Operation-specific encoding in single-digit arithmetic

The involvement of the semantic neural network in rule identification of mathematical processing

The role of the visuospatial network in mathematical processing has been established, but the involvement of the semantic network in mathematical processing is still poorly understood. The current study utilized a number series completion paradigm with the event-related potential (ERP) technique to examine whether the semantic network supports mathematical processing and to find the corresponding spatiotemporal neural marker. In total, 32 right-handed undergraduate students were recruited and asked to complete the number series completion as well as the arithmetical computation task in which numbers were presented in sequence. The event-related potential and multi-voxel pattern analysis showed that the rule identification process involves more semantic processing when compared with the arithmetical computation processes, and it elicited higher amplitudes for the late negative component (LNC) in left frontal and temporal lobes. These results demonstrated that the semantic network supports the rule identification in mathematical processing, with the LNC acting as the neural marker.

Oscillatory electroencephalographic patterns of arithmetic problem solving in fourth graders

Numerous studies have identified neurophysiological correlates of performing arithmetic in adults. For example, oscillatory electroencephalographic (EEG) patterns associated with retrieval and procedural strategies are well established. Whereas fact retrieval has been linked to enhanced left-hemispheric theta ERS (event-related synchronization), procedural strategies are accompanied by increased bilateral alpha ERD (event-related desynchronization). It is currently not clear if these findings generalize to children. Our study is the first to investigate oscillatory EEG activity related to strategy use and arithmetic operations in children. We assessed ERD/ERS correlates of 31 children in fourth grade (aged between nine and ten years) during arithmetic problem solving. We presented multiplication and subtraction problems, which children solved with fact retrieval or a procedure. We analyzed these four problem categories (retrieved multiplications, retrieved subtractions, procedural multiplications, and procedural subtractions) in our study. In summary, we found similar strategy-related patterns to those reported in previous studies with adults. That is, retrieval problems elicited stronger left-hemispheric theta ERS and weaker alpha ERD as compared to procedural problems. Interestingly, we observed neurophysiological differences between multiplications and subtractions within retrieval problems. Although there were no response time or accuracy differences, retrieved multiplications were accompanied by larger theta ERS than retrieved subtractions. This finding could indicate that retrieval of multiplication and subtraction facts are distinct processes, and/or that multiplications are more frequently retrieved than subtractions in this age group.

Specific Mental Arithmetic Difficulties and General Arithmetic Learning Difficulties: The Role of Phonological Working Memory

The aim of this paper was to examine the role of phonological working memory in specific mental arithmetic difficulties and general arithmetic learning difficulties (ALD; difficulties presenting in both mental arithmetic and written arithmetic). In Study 1, we categorized 53 sixth graders into a control group, a group with specific mental arithmetic difficulties, and a group with general ALD. The findings indicated the group with specific mental arithmetic difficulties performed significantly worse on the task involving phonological working memory than did the control group. However, a significant difference was not found between the group with general ALD and the control group. In Study 2 involving 54 sixth graders, we decreased the load of phonological working memory by changing the format of the problems from horizontal (more reliance on phonological codes) to vertical (more reliance on visual resources). We found that the group with specific mental arithmetic difficulties performed comparably to the control group. In other words, when the working memory load is reduced, they no longer lag significantly behind on mental arithmetic. However, the group with general ALD still performed significantly worse than the control group when the problems were presented vertically, indicating that reduced phonological working memory load did not alleviate their arithmetic difficulties. The findings in both studies suggested that poor phonological working memory might contribute to the underlying mechanism for specific mental arithmetic difficulties but not as much for general ALD.

Differential recruitment of brain networks in single-digit addition and multiplication: Evidence from EEG oscillations in theta and lower alpha bands

Previous neuroimaging research investigating dissociation between single-digit addition and multiplication has suggested that the former placed more reliance on the visuo-spatial processing whereas the latter on the verbal processing. However, there has been little exploration into the disassociation in spatio-temporal dynamics of the oscillatory brain activity in specific frequency bands during the two arithmetic operations. To address this issue, the electroencephalogram (EEG) data were recorded from 19 participants engaged in a delayed verification arithmetic task. By analyzing oscillatory EEG activity in theta (5-7 Hz) and lower alpha frequency (9-10 Hz) bands, we found different patterns of oscillatory brain activity between single-digit addition and multiplication during the early processing stage (0-400 ms post-operand onset). Experiment results in this study showed a larger phasic increase of theta-band power for addition than for multiplication in the midline and the right frontal and central regions during the operator and operands presentation intervals, which was extended to the right parietal and the right occipito-temporal regions during the interval immediately after the operands presentation. In contrast, during multiplication higher phase-locking in lower alpha band was evident in the centro-parietal regions during the operator presentation, which was extended to the left fronto-central and anterior regions during the operands presentation. Besides, we found stronger theta phase synchrony between the parietal areas and the right occipital areas for single-digit addition than for multiplication during operands encoding. These findings of oscillatory brain activity extend the previous observations on functional dissociation between the two arithmetic operations.