Includes the use of various techniques to either directly or indirectly image the structure, function/pharmacology of the brain. It is a relatively new discipline within medicine and neuroscience/psychology.
A type of specialized MRI scan. A noninvasive tool used to observe functioning in the brain or other organs by determining which part of the brain and spinal cord is active during a given task by tracking blood oxygen levels in the brain.
The performance of some composite cognitive activity; an operation that affects mental contents; the process of thinking.
Of or pertaining to neuropsychology, the basic scientific discipline that studies the structure and function of the brain related to specific psychological processes and overt behaviors.
The area of neuroscience (the study of the brain and central nervous system) that focuses on understanding perception, action, attention, memory, and language.
A subdiscipline of cognitive science that studies the cognitive, developmental and neural bases of numbers and mathematics.
Noninvasive tools used to observe function and structures in the brain.
Area within the parietal lobe in the brain.
A study that statistically analyzes data by pooling results from a number of studies that have used similar methods to investigate similar topics; the data is re-analyzed as a whole and used to make stronger conclusions based on the results.
A groove or depression on the brain surface separating two ridges of the parietal lobe. Its principal functions are related to perceptual-motor coordination (for directing eye movements and reaching) and visual attention.
A brain region located in the parietal lobe of the brain, behind the supramarginal gyrus and in front of the occipital lobe. It is involved in the processing of auditory and visual perception and in the comprehension of language.
Pertaining to the perception of the spatial relationships between objects in one's field of vision.
A specific learning disability affecting the acquisition of arithmetic skills in an otherwise normal child. Current data indicate that this learning disability is a brain-based disorder with a familial-genetic predisposition.
Scientifically based research that applies rigorous, systematic, and objective procedures to obtain valid knowledge that can be generalized. This type of research draws on observation or experiement and has been accepted by a peer-reviewed journal or approved by an independent panel that conducts a comparable, objective scientific review.
The degree to which one variable is related to another. Used to look for relationships and the strength of the relationship between variables. Does not determine cause or the direction of the relationship.
A person's age measured from the year, month and day they were born.
A fold or ridge on the surface of the brain involved in spatial orientation and word representation.
A brain region located near the top of the frontal lobes and along the walls that divide the left and right hemispheres. It is involved in a wide variety of cognitive and emotional functions. It plays a key role in the brain's ability to process particularly complex and challenging cognitive tasks.
The regions of the brain that are below cortex level; i.e., within the lobes of the brain.
An area in the brain that helps regulate emotion and memory.
A brain region located at the base or "basement" of the brain responsible for a variety of functions, including motor control and learning. The basal ganglia are abnormal in a number of important neurologic conditions (e.g., Parkinson disease).
Refers to the memory system used to store and actively manipulate temporary information for use; can also be called short-term memory.
A system for permanently storing, managing, and retrieving information for later use.
Either of the two symmetrical halves of the brain. Each hemisphere is responsible for different body functions and skills.
The field that concerns itself with linking function with brain structure.
Having or involving two sides.
A non-invasive imaging method using magnetic fields and radio waves to create images of the inside of the body.
One of the two components of the central nervous system located in the cortex on the outer part of the brain, which contains the neurons that fire and receive the signals. The gray matter includes regions of the brain involved in muscle control, sensory perceptions, such as seeing and hearing, memory, emotions and speech.
Part of the central nervous system and composed of neuron projections which are coated in an insulating layer of myelin, giving it a white appearance.
Studies that use working hypotheses that are testable using observation or experiment.
In recent years, the advent of non-invasive neuroimaging methods
, such as functional Magnetic Resonance Imaging (fMRI)
has provided an important complement to behavioral investigations of cognitive processes
. Together with traditional neuropsychological
studies of brain-damaged patients, these investigations have lead to the creation of a new field of research: Cognitive Neuroscience
. The combination of behavioral and neuroscientific empirical studies
is starting to reveal how the brain enables the mind. More recently, this approach has been applied to the study of the typical and atypical developmental trajectories of cognitive processes, such as numerical cognition
This entry reviews the current state of the insights, which have been gleaned from the application of modern functional and structural neuroimaging methods
into the development of children's numerical and mathematical skills.
