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Imaging early practice effects in arithmetic
Abstract
A better understanding of learning processes in arithmetic in healthy adults can guide research into learning disabilities such as dyscalculia. The goal of the present functional magnetic resonance imaging study was to investigate the ongoing process of learning itself. No training was provided prior to the scanning session. Training consisted in a higher frequency of repetition for one set of complex multiplication problems (repeated) and a lower frequency for the other set (novel). Repeated and novel problems were presented randomly in an event-related design. We observed activation decreases due to training in fronto-parietal areas and the caudate nucleus, and activation increases in temporo-parietal regions such as the left angular gyrus. Training effects became significant after approximately eight repetitions of a problem and remained stable over the course of the experiment. The change in brain activation patterns observed was similar to the results of previous neuroimaging studies investigating training effects in arithmetic after a week of extensive training. The paradigm employed seems to be a suitably sensitive tool to investigate and compare learning processes on group level for different populations. Furthermore, on a more general level, the early and robust changes in brain activation in healthy adults observed here indicate that repeating stimuli can profoundly and quickly affect fMRI results.
... This shift is parallel to age-related changes in brain activity (for a detailed review see Peters and De Smedt (2018) [22]). Neuroimaging studies in both children and adults have shown that the frontoparietal network is activated during arithmetic problem solving [23,24]. Interestingly, this activation shifts from frontal to parietal areas when age increases [23]. ...
... Besides the importance of frequency analysis during task performance, an association between mathematical ability and frequency analysis during rest has also been found. Namely, in one recent brain stimulation study it was observed that frontal resting state activity (rs-EEG) in the beta frequency range (14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30) was linked to high mathematical performance [36]. Adults with average and high mathematical baseline skills improved more on a mathematical task when receiving stimulation in the beta range compared to stimulation in other frequency bands. ...
... with the aperiodic signal (offset and exponent) indicated in black and the periodic signal indicated in blue. The shaded blue area is the beta frequency range (14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30). The relative power as calculated with the traditional method is not considering aperiodic signals while the parameterization analysis is (i.e., periodic power). ...
Previous work has shown relations between domain-general processes, domain-specific processes, and mathematical ability. However, the underlying neurophysiological effects of mathematical ability are less clear. Recent evidence highlighted the potential role of beta oscillations in mathematical ability. Here we investigate whether domain-general (working memory) and domain-specific (number sense) processes mediate the relation between resting-state beta oscillations and mathematical ability, and how this may differ as a function of development (children vs. adults). We compared a traditional analysis method normally used in EEG studies with a more recently developed parameterization method that separates periodic from aperiodic activity. Regardless of methods chosen, we found no support for mediation of working memory and number sense, neither for children nor for adults. However, we found subtle differences between the methods. Additionally, we showed that the traditional EEG analysis method conflates periodic activity with aperiodic activity; in addition, the latter is strongly related to mathematical ability and this relation differs between children and adults. At the cognitive level, our findings do not support previous suggestions of a mediation of working memory and number sense. At the neurophysiological level our findings suggest that aperiodic, rather than periodic, activity is linked to mathematical ability as a function of development.
... This short-term training study of arithmetic multiplication items was designed to manipulate arithmetic learning and strategy change from procedural use to fact retrieval and to investigate the corresponding changes in brain activity. fMRI short-term training designs have been applied in a wide range of studies in adults already (Delazer et al., 2003(Delazer et al., , 2005Grabner et al., 2009;Ischebeck et al., 2006Ischebeck et al., , 2007, but they have not been used to study arithmetic learning in children. Earlier brain imaging studies in children have used either cross-sectional (Cho et al., 2011(Cho et al., , 2012Prado et al., 2014;Rivera et al., 2005) or longitudinal designs (Qin et al., 2014), yet they did not investigate the effect of an experimental manipulation of arithmetic strategy use via training on brain activity. ...
... Another possibility for the lack of greater HC activation might be that the duration of the training in children was not long enough to induce training-related changes in brain activity, particularly not in the HC. However, the current training protocol was longer and more intensive than the adult training studies (Grabner et al., 2009;Ischebeck et al., 2006Ischebeck et al., , 2007 and the data at the behavioral level showed that training indeed was sufficient. We observed a clear behavioral decrease over all training days for response time, i.e. from seven seconds to three seconds, and accuracy quickly reached ceiling. ...
... Participants' use of fact retrieval is further supported by the strategy assessment data before the training: 93.2 % of the singledigit items were reported to be solved using arithmetic fact retrieval. Increases in left lateralized activation in the AG is a common finding in adults studies (Delazer et al., 2003(Delazer et al., , 2005Grabner et al., 2009;Ischebeck et al., 2006Ischebeck et al., , 2007, and in some studies on arithmetic in children (Polspoel et al., 2017), and these activation increases have been interpreted as reflective of arithmetic fact retrieval. ...
Arithmetic learning is characterized by a change from procedural strategies to fact retrieval. fMRI training studies in adults have revealed that this change coincides with decreased activation in the prefrontal cortex (PFC) and that within the parietal lobe, a shift occurs from the intraparietal sulcus (IPS) to the angular gyrus (AG) during this change. It remains to be determined whether similar changes can be observed in children, particularly because children often recruit the hippocampus (HC) during fact retrieval, an observation that has not consistently been found in adults. In order to experimentally manipulate arithmetic strategy change, 26 typically developing 9- to-10-year-olds completed a six day at-home training of complex multiplication items (e.g. 16 × 4). Before and after training, children were presented with three multiplication conditions during fMRI: (1) complex to-be-trained/trained items, (2) complex untrained items and (3) single-digit items. Behavioral data indicated that training was successful. Similar to adults, children showed greater activity in the IPS and PFC for the untrained condition post-training, indicating that the fronto-parietal network during procedural arithmetic problem solving is already in place in children of this age. We did not observe the expected training-related changes in the HC. In contrast to what has been observed in adults, greater activity in the AG was not observed for the trained items. These results show that the brain processes that accompany the learning of arithmetic facts are different in children as compared to adults.
... Studies in arithmetical cognition have been focusing on how experience, training and teaching practices can impact the neurocognitive substrates supporting arithmetic processing [1]. So far, studies have shown real-time learning effects [2][3][4][5], focused strategies training effects [2,5] and even cultural-linguistic differences [6] to determine the extent to which the neural substrates as well as the cognitive strategies used in arithmetic can be and are malleable. A question that has been overlooked is whether language modality, signed instead of spoken, may impact the neural network and strategies involved in single-digit arithmetic processing. ...
... Solving multiplication problems, on the other hand, activates a left-lateralized network in the temporal (superior and middle temporal gyri, STG and MTG) and inferior frontal cortices (inferior frontal gyrus, IFG) commonly activated in phonological processing [24,26]. This differentiation of brain networks appears to be experience-driven, where practice and training increase the observed neural differentiation [3][4][5][28][29][30]. Additionally, problem size has been shown to modulate the reliance on the different networks, with larger problems being more likely solved through computation-based strategies [26,[31][32][33][34]. ...
... What we observe here is that even through very different prolonged language and sensory experiences, the distinction between the operations remains, and the attentional and cognitive processes involved are surprisingly similar across groups. Subtle educational and short training manipulations have shown changes in brain networks and strategies [3,4]; how is it that the use of a visual and manual language does not modify more extensively the processes involved? One possible reason might be that language is foundational to abstract thought and that the modality is processed early in the cognitive stream and then filtered out as to leave only abstract reasoning at play. ...
Does experience with signed language impact the neurocognitive processes recruited by adults solving arithmetic problems? We used event-related potentials (ERPs) to identify the components that are modulated by operation type and problem size in Deaf American Sign Language (ASL) native signers and in hearing English-speaking participants. Participants were presented with single-digit subtraction and multiplication problems in a delayed verification task. Problem size was manipulated in small and large problems with an additional extra-large subtraction condition to equate the overall magnitude of large multiplication problems. Results show comparable behavioral results and similar ERP dissociations across groups. First, an early operation type effect is observed around 200 ms post-problem onset, suggesting that both groups have a similar attentional differentiation for processing subtraction and multiplication problems. Second, for the posterior-occipital component between 240 ms and 300 ms, subtraction problems show a similar modulation with problem size in both groups, suggesting that only subtraction problems recruit quantity-related processes. Control analyses exclude possible perceptual and cross-operation magnitude-related effects. These results are the first evidence that the two operation types rely on distinct cognitive processes within the ASL native signing population and that they are equivalent to those observed in the English-speaking population.
... Whereas former research has laid out the general neural networks that play a role in arithmetic learning (Zamarian, Ischebeck, & Delazer, 2009) and the transition from effortful controlled processing to resource-minimal processing has begun to be addressed (Ischebeck, Zamarian, Egger, Schocke, & Delazer, 2007), additional work is necessary to substantiate and further specify the underlying dynamics of what happens to the procedural system and/or whether a separate retrieval-based system is created. Moreover, it remains to be determined how the transition is embedded at the neural level: Are new functional neural circuits developed, or are the original circuits reshaped to operate in a less effortful manner? ...
... Counting can be expected to rely on procedure-based neural networks that comprise frontostriatal regions known to subserve skill acquisition (Poldrack & Gabrieli, 2001) and sequence learning (Gheysen, Van Opstal, Roggeman, Van Waelvelde, & Fias, 2011). The network supporting memory retrieval is expected to comprise the angular gyrus (AG), known to be involved in conceptual knowledge in general (Seghier, 2013), including arithmetic facts (Grabner et al., 2009;Ischebeck et al., 2007;Delazer et al., 2005). In addition, the medial temporal lobes may be involved, especially because they support initial stages of learning, although their role is still a matter of discussion. ...
... In addition, the medial temporal lobes may be involved, especially because they support initial stages of learning, although their role is still a matter of discussion. Some have found involvement of the hippocampus (HC; De Smedt, Holloway, & Ansari, 2011), whereas others did not (Ischebeck et al., 2007). ...
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.
... Studies in arithmetical cognition have been focusing on how experience, training and teaching practices can impact the neurocognitive substrates supporting arithmetic processing [1]. So far, studies have shown real-time learning effects [2][3][4][5], focused strategies training effects [2,5] and even cultural-linguistic differences [6] to determine the extent to which the neural substrates as well as the cognitive strategies used in arithmetic can be and are malleable. A question that has been overlooked is whether language modality, signed instead of spoken, may impact the neural network and strategies involved in single-digit arithmetic processing. ...
... Solving multiplication problems, on the other hand, activates a left-lateralized network in the temporal (superior and middle temporal gyri, STG and MTG) and inferior frontal cortices (inferior frontal gyrus, IFG) commonly activated in phonological processing [24,26]. This differentiation of brain networks appears to be experience-driven, where practice and training increase the observed neural differentiation [3][4][5][28][29][30]. Additionally, problem size has been shown to modulate the reliance on the different networks, with larger problems being more likely solved through computation-based strategies [26,[31][32][33][34]. ...
... What we observe here is that even through very different prolonged language and sensory experiences, the distinction between the operations remains, and the attentional and cognitive processes involved are surprisingly similar across groups. Subtle educational and short training manipulations have shown changes in brain networks and strategies [3,4]; how is it that the use of a visual and manual language does not modify more extensively the processes involved? One possible reason might be that language is foundational to abstract thought and that the modality is processed early in the cognitive stream and then filtered out as to leave only abstract reasoning at play. ...
In this study, we investigate the impact of experience with a signed language on the neurocognitive processes recruited by adults solving single-digit arithmetic problems. We use event-related potentials (ERPs) to identify the components that are modulated by problem size and operation type in Deaf American Sign Language (ASL) native signers as well as in hearing English-speaking participants. Participants were presented with subtraction and multiplication problems in a delayed verification task. Problem size was manipulated in small and large with an additional extra-large subtraction condition to equate the overall magnitude with large multiplication problems. Results show overall comparable behavioral results across groups and similar ERP dissociations between operation types. First, an early operation type effect is observed between 180ms and 210ms post problem onset, suggesting that both groups have a similar attentional differentiation for processing subtraction and multiplication problems. Second, on the posterior-occipital component between 240ms and 300ms, similarly for both groups only subtraction problems show modulation with problem size suggesting that only this category recruit quantity-related processes. Control analyses exclude this effect as being perceptual and magnitude related. These results are the first evidence that the two operations rely on distinct cognitive processes within the ASL native signing population and this distinction is equivalent to the one observed in the English-speaking population.
... Similarly, a recent study on arithmetic skills highlighted the individual differences in both neural correlates and behavioral response in healthy people [29]. The left frontoparietal network has been implicated in playing an important role in arithmetic processing and can be targeted by tACS [30,31]. We recognize that other brain stimulation techniques have been used in the field of arithmetic [32][33][34][35][36][37], for reviews see [31,38,39]. ...
... theta/beta ratio, and beta (14-30 Hz) connectivity (all p > .1). However, our findings from the pBO models highlight an optimal performance effect in the beta frequency range (14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30) in subjects with average and high baseline ability, whilst low baseline ability individuals benefit from stimulation in the gamma frequency range (> 30 Hz). We therefore examined the relationship between baseline ability and baseline frontal beta power in an exploratory manner. ...
