Mathematical difficulties as decoupling of expectation and developmental trajectories

Recent years have seen an increase in research articles and reviews exploring mathematical difficulties (MD). Many of these articles have set out to explain the etiology of the problems, the possibility of different subtypes, and potential brain regions that underlie many of the observable behaviors. These articles are very valuable in a research field, which many have noted, falls behind that of reading and language disabilities. Here will provide a perspective on the current understanding of MD from a different angle, by outlining the school curriculum of England and the US and connecting these to the skills needed at different stages of mathematical understanding. We will extend this to explore the cognitive skills which most likely underpin these different stages and whose impairment may thus lead to mathematics difficulties at all stages of mathematics development. To conclude we will briefly explore interventions that are currently available, indicating whether these can be used to aid the different children at different stages of their mathematical development and what their current limitations may be. The principal aim of this review is to establish an explicit connection between the academic discourse, with its research base and concepts, and the developmental trajectory of abstract mathematical skills that is expected (and somewhat dictated) in formal education. This will possibly help to highlight and make sense of the gap between the complexity of the MD range in real life and the state of its academic science

The Relation between Finger Gnosis and Mathematical Ability: Why Redeployment of Neural Circuits Best Explains the Finding

This paper elaborates a novel hypothesis regarding the observed predictive relation between finger gnosis and mathematical ability. In brief, we suggest that these two cognitive phenomena have overlapping neural substrates, as the result of the re-use ( redeployment ) of part of the finger gnosis circuit for the purpose of representing numbers. We offer some background on the relation and current explanations for it; an outline of our alternate hypothesis; some evidence supporting redeployment over current views; and a plan for further research

The development of number processing and its relation to other parietal functions in early childhood

The project has explored the developmental trajectories of several cognitive functions related to different brain regions: parietal cortex (quantity manipulation, finger gnosis, visuo-spatial memory and grasping abilities) and occipito-temporal cortex (face and object processing), in order to investigate their contributions to the acquisition of formal arithmetic in the first year of schooling. We tested preschooler, first grader and adult subjects, using correlational cross-sectional and longitudinal approaches. Results show that anatomical proximity is a strong predictor of behavioural correlations and of segregation between dorsal and ventral streams’ functions. This observation is particularly prominent in children: within parietal functions, there is a progressive separation across functions during development. During preschool age, presymbolic and symbolic number systems follow distinct developmental trajectories that converge during the first year of primary school. Indeed a possible cause of this phenomenon could be due to the refinement of the numerosity acuity during the acquisition of symbolic knowledge for numbers. Among the tested parietal functions, we observe a strong association between the numerical and the finger domain, especially in children. In preschoolers, finger gnosis is strongly associated with non-symbolic quantity processing, while in first graders it links up to symbolic mental arithmetic. This finding may reflect a pre-existing anatomical connection between the cortical regions supporting the quantity and finger-related functions in early childhood. In contrast, first graders exhibit a finger-arithmetic association more influenced by functional factors and cultural-based strategies (e.g. finger counting). Longitudinal data has allowed us to individuate which cognitive functions measured in kindergarteners predicts better the success in mental arithmetic in the first year of school. Results show that finger gnosis, as well as quantity and space–related abilities all concur at shaping the success in mental calculation in first graders. These results are important because, primarily, they are the first to observe a strong relation between visuo-spatial, finger and quantity related abilities in young children, and, secondly, because the longitudinal design provides strong evidence for a causal link between these functions and the success in formal arithmetic. These results suggest that educational programs should include training in each of these cognitive domains in mathematic classes. Finally, specific applications of these findings can be found within the domain of educational neuroscience and for the rehabilitation of children with numerical deficits (dyscalculia)

Competências matemáticas emergentes : desempenho neuropsicológico de crianças em cidade pré-escolar = emergent math skills : neuropsychological performance in prescholl - aged children

