Spontaneous Focusing on Numerosity in the Development of Early Mathematical Skills

The aim of the present set of longitudinal studies was to explore 3-7-year-old children.s Spontaneous FOcusing on Numerosity (SFON) and its relation to early mathematical development. The specific goals were to capture in method and theory the distinct process by which children focus on numerosity as a part of their activities involving exact number recognition, and individual differences in this process that may be informative in the development of more complex number skills. Over the course of conducting the five studies, fifteen novel tasks were progressively developed for the SFON assessments. In the tasks, confounding effects of insufficient number recognition, verbal comprehension, other procedural skills as well as working memory capacity were aimed to be controlled. Furthermore, how children.s individual differences in SFON are related to their development of number sequence, subitizing-based enumeration, object counting and basic arithmetic skills was explored. The effect of social interaction on SFON was tested. Study I captured the first phase of the 3-year longitudinal study with 39 children. It was investigated whether there were differences in 3-year-old children.s tendency to focus on numerosity, and whether these differences were related to the children.s development of cardinality recognition skills from the age of 3 to 4 years. It was found that the two groups of children formed on the basis of their amount of SFON tendency at the age of 3 years differed in their development of recognising and producing small numbers. The children whose SFON tendency was very predominant developed faster in cardinality related skills from the age of 3 to 4 years than the children whose SFON tendency was not as predominant. Thus, children.s development in cardinality recognition skills is related to their SFON tendency. Studies II and III were conducted to investigate, firstly, children.s individual differences in SFON, and, secondly, whether children.s SFON is related to their counting development. Altogether nine tasks were designed for the assessments of spontaneous and guided focusing on numerosity. The longitudinal data of 39 children in Study II from the age of 3.5 to 6 years showed individual differences in SFON at the ages of 4, 5 and 6 years, as well as stability in children.s SFON across tasks used at different ages. The counting skills were assessed at the ages of 3.5, 5 and 6 years. Path analyses indicated a reciprocal tendency in the relationship between SFON and counting development. In Study III, these results on the individual differences in SFON tendency, the stability of SFON across different tasks and the relationship of SFON and mathematical skills were confirmed by a larger-scale cross-sectional study of 183 on average 6.5-year-old children (range 6;0-7;0 years). The significant amount of unique variance that SFON accounted for number sequence elaboration, object counting and basic arithmetic skills stayed statistically significant (partial correlations varying from .27 to .37) when the effects of non-verbal IQ and verbal comprehension were controlled. In addition, to confirm that the SFON tasks assess SFON tendency independently from enumeration skills, guided focusing tasks were used for children who had failed in SFON tasks. It was explored whether these children were able to proceed in similar tasks to SFON tasks once they were guided to focus on number. The results showed that these children.s poor performance in the SFON tasks was not caused by their deficiency in executing the tasks but on lacking focusing on numerosity. The longitudinal Study IV of 39 children aimed at increasing the knowledge of associations between children.s long-term SFON tendency, subitizing-based enumeration and verbal counting skills. Children were tested twice at the age of 4-5 years on their SFON, and once at the age of 5 on their subitizing-based enumeration, number sequence production, as well as on their skills for counting of objects. Results showed considerable stability in SFON tendency measured at different ages, and that there is a positive direct association between SFON and number sequence production. The association between SFON and object counting skills was significantly mediated by subitizing-based enumeration. These results indicate that the associations between the child.s SFON and sub-skills of verbal counting may differ on the basis of how significant a role understanding the cardinal meanings of number words plays in learning these skills. The specific goal of Study V was to investigate whether it is possible to enhance 3-year old children.s SFON tendency, and thus start children.s deliberate practice in early mathematical skills. Participants were 3-year-old children in Finnish day care. The SFON scores and cardinality-related skills of the experimental group of 17 children were compared to the corresponding results of the 17 children in the control group. The results show an experimental effect on SFON tendency and subsequent development in cardinality-related skills during the 6-month period from pretest to delayed posttest in the children with some initial SFON tendency in the experimental group. Social interaction has an effect on children.s SFON tendency. The results of the five studies assert that within a child.s existing mathematical competence, it is possible to distinguish a separate process, which refers to the child.s tendency to spontaneously focus on numerosity. Moreover, there are significant individual differences in children.s SFON at the age of 3-7 years. Moderate stability was found in this tendency across different tasks assessed both at the same and at different ages. Furthermore, SFON tendency is related to the development of early mathematical skills. Educational implications of the findings emphasise, first, the importance of regarding focusing on numerosity as a separate, essential process in the assessments of young children.s mathematical skills. Second, the substantial individual differences in SFON tendency during the childhood years suggest that uncovering and modeling this kind of mathematically meaningful perceiving of the surroundings and tasks could be an efficient tool for promoting young children.s mathematical development, and thus prevent later failures in learning mathematical skills. It is proposed to consider focusing on numerosity as one potential sub-process of activities involving exact number recognition in future studies.