... Arithmetic performance was tested using an arithmetic calculation paradigm, consisting of problems involving a single-digit number multiplied by a two-digit number, with a three-digit outcome. This paradigm was presented using Matlab's psychtoolbox version 3. A calculation paradigm was used instead of a retrieval paradigm since calculation has been associated with an increased activation in the frontoparietal network [30,56,57]. None of the multiplications included operands with the digits 0, 1, or 2 to prevent variations in difficulty. ...
Accumulating evidence from human-based research has highlighted that the prevalent one-size-fits-all approach for neural and behavioral interventions is inefficient. This approach can benefit one individual, but be ineffective or even detrimental for another. Studying the efficacy of the large range of different parameters for different individuals is costly, time-consuming and requires a large sample size that makes such research impractical and hinders effective interventions. Here an active machine learning technique is presented across participants—personalized Bayesian optimization (pBO)—that searches available parameter combinations to optimize an intervention as a function of an individual’s ability. This novel technique was utilized to identify transcranial alternating current stimulation (tACS) frequency and current strength combinations most likely to improve arithmetic performance, based on a subject’s baseline arithmetic abilities. The pBO was performed across all subjects tested, building a model of subject performance, capable of recommending parameters for future subjects based on their baseline arithmetic ability. pBO successfully searches, learns, and recommends parameters for an effective neurointervention as supported by behavioral, simulation, and neural data. The application of pBO in human-based research opens up new avenues for personalized and more effective interventions, as well as discoveries of protocols for treatment and translation to other clinical and non-clinical domains.
... Changes in deactivation in both the left and right SMG (together with the AG) have been detected in many other arithmetic studies (Bloechle et al., 2016;Grabner et al., 2009a,b;Pesenti et al., 2001;Rickard et al., 2000;Rivera et al., 2005;van Harskamp et al., 2002) and they have been linked to processes supporting memory retrieval (Ischebeck et al., 2007). Similar to the current study, two studies (Ischebeck et al., 2007;Rickard et al., 2000) have observed deactivation in the right SMG while participants worked on a multiplication verification task. ...
... Changes in deactivation in both the left and right SMG (together with the AG) have been detected in many other arithmetic studies (Bloechle et al., 2016;Grabner et al., 2009a,b;Pesenti et al., 2001;Rickard et al., 2000;Rivera et al., 2005;van Harskamp et al., 2002) and they have been linked to processes supporting memory retrieval (Ischebeck et al., 2007). Similar to the current study, two studies (Ischebeck et al., 2007;Rickard et al., 2000) have observed deactivation in the right SMG while participants worked on a multiplication verification task. Whereas Rickard et al. (2000) found increased deactivation in the right SMG for a multiplication verification task relative to two low-level control tasks (i. ...
... Whereas Rickard et al. (2000) found increased deactivation in the right SMG for a multiplication verification task relative to two low-level control tasks (i. e., numerical judgment and perceptual-motor control task), Ischebeck et al. (2007) observed decreased deactivation in the same brain region for repeated (trained) multiplications as compared to novel ones. 1 In contrast to previous findings (Grabner et al., 2007;Grabner et al., 2009a,b), we did not observe any relationship between individual differences in arithmetic competence and activation in the AG. However, the competence-related training effect observed in the right SMG shows a high similarity with the findings from the arithmetic fact training study by Grabner, Ischebeck and colleagues (2009). ...
Single-digit multiplications are thought to be associated with different levels of interference because they show different degrees of feature overlap (i.e., digits) with previously learnt problems. Recent behavioral and neuroimaging studies provided evidence for this interference effect and showed that individual differences in arithmetic fact retrieval are related to differences in sensitivity to interference (STI). The present study investigated whether and to what extent competence-related differences in STI and its neurophysiological correlates can be modulated by a multiplication facts training.
Participants were 23 adults with high and 23 adults with low arithmetic competencies who underwent a five-day multiplication facts training in which they intensively practiced sets of low- and high-interfering multiplication problems. In a functional magnetic resonance imaging (fMRI) test session after the training, participants worked on a multiplication verification task that comprised trained and untrained problems.
Analyses of the behavioral data revealed an interference effect only in the low competence group, which could be reduced but not resolved by training. On the neural level, competence-related differences in the interference effect were observed in the left supramarginal gyrus (SMG), showing activation differences between low- and high-interfering problems only in the low competent group. These findings support the idea that individuals’ low arithmetic skills are related to the development of insufficient memory representations because of STI. Further, our results indicate that a short training by drill (i.e., learning associations between operands and solutions) was not fully effective to resolve existing interference effects in arithmetic fact knowledge.
... Little is known about neurophysiological changes during the course of learning. One of the few functional magnetic resonance imaging (fMRI) studies revealed increased activation of the left angular gyrus after 8 repetitions of complex multiplication problems (Ischebeck, Zamarian, Egger, Schocke, & Delazer, 2007), which partially resembled earlier post-training findings in adults. However, this finding might not be readily generalized to children. ...
... In this way, we can relate our findings to other literature in adults. The only neuroimaging study, which investigated neural changes during the course of arithmetic learning in adults, used multiplication operation as well (Ischebeck et al., 2007). Multiplication is also the only operation which was used in oscillatory EEG studies of arithmetic learning in both adults (Grabner & De Smedt, 2012) and children . ...
... Simultaneous EEG-fMRI studies also revealed that theta oscillation in frontal and parietal areas, including the midline electrodes, is associated with activation of the hippocampus, angular gyrus, superior parietal cortex, insular and cingulate cortices, superior temporal areas, and frontal areas (Mizuhara et al., 2004;Sammer et al., 2007). Interestingly, these brain areas have been frequently reported in fMRI studies of multiplication learning in adults (Bloechle et al., 2016;Ischebeck et al., 2007). Therefore, observed theta activity in the midline electrodes in our study is supported by the activation of several brain areas, which are involved in fMRI studies of multiplication problem-solving. ...
Most studies have investigated brain activation changes after the course of arithmetic learning, and the question remains whether these changes are detectable during the course of learning, i.e., before memory consolidation. Twenty-four fifth graders solved multiplication problems while ongoing electroencephalography (EEG) was recorded. The arithmetic training revealed reduced errors together with a power increase in theta (4–7 Hz) but not in lower alpha (8–10 Hz) or upper alpha (10–13 Hz) bands. We conclude that increases in theta power subserved a shift from slow, procedural strategies to more efficient, automated procedural and retrieval strategies, which led to more efficient performance.
... Activation patterns in the brain can be imaged using fMRI, and several studies have reported working memory being served by frontal areas of the brain, specifically the frontoparietal areas and the basal ganglia (cited in Ischebeck, Zamarian, Egger, Schoke, & Delazer, 2007). However, studies with adults previously trained in arithmetic operations showed different regions of brain activation, specifically in the left angular gyrus, representing the brain retrieving information from long-term memory rather than from working memory (or short-term memory) (Ischebeck et al, 2007). ...
... Activation patterns in the brain can be imaged using fMRI, and several studies have reported working memory being served by frontal areas of the brain, specifically the frontoparietal areas and the basal ganglia (cited in Ischebeck, Zamarian, Egger, Schoke, & Delazer, 2007). However, studies with adults previously trained in arithmetic operations showed different regions of brain activation, specifically in the left angular gyrus, representing the brain retrieving information from long-term memory rather than from working memory (or short-term memory) (Ischebeck et al, 2007). This shift in brain activity demonstrates to the educator that learning has been successful, and has resulted in long-term knowledge for the individual. ...
... This shift in brain activity demonstrates to the educator that learning has been successful, and has resulted in long-term knowledge for the individual. Ischebeck et al (2007) presented complex multiplication problems to healthy adults on a repeated basis and novel problems less frequently, and demonstrated that repetition after eight times showed a significant change in brain activation patterns with higher input from the left angular gyrus (linked with long-term memory). This valuable insight contradicts common perceptions in higher education, where a new topic or concept need be taught only once, rapidly disseminated to students, followed immediately by another. ...
One way that higher education transforms lives is by fostering the development of cognitive complexity in students. This development is demonstrated in many
ways in the classroom, and can be explained using the Perry Scheme of Intellectual and
Ethical Development. Cognitive complexity is imperative for the helping professions, and
students who develop complexity will be better able to facilitate complex changes in clients. Additionally, this kind of development can result in dramatic changes in the students’ own lives, which can lead to transformation at all levels of society
... The cognitive method as well as the statistical analysis of the current study enabled us not only to study the differences between automatic processing of area vs. perimeter (i.e., investigating magnitude sense in DD), but also to investigate whether DD participants indeed perform poorly or differently on continuous magnitude processing tasks in initial vs. proficiency stages of learning (i.e., to investigate learning functions in DD). Earlier studies showed that even a small number of rehearsals of numerical problems led to automatic processing and to changes in brain functions (Ischebeck et al., 2007;Aubin et al., 2016). For instance, Ischebeck et al. (2007) found that very short training (eight repetitions) in multiplication problems led to a decrease in the activity of fronto-parietal brain areas related to calculation and numerical processing (Menon et al., 2000;Dehaene et al., 2003). ...
... Earlier studies showed that even a small number of rehearsals of numerical problems led to automatic processing and to changes in brain functions (Ischebeck et al., 2007;Aubin et al., 2016). For instance, Ischebeck et al. (2007) found that very short training (eight repetitions) in multiplication problems led to a decrease in the activity of fronto-parietal brain areas related to calculation and numerical processing (Menon et al., 2000;Dehaene et al., 2003). On the other hand, the training also resulted in increased activity in temporo-parietal regions known to be involved in arithmetic fact retrieval (Dehaene et al., 2003). ...
... On the other hand, the training also resulted in increased activity in temporo-parietal regions known to be involved in arithmetic fact retrieval (Dehaene et al., 2003). Recently, it was proposed that DDs' deficits in inhibition of irrelevant numerical information can also represent difficulties with consolidating learned information and with performing the shift from initial computing based processing to automatic retrieval based processing (Ischebeck et al., 2007;Aubin et al., 2016). Indeed, Aubin et al. (2016) suggested that people with DD may be less able to consolidate a numerical task within the frontal-parietal region and must instead rely on their working memory. ...
The relationship between numbers and other magnitudes has been extensively investigated in the scientific literature. Here, the objectives were to examine whether two continuous magnitudes, area and perimeter, are automatically processed and whether adults with developmental dyscalculia (DD) are deficient in their ability to automatically process one or both of these magnitudes. Fifty-seven students (30 with DD and 27 with typical development) performed a novel Stroop-like task requiring estimation of one aspect (area or perimeter) while ignoring the other. In order to track possible changes in automaticity due to practice, we measured performance after initial and continuous exposure to stimuli. Similar to previous findings, current results show a significant group × congruency interaction, evident beyond exposure level or magnitude type. That is, the DD group systematically showed larger Stroop effects. However, analysis of each exposure period showed that during initial exposure to stimuli the DD group showed larger Stroop effects in the perimeter and not in the area task. In contrast, during continuous exposure to stimuli no triple interaction was evident. It is concluded that both magnitudes are automatically processed. Nevertheless, individuals with DD are deficient in inhibiting irrelevant magnitude information in general and, specifically, struggle to inhibit salient area information after initial exposure to a perimeter comparison task. Accordingly, the findings support the assumption that DD involves a deficiency in multiple cognitive components, which include domain-specific and domain-general cognitive functions.
... Furthermore, it is assumed to induce more specific processing of number magnitude information in parietal and language-related processes in left temporal areas of the brain. Such a shift in solution strategy was repeatedly observed to be accompanied by reduced activation in the fronto-parietal network of number processing and increased activation in language-related parieto-temporal areas in the left hemisphere in adults (Delazer et al., 2003(Delazer et al., , 2005Grabner, Ischebeck et al., 2009;Ischebeck et al., 2006;Ischebeck, Zamarian, Egger, Schocke, & Delazer, 2007;Ischebeck, Zamarian, Schocke, & Delazer, 2009;Pauli et al., 1994; for a review see Zamarian et al., 2009). Generally, there seems to be a shift from frontal to parietal regions, and then within parietal regions with increasing proficiency reflecting reduced demands on domain-general cognitive processes and increased domain-specific numerical processes . ...
... Generally, there seems to be a shift from frontal to parietal regions, and then within parietal regions with increasing proficiency reflecting reduced demands on domain-general cognitive processes and increased domain-specific numerical processes . Interestingly, it was found that this shift in brain activation can already happen after eight repetitions of arithmetic problems in adults (Ischebeck et al., 2007). ...
... A decrease in parietal activation, which is usually associated with processing numerical magnitude, may indicate that after the training, children seemed to rely less on manipulations of numerical magnitudes to solve the task. This finding is in line with an fMRI study by Ischebeck et al. (2007) that reported similar brain activation changes in adults after a training on complex multiplication problems. In sum, this decrease seems to indicate reduced demands on exact calculation (e.g., Dehaene, Molko, Cohen, & Wilson, 2004). ...