O presente trabalho insere-se no âmbito do emergente campo científico da Neurociência Educacional (também conhecida como Neuroeducação) e está organizado em duas principais abordagens, nas quais se estudam duas populações diferentes. A primeira abordagem subscreve a recomendação internacional sobre a importância de adotar uma visão da neurociência educacional para resolver alguns dos problemas educacionais. Nesta linha, uma pesquisa nacional foi realizada para analisar o conhecimento neurocientífico dos professores e as suas percepções sobre o significado da “ponte” entre a neurociência e a educação. Assim, dois estudos originais foram projetados para fornecer informação sobre o conhecimento dos professores e as suas crenças sobre o recente campo científico da neurociência educacional. Neste caso, a amostra coletada foi junto de professores do ensino pré-escolar ao ensino secundário [Estudo 1: Amostra com 627 professores de diferentes áreas de especialização com idades entre 25 e 65 anos (M = 41, DP = 9); Estudo 2: Participaram 583 professores com idades entre 25 e 61 anos (M = 41, DP = 9)]. A segunda abordagem refere-se à avaliação neuropsicológica e aborda um dos principais problemas atribuídos pela comunidade científica – os escassos instrumentos de medida (adaptados para o Português) para avaliar vários domínios neuropsicológicos. Três estudos experimentais foram realizados e um protocolo de avaliação neuropsicológica foi desenvolvido para este fim. Funções executivas, memória de trabalho visual-espacial, contagem dos dedos, percepção de pequenas quantidades sem proceder à contagem (subitizing) e a habilidade de usar funcionalmente os dedos e de os representar mentalmente (finger gnosis) foram os domínios trabalhados, a partir dos quais foram analisadas as suas relações com as competências matemáticas emergentes. Aqui, a população estudada foram crianças com idade pré-escolar [Estudo 3: Amostra composta por 137 crianças dos 3 aos 5 anos (M = 60, DP = 9; em meses); Estudo 4: Os participantes foram 30 crianças com 5 anos de idade ( 60-71 meses, M = 68, DP = 2.78 ); Estudo 5: Participaram 35 crianças com 5 anos de idade (M = 67.26, DP = 5.43), em meses]. Cada grupo de estudos experimentais, ou seja, os estudos correspondentes a cada abordagem, foram precedidos por revisões de literatura. Assim, são três os objetivos estruturais desta tese doutoral: (i) determinar se as perspectivas dos professores sobre a relação entre neurociência e educação (e seu conhecimento neurocientífico) dá a este campo científico a importância merecida (Estudos 1&2), (ii) adaptar para o Português o teste The Shape School para a sua utilização com crianças pré-escolares (Estudo 3), (iii) determinar se as capacidades matemáticas emergentes (pelo sistema do número aproximado e pelo conhecimento numérico) de crianças com idade pré-escolar é facilitada pelas funções executivas, memória de trabalho visuo-espacial, contagem de dedos, subitizing e a habilidade de usar funcionalmente os dedos (Estudos 4&5). Quanto aos resultados obtidos, na primeira abordagem, os estudos 1 e 2 fornecem evidências do interesse dos professores e do seu reconhecimento sobre o potencial da investigação neurocientífica na educação. No entanto, verificou-se também uma lacuna entre este interesse demonstrado e a proficiência na interpretação de informação científica, uma vez que os professores mostraram dificuldade em distinguir mitos de factos neurocientíficos. Os mitos “inteligências múltiplas”, “ensino dirigido aos estilos de aprendizagem (modelo VAK-Visual, Auditory, Kinaesthesic)” e “lado esquerdo do cérebro contra o lado direito do cérebro” foram os mais prevalentes. Os estudos desenvolvidos destacaram a importância de um processo de translação para que professores e neurocientistas possam colaborar. Em relação à avaliação neuropsicológica, ou seja, a segunda abordagem aqui tratada, os resultados do estudo 3 permitiram obter a adaptação Portuguesa do teste The Shape School que se revelou adequado para utilização quer em investigação, quer em contextos educacionais e