Analysing Strategy Use in Terms of the Four Parameters of Strategic Competence : Contributions from a Numerosity Judgement Task.'Analizando el uso de estrategias en términos de cuatro parámetros de la competencia estratégica: contribuciones de una tarea de juicio de cantidad'.

Resumen tomado parcialmente de la revista.- El artículo forma parte de un monográfico de la revista dedicado a Psicología de las Matemáticas

A capacidade de subitizing em crianças de 4 anos

Dissertação apresentada à escola Superior de Educação de Lisboa para obtenção de grau de mestre em Educação Matemática na Educação Pré-Escolar e nos 1º e 2º Ciclos do Ensino Básico

Mapping numbers onto space in preschool children and adults

Tese de Doutoramento em Psicologia - Especialidade em Psicologia Experimental e Ciências Cognitivas

Sensory enhancement, a pilot perceptual study of subdermal magnetic implants

Subdermal magnetic implants originated as an art form in the world of body modification. To date an in depth scientific analysis of the benefits of this implant has yet to be established. This research explores the concept of sensory extension of the tactile sense utilising this form of implantation. This relatively simple procedure enables the tactile sense to respond to static and alternating magnetic fields. This is not to say that the underlying biology of the system has changed; i.e. the concept does not increase our tactile frequency response range or sensitivity to pressure, but now does invoke a perceptual response to a stimulus that is not innately available to humans. Within this research two social surveys have been conducted in order to ascertain one, the social acceptance of the general notion of human enhancement, and two the perceptual experiences of individuals with the magnetic implants themselves. In terms of acceptance to the notion of sensory improvement (via implantation) ~39% of the general population questioned responded positively with a further ~25% of the respondents answering with the indecisive response. Thus with careful dissemination a large proportion of individuals may adopt this technology much like this if it were to become available for consumers. Interestingly of the responses collected from the magnetic implants survey ~60% of the respondents actually underwent the implant for magnetic vision purposes. The main contribution of this research however comes from a series of psychophysical testing. In which 7 subjects with subdermal magnetic implants, were cross compared with 7 subjects that had similar magnets superficially attached to their dermis. The experimentation examined multiple psychometric thresholds of the candidates including intensity, frequency and temporal. Whilst relatively simple, the experimental setup for the perceptual experimentation conducted was novel in that custom hardware and protocols were created in order to determine the subjective thresholds of the individuals. Abstract iv The overall purpose of this research is to utilise this concept in high stress scenarios, such as driving or piloting; whereby alerts and warnings could be relayed to an operator without intruding upon their other (typically overloaded) exterior senses (i.e. the auditory and visual senses). Hence each of the thresholding experiments were designed with the intention of utilising the results in the design of signals for information transfer. The findings from the study show that the implanted group of subjects significantly outperformed the superficial group in the absolute intensity threshold experiment, i.e. the implanted group required significantly less force than the superficial group in order to perceive the stimulus. The results for the frequency difference threshold showed no significant difference in the two groups tested. Interestingly however at low frequencies, i.e. 20 and 50 Hz, the ability of the subjects tested to discriminate frequencies significantly increased with more complex waveforms i.e. square and sawtooth, when compared against the typically used sinewave. Furthermore a novel protocol for establishing the temporal gap detection threshold during a temporal numerosity study has been established in this thesis. This experiment measured the subjects’ capability to correctly determine the number of concatenated signals presented to them whilst the time between the signals, referred to as pulses, tended to zero. A significant finding was that when altering the length of, the frequency of, and the number of cycles of the pulses, the time between pulses for correct recognition altered. This finding will ultimately aid in the design of the tactile alerts for this method of information transfer. Preliminary development work for the use of this method of input to the body, in an automotive scenario, is also presented within this thesis in the form of a driving simulation. The overall goal of which is to present warning alerts to a driver, such as rear-to-end collision, or excessive speeds on roads, in order to prevent incidents and penalties from occurring. Discussion on the broader utility of this implant has been presented, reflecting on its potential use as a basis for vibrotactile, and sensory substitution, devices. This discussion furthers with postulations on its use as a human machine interface, as well as how a similar implant could be used within the ear as a hearing aid device.

