This fMRI study aimed at unraveling the neural basis of learning alphabet arithmetic facts, as a proxy of the transition from slow and effortful procedural counting-based processing to fast and effortless processing as it occurs in learning addition arithmetic facts. Neural changes were tracked while participants solved alphabet arithmetic problems in a verification task (e.g., F + 4 = J). Problems were repeated across four learning blocks. Two neural networks with opposed learning-related changes were identified. Activity in a network consisting of basal ganglia and parieto-frontal areas decreased with learning, which is in line with a reduction of the involvement of procedure-based processing. Conversely, activity in a network involving the left angular gyrus and, to a lesser extent, the hippocampus gradually increases with learning, evidencing the gradual involvement of retrieval-based processing. Connectivity analyses gave insight in the functional relationship between the two networks. Despite the opposing learning-related trajectories, it was found that both networks become more integrated. Taking alphabet arithmetic as a proxy for learning arithmetic, the present results have implications for current theories of learning arithmetic facts and can give direction to future developments.

Visuospatial working memory (VSWM) plays an important role in arithmetic problem solving, and the relationship between these two skills is thought to change over development. Even though neuroimaging studies have demonstrated that VSWM and arithmetic both recruit frontoparietal networks, inferences about common neural substrates have largely been made by comparisons across studies. Little work has examined how brain activation for VSWM and arithmetic converge within the same participants and whether there are age-related changes in the overlap of these neural networks. In this study, we examined how brain activity for VSWM and arithmetic overlap in 38 children and 26 adults. Although both children and adults recruited the intraparietal sulcus (IPS) for VSWM and arithmetic, children showed more focal activation within the right IPS, whereas adults recruited the bilateral IPS, superior frontal sulcus/middle frontal gyrus, and right insula. A comparison of the two groups revealed that adults recruited a more left-lateralized network of frontoparietal regions for VSWM and arithmetic compared with children. Together, these findings suggest possible neurocognitive mechanisms underlying the strong relationship between VSWM and arithmetic and provide evidence that the association between VSWM and arithmetic networks changes with age.

It is well established that, when comparing nonsymbolic magnitudes (e.g., dot arrays), adults can use both numerical (i.e., the number of items) and nonnumerical (density, total surface areas, etc.) magnitudes. It is less clear which of these magnitudes is more salient or processed more automatically. In this fMRI study, we used a nonsymbolic comparison task to ask if different brain areas are responsible for the automatic processing of numerical and nonnumerical magnitudes, when participants were instructed to attend to either the numerical or the nonnumerical magnitudes of the same stimuli. An interaction of task (numerical vs. nonnumerical) and congruity (congruent vs. incongruent) was found in the right TPJ. Specifically, this brain region was more strongly activated during numerical processing when the nonnumerical magnitudes were negatively correlated with numerosity (incongruent trials). In contrast, such an interference effect was not evident during nonnumerical processing when the task-irrelevant numerical magnitude was incongruent. In view of the role of the right TPJ in the control of stimulus-driven attention, we argue that these data demonstrate that the processing of nonnumerical magnitudes is more automatic than that of numerical magnitudes and that, therefore, the influence of numerical and nonnumerical variables on each other is asymmetrical.

The ability to process the numerical magnitude of sets of items has been characterized in many animal species. Neuroimaging data have associated this ability to represent nonsymbolic numerical magnitudes (e.g., arrays of dots) with activity in the bilateral parietal lobes. Yet the quantitative abilities of humans are not limited to processing the numerical magnitude of nonsymbolic sets. Humans have used this quantitative sense as the foundation for symbolic systems for the representation of numerical magnitude. Although numerical symbol use is widespread in human cultures, the brain regions involved in processing of numerical symbols are just beginning to be understood. Here, we investigated the brain regions underlying the semantic and perceptual processing of numerical symbols. Specifically, we used an fMRI adaptation paradigm to examine the neural response to Hindu-Arabic numerals and Chinese numerical ideographs in a group of Chinese readers who could read both symbol types and a control group who could read only the numerals. Across groups, the Hindu-Arabic numerals exhibited ratio-dependent modulation in the left IPS. In contrast, numerical ideographs were associated with activation in the right IPS, exclusively in the Chinese readers. Furthermore, processing of the visual similarity of both digits and ideographs was associated with activation of the left fusiform gyrus. Using culture as an independent variable, we provide clear evidence for differences in the brain regions associated with the semantic and perceptual processing of numerical symbols. Additionally, we reveal a striking difference in the laterality of parietal activation between the semantic processing of the two symbols types.