Recent years have seen a considerable increase in informal educational environments complementing formal educational settings such as schools. In this chapter, we will report results on the efficacy of a web-platform for game-based learning of orthography and numeracy. Besides the behavioral assessment of the platform, we focused specifically on neurocognitive changes due to training on the platform. These neurocognitive data are particularly informative to understand how game-based learning leads to performance improvements, and also might help us to develop new instructional designs. Our web-based platform hosts several learning games, aiming at fostering orthography and numeracy skills. Learning games enable individual learning independent from formal learning environments—anytime and anywhere. Behavioral results revealed promising learning effects, particularly for orthography. In the next step, neurocognitive changes during arithmetic learning were assessed. Results indicated that arithmetic learning in our informal environment led to strategy changes, previously reported for the development of arithmetic competencies in formal learning settings for both adults and children. Altogether, the findings suggest that improvements in orthography and numeracy can be achieved in joyful and less stressful informational environments such as our web-platform for game-based learning. We suggest that the additional implementation of adaptivity in such learning games to better meet individual needs should further increase obtained training effects in the future. Instructional implications of these findings and the relevance of neurocognitive data for learning are discussed.
... Thus, the question arises whether or not the described areas and connections are indeed causally involved in the numerical processes suggested and, thus, whether the two-network framework can sufficiently explain numerical performance of cognitively impaired participants as well. Especially in arithmetic fact retrieval, it has been criticized that several of the areas, which are typically found activated during arithmetic fact retrieval, may neither be specific to nor necessary for arithmetic fact retrieval (e.g., Bloechle et al. 2016;Grabner et al. 2009a, b;Grabner et al. 2009a, b;Ischebeck et al. 2007). The angular gyrus, for instance, has been frequently associated with arithmetic fact retrieval (e.g., Delazer et al. 2003a, b; for a meta-analysis see Dehaene et al. 2003), but was also modulated by learning of mathematical, but also nonmathematical content (Ischebeck et al. 2007). ...
... Especially in arithmetic fact retrieval, it has been criticized that several of the areas, which are typically found activated during arithmetic fact retrieval, may neither be specific to nor necessary for arithmetic fact retrieval (e.g., Bloechle et al. 2016;Grabner et al. 2009a, b;Grabner et al. 2009a, b;Ischebeck et al. 2007). The angular gyrus, for instance, has been frequently associated with arithmetic fact retrieval (e.g., Delazer et al. 2003a, b; for a meta-analysis see Dehaene et al. 2003), but was also modulated by learning of mathematical, but also nonmathematical content (Ischebeck et al. 2007). In addition, neuropsychological single-case studies do not unequivocally support a causal role as some patients with a multiplication deficit had a preserved AG (Cohen and Dehaene 2000;Dehaene and Cohen 1997;Zaunmuller et al. 2009), while others with a lesion of the left AG did not show a multiplication deficit (e.g., Van Harskamp and Cipolotti 2001). ...
Developmental dyscalculia is a specific learning disorder that persists over lifetime and can have an enormous impact on personal, health-related, and professional aspects of life. Despite its central importance, the origin both at the cognitive and neural level is not yet well understood. Several classification schemas of dyscalculia have been proposed, sometimes together with an associated deficit at the neural level. However, these explanations are (a) not providing an exhaustive framework that is at levels with the observed complexity of developmental dyscalculia at the behavioral level and (b) are largely mono-causal approaches focusing on gray matter deficits. We suggest that number processing is instead the result of context-dependent interaction of two anatomically largely separate, distributed but overlapping networks that function/cooperate in a closely integrated fashion. The proposed two-network framework (TNF) is the result of a series of studies in adults on the neural correlates underlying magnitude processing and arithmetic fact retrieval, which comprised neurofunctional imaging of various numerical tasks, the application of probabilistic fiber tracking to obtain well-defined connections, and the validation and modification of these results using disconnectome mapping in acute stroke patients. Emerged from data in adults, it represents the endpoint of the acquisition and use of mathematical competencies in adults. Yet, we argue that its main characteristics should already emerge earlier during development. Based on this TNF, we develop a classification schema of phenomenological subtypes and their underlying neural origin that we evaluate against existing propositions and the available empirical data.
... These findings have also been replicated across different operation types (Delazer et al. 2005;Ischebeck et al. 2006). Additionally, an innovative design where participants were trained on problems within the scanner revealed that participants exhibited training-related activation decreases in fronto-parietal regions, and increases in temporo-parietal regions including the left AG over the duration of the fMRI scan (Ischebeck et al. 2007). Together, findings showing that activation in the AG is associated with trained arithmetic problems have been taken to suggest that the AG is related to the retrieval of arithmetic facts. ...
... Another unresolved question about AG function during arithmetic is the distinction between the left and right AG during mathematical problem-solving. Specifically, many studies report left-lateralized activation for arithmetic factretrieval (Delazer et al. 2003;Grabner et al. 2009;Ischebeck et al. 2007), whereas others report bilateral activation in the AG (De Smedt et al. 2011;Polspoel et al. 2017;Stanescu-Cosson et al. 2000). Further, one of the only rTMS studies to simultaneously examine both the left and right AG found that disruption of the AG in both hemispheres affected addition performance to a similar degree (Montefinese et al. 2017). ...
Since the pioneering work of the early 20th century neuropsychologists, the angular gyrus (AG), particularly in the left hemisphere, has been associated with numerical and mathematical processing. The association between the AG and numerical and mathematical processing has been substantiated by neuroimaging research. In the present review article, we will examine what is currently known about the role of the AG in numerical and mathematical processing with a particular focus on arithmetic. Specifically, we will examine the role of the AG in the retrieval of arithmetic facts in both typically developing children and adults. The review article will consider alternative accounts that posit that the involvement of the AG is not specific to arithmetic processing and will consider how numerical and mathematical processing and their association with the AG overlap with other neurocognitive processes. The review closes with a discussion of future directions to further characterize the relationship between the angular gyrus and arithmetic processing.
... Evidence for the left angular gyrus being more important during multiplication than subtraction comes largely from training studies in typical adults [56]. Ischebeck and colleagues [65] demonstrated that increasing familiarity of multiplication problems led to a shift in activity from bilateral IPS to left AG over the course of a single scanning session. While this was initially interpreted as evidence for the involvement of the AG in arithmetic fact retrieval, subsequent studies suggested that the increasing activity in AG did not reflect numberspecific fact retrieval but rather a general signature of learning that can be found with various contents [34,66]. ...
... In line with the previous literature, we found a largely left-lateralized network including the AG during multiplication [34,65,67,138], while subtraction was associated with a bilateral activation pattern including both left and right IPS [54,60,63]. However, regarding the left IPS and left AG this distinction was not as clear-cut as proposed in the literature. ...
Developmental dyscalculia (DD) is a developmental disorder characterized by arithmetic difficulties. Recently, it has been suggested that the neural networks supporting procedure-based calculation (e.g., in subtraction) and left-hemispheric verbal arithmetic fact retrieval (e.g., in multiplication) are partially distinct. Here we compared the neurofunctional correlates of subtraction and multiplication in a 19-year-old student (RM) with DD to 18 age-matched controls. Behaviorally, RM performed significantly worse than controls in multiplication, while subtraction was unaffected. Neurofunctional differences were most pronounced regarding multiplication: RM showed significantly stronger activation than controls not only in left angular gyrus but also in a fronto-parietal network (including left intraparietal sulcus and inferior frontal gyrus) typically activated during procedure-based calculation. Region-of-interest analyses indicated group differences in multiplication only, which, however, did not survive correction for multiple comparisons. Our results are consistent with dissociable and processing-specific, but not operation-specific neurofunctional networks. Procedure-based calculation is not only associated with subtraction but also with (untrained) multiplication facts. Only after rote learning, facts can be retrieved quasi automatically from memory. We suggest that this learning process and the associated shift in activation patterns has not fully occurred in RM, as reflected in her need to resort to procedure-based strategies to solve multiplication facts.
... Fact retrieval, in contrast, was associated with stronger activation (or less deactivation) of the angular gyrus (AG; Arsalidou and Taylor, 2011;Delazer et al., 2005;Grabner et al., 2009;Menon, 2015;Zamarian et al., 2009), indicating the reliance on memory networks, which the AG is thought to be part of (Destefano and LeFevre, 2004;Menon, 2015). Training studies further corroborated this neural dissociation by showing that fact learning is accompanied by a change from procedural activation patterns to retrieval patterns (Pauli et al., 1994;Ischebeck et al., 2007;Grabner and De Smedt, 2012;Soltanlou et al., 2019). ...
... Many studies investigating the brain regions and networks relevant for arithmetic processes speculate the AG to be important for fact retrieval (probably relevant for establishing the connection between arithmetic problems and their solution; Grabner et al., 2013), or supporting activation control in longterm memory networks (Bloechle et al., 2016). Frontal regions, in contrast, have mainly been associated with procedural calculation (Ischebeck et al., 2007;Grabner et al., 2009). However, the strong effects of frontal stimulation might be based on the relevance of frontal regions and frontal theta band oscillations for executive functions. ...
Over the last decades, interest in transcranial electrical stimulation (tES) has grown, as it might allow for causal investigations of the associations between cortical activity and cognition as well as to directly influence cognitive performance. The main objectives of the present work were to assess whether tES can enhance the acquisition and application of arithmetic abilities, and whether it enables a better assessment of underlying neurophysiological processes. To this end, the present, double-blind, sham-controlled study assessed the effects of six active stimulations (three tES protocols: anodal transcranial direct current stimulation (tDCS), alpha band transcranial alternating current stimulation (tACS), and theta band tACS; targeting the left dorsolateral prefrontal cortex or the left posterior parietal cortex) on the acquisition of an arithmetic procedure, arithmetic facts, and event-related synchronization/desynchronization (ERS/ERD) patterns. 137 healthy adults were randomly assigned to one of seven groups, each receiving one of the tES-protocols during learning. Results showed that frontal theta band tACS reduced the repetitions needed to learn novel facts and both, frontal and parietal theta band tACS accelerated the decrease in calculation times in fact learning problems. The beneficial effect of frontal theta band tACS may reflect enhanced executive functions, allowing for better control and inhibition processes and hence, a faster acquisition and integration of novel fact knowledge. However, there were no significant effects of the stimulations on procedural learning or ERS/ERD patterns. Overall, theta band tACS appears promising as a support for arithmetic fact training, but effects on procedural calculations and neurophysiological processes remain ambiguous.
... However, it is still unclear how, exactly, information processing is handled by such a distributed network (Menon 2015). Furthermore, with regard to retrieval processes within multiplication, different studies have suggested that the left angular gyrus (ANG) may change its activity during an automated multiplication task (Delazer et al. 2003;Ischebeck et al. 2007;Zamarian et al. 2009). Studies using verification tasks (vs. ...
... When related solutions are encountered, they would be already partly activated, and this activation would have to be overcome. This preactivation explains the involvement of the left DLPFC-OFC and the left IPL, the store for arithmetic facts, as has been previously shown (Dehaene et al. 2003;Delazer et al. 2003;Ischebeck et al. 2007). The resolution of the competition needs the frontal areas. ...
Our ability to calculate implies more than the sole retrieval of the correct solution. Essential processes for simple calculation are related to the spreading of activation through arithmetic memory networks. There is behavioral and electrophysiological evidence for these mechanisms. Their brain location is, however, still uncertain. Here, we measured magnetoencephalographic brain activity during the verification of simple multiplication problems. Following the operands, the solutions to verify could be preactivated correct solutions, preactivated table-related incorrect solutions, or unrelated incorrect solutions. Brain source estimation, based on these event-related fields, revealed 3 main brain networks involved in simple calculation: 1) bilateral inferior frontal areas mainly activated in response to correct, matching solutions; 2) a left-lateralized frontoparietal network activated in response to incorrect table-related solutions; and (3) a strikingly similar frontoparietal network in the opposite hemisphere activated in response to unrelated solutions. Directional functional connectivity analyses revealed a bidirectional causal loop between left parietal and frontal areas for table-related solutions, with frontal areas explaining the resolution of arithmetic competition behaviorally. Hence, this study isolated at least 3 neurofunctional networks orchestrated between hemispheres during calculation.
... We are therefore in a position to suggest hypotheses that can be tested with the experimental paradigm we are using in this study. 1) We propose that our training reproduces the previously observed reduction in frontal activation found by Ischebeck, Delazer and colleagues using fMRI (Ischebeck, Zamarian, Egger, Schocke, & Delazer, 2007;Ischebeck, Zamarian, Schocke, & Delazer, 2009;Ischebeck et al., 2006) and differential hemodynamic effects of training on multiplication and subtraction. 2) By studying RSFC we can then establish for the first time: a) whether the initial state of functional connectivity predicts the effectiveness of the learning arithmetic in adults, as it has in motor tasks (Sampaio-Baptista et al., 2015) and learning to read (Hoeft et al., 2011) in children. ...
... This confirms that our training procedure was effective both in improving performance and in modifying neural activity in the fronto-parietal neural network for arithmetical processing established by neuropsychological and neuroimaging studies (e.g., Andres et al., 2011;Cipolotti & van Harskamp, 2001). Moreover, we also replicated the differential effects of training in multiplication and subtraction (Ischebeck et al., 2006(Ischebeck et al., , 2007(Ischebeck et al., , 2009. Training reduced activation in the parietal lobes for subtraction but not for multiplication. ...