Probabilidade de emergência de classes ordinais após o ensino de relações numéricas

O paradigma de equivalência de estímulos tem se mostrado útil na explicação de processos comportamentais complexos, como aqueles envolvidos em comportamentos conceituais numéricos. Vários estudos têm buscado a compreensão de como desempenhos sob controle da função de ordem são estabelecidos e mantidos. O objetivo do presente trabalho foi verificar se classes ordinais poderiam emergir após o ensino por emparelhamento arbitrário e de produção de seqüência. Participaram do estudo três alunos com atraso no desenvolvimento. Os estímulos visuais foram formas abstratas indicando numerosidade (A), numerais cardinais (B)e nomes escritos em letras maiúsculas de numerais (C). As sessões experimentais foram conduzidas em uma sala da APAE-BELÉM e um software controlou e registrou os dados comportamentais. As relações AB/AC foram ensinadas e testou-se a emergência de três classes de equivalência. Em seguida, houve um ensino por encadeamento de respostas com estímulos de um dos conjuntos (A1A2A3) e uma sonda de seqüenciação. Então, foi avaliada a emergência de novas seqüências (B1B2B3 e C1C2C3). Posteriormente, testes de substitutabilidade foram aplicados para verificar a formação de classes ordinais (por exemplo: A1B2C3). Testes de generalização também foram apresentados para verificar se um responder envolvendo numerosidade ocorreria com novos estímulos (por exemplo: E1E2E3). Os resultados demonstraram que os participantes responderam a novas seqüências prontamente ou com emergência gradual. A análise de topografias de controle de estímulos envolvidas nesse tipo de tarefa mostrou-se útil para a compreensão da ordinalidade. Todos os participantes responderam a seqüências com novos estímulos (generalização). O procedimento mostrou-se também eficiente na transferência de funções ordinais em pessoas com atraso no desenvolvimento.

A Test of Absolute Numerousness Judgments in Lion-Tailed Macaques (Macaca Silenus)

Numerous studies have shown that animals have a sense of quantity and can distinguish between relative amounts. The concepts of relative numerousness, estimation, and subitizing are well established in species as diverse as chimpanzees and salamanders. Mobile animals have practical use for an understanding of number in common situations such as predation, mating, and competition. However, the ability to identify discrete quantities has only been firmly established in humans. The purpose of this study was to test for such “absolute numerousness” judgments in three lion-tailed macaques (Macaca silenus), a non-human primate. The three macaques tested had previously been trained on a computerized matchto- sample (MTS) task using geometric shapes. In this study, they were introduced to a MTS task containing a numerical cue, which required the monkeys to match stimuli containing either one or two items for rewards. If monkeys were successful at the initial matching task, they were tested with stimuli in which the position of the items and then the surface area of the items was controlled. If the monkeys could match successfully without using these non-numerical cues, they would demonstrate the capability to make absolute numerousness judgments. None of the monkeys matched successfully using the numerical cue, so no evidence of absolute numerosity was found. Each macaque progressed through the experiment in an individualized manner, attempting a variety of strategies to obtain rewards. These included side preferences and an alternating-side strategy that were unrelated to the numerical cues in the stimuli. When it became clear that the monkeys were not matching based on a stimulus-based cue, they were tested again on matching geometric shapes. All three macaques stopped using their alternate strategies and were able to match shapes successfully, demonstrating that they were still capable of completing the matching task. The data suggest that the monkeys could not transfer this ability to the numerical stimuli. This indicates that the macaques lack a sense of exact quantity, or that they could not recognize the numerical cues in the stimuli as being relevant to the task.

