The Developmental Characteristic And Neural Mechanism Of Mathematical Sequence Rule Learning

Rule learning plays a significant role in human cognition. It helps people to generalize the common rule and masters the nature of whole world. There are a large number of literatures have focused on the sentential tasks. Most of them have adopted habituation-dishabituation paradigm to explore the development of infants’ rule learning. Although many studies proved that infants and even animals had the ability of rule learning, they all focus on the grammar rule that is very simple to detect. The main cognitive process of infants’rule learning is to distinguish two patterns of rules, the one is regularity and another is irregularity. Infants are able to generalize the inner structure of stimuli when they stay in habituated phase (rule-detection phase). In other words, the pattern (rule) that is discovered by infants is the similar pronounce between the first and the last one. The main cognitive process is the pattern recognition. Nonetheless, we have to deal with a huge amount of information every day. The method of rule-detection is more than discriminating between regularities and irregularities. To learn the abstract rules, we have adopted not only pattern cognition, but also inductive inference and hypothesis testing. The present research employs the modified Brixton test. We present a clock-like card, which contains12circles with one is blue and others are white to all subjects. There are two conditions of the moving blue circle. In one condition, the moving circle follows the hidden rule. The other moving is at random. The purpose of the task is to judge which condition the moving is. As we all know, rule-attainment and rule-application is the key parts of numerical sequences. The nature of former one is rule-induction that contains hypothesis formulation and hypothesis test. The later one is rule application. The indispensable part of rule-detection is rule searching phase and rule discovery phase that are involved in the process of rule-attainment. Therefore, we continue to explore the brain region related to this process, especially the rule-discovery phase. Moreover, rule violation is also closely related to rule learning. After a sequence of stimuli, the random stimulus appears to distract the subject. The identified ability of violated stimuli and the active region of rule violation phase are still unknown. The purpose of the present study is to explore the rule-detection ability of numerical sequences and the brain mechanism of rule-detection. The first section involves two experiments. We discussed the young children before the formal operational stage (Piaget.1970), could generalize the abstract rule hide behind the stimulus sequence. Importantly, the present study would examine the developmental characteristics of rule-detection for children range from4to6years old. In section two, we measured event-related functional magnetic resonance imaging (fMRI) during the distinct phases of rule learning.Section one focuses on the capacity of rule detection for4to6-year-olds. The purpose is:(1) to examine the developmental characteristics of learning mathematical rules for children and different performances between easy and difficult conditions;(2) to explore whether children could discover mathematic rules when Arabic numbers were not used in the material. Results:(1) children who over4-year-old can detect most (80%) of the easy rules;(2) children who over4-year-old can detect most (80%)of the difficult rules;(3) children use the same searching trials among the successful samples;(4) in Experiment2, the ability of rule-detection showed a positive correlation with mathematical performance. Conclusion:(1)5-year-olds are capable of detected most of the mathematical rules;(2) the extra digital information may interfere with the performance of rule-attainment.Section two focuses on the mechanism of separate rule-detection phase. The purpose is:(1) to explore the cerebral regions involved in the four phases;(2) to study the brain regions sensitive to the rule-violation phase;(3) to investigate the region of interest (ROI) of mathematical sequences learning. Results:(1) Compared with the rule search phase, the rule discovery phase evoked many clusters, including the medial frontal gyrus (BA10), the left middle frontal gyrus (BA11), right inferior frontal gyrus (BA47), left parahippocampal gyrus (BA35), right supramarginal gyrus (BA40). bilateral cingulate (BA24), bilateral inferior parietal lobule (BA39). In difficult conditions, the medial frontal gyrus (BA9,10), the cingulate gyrus (BA24). right supramarginal gyrus (BA40), bilateral inferior parietal lobule (BA40), and bilateral temporal areas (BA20) are activated.(2)the cerebral regions specific to the following(following minus violation) include:bilateral medial frontal gyrus (BA10), left middle frontal gyrus (BA11), bilateral cingulate (BA31), and left precuneus were activated in the easy condition. The difficult condition evoked the following clusters:bilateral medial frontal gyrus (BA10), left middle frontal gyrus (BA11), left cingulate (BA31), bilateral parahippocampal gyrus (BA28), left temporal gyrus (BA20,21), and bilateral fusiform gyrus (BA37).(3) the rule violation phase minus the rule following phase also activated some clusters. In the easy condition, the left superior frontal gyrus (BA6), left medial frontal gyrus (BA6), bilateral middle frontal gyrus (BA6,8,9,46), bilateral inferior frontal gyrus (BA47), and left parietal lobule (BA7).Only the right inferior parietal lobule (BA40) was evoked in the difficult condition.(4) In lateral OFC and SPL, the ROI analysis revealed that the time-gignal strength curve under the rule following phase is much lower than other three phases; the ROI of DLPFC, the time-signal strength curve under the rule searching phase is the highest, while the rule following phase is the lowest; the ROI of MTG, the rule searching phase has the highest time-signal strength. The results suggest that (1) the cerebral regions involved in the rule-searching phase and the rule-discovery phase is different. Middle dorsolateral prefrontal cortex (mid-DLPFC) is more activated under the rule-searching phase than the rule-discovery phase. Moreover, compared with the rule-discovery phase, the left medial orbitofrontal cortex (OFC), bilateral cingulates, bilateral inferior parietal lobule (IPL). and right inferior/middle temporal gyrus are more activated in the rule-searching phase;(2) the rule violation phase evoked more activations in the lateral OFC and superior parietal lobule(SPL) than the rule following phase.