How Resting-State Functional Connectivity (RSFC) is modified by learning is an important but rarely asked question. Here we used functional near-infrared spectroscopy (fNIRS) to measure changes in RSFC after learning novel subtraction and multiplication facts by forty-one young adult volunteers. We also measured changes in regional hemoglobin concentration. Fronto-parietal RSFC was modified by arithmetic learning and the fronto-parietal RSFC configuration before learning predicted the effectiveness of arithmetic learning. We also found a significant learning effect indicated by a monotonic decrease in reaction time and an increase in accuracy. Regional task-dependent oxy-hemoglobin concentration differentiated subtraction from multiplication learning supporting previous fMRI findings. These results suggest the sensitivity and importance of fronto-parietal connectivity to arithmetic learning.
... Lin, Imada, and Kuhl (2012) as well as Ischebeck, Zamarian, Egger, Schocke, and Delazer (2007) through fMRI tests observe the brain activation of bilingual children before and after receiving extensive training. The left hemispheric gyrus is likely to be more active and sensitive after eight repetitive tasks and the arithmetical codes remain stable over the experiment. ...
... The brain activation investigation indicates that repetition of several stimuli in the early bilinguals profoundly affects the preservation of arithmetic code in the bilinguals' language specific operation format. Ischebeck, Zamarian, Egger, Schocke, and Delazer (2007), furthermore, suggest the balanced training of arithmetic repetitive problem solving in both languages to eliminate the activation of the fronto-parietal area which brings a controlled translation tool. In contrary, an extensive training for late bilinguals brings only little pattern changes in the fronto-parietal area of the brain which may not preserve memory for a long time. ...
This study talks about what aspects correlated between the language specific operation and arithmetic processing skills that occur in bilingual people’s brains. Some studies toward the behaviour and neurology’s aspects are discussed as well as their findings in order to answer the research questions of the study. The discussions reveal that both skills have a positive correlation and that both occur in the brain’s left hemisphere; however, the left hemisphere largely participates in automatic language specific operations and simple calculations, while the right hemisphere dominates advanced control processing operations in calculation (e.g. calculus, logarithm) and language information transfer. In addition, studies show that the bilinguals’ language dominance does not clearly determine the correlation between the language and arithmetic skills. Further, in order to retain better arithmetic concepts, comprehensive and simultaneous training should be conducted in both languages and in the early stage of language development, especially during bilinguals’ critical age of language learning.
... Specifically, it has been suggested that multiplication equations almost exclusively depend on fact retrieval from memory (Grabner et al., 2022). This notion has been supported by brain imaging studies which show neural activity that is involved in retrieving semantic knowledge from memory while engaging with multiplication equations (Chochon et al., 1999;Ischebeck et al., 2007;Jost et al., 2004;Zhou et al., 2007). Some of the studies that tested neuronal markers for multiplication equations, found a specific multiplication-related activity in the precentral gyrus and the supplementary motor areas and stronger activity for large equations (8 × 9 = 72) compared to small equations (2 × 5 = 10; Jost et al., 2004;Zhou et al., 2007). ...
Certain stimuli can automatically trigger different behaviors in a stimulus-driven manner. To investigate whether mathematical equations automatically trigger the tendency to engage in arithmetic processing, we asked whether the presentation of multiplication equations in an irrelevant dimension can trigger the automatic task of arithmetic processing and if so, which processes are involved. To that end, we employed a color-naming task in which participants had to name the color of different stimuli, such as: mathematical equations (e.g., 4 × 6 = 24), neutral-symbols (e.g., ####), neutral-words (e.g., building), and same-number strings (e.g., 11111), which appeared as one of four different colors. We found that mathematical equations and regular words in the irrelevant dimension triggered more task conflict (i.e., color naming's reaction time was longer) as compared to same-number strings. In addition, we found evidence for the automatic activation of different numerical processes; such that large-size equations (7 × 9 = 63) triggered more conflict as compared with small-size (2 × 3 = 6) equations and same-parity incorrect equations (3 × 2 = 8) triggered more conflict as compared to different-parity incorrect equations (4 × 2 = 9). We found no evidence indicating a distinction between the correct and incorrect equations. We discussed the relevance of the findings to the automaticity of arithmetic abilities and other domains in numerical cognition.
... Delazer et al., 2004); or they trialled interventions with healthy adults (e.g. Ischebeck et al. 2007). Fourteen articles were identified as potentially suitable for inclusion, and were evaluated in detail. ...
Acalculia is an acquired deficit in numerical skills following a brain-injury, which impacts independence (traveling, managing money, counting medications) and wellbeing. It is estimated to affect 30%-65% of brain-injury survivors.In the past, there have been four reviews (two of which were systematic) covering the available intervention for acalculia, however, all of these reviews have missed some studies, and the last systematic review is over 10 years old.The current work had systematically searched Web of Knowledge (WoK) and UMI Dissertation Abstracts for studies describing interventions for Acalculia published up until 29th of September 2023. To be included, studies had to be written in English and involve an intervention for acalculia that occurred as a result of a stroke or a brain injury, to directly address numerical difficulties, and to report the outcomes of the intervention, with no limit on the type or timing of measures. The search identified only 16 publications that describe interventions for acalculia, with a total of N=31 patients, and one unpublished public report of app-based intervention involving 18 patients. The majority of interventions (10) were designed to improve relearning of multiplication tables, followed by those designed to improve transcoding skills (4). All identified interventions were delivered individually (i.e., no group interventions), and were largely tailored to individual patients. The most common method used by interventions was intense repetition (‘drill’), and the majority of interventions were conducted in French or German. We found only one intervention in non-European language (Japanese), despite evidence of linguistic effects on performance across languages and cultures. While all interventions were effective, there were important differences in the transferability of improvement from trained to untrained problems. Overall, the review highlights the scarcity of evidence of interventions for acalculia, despite the high prevalence and devastating impact of the condition. It also highlights obvious gaps, and makes suggestions for further investigation in order to improve the quality of interventions and outcomes for patients.
... According to this theory, interactions within a network of frontal and parietal association cortices, including bilateral dorsolateral prefrontal cortices (DLPFCs) and superior and inferior parietal areas, are critical in supporting human reasoning and intelligence (Jung & Haier, 2007). Many functional MRI (fMRI) and electroencephalography (EEG) studies have supported this view by showing activation in these brain areas when participants engage in Gf tasks (Christoff et al., 2001;Conway et al., 2002;Duncan, 2005;Duncan et al., 1995;Engle et al., 1999;Ischebeck et al., 2006Ischebeck et al., , 2007Kroger et al., 2002;Langer et al., 2012;Lee et al., 2006;Li et al., 2009;Miasnikova et al., 2019). Further, much of this previous work has also shown that an inverse relationship exists between activation of brain regions and performance on tasks targeting Gf, with decreased activation in these cortical networks being associated with better task performance (Haier et al., 1983(Haier et al., , 1988Neubauer & Fink, 2009;Parks et al., 1988). ...
Fluid intelligence (G f ) involves logical reasoning and novel problem‐solving abilities. Often, abstract reasoning tasks like Raven's progressive matrices are used to assess G f . Prior work has shown an age‐related decline in fluid intelligence capabilities, and although many studies have sought to identify the underlying mechanisms, our understanding of the critical brain regions and dynamics remains largely incomplete. In this study, we utilized magnetoencephalography (MEG) to investigate 78 individuals, ages 20–65 years, as they completed an abstract reasoning task. MEG data was co‐registered with structural MRI data, transformed into the time–frequency domain, and the resulting neural oscillations were imaged using a beamformer. We found worsening behavioral performance with age, including prolonged reaction times and reduced accuracy. MEG analyses indicated robust oscillations in the theta, alpha/beta, and gamma range during the task. Whole brain correlation analyses with age revealed relationships in the theta and alpha/beta frequency bands, such that theta oscillations became stronger with increasing age in a right prefrontal region and alpha/beta oscillations became stronger with increasing age in parietal and right motor cortices. Follow‐up connectivity analyses revealed increasing parieto‐frontal connectivity with increasing age in the alpha/beta frequency range. Importantly, our findings are consistent with the parieto‐frontal integration theory of intelligence (P‐FIT). These results further suggest that as people age, there may be alterations in neural responses that are spectrally specific, such that older people exhibit stronger alpha/beta oscillations across the parieto‐frontal network during abstract reasoning tasks.
... Indeed, the functional domain of two prominent subcortical structures, the cerebellum and basal ganglia has been recognized to extend beyond the motor domain (Owen et al., 1992;Middleton and Strick, 1994;Balsters et al., 2013;Sokolov et al., 2017;Bostan and Strick, 2018;Schmahmann, 2019). Both regions have reciprocal connectivity with many of the cortical areas associated with mathematical cognition (Ide et al., 2011;Bostan and Strick, 2018;Milardi et al., 2019) and, although outside the focus of neuroimaging studies, activation changes in both the cerebellum and basal ganglia have been consistently observed even in contrasts that control for overt motor responses (Ischebeck et al., 2007;Zago et al., 2008). ...
Humans exhibit complex mathematical skills attributed to the exceptional enlargement of neocortical regions throughout evolution. In the current work, we initiated a novel exploration of the ancient subcortical neural network essential for mathematical cognition. Using a neuropsychological approach, we report that degeneration of two subcortical structures, the cerebellum and basal ganglia, impairs performance in symbolic arithmetic. We identify distinct computational impairments in male and female participants with cerebellar degeneration (CD) or Parkinson's disease (PD). The CD group exhibited a disproportionate cost when the arithmetic sum increased, suggesting that the cerebellum is critical for iterative procedures required for calculations. The PD group showed a disproportionate cost for equations with increasing addends, suggesting that the basal ganglia are critical for chaining multiple operations. In Experiment 2, the two patient groups exhibited intact practice gains for repeated equations at odds with an alternative hypothesis that these impairments were related to memory retrieval. Notably, we discuss how the counting and chaining operations relate to cerebellar and basal ganglia function in other task domains (e.g., motor processes). Overall, we provide a novel perspective on how the cerebellum and basal ganglia contribute to symbolic arithmetic. Our studies demonstrate the constraints on the computational role of two subcortical regions in higher cognition.
... Brain imaging studies with short and simple arithmetic tasks suggest that learning of mathematical knowledge is accompanied by a shift from more frontal to more parietal regions [26][27][28][29] . Electroencephalography (EEG) studies suggest that brain processes measured with cortical oscillation and event-related potentials (ERPs) differences are associated with brain functions are modified through expertise, such as including processes related to rote learning and strategy selection for solving the tasks at hand (Hinault and Lemaire for a review 30 ). ...
Current trend in neurosciences is to use naturalistic stimuli, such as cinema, class-room biology or video gaming, aiming to understand the brain functions during ecologically valid conditions. Naturalistic stimuli recruit complex and overlapping cognitive, emotional and sensory brain processes. Brain oscillations form underlying mechanisms for such processes, and further, these processes can be modified by expertise. Human cortical functions are often analyzed with linear methods despite brain as a biological system is highly nonlinear. This study applies a relatively robust nonlinear method, Higuchi fractal dimension (HFD), to classify cortical functions of math experts and novices when they solve long and complex math demonstrations in an EEG laboratory. Brain imaging data, which is collected over a long time span during naturalistic stimuli, enables the application of data-driven analyses. Therefore, we also explore the neural signature of math expertise with machine learning algorithms. There is a need for novel methodologies in analyzing naturalistic data because formulation of theories of the brain functions in the real world based on reductionist and simplified study designs is both challenging and questionable. Data-driven intelligent approaches may be helpful in developing and testing new theories on complex brain functions. Our results clarify the different neural signature, analyzed by HFD, of math experts and novices during complex math and suggest machine learning as a promising data-driven approach to understand the brain processes in expertise and mathematical cognition.
... Studies on complex arithmetic training, specifically complex multiplication training, in adult participants have revealed a decreased activation in the frontal gyri, IPS, and superior parietal lobule, while displaying an increased activation in the angular gyrus (see, e.g., , for a review). This shift in brain activity indicates a transition from relying on effortful and procedural processes to utilizing memory and retrieval-based strategies (Grabner & De Smedt, 2012;Grabner et al., 2009;Ischebeck, Zamarian, Schocke, & Delazer, 2009;Ischebeck, Zamarian, Egger, Schocke, & Delazer, 2007;Ischebeck et al., 2006;Delazer et al., 2003Delazer et al., , 2005. Consistently, developmental imaging studies in the field of arithmetic reasoning also support the notion that the automation of mathematical processes is accompanied by a shift in activation from frontal to parietal regions (Rivera, Reiss, Eckert, & Menon, 2005). ...