Because number is an abstract quality of a set, the way in which a number is externally represented does not change its quantitative meaning. In this study, we examined the development of the brain regions that support format-independent representation of numerical magnitude. We asked children and adults to perform both symbolic (Hindu-Arabic numerals) and nonsymbolic (arrays of squares) numerical comparison tasks as well as two control tasks while their brains were scanned using fMRI. In a preliminary analysis, we calculated the conjunction between symbolic and nonsymbolic numerical comparison. We then examined in which brain regions this conjunction differed between children and adults. This analysis revealed a large network of visual and parietal regions that showed greater activation in adults relative to children. In our primary analysis, we examined age-related differences in the conjunction of symbolic and nonsymbolic comparison after subtracting the control tasks. This analysis revealed a much more limited set of regions including the right inferior parietal lobe near the intraparietal sulcus. In addition to showing increased activation to both symbolic and nonsymbolic magnitudes over and above activation related to response selection, this region showed age-related differences in the distance effect. Our findings demonstrate that the format-independent representation of numerical magnitude in the right inferior parietal lobe is the product of developmental processes of cortical specialization and highlight the importance of using appropriate control tasks when conducting developmental neuroimaging studies.

Although significant insights into the neural basis of numerical and mathematical processing have been made, the neural processes that enable abstract symbols to become numerical remain largely unexplored in humans. In the present study, adult participants were trained to associate novel symbols with nonsymbolic numerical magnitudes (arrays of dots). Functional magnetic resonance imaging was used to examine the neural correlates of numerical comparison versus recognition of the novel symbols after each of two training stages. A left-lateralized fronto-parietal network, including the intraparietal sulcus, the precuneus, and the dorsal prefrontal cortex, was more active during numerical comparison than during perceptual recognition. In contrast, a network including bilateral temporal–occipital regions was more active during recognition than comparison. A whole-brain three-way interaction revealed that those individuals who had higher scores on a postscan numerical task (measuring their understanding of the global numerical organization of the novel symbols) exhibited increasing segregation between the two tasks in the bilateral intraparietal sulci as a function of increased training. Furthermore, whole-brain regression analysis showed that activity in the left intraparietal sulcus was systematically related to the effect of numerical distance on accuracy. These data provide converging evidence that parietal and left prefrontal cortices are involved in learning to map numerical quantities onto visual symbols. Only the parietal cortex, however, appeared systematically related to the degree to which individuals learned to associate novel symbols with their numerical referents. We conclude that the left parietal cortex, in particular, may play a central role in imbuing visual symbols with numerical meaning.

There exists a long-standing debate regarding whether small and large numerosities engage different networks of processing. The ability to rapidly enumerate small (1–4) numerosities is referred to as “subitizing” and is thought to be qualitatively different from large numerosity processing. Functional neuro-imaging studies have attempted to dissociate neural correlates of small and large number processing by contrasting subitizing with counting of numerosities just outside the subitizing range. In the present study, we used functional magnetic resonance imaging (fMRI) to contrast the processing of numerosities in the “subitizing range” with numerosities requiring estimation. Participants compared sequentially presented slides of either dots or Arabic numerals for their relative magnitude. We show that comparison of nonsymbolic numerosities in the subitizing range led to activation of the right temporo-parietal junction, while at the same time this region was found to be suppressed during large numerosity processing. Furthermore, relative suppression of this region was strongly associated with faster response times. In previous studies, this region has been implicated in stimulus-driven attention.We therefore contend that activation of the temporo-parietal junction during small number processing and the suppression thereof during large numerosity comparisons reflects differential reliance on stimulus-driven versus goal-directed attentional networks in the brain.

Numerical magnitude processing is an essential everyday skill. Functional brain imaging studies with human adults have repeatedly revealed that bilateral regions of the intraparietal sulcus are correlated with various numerical and mathematical skills. Surprisingly little, however, is known about the development of these brain representations. In the present study, we used functional neuroimaging to compare the neural correlates of nonsymbolic magnitude judgments between children and adults. Although behavioral performance was similar across groups, in comparison to the group of children the adult participants exhibited greater effects of numerical distance on the left intraparietal sulcus. Our findings are the first to reveal that even the most basic aspects of numerical cognition are subject to age-related changes in functional neuroanatomy. We propose that developmental impairments of number may be associated with atypical specialization of cortical regions underlying magnitude processing.

The role of language in performing numerical computations has been a topic of special interest in cognition. The “Triple Code Model” proposes the existence of a language-dependent verbal code involved in retrieving arithmetic facts related to addition and multiplication, and a language-independent analog magnitude code subserving tasks such as number comparison and estimation. Neuroimaging studies have shown dissociation between dependence of arithmetic computations involving exact and approximate processing on language-related circuits. However, a direct manipulation of language using different arithmetic tasks is necessary to assess the role of language in forming arithmetic representations and in solving problems in different languages. In the present study, 20 English-Chinese bilinguals were trained in two unfamiliar arithmetic tasks in one language and scanned using fMRI on the same problems in both languages (English and Chinese). For the exact “base-7 addition” task, language switching effects were found in the left inferior frontal gyrus (LIFG) and left inferior parietal lobule extending to the angular gyrus. In the approximate “percentage estimation” task, language switching effects were found predominantly in the bilateral posterior intraparietal sulcus and LIFG, slightly dorsal to the LIFG activation seen for the base-7 addition task. These results considerably strengthen the notion that exact processing relies on verbal and language-related networks, whereas approximate processing engages parietal circuits typically involved in magnitude-related processing.