Number-related Brain Potentials Are Differentially Affected by Mapping Novel Symbols on Small versus Large Quantities in a Number Learning Task

The nature of the mapping process that imbues number symbols with their numerical meaning-known as the "symbolgrounding process"-remains poorly understood and the topic of much debate. The aim of this study was to enhance insight into how the nonsymbolic-symbolic number mapping process and its neurocognitive correlates might differ between small (1-4; subitizing range) and larger (6-9) numerical ranges. Hereto, 22 young adults performed a learning task in which novel symbols acquired numerical meaning by mapping them onto nonsymbolic magnitudes presented as dot arrays (range 1-9). Learning-dependent changes in accuracy and RT provided evidence for successful novel symbol quantity mapping in the subitizing (1-4) range only. Corroborating these behavioral results, the number processing related P2p component was only modulated by the learning/mapping of symbols representing small numbers 1-4. The symbolic N1 amplitude increased with learning independent of symbolic numerical range but dependent on the set size of the preceding dot array; it only occurred when mapping on one to four item dot arrays that allow for quick retrieval of a numeric value, on the basis of which, with learning, one could predict the upcoming symbol causing perceptual expectancy violation when observing a different symbol. These combined results suggest that exact nonsymbolic-symbolic mapping is only successful for small quantities 1-4 from which one can readily extract cardinality. Furthermore, we suggest that the P2p reflects the processing stage of first access to or retrieval of numeric codes and might in future studies be used as a neural correlate of nonsymbolic-symbolic mapping/symbol learning

The Neuroscience of Mathematical Cognition and Learning

The synergistic potential of cognitive neuroscience and education for efficient learning has attracted considerable interest from the general public, teachers, parents, academics and policymakers alike. This review is aimed at providing 1) an accessible and general overview of the research progress made in cognitive neuroscience research in understanding mathematical learning and cognition, and 2) understanding whether there is sufficient evidence to suggest that neuroscience can inform mathematics education at this point. We also highlight outstanding questions with implications for education that remain to be explored in cognitive neuroscience. The field of cognitive neuroscience is growing rapidly. The findings that we are describing in this review should be evaluated critically to guide research communities, governments and funding bodies to optimise resources and address questions that will provide practical directions for short- and long-term impact on the education of future generations

When smaller is more – investigating the interplay between continuous sensory cues and numerical information

Research on numerical cognition is not limited to symbolic numbers and mathematics but it also includes discrete and continuous magnitudes. Continuous magnitudes are ubiquitous in nature and serve as important cues in everyday life situations. When one tries to choose the plate with more cookies in the cafeteria, they usually do not count the cookies but rather arrive at a fair estimate by comparing such continuous magnitudes. For example, nine cookies on a plate will occupy a larger area and have to be placed denser to each other than five cookies. Recent research has shown that, as opposed to the classical view, the processing of symbolic numbers and non-symbolic numerosities is not independent from such sensory cues. The present dissertation consists of two studies that investigate what psychological processes underlie the interaction between sensory cues and numerical information. Study 1 aimed to replicate and extend the findings of Gebuis & Reynvoet who systematically manipulated the relationship between continuous and discrete magnitudes in a non-symbolic numerical comparison task. The main goal was to assess the stability and the robustness of the influence of sensory cues on numerical comparisons as the originally reported patterns suggest a complex interaction between these two kinds of information that are difficult to reconcile with the classic views on numerical processing. Indeed, the results confirmed that continuous magnitudes have a complex effect on numerical judgements and that their interaction can be either due to incomplete inhibition or due to integration of continuous magnitudes during numerical tasks. Study 2 turned to symbolic numbers and investigated whether inhibition underlies the interaction of continuous sensory properties and numerical information. To this end a novel paradigm was introduced that allowed to investigate well-established electrophysiological correlates of inhibition with numerical stimuli. The results provide evidence that inhibition underlies the interaction between sensory cues and numerical information. Additionally, they show that the paradigm introduced in Study 2 may suitable to investigate these processes across different developmental stages and numeracy levels