Human populations show large individual differences in math performance and math learning abilities. Early math skill acquisition is critical for providing the foundation for higher quantitative skill acquisition and succeeding in modern society. However, the neural bases underlying individual differences in math competence remain unclear. Modern neuroimaging techniques allow us to not only identify distinct local cortical regions but also investigate large-scale neural networks underlying math competence both structurally and functionally. To gain insights into the neural bases of math competence, this review provides an overview of the structural and functional neural markers for math competence in both typical and atypical populations of children and adults. Although including discussion of arithmetic skills in children, this review primarily focuses on the neural markers associated with complex math skills. Basic number comprehension and number comparison skills are outside the scope of this review. By synthesizing current research findings, we conclude that neural markers related to math competence are not confined to 1 particular region; rather, they are characterized by a distributed and interconnected network of regions across the brain, primarily focused on frontal and parietal cortices. Given that human brain is a complex network organized to minimize the cost of information processing, an efficient brain is capable of integrating information from different regions and coordinating the activity of various brain regions in a manner that maximizes the overall efficiency of the network to achieve the goal. We end by proposing that frontoparietal network efficiency is critical for math competence, which enables the recruitment of task-relevant neural resources and the engagement of distributed neural circuits in a goal-oriented manner. Thus, it will be important for future studies to not only examine brain activation patterns of discrete regions but also examine distributed network patterns across the brain, both structurally and functionally.
... Notwithstanding, mathematics would make a useful and approachable higher power. The practice of working mathematics problems can be seen as having a calming e↵ect [11]. The social nature of sharing in the gospel of mathematics can highlight how appealing mathematics is to some people and allow for bonds of friendship to arise out of a common interest [4]. ...
Conversion of strangers, or proselytizing, is a feature of a range of groups for religious, organizational and other aims. In twelve-step recovery programs, such as Alcoholics Anonymous, belief in a higher power is a requirement for working the steps to recovery. People are encouraged to find a higher power of their own understanding. This paper presents a model for using mathematics as a higher power, and shows how recovery works with mathematics in that role instead of a more traditional higher power such as God. A contemplative definition of math is given along with a description of a three-categoried epistemology: mathematics, science, and the personal. This epistemology is shown to be sufficient to work the Twelve Steps, with mathematics as a higher power. Proselytizing is not required.
... Researchers established that targeted academic training for schooled children and adolescents can meaningfully alter the brain's patterns of activity, and hence expertise in specific cognitive spheres. Following arithmetic training and the consequent heightened activation of the students' brains, the attention and executive processing-rich zones of the frontoparietal areas became more automatic and efficient knowledge retrieval zones (Ischebeck, Laura, Karl, Michael & Margarete, 2007). ...
Secondary education as a predictor of aptitude: Implications for selection in the automotive sector
... The left angular gyrus, which is an essential part of the language-based code, was found to be more deactivated during estimation than exact knowledge [26,27]. Some studies have reported greater responses in the left angular gyrus during more automated calculation tasks [28,29]. A few studies have reported relative decreases or deactivation in the left angular gyrus during a simple calculation task [30,31]. ...
The current study examined whether discrete numerical estimation is based on the same cognitive process as estimation of continuous magnitudes such as weight and time. While the verbal estimation of numerical quantities has a contingent unit of measurement (e.g., how many cookies fit in a cookie jar? _X_ cookies), estimation of time and weight does not (e.g., how much time does it take to fill a bath with water? _X_ minutes/hours/seconds). Therefore, estimation of the latter categories has another level of difficulty, requiring extensive involvement of cognitive control. During a functional magnetic resonance imaging (fMRI) scan, 18 students performed estimations with three estimation categories: number, time, and weight. Estimations elicited activity in multiple brain regions, mainly: (1) visual regions including bilateral lingual gyrus), (2) parietal regions including the left angular gyrus and right supramarginal gyrus, and (3) the frontal regions (cingulate gyrus and the inferior frontal cortex). Continuous magnitude estimations (mostly time) produced different frontal activity than discrete numerical estimations did, demonstrating different profiles of brain activations between discrete numerical estimations and estimations of continuous magnitudes. The activity level in the right middle and inferior frontal gyrus correlated with the tendency to give extreme responses, signifying the importance of the right prefrontal lobe in estimations.
... These areas were the bilateral angular gyrus, the left orbital sulcus and the left middle frontal gyrus. Although the angular gyrus has been shown to be activated in various cognitive domains (perceptual and motor reorienting, number processing, attention and spatial cognition, episodic memory retrieval and encoding, language processing, theory of mind; Cabeza, Ciaramelli, & Moscovitch, 2012), fMRI and neuropsychological studies have shown that the left angular gyrus plays an important role also during calculation processing, in particular during multiplication and arithmetical fact retrieval from memory (Chochon et al., 1999;Delazer et al., 2003;Gerstmann, 1940;Grabner et al., 2007Grabner et al., , 2013Grabner, Ansari, et al., 2009;Grabner, Ischebeck, et al., 2009;Ischebeck, Zamarian, Egger, Schocke, & Delazer, 2007;Lee, 2000;Stanescu-Cosson et al., 2000; see also: Dehaene et al., 2003, for a review). However, some studies have reported bilateral activation of the angular gyrus during exact calculation tasks, suggesting that also the right angular gyrus has a role in arithmetic processing, although the left hemisphere showed a larger effect (Göbel, Walsh, & Rushworth, 2001;Menon et al., 2000;Stanescu-Cosson et al., 2000). ...
Numerical estimation of arrays of objects is faster and more accurate when items can be clustered into groups, a phenomenon termed “groupitizing.” Grouping can facilitate segregation into subitizable “chunks,” each easily estimated, then summed. The current study investigates whether spatial grouping of arrays drives specific neural responses during numerical estimation, reflecting strategies such as exact calculation and fact retrieval. Fourteen adults were scanned with fMRI while estimating either the numerosity or shape of arrays of items, either randomly distributed or spatially grouped. Numerosity estimation of both classes of stimuli elicited common activation of a right lateralized frontoparietal network. Grouped stimuli additionally recruited regions in the left hemisphere and bilaterally in the angular gyrus. Multivariate pattern analysis showed that classifiers trained with the pattern of neural activations read out from parietal regions, but not from the primary visual areas, can decode different numerosities both within and across spatial arrangements. The behavioral numerical acuity correlated with the decoding performance of the parietal but not with occipital regions. Overall, this experiment suggests that the estimation of grouped stimuli relies on the approximate number system for numerosity estimation, but additionally recruits regions involved in calculation. Numerosity estimation is more accurate when items can be clustered into groups. Common frontoparietal areas are activated by different spatial arrangements. Estimation of grouped stimuli recruits additional areas such as angular gyrus.
... Indeed, the functional domain of two prominent subcortical structures, the cerebellum and basal ganglia has been recognized to extend well beyond the motor domain [24][25][26][27][28][29][30] . Both regions have reciprocal connectivity with many of the cortical areas associated with mathematical cognition 27,31−33 and, although outside the focus of most neuroimaging studies, activation changes in both the cerebellum and basal ganglia have been consistently observed even in contrasts that control for overt motor responses [34][35][36] . ...
Humans exhibit complex mathematical skills, often attributed to the exceptionally large neocortex. Using a neuropsychological approach, we report that degeneration within two subcortical structures, the basal ganglia and cerebellum, impairs performance in symbolic arithmetic. Moreover, we identify distinct computational impairments in individuals with Parkinson’s disease (PD) or cerebellar degeneration (CD). The CD group exhibited a disproportionate cost when arithmetic sum increased, suggesting that the cerebellum is critical for iterative procedures required for calculations. The PD group exhibited a disproportionate cost for equations with an increasing number of addends, suggesting that the basal ganglia are critical for the coordination of multiple cognitive operations. In Experiment 2, the two patient groups exhibited intact practice gains for repeated equations at odds with an alternative hypothesis that these impairments were related to memory retrieval. Overall, the results provide a novel demonstration of the contribution of subcortical structures to the computations required for complex cognition.
... Moreover, Bloechle et al. (2016) measured brain activation in healthy participants before and after an extensive multiplication training to evaluate the neural correlates of arithmetic fact acquisition more speci cally. When comparing activation patterns for trained and untrained problems in the post-training fMRI session, the authors replicated a higher activation of the left AG for trained problems as observed previously (Delazer et al., 2003;Ischebeck et al., 2007). However, in a pre-post comparison of activation for trained problems and the same problems in the pretraining fMRI session, no signal change in the AG was observed. ...
... Unfortunately, P-FIT does not expand on the nature of such dynamic interactions between cortical regions. Nonetheless, in support of this theory, many fMRI and PET studies have shown Gƒ-related activations in these regions (Duncan et al. 2000;Ischebeck et al. 2006Ischebeck et al. , 2007 and seminal work from Neubauer and colleagues has shown an inverse correlation between intelligence and cerebral activity on logical reasoning tasks Neubauer & Fink, 2009). The latter findings support the idea of neural efficiency and thereby another leading theory in this literature, the neural efficiency hypothesis (NEH) of intelligence, which was first put forward by Haier and colleagues (Haier et al. 1988). ...
Fluid intelligence (Gƒ) includes logical reasoning abilities and is an essential component of normative cognition. Despite the broad consensus that parieto‐prefrontal connectivity is critical for Gƒ (e.g. the parieto‐frontal integration theory of intelligence, P‐FIT), the dynamics of such functional connectivity during logical reasoning remains poorly understood. Further, given the known importance of these brain regions for Gƒ, numerous studies have targeted one or both of these areas with non‐invasive stimulation with the goal of improving Gƒ, but to date there remains little consensus on the overall stimulation‐related effects. To examine this, we applied high‐definition direct current anodal stimulation to the left and right dorsolateral prefrontal cortex (DLPFC) of 24 healthy adults for 20 min in three separate sessions (sham, left, and right active). Following stimulation, participants completed a logical reasoning task during magnetoencephalography (MEG). Significant neural responses at the sensor‐level were imaged using a beamformer, and peak task‐induced activity was subjected to dynamic functional connectivity analyses to evaluate the impact of distinct stimulation montages on network activity. We found that participants responded faster following right DLPFC stimulation vs. sham. Moreover, our neural findings followed a similar trajectory of effects such that left parieto‐frontal connectivity decreased following right and left DLPFC stimulation compared to sham, with connectivity following right stimulation being significantly correlated with the faster reaction times. Importantly, our findings are consistent with P‐FIT, as well as the neural efficiency hypothesis (NEH) of intelligence. In sum, this study provides evidence for beneficial effects of right DLPFC stimulation on logical reasoning.
Key points
Logical reasoning is an indispensable component of fluid intelligence and involves multispectral oscillatory activity in parietal and frontal regions.
Parieto‐frontal integration is well characterized in logical reasoning; however, its direct neural quantification and neuromodulation by brain stimulation remain poorly understood.
High‐definition transcranial direct current stimulation of dorsolateral prefrontal cortex (DLPFC) had modulatory effects on task performance and neural interactions serving logical reasoning, with right stimulation showing beneficial effects.
Right DLPFC stimulation led to a decrease in the response time (i.e. better task performance) and left parieto‐frontal connectivity with a marginal positive association between behavioural and neural metrics.
Other modes of targeted stimulation of DLPFC (e.g. frequency‐specific) can be employed in future studies.
... To elaborate, processing of mathematical operations has been attributed mainly to involvement of the human frontoparietal network (Grabner et al., 2009;Klein et al., 2013;Matejko & Ansari, 2015;Nieder, 2016). A shift from the involvement of the prefrontal regions in this network to the parietal regions, mostly lateralized to the left hemisphere, has been observed with fMRI when expertise increases as consequence of a mathematical training paradigm (Kucian et al., 2008;Ischebeck et al., 2007;Rivera et al., 2005). ...
Numerical skills encompass a variety of cognitive processes and are crucial for performance in today’s modern world but vary greatly between individuals. Several approaches of numerical cognition have been studied ranging from behavioral to neuroimaging studies. Transcranial electrical stimulation (tES) has become a promising tool to influence numerical cognition and is frequently used in clinical settings. The main aim of this chapter is to shed light onto current tES research as an intervention in this domain. We first provide a brief overview of the underlying neurocognitive mechanisms of basic and advanced mathematical skills, such as working memory, executive functions, and (non)symbolic number skills, since tES allows to intervene and further unravel the role of these mechanisms. In addition, we discuss the need for tES research to focus on the transfer of these skills to a similar numerical task to determine facilitation by means of neuroplasticity. Therefore we emphasize studies using tES as a numerical intervention and focus on transfer effects since these outcomes could contribute to implications for educational practice.
... This is a core parietal region implicated in numerical cognition (i.e., number sense) and in magnitude judgment. We also observed GM changes in bilateral AG, which is functionally involved in the transition from quantity-based processing to automatic fact retrieval (Dehaene et al., 1999;Grabner et al., 2007Grabner et al., , 2009aIschebeck et al., 2007), the processing of digits (Price and Ansari, 2011), or the mapping between a symbol and its referents (Ansari, 2008;Grabner et al., 2009b). Interestingly, the AG has also been involved in non-symbolic number processing (Göbel et al., 2001;Kaufmann et al., 2011). ...
... Por último, se ha propuesto que el núcleo caudado participaría también en el procesamiento numérico y el cálculo, aunque se desconoce cuál sería exactamente su papel. Se ha observado su implicación en tareas de cálculo aritmético complejo [13], hallazgo replicado en otras investigaciones, donde se estudia el efecto del entrenamiento en la resolución de problemas aritméticos [56]. En concreto, se observa una mayor activación del núcleo caudado cuando los problemas son novedosos (no entrenados) respecto a los entrenados. ...