Investigation on Heart Rate Variability (HRV) and psycho-social-affective adjustment in Italian women with ovarian cancer

INTRODUZIONE: L’integrazione mente-corpo applicata ad un ambito patologico predominante in questi tempi, come il cancro, è il nucleo di questa tesi. Il background teorico entro cui è inserita, è quello della Psiconeuroendocrinoimmunologia (Bottaccioli, 1995) e Psico-Oncologia. Sono state identificate, nella letteratura scientifica, le connessioni tra stati psicologici (mente) e condizioni fisiologiche (corpo). Le variabili emerse come potenzialmente protettive in pazienti che si trovano ad affrontare il cancro sono: il supporto sociale, l’immagine corporea, il coping e la Qualità della Vita, insieme all’indice fisiologico Heart Rate Variability (HRV; Shaffer & Venner, 2013). Il potenziale meccanismo della connessione tra queste variabili potrebbe essere spiegato dall’azione del Nervo Vago, come esposto nella Teoria Polivagale di Stephen Porges (2007; 2009). OBIETTIVI: Gli obiettivi principali di questo studio sono: 1. Valutare l’adattamento psicologico alla patologia in termini di supporto sociale percepito, immagine corporea, coping prevalente e qualità della vita in donne con cancro ovarico; 2. Valutare i valori di base HRV in queste donne; 3. Osservare se livelli più elevati di HRV sono associati ad un migliore adattamento psicologico alla patologia; 4. Osservare se una peggiore percezione dell’immagine corporea e l’utilizzo di strategie di coping disadattive sono associate ad una Qualità della Vita più scarsa. METODO: 38 donne affette da cancro ovarico, al momento della valutazione libere da patologia, sono state reclutate presso la clinica oncologica del reparto di Ginecologia dell’Azienda Ospedaliero-Universitaria di Parma, Italia. Ad ogni partecipante è stato chiesto di compilare una batteria di test composta da: MSPSS, per la valutazione del supporto sociale percepito; DAS-59, per la valutazione dell’immagine corporea; MAC, per la valutazione delle strategie di coping prevalenti utilizzate verso il cancro; EORTC-QLQ30, per la valutazione della Qualità della Vita. Per ogni partecipante è stato registrato HRV di base utilizzando lo strumento emWave (HeartMath). RISULTATI PRINCIPALI: Rispondendo agli obiettivi 1 e 2, in queste donne si è rilevato una alto tasso di supporto sociale percepito, in particolare ricevuto dalla persona di riferimento. L’area rivelatasi più critica nel supporto sociale è quella degli amici. Per quanto riguarda l’immagine corporea, la porzione di campione dai 30 ai 61 anni, ha delle preoccupazioni globali legate all’immagine corporea paragonabili ai dati provenienti dalla popolazione generale con preoccupazioni riguardo l’aspetto corporeo. Invece, nella porzione di campione dai 61 anni in su, il pattern di disagio verso l’aspetto fisico sembra decisamente peggiorare. Inoltre, in questo campione, si è rilevato un disagio globale verso l’immagine corporea significativamente più alto rispetto ai valori normativi presenti in letteratura riferiti a donne con cancro al seno con o senza mastectomia (rispettivamente t(94)= -4.78; p<0.000001; t(110)= -6.81;p<0.000001). La strategia di coping più utilizzata da queste donne è lo spirito combattivo, seguito dal fatalismo. Questo campione riporta, inoltre, una Qualità della Vita complessivamente soddisfacente, con un buon livello di funzionamento sociale. L’area di funzionalità più critica risulta essere il funzionamento emotivo. Considerando i sintomi prevalenti, i più riferiti sono affaticamento, disturbi del sonno e dolore. Per definire, invece, il pattern HRV, sono stati confrontati i dati del campione con quelli presenti in letteratura, riguardanti donne con cancro ovarico. Il campione valutato in questo studio, ha un HRV SDNN (Me=28.2ms) significativamente più alto dell’altro gruppo. Tuttavia, confrontando il valore medio di questo campione con i dati normativi sulla popolazione sana (Me=50ms), i nostri