Both the study of brain-damaged patients and, more recently, non-invasive neuroimaging studies of healthy participants, have revealed a set of brain areas that are associated with the processing of numeracy and arithmetic. Specifically, a wide range of functional neuroimaging studies point to areas of the parietal cortex
(see Figure 1 below) as playing a critical role in the processing of both numerical and mathematical problems. In a recent meta-analysis
(Dehaene, Piazza, Pinel, & Cohen, 2003) of neuroimaging studies in which adult participants were asked to solve numerical (e.g., number comparison and estimation) or mathematical (e.g., mental arithmetic) tasks, the authors reported the presence of three key areas in the parietal cortex that are thought to subserve numerical and mathematical cognition. Specifically, the meta-analysis suggests that when participants process numerical quantity (e.g., while deciding which of two numbers is numerically larger), they activate bilateral (left and right side) areas of the so-called intraparietal sulcus (IPS)
. In contrast, when adults are asked to calculate, activation is most commonly found in a left-lateralized parietal region called the angular gyrus (AG)
. In addition to these two regions, Dehaene et al. identified a third region in both the left and right superior parietal cortex that, according to these authors, is associated with the attentional and visuo-spatial
resources required by numerical and mathematical processing tasks.
Figure 1. Key areas in the parietal cortex.
This meta-analysis demonstrates the significant progress that has been made in our understanding of the brain regions involved in both numerical and mathematical processing. However, to date, most of the neuroimaging studies investigating the neural mechanisms underlying numeracy and mathematical processing have been conducted with healthy adult participants. Therefore, much less is known about whether, and if so how, the brain areas associated with numerical and mathematical processing change over developmental time and how such developmental processes differ among children who present with mathematical difficulties (i.e., Developmental Dyscalculia
Key Research Questions
Based on the background of the information discussed above, two key research questions can be delineated:
1. Do the brain mechanisms underlying numeracy and mathematics change over developmental time? If so, how?
2. Do children with DD activate the same brain regions as their typically developing peers?
Recent Research Results
While neuroimaging studies into the developmental trajectories underlying numeracy and mathematics lag significantly behind empirical research
that has investigated the neural correlates of these functions in the adult brain, there now exists a growing body of both functional and structural neuroimaging studies with developmental subject populations.
Do the brain mechanisms underlying numeracy and mathematics change over developmental time? If so, how?
In one of the first neuroimaging studies of arithmetic development, Rivera, Reiss, Eckert, and Menon (2005) used fMRI to study the neural correlates of addition and subtraction in healthy participants between the ages of 8 and 19 years. Participants viewed addition and subtraction problems (e.g., 5+3=8 or 7-4=2) and had to judge whether the result displayed was correct or incorrect. Moreover, participants completed a control task in which they had to judge whether a sequence of 5 digits contained a 0 or not (e.g., 61059 or 93263). When brain activation associated with the arithmetic task was subtracted from that associated with the control task, the brain areas involved in calculation could be revealed. The authors then correlated
the results of the difference between the calculation and the control task with the chronological ages
of the participants. Using this analysis, Rivera et al. could reveal in which brain areas the activation either positively or negatively correlated with chronological age. This correlational analysis uncovered both brain circuits whose activation during mental arithmetic increases with chronological age as well as brain regions in which the younger participants exhibited greater activation than their older peers. More specifically, Rivera et al. found that activation in the left inferior parietal cortex (including the left supramarginal gyrus
and the anterior aspect of the left angular gyrus) increased with the chronological age of the participants. In contrast, areas of the prefrontal and anterior cingulate cortex
as well as subcortical regions
such as the hippocampus
and basal ganglia
exhibited decreasing activation related to the arithmetic task with increasing age. These findings therefore suggest that there are indeed dramatic changes in the neural correlates of addition and subtraction as a function of chronological age. The increasing activation of the left inferior parietal cortex suggests that the involvement of this region in adults is the outcome of a process of developmental specialization. Furthermore, the decreasing activation of the prefrontal cortex may suggest that functions such as attention and working memory
as well as the use of immature problem-solving strategies, which have frequently been associated with these frontal brain regions, are more engaged during calculation by young children, compared to adolescents and young adults. Finally, the decreasing activation in the hippocampus may be evidence that over developmental time calculation requires less engagement of systems involved in the formation of long-term memory
(such as arithmetic facts) in the brain.