Number Processing in Infants and Children Born Very Preterm

Individuals born very preterm (<32 weeks; VP) have notably poorer attainment in mathematics than their term-born peers. Only a handful of studies have investigated basic numerical skills in VP children and the underlying mechanisms associated with problems with mathematics in this population are still not fully comprehended. Basic processes underlying numerical cognition can go awry very early in development and there is a lack of knowledge of early trajectories of acquisition of numerical skills in infants born prematurely. This thesis reports on a series of studies investigating number processing in very preterm infants and children. These make use of a combination of tools, such as neurodevelopmental assessments, eye-tracking, event-related-potentials, neuropsychological evaluations and experimental tasks. Specifically, cross-sectional studies investigated numerical sensitivity in VP infants aged six and twelve months. Behavioural and electrophysiological measures assessing a range of domain-general and domain-specific skills associated with mathematics performance were also investigated in VP school-aged children. The results showed that, during the first year of post-natal life, VP infants do not exhibit differential developmental trajectories in the basic ability to discriminate numerosities compared to infants born at full term, although they required a longer time to discriminate the new number of elements. Later in development, school-aged VP children demonstrated difficulties in processing basic numerical information. Electrophysiological data demonstrated that this might be associated with deficits in sensory and attention resources and not necessarily in how VP children encode number-related information. Difficulties in processing numerical information, however, have only a marginal impact on their performance in mathematics. We tentatively conclude that difficulties in mathematics in individuals born very prematurely are largely associated with domain-general skills

Number Representation in Bilinguals. The role of early learning in the Mental Number Line representation