... We further found that the left AG was engaged more for nonsymbolic relative to symbolic addition. At first blush, this may seem surprising because the left AG is commonly found to be involved in the verbal coding and retrieval of arithmetic facts and so it might have been expected to be more involved in the symbolic arithmetic task (Dehaene et al., 2003;Grabner, Ansari, et al., 2009;Grabner, Ansari, Koschutnig, & Reishofer, 2013;Ischebeck, Zamarian, Egger, Schocke, & Delazer, 2007). An alternate proposal suggests that the left AG supports the automatic mapping of overlearned arithmetic problems to their respective solutions in memory (Ansari, 2008;Grabner et al., 2013). ...
Symbolic arithmetic is a complex, uniquely human ability that is acquired through direct instruction. In contrast, the capacity to mentally add and subtract nonsymbolic quantities such as dot arrays emerges without instruction and can be seen in human infants and nonhuman animals. One possibility is that the mental manipulation of nonsymbolic arrays provides a critical scaffold for developing symbolic arithmetic abilities. To explore this hypothesis, we examined whether there is a shared neural basis for nonsymbolic and symbolic double‐digit addition. In parallel, we asked whether there are brain regions that are associated with nonsymbolic and symbolic addition independently. First, relative to visually matched control tasks, we found that both nonsymbolic and symbolic addition elicited greater neural signal in the bilateral intraparietal sulcus (IPS), bilateral inferior temporal gyrus, and the right superior parietal lobule. Subsequent representational similarity analyses revealed that the neural similarity between nonsymbolic and symbolic addition was stronger relative to the similarity between each addition condition and its visually matched control task, but only in the bilateral IPS. These findings suggest that the IPS is involved in arithmetic calculation independent of stimulus format.
... Although these previous studies have suggested that the IPL is related to processing of magnitude or numerosity of presented stimuli, it has been also observed that the functional/anatomical network between left IFG and IPL is important for arithmetic performance 47,48 . It is likely that IFG is involved in arithmetic or more complex mathematical tasks rather than elementary number processing 28,49,50 . The current RS effect in the IFG suggests that structural aspect of arithmetic is beyond the processing of numerosity or magnitude. ...
Abstract The presence of a shared neural system for the syntactic processing in language and arithmetic is controversial. Recent behavioral studies reported a cross-domain structural priming between language and arithmetic. Using functional magnetic resonance imaging, we examined whether the neural activation reflects the structural interaction between language and arithmetic. We prepared sentences and arithmetic expressions (A-expressions) with same and different syntactic structures and presented structurally congruent/incongruent pairs consecutively. By directly comparing activations in the congruent and incongruent conditions, we observed significant repetition suppression effect in the regions including the bilateral inferior frontal gyrus, i.e., neural activation with an A-expression decreased after a sentence with the same syntactic structure (and vice versa). The results strongly support the idea that arithmetic and language share the neural basis for processing syntactic structures.
... Studies with younger adults adopting functional magnetic resonance imaging (fMRI) methods have shown that a short but intensive training on complex arithmetic problems yields significant performance improvements (i.e., higher accuracy and faster response times) that go along with specific changes in brain activation patterns. Specifically, arithmetic skill acquisition following intensive training is associated with an activation decrease in fronto-parietal brain areas including the intraparietal sulcus (IPS) related to a reduced reliance on working memory and quantity processing, whereas a relative activation increase is found in parietal brain areas including the angular gyrus (AG) in association with an increased reliance on automated arithmetic fact retrieval [36][37][38][39][40][41][42][43][44] (but see [45] for a different point of view). It has also been shown that successful transfer of the newly acquired arithmetic knowledge (multiplication) to a new situation (related division) appears in association with activation in the left AG and is strongly influenced by inter-individual differences in arithmetic competence [41] (see also [38]). ...
Acquisition of numerical knowledge and understanding of numerical information are crucial for coping with the changing demands of our digital society. In this study, we assessed arithmetic learning in older and younger individuals in a training experiment including brain imaging. In particular, we assessed age-related effects of training intensity, prior arithmetic competence, and neuropsychological variables on the acquisition of new arithmetic knowledge and on the transfer to new, unknown problems. Effects were assessed immediately after training and after 3 months. Behavioural results showed higher training effects for younger individuals than for older individuals and significantly better performance after 90 problem repetitions than after 30 repetitions in both age groups. A correlation analysis indicated that older adults with lower memory and executive functions at baseline could profit more from intensive training. Similarly, training effects in the younger group were higher for those individuals who had lower arithmetic competence and executive functions prior to intervention. In younger adults, successful transfer was associated with higher executive functions. Memory and set-shifting emerged as significant predictors of training effects in the older group. For the younger group, prior arithmetic competence was a significant predictor of training effects, while cognitive flexibility was a predictor of transfer effects. After training, a subgroup of participants underwent an MRI assessment. A voxel-based morphometry analysis showed a significant interaction between training effects and grey matter volume of the right middle temporal gyrus extending to the angular gyrus for the younger group relative to the older group. The reverse contrast (older group vs. younger group) did not yield any significant results. These results suggest that improvements in arithmetic competence are supported by temporo-parietal areas in the right hemisphere in younger participants, while learning in older people might be more widespread. Overall, our study indicates that arithmetic learning depends on the training intensity as well as on person-related factors including individual age, arithmetic competence before training, memory, and executive functions. In conclusion, we suggest that major progress can be also achieved by older participants, but that interventions have to take into account individual variables in order to provide maximal benefit.
... Researchers established that targeted academic training for schooled children and adolescents can meaningfully alter the brain's patterns of activity, and hence expertise in specific cognitive spheres. Following arithmetic training and the consequent heightened activation of the students' brains, the attention and executive processing-rich zones of the frontoparietal areas became more automatic and efficient knowledge retrieval zones (Ischebeck, Laura, Karl, Michael & Margarete, 2007). ...
Orientation: Details of applicants’ secondary education (incorporating subject choice) could be a useful screening tool when processing large applicant pools. Here, the relationships between secondary education (incorporating subject choice) and the reasoning and visual perceptual speed components of the Differential Aptitude Test are explored.
Research purpose: The objective of the study was to determine whether type of secondary education (incorporating subject choice) could be used as a substitute for reasoning (verbal and non-verbal) and/or visual perceptual speed aptitudes in the selection of operators for an automotive plant in South Africa.
Motivation for the study: The motivation for this study arose from the evident gap in academic literature as well as the selection needs of the automotive industry.
Research design, approach and method: This research adopted a quantitative approach. It involved a non-probability convenience quota sample of 2463 work-seeking applicants for an automotive operator position in South Africa. Participants completed a biographical questionnaire and three subtests from the Differential Aptitude Test battery. The Chi-square test was used to determine the relationship between type of secondary education (incorporating subject choice) and selected cognitive aptitudes.
Main findings: The study’s findings revealed statistically and practically significant relationships between type of secondary education (incorporating subject choice), verbal reasoning, non-verbal reasoning and visual perceptual speed. Broad performance levels in the three aptitude subtests employed in this study were significantly associated with the type of matriculation certificate held by applicants. The findings specifically indicated that the secondary education types that included the subjects mathematics or both mathematics and science were associated with higher levels of performance in the three aptitudes. This had consequences for these applicants’ success in the screening process which could lead to enhanced chances of employability.
Practical and managerial implications: Applicants’ type of secondary education (incorporating subject choice) could be regarded as a key criterion in human resource selection and be instructive in the screening process. This could reduce the candidate pool prior to more costly psychometric assessments.
Contribution or value-add: The findings are specifically relevant to the South African automotive industry in terms of their human resource selection practices. The insights gained from the findings may also be used as a guide to human resource practitioners in the selection of similar level employees in other working contexts. The study makes a case for a multiple-hurdle approach to selection.
Mathematical operations are cognitive actions we take to calculate relations among numbers. Arithmetic operations, addition, subtraction, multiplication, and division are elemental in education. Addition is the first one taught in school and is most popular in functional magnetic resonance imaging (fMRI) studies. Division, typically taught last is least studied with fMRI. fMRI meta-analyses show that arithmetic operations activate brain areas in parietal, cingulate and insular cortices for children and adults. Critically, no meta-analysis examines concordance across brain correlates of separate arithmetic operations in children and adults. We review and examine using quantitative meta-analyses data from fMRI articles that report brain coordinates separately for addition, subtraction, multiplication, and division in children and adults. Results show that arithmetic operations elicit common areas of concordance in fronto-parietal and cingulo-opercular networks in adults and children. Between operations differences are observed primarily for adults. Interestingly, higher within-group concordance, expressed in activation likelihood estimates, is found in brain areas associated with the cingulo-opercular network rather than the fronto-parietal network in children, areas also common between adults and children. Findings are discussed in relation to constructivist cognitive theory and practical directions for future research.
Arithmetic fact retrieval has been suggested to recruit a left-lateralized network comprising perisylvian language areas, parietal areas such as the angular gyrus (AG), and non-neocortical structures such as the hippocampus. However, the underlying white matter connectivity of these areas has not been evaluated systematically so far. Using simple multiplication problems, we evaluated how disconnections in parietal brain areas affected arithmetic fact retrieval following stroke. We derived disconnectivity measures by jointly considering data from n=73 patients with acute unilateral lesions in either hemisphere and a white-matter tractography atlas (HCP-842) using the Lesion Quantification Toolbox (LQT). Whole-brain voxel-based analysis indicated a left-hemispheric cluster of white matter fibers connecting the AG and superior temporal areas to be associated with a fact retrieval deficit. Subsequent analyses of direct grey-to-grey matter disconnections revealed that disconnections of additional left-hemispheric areas (e.g., between the superior temporal gyrus and parietal areas) were significantly associated with the observed fact retrieval deficit. Results imply that disconnections of parietal areas (i.e., the AG) with language-related areas (i.e., superior and middle temporal gyri) seem specifically detrimental to arithmetic fact retrieval. This suggests that arithmetic fact retrieval recruits a widespread left-hemispheric network and emphasizes the relevance of white matter connectivity for number processing.
The ability to perceive the numerosity of items in the environment is critical for behavior of species across the evolutionary tree. Though the focus of studies of numerosity perception lays on the parietal and frontal cortices, the ability to perceive numerosity by a range of species suggests that subcortical nuclei may be implicated in the process. Recently, we have uncovered tuned neural responses to haptic numerosity in the human cortex. Here, we questioned whether subcortical nuclei are also engaged in perception of haptic numerosity. To that end, we utilized a task of haptic numerosity exploration, together with population receptive field model of numerosity selective responses measured at ultra-high field MRI (7T). We found tuned neural responses to haptic numerosity in the bilateral putamen. Similar to the cortex, the population receptive fields tuning width increased with numerosity. The tuned responses to numerosity in the putamen extend its role in cognition and propose that the motor-sensory loops of the putamen and basal ganglia might take an active part in numerosity perception and preparation for future action.
Strong foundational skills in mathematical problem solving, acquired in early childhood, are critical not only for success in the science, technology, engineering, and mathematical (STEM) fields but also for quantitative reasoning in everyday life. The acquisition of mathematical skills relies on protracted interactive specialization of functional brain networks across development. Using a systems neuroscience approach, this review synthesizes emerging perspectives on neurodevelopmental pathways of mathematical learning, highlighting the functional brain architecture that supports these processes and sources of heterogeneity in mathematical skill acquisition. We identify the core neural building blocks of numerical cognition, anchored in the posterior parietal and ventral temporal-occipital cortices, and describe how memory and cognitive control systems, anchored in the medial temporal lobe and prefrontal cortex, help scaffold mathematical skill development. We highlight how interactive specialization of functional circuits influences mathematical learning across different stages of development. Functional and structural brain integrity and plasticity associated with math learning can be examined using an individual differences approach to better understand sources of heterogeneity in learning, including cognitive, affective, motivational, and sociocultural factors. Our review emphasizes the dynamic role of neurodevelopmental processes in mathematical learning and cognitive development more generally.
Background
Functional MRI studies have suggested a ‘frontoparietal shift’ over the course of development, whereby children tend to engage prefrontal neural regions to a greater extent than adults when completing mathematics tasks. Although this literature hints that lateral prefrontal regions may be involved in acquiring mathematics knowledge, a key limitation of existing studies is that they have included mathematics content that children already are familiar with as opposed to examining the dynamic learning process. We aimed to address this gap by examining children's neural responses when exposed to a new, unfamiliar mathematics concept.
Method
Eighteen 8 – 11 year old children viewed blocked demonstrations of base-2/binary (unfamiliar) and base-10/decimal (familiar) number systems while undergoing functional MRI (fMRI). Children's behavioral understanding of binary numbers was measured between fMRI runs.
Results
Counter to hypotheses, there were no overall differences in prefrontal activity for binary relative to decimal blocks. However, children with higher levels of behavioral understanding of the novel, binary concept showed enhanced neural activity in the left rostral middle frontal gyrus specifically during binary concept exposure. They also showed enhanced connectivity between this region and pre-and post-central gyri and left parahippocampal regions.
