than Others and Some Numbers May Be "More Even" Than Others.

Numerical categories such as parity, i.e., being odd or even, have frequently been shown to influence how particular numbers are processed. Mathematically, number parity is defined categorically. So far, cognitive, and psychological accounts have followed the mathematical definition and defined parity as a categorical psychological representation as well. In this manuscript, we wish to test the alternative account that cognitively, parity is represented in a more gradual manner such that some numbers are represented as "more odd" or "more even" than other odd or even numbers, respectively. Specifically, parity processing might be influenced by more specific properties such as whether a number is a prime, a square number, a power of 2, part of a multiplication table, divisible by 4 or by 5, and many others. We suggest that these properties can influence the psychologically represented parity of a number, making it more or less prototypical for odd- or evenness. In the present study, we tested the influence of these numerical properties in a bimanual parity judgment task with auditorily presented two-digit numbers. Additionally, we further investigated the interaction of these numerical properties with linguistic factors in three language groups (English, German, and Polish). Results show significant effects on reaction times of the congruity of parity status between decade and unit digits, even if numerical magnitude and word frequency are controlled. We also observed other effects of the above specific numerical properties, such as multiplication attributes, which facilitated or interfered with the speed of parity judgment. Based on these effects of specific numerical properties we proposed and elaborated a parity continuum account. However, our cross-lingual study also suggests that parity representation and/or access seem to depend on the linguistic properties of the respective language or education and culture. Overall, the results suggest that the "perceived" parity is not the same as objective parity, and some numbers are more prototypical exemplars of their categories.

Impaired recognition of communicative interactions from biological motion in schizophrenia.

BACKGROUND: Patients with schizophrenia are deficient in multiple aspects of social cognition, including biological motion perception. In the present study we investigated the ability to read social information from point-light stimuli in schizophrenia. METHODOLOGY/PRINCIPAL FINDINGS: Participants with paranoid schizophrenia and healthy controls were presented with a biological motion task depicting point-light actions of two agents either engaged in a communicative interaction, or acting independently of each other. For each stimulus, participants were asked to decide whether the two agents were communicating vs. acting independently of each other (task A), and to select the correct action description among five response alternatives (task B). Participants were also presented with a mental rotation task to assess their visuospatial abilities, and with a facial emotion recognition task tapping social cognition. Results revealed that participants with schizophrenia performed overall worse than controls both in discriminating communicative from non-communicative actions (task A) and in selecting which of the 5 response alternatives best described the observed actions (task B). Interestingly, the impaired performance of schizophrenic participants was mainly due to misclassification of non-communicative stimuli as communicative actions. Correlation analysis revealed that visuospatial abilities predicted performance in task A but not in task B, while facial emotion recognition abilities was correlated with performance in both task A and task B. CONCLUSIONS/SIGNIFICANCE: These findings are consistent with theories of "overmentalizing" (excessive attribution of intentionality) in schizophrenia, and suggest that processing social information from biological motion does rely on social cognition abilities.

The Multilingual CID-5: A New Tool to Study the Perception of Communicative Interactions in Different Languages.

The investigation of the ability to perceive, recognize, and judge upon social intentions, such as communicative intentions, on the basis of body motion is a growing research area. Cross-cultural differences in ability to perceive and interpret biological motion, however, have been poorly investigated so far. Progress in this domain strongly depends on the availability of suitable stimulus material. In the present method paper, we describe the multilingual CID-5, an extension of the CID-5 database, allowing for the investigation of how non-conventional communicative gestures are classified and identified by speakers of different languages. The CID-5 database contains 14 communicative interactions and 7 non-communicative actions performed by couples of agents and presented as point-light displays. For each action, the database provides movie files with the point-light animation, text files with the 3-D spatial coordinates of the point-lights, and five different response alternatives. In the multilingual CID-5 the alternatives were translated into seven languages (Chinese, Dutch, English, French, German, Italian, and Polish). Preliminary data collected to assess the recognizability of the actions in the different languages suggest that, for most of the action stimuli, information presented in point-light displays is sufficient for the distinctive classification of the action as communicative vs. individual, as well as for identification of the specific communicative gesture performed by the actor in all the available languages.

How number-space relationships are assessed before formal schooling: A taxonomy proposal.

The last years of research on numerical development have provided evidence that spatial-numerical associations (SNA) can be formed independent of formal school training. However, most of these studies used various experimental paradigms that referred to slightly different aspects of number and space processing. This poses a question of whether all SNAs described in the developmental literature can be interpreted as a unitary construct, or whether they are rather examples of different, but related phenomena. Our review aims to provide a starting point for a systematic classification of SNA measures used from infancy to late preschool years, and their underlying representations. We propose to distinguish among four basic SNA categories: (i) cross-dimensional magnitude processing, (ii) associations between spatial and numerical intervals, (iii) associations between cardinalities and spatial directions, (iv) associations between ordinalities and spatial directions. Such systematization allows for identifying similarities and differences between processes and representations that underlie the described measures, and also for assessing the adequacy of using different SNA tasks at different developmental stages.