La presente tesis tiene como objetivo el estudio de la matemática bilingüe dentro del ámbito científico de la Cognición Numérica y Bilingüismo. El abordaje de cómo las personas bilingües representan y acceden a la magnitud es actualmente una cuestión de creciente interés que responde a la necesidad de entender el papel que desempeña el lenguaje en la adquisición temprana de las matemáticas. Esa importancia se ve reflejada habitualmente en el contexto de la educación, en donde el aprendizaje de la aritmética y el bilingüismo concurren de forma natural. Dada la importancia que tiene en nuestra sociedad tanto la adquisición de las matemáticas como el aprendizaje de una segunda lengua en edades tempranas, es necesario su estudio y abordaje desde el ámbito de la Neurociencia Cognitiva. Con el fin de entender en mayor profundidad los mecanismos neurocognitivos que subyacen al manejo de los números en las personas bilingües, el presente estudio aborda la cuestión del papel que el aprendizaje temprano de las matemáticas en una de las dos lenguas naturales del bilingüe, tiene en la representación del número. Para ello, se han diseñado tres experimentos utilizando la técnica de electroencefalografía, la cual permite una buena resolución temporal de la actividad neuronal que acompaña a la función cognitiva. Siguiendo la línea de investigación de Salillas y Carreiras (2014) sobre el impacto de la llamada "Lengua de aprendizaje de las matemáticas" (LLmath) en el código básico de la magnitud numérica, este estudio indaga en los efectos que tienen el aprendizaje temprano de las matemáticas en la relación entre número y espacio. Por tanto, el principal objetivo ha sido la investigación de cómo los bilingües activan y recuperan la línea numérica mental cuando la información numérica coincide con la LLmath en comparación con la "Otra Lengua" (OL). Un segundo objetivo se ha centrado en evaluar cómo impactan en la memoria de trabajo la manipulación y retención de la información numérico-espacial cuando ésta se presenta verbalmente en cada una de las dos lenguas (LLmath y OL).The implications of bilingualism in Math Cognition might be particularly visible in social, cultural and educational contexts. The clearest proof is the fact that bilinguals often switch languages when carrying out arithmetic computations such as fact retrieval or even number comparison, regardless of proficiency (Kolers, 1968). Thus, the main assumption is that arithmetic is sensitive to the language in which it was learned or trained (Frenk-Mestre and Vaid, 1993; Spelke and Tsivkin, 2001; Salillas and Wicha, 2012). More recently, we have proposed that this preference for one language has also an impact in the basic numerical magnitude representation. We suggested that the Language of Learning Math (herein LLmath) entails a preferred verbal code also for the most basic numerical knowledge: When bilinguals manage two different wording systems for naming quantity, the system pertaining to LLmath, and not L1, automatically gets activated and modulates the distance effect (Salillas and Carreiras, 2014; Salillas et al., 2015). The present study aims to further investigate the relationship between the LLmath and the evolved magnitude representation that implies an spatial component, the so-called “Mental Number Line” (MNL; Restle, 1970; Deahene, 1992).Given that previous research has provided evidence of the role of language in basic aspects of numerical representation in bilinguals, we aimed to investigate the neural bases of early math learning influence in the MNL representation. For such purpose, we tested a sample of Spanish-Basque bilinguals, equally proficient in both languages. We conducted two experiments based on a visual and an auditory working memory paradigm. It is well-known that specific working memory (WM) resources (e.g. phonological loop, visuospatial sketchpad) have an active role in number processing (Baddeley, 1986; DeStefano and LeFevre, 2004; Hecht, 2002; LeFevre et al., 2005; Raghubar et al., 2010; Seitz and Schumann-Hengsteler, 2000). Working memory entails a number of operations, needed to keep information active, each one related to a transient cognitive stage (encoding, retention, retrieval) (Baddeley, 1984; Friedman and Johnson, 2000). EEG-ERPs methods have been used in previous studies to isolate neural activity associated to the time course in each WM stage (Berti et at., 2000; McEvoy et al., 1998; Ruchkin et al., 1992, 1994, 1997; Shucard et al., 2009). In our study, we measured EEG during a match-to-sample task to investigate numerical-spatial processing signatures as a function of early learning math (LLmath vs Other Language (OL)) during the different WM stages. Participants were instructed to memorize the spatial location of a set of numbers presented visually (Experiment 1) or auditory (Experiment 2) either in the LLmath or in OL, and respond accordingly to a test number. Number-words could be congruent or incongruent with the spatial arrangement of the MNL (small numbers-left side/ large numbers-right side). We manipulated the memory load using 4 or 6 items in parallel versions of visual and auditory match-to-sample tasks (Sternberg task, Sternberg, 1966). This allowed us to better investigate the WM cognitive cost associated to each language during numerical-spatial information management. In general, our study provides neuroimaging evidence supporting different brain mechanisms for LLmath and OL in bilinguals´ MNL representation that agrees with previous findings. The results suggest an important role of language in the access to the MNL consistent with the early math leaning impact hypothesis. Further research should consider the results of this study to further investigate the neural mechanisms and core cognitive processes underlying the bilingual math case in order to enhance development of math competence and optimize learning

A developmental model of number representation

We delineate a developmental model of number representations. Notably, developmental dyscalculia (DD) is rarely associated with an all-or-none deficit in numerosity processing as would be expected if assuming abstract number representations. Finally, we suggest that the "generalist genes” view might be a plausible - though thus far speculative - explanatory framework for our model of how number representations develo