Conclusions
Individual differences in children's behavioral grasp of a new mathematics concept correlate with prefrontal activity and functional connectivity during exposure to the concept, suggesting that rostral prefrontal cortex may play a role in mathematics learning.
The functional overlap of language and arithmetic is debatable. Although some studies have reported independent representations of arithmetic and language in the brain, other studies have reported shared activity of the two cognitive domains in the inferior frontal gyrus. Although most previous studies have evaluated right-handed individuals, variability of hemispheric dominance in non-right-handed individuals should provide important information on the functional collateralization of these two cognitive domains. The present study evaluated the cortical lateralization patterns of the two cognitive domains using functional magnetic resonance imaging in 30 non-right-handed participants who performed language and arithmetic tasks. We found that language and arithmetic tasks demonstrated shared activity in the bilateral inferior frontal gyrus (IFG). Furthermore, the lateralization patterns of language and arithmetic tasks were correlated with each other. Most participants with language dominance in the left hemisphere also exhibited dominance of arithmetic tasks in the left hemisphere; similarly, most participants with language dominance in the right hemisphere exhibited dominance of arithmetic tasks in the right hemisphere. Among all the brain regions, the precentral gyrus, which is located slightly posterior to the IFG, exhibited the highest correlation coefficient between laterality indices of language and arithmetic tasks. These results suggest a shared functional property between language and arithmetic in the brain.
This commentary reviews and summarises the strides which neuroscience has made in our present understanding of the development of literacy and numeracy in children. Specifically, it draws attention to key insights from studies which have elucidated the possible neural mechanisms that may account for difficulties in the development of these fundamental learning abilities. It also discusses the possible future applications of neuroscience in providing early detection of these learning difficulties in children, and in guiding the design of appropriate interventions aimed at mitigating these difficulties. Finally, it identifies challenges that will arise as the field of educational neuroscience matures. Importantly, it emphasises that educational neuroscience research must be considered in tandem with research in other fields in order to develop a holistic understanding of the process of learning.
Recent studies have highlighted that people with mathematical and scientific talents develop a different brain structure from those with typical development. However, most of these studies have focused on the relationship between cognitive functions
of the brain and the operation of a single area of the brain. This study explores the connections among the network structures with relation to mathematical and scientific talents, intelligence, and white matter. The study recruited 42 men with normal
nerve functions. The experimental group comprised 21 participants with mathematical and scientific talents and an age of 21.00 ± 1.67 years; the control group comprised 21 participants with typical developmental and an age of 21.48 ± 2.29 years.
The mathematical and scientific talent and typical developmental groups consisted of 21 people each. The researchers adopted the third version of the Wechsler Adult Intelligence Test to evaluate individual intelligence, conduct diffusion tensor imaging of participants, and construct a network of white matter to analyze the overall network attributes and nodal efficiencies using graph theory. The results show that the communication efficiency among the nodes inside the local region is relatively better in people with mathematical and scientific talents, particularly the in the superior prefrontal gyrus.
Moreover, when intelligence was equal between the two groups, the mathematical and scientific talent group outperformed the other in terms of node efficiency in local regions and the clustering coefficient in the superior occipital gyrus. The relationship between the topological properties and the intelligence of the mathematical and scientific talent group and the typical developmental group showed that only the intelligence of the typical developmental group was positively connected with integrated efficiency across several regions of the brain; however, no direct correlation was shown in the mathematical
and scientific talents group. The results not only provided empirical evidence for the disparity in white matter structure between mathematical and scientific talent and typical development groups but also distinguished mathematical and scientific talents, mathematical ability, and intelligence based on the topological network of the brain, which can be used in future assessments for people with mathematical and scientific talents.
Mathematical cognition provides a foundation for the development of skills critical for success in the 21st century. The use of mathematics to categorize, visualize, and manipulate information now extends to virtually all domains of human activity, making the necessity for basic mathematical skills more pressing than ever. This chapter summarizes current knowledge about the developmental and neurocognitive basis of mathematical reasoning. We review central cognitive theories and summarize emerging findings on the perceptual and cognitive building blocks of numerical cognition, the functional brain circuits associated with them, and the multiple memory and cognitive‐control systems that play a critical role in scaffolding children's mathematical skill development. We highlight neurodevelopmental models and functional brain circuits that go beyond individual regions involved in number processing and demonstrate that brain systems and circuits engaged by the developing brain are not the same as those engaged in adult brains sculpted by years of learning.
Neurocognitive studies of arithmetic learning in adults have revealed decreasing brain activation in the fronto-parietal network, along with increasing activation of specific cortical and subcortical areas during learning. Both changes are associated with a shift from procedural to retrieval strategies for problem-solving. Here we address the critical, open question of whether similar neurocognitive changes are also evident in children. In this study, 20 typically developing children were trained to solve simple and complex multiplication problems. The one-session and two-week training effects were monitored using simultaneous functional near-infrared spectroscopy (fNIRS) and electroencephalography (EEG). FNIRS measurement after one session of training on complex multiplication problems revealed decreased activation at the left angular gyrus (AG), right superior parietal lobule, and right intraparietal sulcus. Two weeks of training led to decreased activation at the left AG and right middle frontal gyrus. For both simple and complex problems, we observed increased alpha power in EEG measurements as children worked on trained versus untrained problems. In line with previous multiplication training studies in adults, reduced activation within the fronto-parietal network was observed after training. Contrary to adults, we found that strategy shifts via arithmetic learning were not contingent on the activation of the left AG in children.
Nine previous positron emission tomography (PET) studies of human visual information processing were reanalyzed to determine the consistency across experiments of blood flow decreases during active tasks relative to passive viewing of the same stimulus array. Areas showing consistent decreases during active tasks included posterior cingulate/precuneous (Brodmann area, BA 31/7), left (BAS 40 and 39/19) and right (BA 40) inferior parietal cortex, left dorsolateral frontal cortex (BA S), left lateral inferior frontal cortex (BA 10/47), left inferior temporal gyrus @A 20), a strip of medial frontal regions running along a dorsal-ventral axis (BAs 8, 9, 10, and 32), and the right amygdala.
Experiments involving language-related processes tended to show larger decreases than nonlanguage experiments. This trend mainly reflected blood flow increases at certain areas in the passive conditions of the language experiments (relative to a fixation control in which no task stimulus was present) and slight blood flow decreases in the passive conditions of the nonlanguage experiments. When the active tasks were referenced to the fixation condition, the overall size of blood flow decreases in language and nonlanguage tasks were the same, but differences were found across cortical areas. Decreases were more pronounced in the posterior cingulate/precuneous (BAS 31/7) and right inferior parietal cortex (BA 40) during language-related tasks and more pronounced in left inferior frontal cortex (BA 10/47) during nonlanguage tasks.
Blood flow decreases did not generally show significant differences across the active task states within an experiment, but a verb-generation task produced larger decreases than a read task in right and left inferior parietal lobe (BA 40) and the posterior cingulate/precuneous (BA 31/7), while the read task produced larger decreases in left lateral inferior frontal cortex (BA 10/47). These effects mirrored those found between experiments in the language-nonlanguage comparison.
Consistent active minus passive decreases may reflect decreased activity caused by active task processes that generalize over tasks or increased activity caused by passive task processes that are suspended during the active tasks. Increased activity during the passive condition might reflect ongoing processes, such as unconstrained verbally mediated thoughts and monitoring of the external environment, body, and emotional state.
Positron emission tomography was used to examine the cerebral networks underlying number comparison and multiplication in eight normal volunteers. Cerebral blood flow was measured within anatomical regions of interest defined in each subject using magnetic resonance imaging. Three conditions were used: rest with eyes closed, mental multiplication of pairs of arabic digits and larger-smaller comparison of the same pairs. Both multiplication and comparison activated the left and right lateral occipital cortices, the left precentral gyrus, and the supplementary motor area. Beyond these common activations, multiplication activated also the left and right inferior parietal gyri, the left fusiform and lingual gyri, and the right cuneus. Relative to comparison, multiplication also yielded superior activity in the left lenticular nucleus and in Brodmann's area 8, and induced a hemispheric asymmetry in the activation of the precentral and inferior frontal gyri. Conversely, relative to multiplication, comparison yielded superior activity in the right superior temporal gyrus, the left and right middle temporal gyri, the right superior frontal gyrus, and the right inferior frontal gyrus. These results underline the role of bilateral inferior parietal regions in number processing and suggest that multiplication and comparison may rest on partially distinct networks.
The area of cognitive arithmetic is concerned with the mental representation of number and arithmetic, and the processes and procedures that access and use this knowledge. In this article, I provide a tutorial review of the area, first discussing the four basic empirical effects that characterize the evidence on cognitive arithmetic: the effects of problem size or difficulty, errors, relatedness, and strategies of processing. I then review three current models of simple arithmetic processing and the empirical reports that support or challenge their explanations. The third section of the review discusses the relationship between basic fact retrieval and a rule-based component or system, and considers current evidence and proposals on the overall architecture of the cognitive arithmetic system. The review concludes with a final set of speculations about the all-pervasive problem difficulty effect, still a central puzzle in the field.
Did evolution endow the human brain with a predisposition to represent and acquire knowledge about numbers? Although the parietal lobe has been suggested as a potential substrate for a domain-specific representation of quantities, it is also engaged in verbal, spatial, and attentional functions that may contribute to calculation. To clarify the organisation of number-related processes in the parietal lobe, we examine the three-dimensional intersection of fMRI activations during various numerical tasks, and also review the corresponding neuropsychological evidence. On this basis, we propose a tentative tripartite organisation. The horizontal segment of the intraparietal sulcus (HIPS) appears as a plausible candidate for domain specificity: It is systematically activated whenever numbers are manipulated, independently of number notation, and with increasing activation as the task puts greater emphasis on quantity processing. Depending on task demands, we speculate that this core quantity system, analogous to an internal "number line," can be supplemented by two other circuits. A left angular gyrus area, in connection with other left-hemispheric perisylvian areas, supports the manipulation of numbers in verbal form. Finally, a bilateral posterior superior parietal system supports attentional orientation on the mental number line, just like on any other spatial dimension.
Sumario: Structural models for counted data -- Maximum likelihood estimates for complete tables -- Formal goodness of it: summary statistics and model selection -- Maximum likelihood estimation for incomplete tables -- Estimating the size of a closed population -- Models for measuring change -- Analysis of square tables: symmetry and marginal homogeneity -- Model selection and assessing closeness of fit: practical aspects -- Other methods for estimation and testing in cross-classifications -- Measures of association and agreement -- Pseudo-bayes estimates of cell probabilities -- Sampling models for discrete data -- Asymptotic methods.
A patient presented with agraphia and acalculia associated with a left frontal (F1, F2) infarction. He made mainly phonological but also lexical errors in writing (syllabograms), but his ability to write kanji (morphograms) was relatively preserved. Although he could add and subtract numbers, he could neither multiply nor divide them because of a difficulty in retrieving the multiplication tables and calculation procedures. Positron emission tomography showed decreased cerebral blood flow and metabolism limited to the infarct site. These findings suggest that agraphia and acalculia may occur associated with a left prefrontal lesion, and that the retrieval of arithmetic processes is modality specific.
Cortical activation during arithmetic calculation (silent subtraction by sevens) was compared to that observed during a control condition for which subjects were required to count forward by ones. Nine normal subjects underwent 1.5-T functional magnetic resonance imaging while performing these tasks. All subjects showed bilateral premotor, posterior parietal, and prefrontal cortex activation during serial calculation. There was a large degree of individual variation in activation outside of these areas. These results confirm the role of posterior parietal cortex in arithmetic calculation and implicate other regions, including prefrontal cortex.
We measured cerebral activation with functional magnetic resonance imaging at 3 Tesla while eight healthy volunteers performed various number processing tasks known to be dissociable in brain-lesioned patients: naming, comparing, multiplying, or subtracting single digits. The results revealed the activation of a circuit comprising bilateral intraparietal, prefrontal, and anterior cingulate components. The extension and lateralization of this circuit was modulated by task demands. The intraparietal and prefrontal activation was more important in the right hemisphere during the comparison task and in the left hemisphere during the multiplication task and was intensely bilateral during the subtraction task. Thus, partially distinct cerebral circuits with the dorsal parietal pathway underlie distinct arithmetic operations.