clínicos. Com os estudos 4 e 5 identificaram-se os componentes que se relacionam com as competências matemáticas emergentes, destacando-se as funções executivas, subitizing e finger gnosis como preditores do conhecimento numérico. Assim, os vários estudos realizados neste âmbito suportam a necessidade de avaliação precoce dos domínios neuropsicológicos analisados, visto que parecem contribuir para uma melhor caracterização das competências matemáticas emergentes em crianças com idade pré-escolar. Considerando todos os resultados no seu conjunto, as conclusões destacam a necessidade de validade científica para a reforma do ensino, em geral, e para a educação da matemática, em particular, sob o campo da neurociência educacionalThe present work falls within the emerging field of Educational Neuroscience and is organized around two main approaches, studying two different populations. The first approach subscribes the international recommendation concerning the importance to adopt an educational neuroscience view to solving some of the educational problems. In this line, a national research was conducted to analyse the teacher’s neuroscientific knowledge and their perceptions about the “neuroscience-education bridge” meaning. Thus, two original researches were designed to analyse the teachers’ knowledge and beliefs concerning educational neuroscience. In this case, the sample collected was the Portuguese teachers from preschool to high school [Study 1: Sample with 627 teachers with ages ranged between 25 and 65 years (M=41; SD=9); Study 2: Participated 583 teachers from different areas of expertise, aged between 25 and 61 years (M=41; SD=9)]. The second approach refers to the neuropsychological assessment and addresses one of the main problems assigned by the research community – the few tools (adapted to Portuguese) to evaluate several neuropsychological domains. Three experimental studies were performed and a neuropsychological assessment protocol was developed for this purpose. Executive functions, visual-spatial working memory, finger counting, finger gnosis and subitizing were the studied domains, which were then correlated with early number knowledge. Here, the population studied was the Portuguese preschool-aged children [Study 3: Sample composed of 137 children from 3 to 5 years (M=60; SD=9; in months); Study 4: Participants were 30 children with 5 years-old (60-71 months; M=68, SD=2.78); Study 5: Collected 35 children with 5 years-old (M=67.26, SD=5.43), in months]. Each group of experimental studies, i.e., concerning each approach, were preceded by literature reviews. Therefore, the structural goals of this thesis are threefold: (i) determine whether the Portuguese teachers’ perspectives on the relationship between neuroscience and education (and their neuroscientific knowledge) gives to this field the significance deserved (Studies 1&2); (ii) adapt The Shape School test for the use of Portuguese preschoolers (Study 3); (iii) determine whether the emergent mathematical ability (by the approximate number system and the number knowledge) of Portuguese preschoolers is facilitated by the executive functions, visual-spatial working memory, finger counting, subitizing and finger gnosis (Studies 4&5). Concerning the findings, in the first approach, present studies provide evidence of the teachers’ interest and acknowledge of the potential of neuroscientific information in education, but also found a gap between their interest and proficiency in the interpretation of scientific information, since they showed difficulty of distinguishing myths from facts. Regarding the neuropsychological assessment, i.e., the second approach discussed here, the current studies support the need for early assessment of the components abilities analysed, which seem to contribute to a better characterisation of emerging numeracy skills in preschoolers. Taken all together, the conclusions highlight the need of scientific validity for reforming education, in general, and mathematics education, in particular, under the field of educational neuroscienc

