Numerical fractions are commonly used to express ratios and proportions (i.e., real numbers), but little is known about how they are mentally represented and processed by skilled adults. Four experiments employed comparison tasks to investigate the distance effect and the effect of the spatial numerical association of response codes (SNARC) for fractions. Results showed that fractions were processed componentially and that the real numerical value of the fraction was not accessed, indicating that processing the fraction's magnitude is not automatic. In contrast, responses were influenced by the numerical magnitude of the components and reflected the simple comparison between numerators, denominators, and reference, depending on the strategy adopted. Strategies were used even by highly skilled participants and were flexibly adapted to the specific experimental context. In line with results on the whole number bias in children, these findings suggest that the understanding of fractions is rooted in the ability to represent discrete numerosities (i.e., integers) rather than real numbers and that the well-known difficulties of children in mastering fractions are circumvented by skilled adults through a flexible use of strategies based on the integer components.
The properties of objects, such as shape, influence the way we grasp them. To quantify the role of different brain regions during grasping, it is necessary to disentangle the processing of visual dimensions related to object properties from the motor aspects related to the specific hand configuration. We orthogonally varied object properties (shape, size, and elongation) and task (passive viewing, precision grip with two or five digits, or coarse grip with five digits) and used representational similarity analysis of functional magnetic resonance imaging data to infer the representation of object properties and hand configuration in the human brain. We found that object elongation is the most strongly represented object feature during grasping and is coded preferentially in the primary visual cortex as well as the anterior and posterior superior-parieto-occipital cortex. By contrast, primary somatosensory, motor, and ventral premotor cortices coded preferentially the number of digits while ventral-stream and dorsal-stream regions coded a mix of visual and motor dimensions. The representation of object features varied with task modality, as object elongation was less relevant during passive viewing than grasping. To summarize, this study shows that elongation is a particularly relevant property of the object to grasp, which along with the number of digits used, is represented within both ventral-stream and parietal regions, suggesting that communication between the two streams about these specific visual and motor dimensions might be relevant to the execution of efficient grasping actions.
Neurons in macaque primary motor cortex (M1) are broadly tuned to arm movement direction. Recent evidence suggests that human M1 contains directionally tuned neurons, but it is unclear which other areas are part of the network coding movement direction and what characterizes the responses of neuronal populations in those areas. Such information would be highly relevant for the implementation of brain-computer interfaces (BCIs) in paralyzed patients. We used functional magnetic resonance imaging adaptation to identify which areas of the human brain show directional selectivity and the degree to which these areas are affected by the type of motor act (to press vs to grasp). After adapting participants to one particular hand movement direction, we measured the release from adaptation during occasional test trials, parametrically varying the angular difference between adaptation and test direction. We identified multiple areas broadly tuned to movement direction, including M1, dorsal premotor cortex, intraparietal sulcus, and the parietal reach region. Within these areas, we observed a gradient of directional selectivity, with highest directional selectivity in the right parietal reach region, for both right-and left-hand movements. Moreover, directional selectivity was modulated by the type of motor act to varying degrees, with the largest effect in M1 and the smallest modulation in the parietal reach region. These data provide an important extension of our knowledge about directional tuning in the human brain. Furthermore, our results suggest that the parietal reach region might be an ideal candidate for the implementation of BCI in paralyzed patients.
The difficulty in processing fractions seems to be related to the interference between the whole-number value of the numerator and the denominator and the real value of the fraction. Here we assess whether the reported problems with symbolic fractions extend to the nonsymbolic domain, by presenting fractions as arrays of black and white dots representing the two operands. Participants were asked to compare a target array with a reference array in two separate tasks using the same stimuli: a numerosity task comparing just the number of white dots in the two arrays; and a proportion task comparing the proportion of black and white dots. The proportion task yielded lower accuracy and slower response, confirming that even with nonsymbolic stimuli accessing proportional information is relatively difficult. However, using a congruity manipulation in which the greater numerosity of white dots could co-occur with a lower proportion of them, and vice versa, it was found that both task-irrelevant dimensions would interfere with the task-relevant dimension suggesting that both numerosity and proportion information was automatically accessed. The results indicate that the magnitude of fractions can be automatically and holistically processed in the nonsymbolic domain.
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