Positron emission tomography (PET) and functional magnetic resonance imaging (fMRI) have been extensively used to explore the functional neuroanatomy of cognitive functions. Here we review 275 PET and fMRI studies of attention (sustained, selective, Stroop, orientation, divided), perception (object, face, space/motion, smell), imagery (object, space/motion), language (written/spoken word recognition, spoken/no spoken response), working memory (verbal/numeric, object, spatial, problem solving), semantic memory retrieval (categorization, generation), episodic memory encoding (verbal, object, spatial), episodic memory retrieval (verbal, nonverbal, success, effort, mode, context), priming (perceptual, conceptual), and procedural memory (conditioning, motor, and nonmotor skill learning). To identify consistent activation patterns associated with these cognitive operations, data from 412 contrasts were summarized at the level of cortical Brodmann's areas, insula, thalamus, medial-temporal lobe (including hippocampus), basal ganglia, and cerebellum. For perception and imagery, activation patterns included primary and secondary regions in the dorsal and ventral pathways. For attention and working memory, activations were usually found in prefrontal and parietal regions. For language and semantic memory retrieval, typical regions included left prefrontal and temporal regions. For episodic memory encoding, consistently activated regions included left prefrontal and medial temporal regions. For episodic memory retrieval, activation patterns included prefrontal, medial temporal, and posterior midline regions. For priming, deactivations in prefrontal (conceptual) or extrastriate (perceptual) regions were consistently seen. For procedural memory, activations were found in motor as well as in non-motor brain areas. Analysis of regional activations across cognitive domains suggested that several brain regions, including the cerebellum, are engaged by a variety of cognitive challenges. These observations are discussed in relation to functional specialization as well as functional integration.
Positron emission tomography was used to localize the cerebral networks specifically involved in three basic numerical processes: arabic numeral processing, numerical magnitude comparison, and retrieval of simple addition facts. Relative cerebral blood flow changes were measured while normal volunteers were resting with eyes closed, making physical judgment on nonnumerical characters or arabic digits, comparing, or adding the same digits. Processing arabic digits bilaterally produced a large nonspecific activation of occipito-parietal areas, as well as a specific activation of the right anterior insula. Comparison and simple addition fact retrieval revealed a fronto-parietal network involving mainly the left intraparietal sulcus, the superior parietal lobule and the precentral gyrus. Comparison also activated, but to a lesser extent, the right superior parietal lobe, whereas addition also activated the orbito-frontal areas and the anterior insula in the right hemisphere. Implications for current anatomo-functional models of numerical cognition are drawn.
Neuropsychological studies have revealed different subtypes of dyscalculia, including dissociations between exact calculation and approximation abilities, and an impact of number size on performance. To understand the origins of these effects, we measured cerebral activity with functional MRI at 3 Tesla and event-related potentials while healthy volunteers performed exact and approximate calculation tasks with small and large numbers. Bilateral intraparietal, precentral, dorsolateral and superior prefrontal regions showed greater activation during approximation, while the left inferior prefrontal cortex and the bilateral angular regions were more activated during exact calculation. Increasing number size during exact calculation led to increased activation in the same bilateral intraparietal regions as during approximation, as well the left inferior and superior frontal gyri. Event-related potentials gave access to the temporal dynamics of calculation processes, showing that effects of task and of number size could be found as early as 200-300 ms following problem presentation. Altogether, the results reveal two cerebral networks for number processing. Rote arithmetic operations with small numbers have a greater reliance on left-lateralized regions, presumably encoding numbers in verbal format. Approximation and exact calculation with large numbers, however, put heavier emphasis on the left and right parietal cortices, which may encode numbers in a non-verbal quantity format. Subtypes of dyscalculia can be explained by lesions disproportionately affecting only one of these networks.
Mental calculation is a complex cognitive operation that is composed of a set of distinct functional processes. Using functional magnetic resonance imaging (fMRI), we mapped brain activity in healthy subjects performing arithmetical tasks and control tasks evoking a comparable load on visuo-constructive, linguistic, attentional and mnemonic functions. During calculation, as well as non-mathematical tasks, similar cortical networks consisting of bilateral prefrontal, premotor and parietal regions were activated, suggesting that most of these cortical areas do not exclusively represent modules for calculation but support more general cognitive operations that are instrumental but not specific to mental arithmetic. Significant differences between calculation and the non-mathematical tasks were found in parietal sub-regions, where non-arithmetic number or letter substitution tasks preferentially activated the superior parietal lobules whereas calculation predominantly elicited activation of the left dorsal angular gyrus and the medial parietal cortices. We interpret the latter activations to reflect sub-processes of mental calculation that are related to the processing of numerical representations during exact calculation and to arithmetical fact retrieval. Finally, we found that more complex calculation tasks involving the application of calculation rules increased activity in left inferior frontal areas that are known to subserve linguistic and working memory functions. Taken together, these findings help to embed the specific cognitive operation of calculation into a neural framework that provides the required set of instrumental components. This result may further inform the cognitive modeling of calculation and adds to the understanding of neuropsychological deficit patterns in patients.
This study reports for the first time a selective impairment for simple addition in patient FS. Moreover, patient VP presented with a selective impairment for simple multiplication and patient DT with a selective impairment for simple subtraction. These findings are discussed in the context of two of the most influential models for the organisation of arithmetical facts in memory (Dehaene and Cohen, 1995, 1997, and Dagenbach and McCloskey, 1992). Dehaene and Cohen (1995, 1997) have proposed that dissociation between arithmetical facts result from a selective impairment to two different types of processing: rote verbal memory for multiplication and simple addition vs. quantity processing for subtraction and division. Dagenbach and McCloskey (1992) suggest dissociation between arithmetical facts result from a selective damage to segregated memory networks specific for each operation. We will argue that our findings are problematic for Dehaene's model and in good accord with McCloskey's view.
Modern neurosurgical concepts call for not only "seeing" but also for "localizing" structures in three-dimensional space in relationship to each other. Hence there is a need for a reference system. This book aims to put this notion into practice by means of anatomical and MRI sections with the same stereotaxic orientation. The purpose is to display the fundamental distribution of structures in three-dimensional space and their spatial evolution within the brain as a whole, while facilitating their identification; to make comparative studies of cortico-subcortical lesions possible on a basis of an equivalent reference system; to exploit the anatomo-functional data such as those furnished by SEEG in epilepsy and to enable the localization of special regions such as the SMA in three-dimensional space; and to apply the anatomical correlations of this reference system to neurophysiological investigations lacking sufficient anatomical back-up (including PET scan).
I Number Words.- 1 Introduction and Overview of Different Uses of Number Words.- 2 The Number-Word Sequence: An Overview of Its Acquisition and Elaboration.- II Correspondence Errors in Counting Objects.- 3 Correspondence Errors in Children's Counting.- 4 Effects of Object Arrangement on Counting Correspondence Errors and on the Indicating Act.- 5 Effects of Object Variables and Age of Counter on Correspondence Errors Made When Counting Objects in Rows.- 6 Correspondence Errors in Children's Counting: A Summary.- III Concepts of Cardinality.- 7 Children's Early Knowledge About Relationships Between Counting and Cardinality.- 8 Later Conceptual Relationships Between Counting and Cardinality: Addition and Subtraction of Cardinal Numbers.- 9 Uses of Counting and Matching in Cardinal Equivalence Situations: Equivalence and Order Relations on Cardinal Numbers.- IV Number Words, Counting, and Cardinality: The Increasing Integration of Sequence, Count, and Cardinal Meanings.- 10 Early Relationships Among Sequence Number Words, Counting Correspondence, and Cardinality.- 11 An Overview of Changes in Children's Number Word Concepts from Age 2 Through 8.- References.- Author Index.
Knowledge of the prevalence of learning disabilities in general, and dyscalculia in particular, has major clinical, educational, and public health ramifications. Determining the prevalence of dyscalculia can also aid in assessing the efficacy of educational programs and instructional methods. Furthermore, in many countries, educational interventions are mandated by law, with consequent budgetary implications. Therefore, generating reliable data on the prevalence of learning disabilities is far from being a theoretical issue. Rather, it is a necessity for those agencies responsible for providing medical services and special educational interventions. Basic research principles need to be implemented. Of prime importance is the definition of learning disability, for which a consensus has not yet been reached and, therefore, is still a topic of ongoing debate. It is imperative to identify medical and environmental conditions that may masquerade as learning disabilities or exacerbate the difficulties of a child who is considered academically weak who does not have a learning disability. In this chapter the epidemiological studies performed in Europe, North America, India, and Israel are reviewed. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
A series of experiments explored the role of information storage in working memory in performing mental arithmetic. Experiment 1 assessed the strategies people report for solving auditorily presented multidigit problems such as 325 + 46. As expected, all subjects reported breaking down the problems into a series of elementary stages, though there were considerable individual differences with regard to the order of their execution. Strategies of this type necessitate both the temporary storage of information and the mobilization of long-term knowledge. Experiments 2 and 3 examined the effects of delaying the output of individual partial results on calculation accuracy and showed that interim information is forgotten if it is not utilized immediately. Experiment 4 showed that forgetting the initial information is also a source of error and suggested that forgetting increases as a function of the number of calculation stages intervening between initial presentation and subsequent utilization of information. Two simple quantitative models were derived from a general task analysis, one of which assumed a decay process in working storage and the other no decay. The decay model gave a reasonable fit to data from Experiments 2–4, and in doing so it coped appreciably well with the effects of a large variety of task variables (e.g., carrying, the provision of written notes, calculation strategy, output order). The decay model is a tractable analysis of a complex task, and it is suggested that similar analyses may prove fruitful for other problem-solving activities which involve the use of working memory.
It has long been debated whether the ability to solve mathematical problems depends on language. In this issue, Dehaene et al. show that exact calculations involve linguistic representations of numbers and are controlled by the speech-related areas of the left frontal lobe in the brain. In contrast, approximate calculations are language-independent, relying on visuo-spatial representations of numbers controlled by the left and right parietal lobes. In an accompanying Perspective, Brian Butterworth discusses these findings and postulates that the parietal lobes may also be involved in finger counting, an almost universal stage in the learning of exact arithmetic.
We report a single case study of a brain-damaged patient with impaired arithmetic performance. Three principal findings are presented: First, in a task involving production of answers to simple arithmetic problems, the patient's performance was far better for subtraction than for addition or multiplication. Second, in all arithmetic operations performance was generally much better for problems potentially solvable by rule (e.g., 5 + 0) than for problems requiring retrieval of specific facts (e.g., 5 + 3). Third, the dissociation between subtraction and the other arithmetic operations obtained in the production task was not observed in a verification task. The implications of these findings for claims concerning the organization of stored arithmetic facts are discussed.
This article discusses cognitive neuropsychological research on acquired dyscalculia (i.e., impaired numerical processing resulting from brain damage), surveying issues of current interest, and illustrating the ways in which analyses of acquired deficits can contribute to an understanding of normal processing. I first review the logic whereby inferences concerning normal cognition are drawn from patterns of impaired performance. I then consider research exploring the general functional architecture of the cognitive numerical processing mechanisms, and finally turn to studies aimed at probing the internal structure and functioning of individual processing components.
Studies of brain-damaged patients have revealed the existence of a selective impairment of face processing, prosopagnosia, resulting from lesions at different loci in the occipital and temporal lobes. The results of such studies have led to the identification of several cortical areas underlying the processing of faces, but it remains unclear what functional aspects of face processing are served by these areas and whether they are uniquely devoted to the processing of faces. The present study addresses these questions in a positron emission tomography (PET) study of regional cerebral blood flow in normal adults, using the 15 oxygen water bolus technique. The subjects participated in six tasks (with gratings, faces and objects), and the resulting level of cerebral activation was mapped on images of the subjects' cerebral structures obtained through magnetic resonance and was compared between tasks using the subtraction method. Compared with a fixation condition, regional cerebral blood flow (rCBF) changes were found in the striate and extrastriate cortex when subjects had to decide on the orientation of sine-wave gratings. A face-gender categorization resulted in activation changes in the right extrastriate cortex, and a face-identity condition produced additional activation of the fusiform gyrus and anterior temporal cortex of both hemispheres, and of the right parahippocampal gyrus and adjacent areas. Cerebral activation during an object-recognition task occurred essentially in the left occipito-temporal cortex and did not involve the right hemisphere regions specifically activated during the face-identity task. The results provide the first empirical evidence from normal subjects regarding the crucial role of the ventro-medial region of the right hemisphere in face recognition, and they offer new information about the dissociation between face and object processing.
Information about the basal ganglia has accumulated at a prodigious pace over the past decade, necessitating major revisions in the authors' concepts of the structural and functional organization of these nuclei. Recent anatomical and physiological findings have further substantiated the concept of segregated basal ganglia-thalamocortical pathways, and reinforced the general principle that basal ganglia influences are transmitted only to restricted portions of the frontal lobe (even though the striatum receives projections from nearly the entire neocortex). Using the 'motor' circuit as a model, the authors have reexamined the available data on other portions of the basal ganglia-thalamocortical pathways and found that the evidence strongly suggests the existence of at least four additional circuits organized in parallel with the 'motor' circuit. In the discussion that follows, they review some of the anatomic and physiologic features of the 'motor circuit,' as well as the data that support the existence of the other proposed parallel circuits, which they have designated the 'oculomotor,' the 'dorsolateral prefrontal,' the 'lateral orbitofrontal,' and the 'anterior cingulate,' respectively. Each of these five basal ganglia-thalamocortical circuits appears to be centered upon a separate part of the frontal lobe. This list of basal ganglia-thalamocortical circuits is not intended to be exhaustive. In fact, if the conclusions suggested in this review are valid, future investigations might be expected to disclose not only further details (or the need for revisions) of these five circuits, but perhaps also the existence of additional parallel circuits whose identification is currently precluded by a paucity of data.