The data reported by Rivera et al. (2005) suggests that the development of calculation skills is associated with a dynamic pattern of changes in the brain circuitry engaged during calculation. These findings raise the question of whether similar developmental changes can also be found when more basic tasks are tested. When participants are asked to compare which of two numbers is numerically larger, the time it takes them to perform this relative magnitude judgment is related to the difference or numerical distance between the two numbers (Moyer & Landauer, 1967). More specifically, it takes longer to judge which of two numbers is numerically larger when the numerical distance is comparatively small. In other words, there exists a highly reliable inverse relationship between reaction times and numerical distance. This effect has become a standard measure in studies of numerical magnitude processing, as it is thought to reveal features of the underlying representations of numerical magnitude. Consequently, in neuroimaging studies with adults, the effect of numerical distance has been investigated and a growing body of research has revealed that numerical distance modulated activation in areas of the IPS in both hemispheres
(Pinel, Dehaene, Riviere, & LeBihan, 2001). Since behavioral studies have shown that the distance effect decreases over developmental time (Holloway & Ansari, 2008; Sekuler & Mierkiewicz, 1977), it is possible that there exist age-related changes in the functional neuroanatomy
associated with numerical distance. In order to address this question, Ansari, Garcia, Lucas, Hamon, and Dhital (2005) used fMRI to measure brain activation in both children (mean age 10 years) and adults while they compared the relative magnitudes of single-digit Arabic numerals. The results of this study revealed that, consistent with prior evidence, numerical distance modulated activation in bilateral
regions of the parietal cortex. In the group of children, however, the strongest effect of numerical distance on brain activation was found in the prefrontal cortex. Thus, consistent with the above-reviewed developmental study of calculation (Rivera et al., 2005) there appears to be a shift away from the engagement of the prefrontal cortex towards increasing engagement of the parietal cortex over developmental time.
In a subsequent study, Ansari and Dhital (2006) examined whether similar age-related changes in the neural correlates of the numerical distance effect could be found when participants were asked to compare non-symbolic numerical magnitudes. In an fMRI study, both adults and children were asked to judge which of two arrays of squares was numerically larger and the numerical distance between the groups of squares was systematically varied. The results, consistent with those reported by Ansari et al. (2005), revealed a greater effect of numerical distance on the parietal cortex in adults compared to children. That is the activation of the parietal cortex was greater when participants were comparing pairs of numbers separated by a relatively small (e.g. 1 vs. 2 squares) compared to a large (2 vs. 9 squares) numerical distance.
Taken together, the studies discussed above demonstrate age-related specialization of brain circuits for both calculation and numerical magnitude processing. The available evidence suggests that the left inferior parietal cortex (comprising the supramarginal and angular gyri) increases in calculation-related activation as a function of chronological age. Conversely, bilateral regions of the IPS are more engaged during numerical magnitude processing in adults compared to children. Other data also support this fronto-parietal shift in the activation underlying both calculation and numerical magnitude processing (Cantlon et al., 2009; Kaufmann et al., 2006; Kucian, von Aster, Loenneker, Dietrich, & Martin, 2008).
It should be noted, however, that Cantlon, Brannon, Carter, and Pelphrey (2006) found similar activation of the parietal cortex in both 4-year-old children and adults during non-symbolic numerical(arrays of dots) magnitude processing. In their study participants were presented with repeated images displaying the same number of dots (e.g., 16) in different spatial configurations. Following several repetitions, participants were presented with a novel numerosity (e.g., 32). By mapping the brain regions activated by the presentation of the novel numerosity it is possible to uncover brain regions that are sensitive to changes in the number of items displayed. The similarity in parietal activation between children and adults revealed by Cantlon et al. in this passive number 'perception' task raises the possibility that developmental differences revealed in other studies have to do with the neurocognitive mechanisms engaged when translating representations of number and arithmetic into responses. Understanding the difference in brain activation in passive compared to active task is an important avenue for future research.
Do children with DD activate the same brain regions as their typically developing peers?