valori risultano drasticamente più bassi. In ultimo, donne che hanno ricevuto diagnosi di cancro ovarico in età fertile, sembrano avere maggiore HRV, migliore funzionamento emotivo e minore sintomatologia rispetto alle donne che hanno ricevuto diagnosi non in età fertile. Focalizzando l’attenzione sulla ricerca di relazioni significative tra le variabili in esame (obiettivo 3 e 4) sono state trovate numerose correlazioni significative tra: l’età e HRV, supporto percepito , Qualità della Vita; Qualità della Vita e immagine corporea, supporto sociale, strategie di coping; strategie di coping e immagine corporea, supporto sociale; immagine corporea e supporto sociale; HRV e supporto sociale, Qualità della Vita. Per verificare la possibile connessione causale tra le variabili considerate, sono state applicate regressioni lineari semplici e multiple per verificare la bontà del modello teorico. Si è rilevato che HRV è significativamente positivamente influenzata dal supporto percepito dalla figura di riferimento, dal funzionamento di ruolo, dall’immagine corporea totale. Invece risulta negativamente influenzata dal supporto percepito dagli amici e dall’uso di strategie di coping evitanti . La qualità della vita è positivamente influenzata da: l’immagine corporea globale e l’utilizzo del fatalismo come strategia di coping prevalente. Il funzionamento emotivo è influenzato dal supporto percepito dalla figura di riferimento e dal fatalismo. DISCUSSIONI E CONCLUSIONI: Il campione Italiano valutato, sembra essere a metà strada nell’adattamento dello stato psicologico e dell’equilibrio neurovegetativo al cancro. Sicuramente queste donne vivono una vita accettabile, in quanto sopravvissute al cancro, ma sembra anche che portino con sé preoccupazioni e difficoltà, in particolare legate all’accettazione della loro condizione di sopravvissute. Infatti, il migliore adattamento si riscontra nelle donne che hanno avuto peggiori condizioni in partenza: stadio del cancro avanzato, più giovani, con diagnosi ricevuta in età fertile. Pertanto, è possibile suggerire che queste condizioni critiche forzino queste donne ad affrontare apertamente il cancro e la loro situazione di sopravvissute al cancro, portandole ad “andare avanti” piuttosto che “tornare indietro”. Facendo riferimento alle connessioni tra variabili psicologiche e fisiologiche in queste donne, si è evidenziato che HRV è influenzata dalla presenza di figure significative ma, in particolare, è presumibile che sia influenzata da un’appropriata condivisione emotiva con queste figure. Si è anche evidenziato che poter continuare ad essere efficaci nel proprio contesto personale si riflette in un maggiore HRV, probabilmente in quanto permette di preservare il senso di sé, riducendo in questo modo lo stress derivante dall’esperienza cancro. Pertanto, HRV in queste donne risulta associato con un migliore adattamento psicologico. Inoltre, si è evidenziato che in queste donne la Qualità della Vita è profondamente influenzata dalla percezione dell’immagine corporea. Si tratta di un aspetto innovativo che è stato rilevato in questo campione e che, invece, nei precedenti studi non è stato indagato. In ultimo, la strategia di coping fatalismo sembra essere protettiva e sembra facilitare il processo di accettazione del cancro. Si spera sinceramente che le ricerche future possano superare i limiti del presente studio, come la scarsa numerosità e l’uso di strumenti di valutazione che, per alcuni aspetti come la scala Evitamento nel MAC, non centrano totalmente il target di indagine. Le traiettorie future di questo studio sono: aumentare il numero di osservazioni, reclutando donne in diversi centri specialistici in diverse zone d’Italia; utilizzare strumenti più specifici per valutare i costrutti in esame; valutare se un intervento di supporto centrato sul miglioramento di HRV (come HRV Biofeedback) può avere una ricaduta positiva sull’adattamento emotivo e la Qualità della Vita.