Know Thyself: Behavioral Evidence for a Structural Representation of the Human Body

Background: Representing one's own body is often viewed as a basic form of self-awareness. However, little is known about structural representations of the body in the brain.Methods and Findings: We developed an inter-manual version of the classical "in-between'' finger gnosis task: participants judged whether the number of untouched fingers between two touched fingers was the same on both hands, or different. We thereby dissociated structural knowledge about fingers, specifying their order and relative position within a hand, from tactile sensory codes. Judgments following stimulation on homologous fingers were consistently more accurate than trials with no or partial homology. Further experiments showed that structural representations are more enduring than purely sensory codes, are used even when number of fingers is irrelevant to the task, and moreover involve an allocentric representation of finger order, independent of hand posture.Conclusions: Our results suggest the existence of an allocentric representation of body structure at higher stages of the somatosensory processing pathway, in addition to primary sensory representation

The role of the right temporoparietal junction in perceptual conflict: detection or resolution?

The right temporoparietal junction (rTPJ) is a polysensory cortical area that plays a key role in perception and awareness. Neuroimaging evidence shows activation of rTPJ in intersensory and sensorimotor conflict situations, but it remains unclear whether this activity reflects detection or resolution of such conflicts. To address this question, we manipulated the relationship between touch and vision using the so-called mirror-box illusion. Participants' hands lay on either side of a mirror, which occluded their left hand and reflected their right hand, but created the illusion that they were looking directly at their left hand. The experimenter simultaneously touched either the middle (D3) or the ring finger (D4) of each hand. Participants judged, which finger was touched on their occluded left hand. The visual stimulus corresponding to the touch on the right hand was therefore either congruent (same finger as touch) or incongruent (different finger from touch) with the task-relevant touch on the left hand. Single-pulse transcranial magnetic stimulation (TMS) was delivered to the rTPJ immediately after touch. Accuracy in localizing the left touch was worse for D4 than for D3, particularly when visual stimulation was incongruent. However, following TMS, accuracy improved selectively for D4 in incongruent trials, suggesting that the effects of the conflicting visual information were reduced. These findings suggest a role of rTPJ in detecting, rather than resolving, intersensory conflict

MORE THAN FINGER COUNTING: SHARED RESOURCES BETWEEN FINGER TAPPING AND ARITHMETIC

Thesis (Ph.D.) - Indiana University, Cognitive Science, 2011Arithmetic is a branch of mathematics upon which many other mathematical content areas are built. The study of the mechanisms underlying arithmetic is crucial for understanding cognition in other domains of mathematics, as well as higher-level cognition. Recent advances in the study of embodied cognition have yielded to a new interest in how mathematical thinking relates to our body and the sensorimotor system. Abundant behavioral, neuroimaging, and neuropsychological evidence have accumulated over the last two decades showing a relationship between number processing and sensorimotor processes. In addition, considerable evidence has been presented that suggest precursors of arithmetic skills in animals. This shows that arithmetic is not uniquely human and some of the relevant mechanisms may exist independent of language. In this dissertation a combination of behavioral and neuroimaging methods were used to explore the embodiment of arithmetic processing, with particular focus on the relation between finger movements and addition. In addition, how bodily measures (e.g. handedness, finger counting habits, finger tapping ability) interact with cognitive measures (e.g. math ability, digit span, spatial ability) was investigated. The results provide evidence for a finger-based representation of numbers, and show that bodily measures can predict elementary numerical skills

A computational model of focused attention meditation and its transfer to a sustained attention task

Although meditation and mindfulness practices are widely discussed and studied more and more in the scientific literature, there is little theory about the cognitive mechanisms that comprise it. Here we begin to develop such a theory by creating a computational cognitive model of a particular type of meditation: focused attention mediation. This model was created within Prims, a cognitive architecture similar to and based on ACT-R, which enables us to make predictions about the cognitive tasks that meditation experience may affect. We implemented a model based on an extensive literature review of how the meditation experience unfolds over time. We then subjected the Prims model to a session of the Sustained Reaction to Response Task, a task typically used to study sustained attention, a faculty that may be trained with meditation practice. Analyses revealed that the model was significantly more sensitive to detecting targets and non-targets after the meditation practice than before. These results agree with empirical findings of a longitudinal study conducted in 2010. These results suggest that our approach to modeling meditation and its effects of cognition is feasible

How does rumination impact cognition? A first mechanistic model.

Rumination is a process of uncontrolled, narrowly-foused neg- ative thinking that is often self-referential, and that is a hall- mark of depression. Despite its importance, little is known about its cognitive mechanisms. Rumination can be thought of as a specific, constrained form of mind-wandering. Here, we introduce a cognitive model of rumination that we devel- oped on the basis of our existing model of mind-wandering. The rumination model implements the hypothesis that rumina- tion is caused by maladaptive habits of thought. These habits of thought are modelled by adjusting the number of memory chunks and their associative structure, which changes the se- quence of memories that are retrieved during mind-wandering, such that during rumination the same set of negative memo- ries is retrieved repeatedly. The implementation of habits of thought was guided by empirical data from an experience sam- pling study in healthy and depressed participants. On the ba- sis of this empirically-derived memory structure, our model naturally predicts the declines in cognitive task performance that are typically observed in depressed patients. This study demonstrates how we can use cognitive models to better un- derstand the cognitive mechanisms underlying rumination and depression