The above reviewed studies demonstrate that, among typically developing children, the functional neuroanatomy underlying numerical and mathematical processing undergoes age-related changes. This raises the question of whether the neural correlates of calculation and numerical magnitude processing differ in children with mathematical difficulties (or DD).
To date, there are only very few empirical studies that can address this question. However some progress has been made. In the first functional neuroimaging study of children with Developmental Dyscalculia (DD; see this Encyclopedia entry by Cohen Kadosh, 2009
) more diffuse and weaker activation was found in the IPS. In a more recent study, Price, Holloway, Rasanen, Vesterinen, and Ansari (2007) investigated the effect of non-symbolic (e.g., arrays of squares) numerical distance on brain activation in children with DD as well as a group of typically developing, age-matched children. These authors found that while the right IPS of typically developing children was modulated by numerical distance, there was lower activation and no distance effect on IPS activation in the group of children with DD. These data suggest that there is an impairment of numerical magnitude representation in DD. A similar pattern of data was recently reported by Mussolin et al. (2010) for symbolic (Arabic numerals) numerical magnitude comparison.
In addition to measuring brain activation patterns and how these differ between individuals with and without DD, it is also possible to compare the physical structure of the brain between participants. In other words, using structural images of the brain acquired using Magnetic Resonance Imaging (MRI)
, the volume of brain tissue (such as gray
matter) can be calculated and compared between participants with and without DD. A recent comparison of gray matter volume (amount of gray matter) between children with DD and their typically developing peers revealed reduced gray matter volumes in the right parietal cortex as well as the frontal brain regions (Rotzer et al., 2007). In other words, the individuals with DD had less brain tissue compared to typically developing children in regions that are well known to be involved in the processing of numerical magnitude. Thus DD is associated with both atypical structure and function of the IPS.
The above overview illustrates that progress towards a greater understanding of the neural mechanisms underlying the typical and atypical development of numeracy and mathematical skills is being made. However, there are many outstanding questions that should be addressed in the future. From a theoretical perspective, it is currently unclear which factors mediate and explain the age-related changes found in brain activation. It is possible that these are the consequence of brain maturation, education, experience or an interaction between these factors. Systematic research is needed to understand what causes the developmental changes in the neural correlates of numeracy and mathematics. Understanding, for example, how education influences the representation of numerical symbols in the brain (such as Arabic numerals) will help to better understand the effects of education on the brain.
A related future direction is the need for more longitudinal studies to provide a more detailed understanding of how the brain activation underlying numeracy and arithmetic changes over developmental time. Such longitudinal studies will also be crucial for a greater understanding of the stability of atypical activation profiles found among children with DD. From an educational perspective, neuroimaging could become an important tool for tracking the outcomes associated with structured intervention/remediation programs. In literature on reading remediation, neuroimaging methods such as fMRI have been used to show brain activation changes mediated by intervention programs (Shaywitz et al., 2004; Shaywitz & Shaywitz, 2009
; Temple et al., 2003) Similar studies should be employed to establish whether research-based remediation programs (for more details, see this Encyclopedia entry by Wilson & Räsänen, 2008
) lead to normalization of atypical brain activation profiles in children with DD.
The present entry provides a broad overview of the existing body of neuroimaging studies of numerical and mathematical development. Taken together the available evidence demonstrates that the neural correlates of numerical and mathematical development change as a function of chronological age. More specifically, for both calculation and basic numerical magnitude processing, areas of the parietal cortex increase in their engagement over developmental time, while prefrontal regions of the brain decrease in their involvement. Furthermore, a growing, but still small, body of research suggests that this developmental specialization of the parietal cortex for numerical and mathematical processing is disrupted in children with DD. Functional activation studies have revealed reduced activation in the parietal cortex during numerical and mathematical processing in individuals with DD and structural evidence suggests that these individuals have less gray matter in the parietal cortex than their typically developing peers.
In conclusion, neuroimaging of numerical and mathematical development is very much in its infancy and much more research is needed to answer questions concerning the specific nature of developmental changes, or absence thereof, in children who have mathematical difficulties. Furthermore, much more work is needed to connect the neuroimaging literature with mathematics education and remediation programs.
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