Neurophysiology of the macaque fronto-parietal magnitude system

In primates, the magnitude system resides in a fronto-parietal network. Single neurons in the monkey prefrontal cortex (PFC) and ventral intraparietal area (VIP) exhibit higher responses to a certain number of stimulus items regardless of their appearance or even sensory modality. Neuroimaging studies in humans show corresponding activation in human fronto-parietal areas during enumeration tasks. However, these areas are also involved in many other executive functions and, thus, the responses of single neurons within the network could be shaped by many factors. Understanding how information about magnitude develops within single neurons in this network was the objective of this thesis. This thesis includes five studies addressing various aspects of the primate frontoparietal magnitude system. First, we determined the role of behavioural relevance in shaping neuronal responses to number. Using enumerable coloured stimuli that naïve macaque monkeys discriminated based on their colour rather than number, we examined the selectivity of neuronal responses towards the number of stimuli. We simultaneously recorded single neurons in VIP and PFC. We compared these neurons to those recorded after a period of training for both monkeys, while they discriminated the stimuli based on number. In all the recording sessions, we also mapped the visual receptive fields (RF) of neurons using a passive fixation task. We created RF maps for a large number of spatially-selective neurons in each area and compared the RFs of pairs of neurons recorded at the same electrode tip. We then differentiated the extent of interaction between the RF and number selectivity in both areas. Neurons in both PFC and VIP were selective for number despite the monkeys being numerically-naïve and number being the behaviourally irrelevant stimulus feature. Post training, neurons in PFC were modulated by behavioural relevance and their selectivity for number became stronger as a result. VIP neurons did not show such an effect. We found that PFC RFs were predominantly contralateral and VIP RFs, foveal. Regardless of RF location and size, we observed heterogeneous and sometimes, inverted RFs in neurons adjacent to each other, more frequently in PFC than in VIP. Lastly, neurons in both PFC and VIP were strongly number-selective even when the number stimuli were shown outside their RFs. Our results provided valuable insight into the organisation of the magnitude system in primates. The presence of number-selective neuronal responses in numerically-naïve monkeys even when the number of stimuli was behaviourally irrelevant confirmed that our magnitude system processes magnitude spontaneously as a natural category. The strict spatiotopic organisation of RFs characteristic of early visual areas is progressively lower in VIP and PFC. Together, these results point to a hierarchy in the fronto-parietal areas we studied, with PFC located at the apex of the magnitude system and VIP upstream to it

Neuromodulation of Spatial Associations: Evidence from Choice Reaction Tasks During Transcranial Direct Current Stimulation

Various portions of human behavior and cognition are influenced by covert implicit processes without being necessarily available to intentional planning. Implicit cognitive biases can be measured in behavioral tasks yielding SNARC effects for spatial associations of numerical and non-numerical sequences, or yielding the implicit association test effect for associations between insect-flower and negative-positive categories. By using concurrent neuromodulation with transcranial direct current stimulation (tDCS), subthreshold activity patterns in prefrontal cortical regions can be experimentally manipulated to reduce implicit processing. Thus, the application of tDCS can test neurocognitive hypotheses on a unique neurocognitive origin of implicit cognitive biases in different spatial-numerical and non-numerical domains. However, the effects of tDCS are not only determined by superimposed electric fields, but also by task characteristics. To outline the possibilities of task-specific targeting of tDCS, task characteristics and instructions can be varied systematically when combined with neuromodulation. In the present thesis, implicit cognitive processes are assessed in different paradigms concurrent to left-hemispheric prefrontal tDCS to investigate a verbal processing hypothesis for implicit associations in general. In psychological experiments, simple choice reaction tasks measure implicit SNARC and SNARC-like effects as relative left-hand vs. right-hand latency advantages for responding to smaller number or ordinal sequence targets. However, different combinations of polarity-dependent tDCS with stimuli and task procedures also reveal domain-specific involvements and dissociations. Discounting previous unified theories on the SNARC effect, polarity-specific neuromodulation effects dissociate numbers and weekday or month ordinal sequences. By considering also previous results and patient studies, I present a hybrid and augmented working memory account and elaborate the linguistic markedness correspondence principle as one critical verbal mechanism among competing covert coding mechanisms. Finally, a general stimulation rationale based on verbal working memory is tested in separate experiments extending also to non-spatial implicit association test effects. Regarding cognitive tDCS effects, the present studies show polarity asymmetry and task-induced activity dependence of state-dependent neuromodulation. At large, distinct combinations of the identical tDCS electrode configuration with different tasks influences behavioral outcomes tremendously, which will allow for improved task- and domain-specific targeting