Mapping and modulating spatial attention asymmetries in young and older adults

Healthy young adults demonstrate a group-level, systematic preference for stimuli presented in the left side of space relative to the right (‘pseudoneglect’) (Bowers & Heilman, 1980). This results in an overestimation of features such as size, brightness, numerosity and spatial frequency in the left hemispace, probably as a result of right cerebral hemisphere dominance for visuospatial attention. This spatial attention asymmetry is reduced in the healthy older population, and can be shifted entirely into right hemispace under certain conditions. Although this rightward shift has been consistently documented in behavioural experiments, there is very little neuroimaging evidence to explain this effect at a neuroanatomical level. In this thesis, I used behavioural methodology and electroencephalography (EEG) to map spatial attention asymmetries in young and older adults. I then use transcranial direct current stimulation (tDCS) to modulate these spatial biases, with the aim of assessing age-related differences in response to tDCS. In the first of three experiments presented in this thesis, I report in Chapter Two that five different spatial attention tasks provide consistent intra-task measures of spatial bias in young adults across two testing days. There were, however, no inter-task correlations between the five tasks, indicating that pseudoneglect is at least partially driven by task-dependent patterns of neural activity. In Chapter Three, anodal tDCS was applied separately to the left (P5) and right (P6) posterior parietal cortex (PPC) in young and older adults, with an aim to improve the detection of stimuli appearing in the contralateral visual field. There were no age differences in response to tDCS, but there were significant differences depending on baseline performance. Relative to a sham tDCS protocol, tDCS applied to the right PPC resulted in maintained visual detection across both visual fields in adults who were good at the task at baseline. In contrast, left PPC tDCS resulted in reduced detection sensitivity across both visual fields in poor performers. Finally, in Chapter Four, I report a right-hemisphere lateralisation of EEG activity in young adults that was present for long (but not short) landmark task lines. In contrast, older adults demonstrated no lateralised activity for either line length, thus providing novel evidence of an age-related reduction of hemispheric asymmetry in older adults. The results of this thesis provide evidence of a highly complex set of factors that underlie spatial attention asymmetries in healthy young and older adults.

TiMMing: developing an innovative suite of bioinformatic tools to harmonize and track the origin of copy number alterations in the evolutive history of multiple myeloma

Multiple Myeloma (MM) is a hematologic cancer with heterogeneous and complex genomic landscape, where Copy Number Alterations (CNAs) play a key role in the disease's pathogenesis and prognosis. It is of biological and clinical interest to study the temporal occurrence of early alterations, as they play a disease "driver" function by deregulating key tumor pathways. This study presents an innovative bioinformatic tools suite created for harmonizing and tracing the origin of CNAs throughout the evolutionary history of MM. To this aim, large cohorts of newly-diagnosed MM (NDMM, N=1582) and Smoldering-MM (SMM, N=282) were aggregated. The tools developed in this study enable the harmonization of CNAs as obtained from different genomic platforms in such a way that a high statistical power can be obtained. By doing so, the high numerosity of those cohorts was harnessed for the identification of novel genes characterized as "driver" (NFKB2, NOTCH2, MAX, EVI5 and MYC-ME2-enhancer), and the generation of an innovative timing model, implemented with a statistical method to introduce confidence intervals in the CNAs-calls. By applying this model on both NDMM and SMM cohorts, it was possible to identify specific CNAs (1q(CKS1B)amp, 13q(RB1)del, 11q(CCND1)amp and 14q(MAX)del) and categorize them as "early"/ "driver" events. A high level of precision was guaranteed by the narrow confidence intervals in the timing estimates. These CNAs were proposed as critical MM alterations, which play a foundational role in the evolutionary history of both SMM and NDMM. Finally, a multivariate survival model was able to identify the independent genomic alterations with the greatest effect on patients’ survival, including RB1-del, CKS1B-amp, MYC-amp, NOTCH2-amp and TRAF3-del/mut. In conclusion, the alterations that were identified as both "early-drivers” and correlated with patients’ survival were proposed as biomarkers that, if included in wider survival models, could provide a better disease stratification and an improved prognosis definition.