*In this contribution, Christine Marques discusses how neuroscience can contribute to Mathematics education by better understanding the cognitive processes involved in mathematical performance.*

Early mathematical abilities provide the foundation for academic and professional success. Identifying and understanding the neural basis of mathematical thinking is of utmost importance not only for studying acquired abilities from an evolutionary perspective (Butterworth & Walsh, 2011) but also to help us understand the origin of mathematical learning disabilities in individuals. Behavioral research, the first field attempting to correlate brain area to numerical abilities, has identified key numerical competencies necessary for math skill acquisition (Siegler, 1987). Nevertheless, neuroimaging methods, in particular functional brain imaging, provide a second and unique level of analysis that complements behavioral methods by providing unique insights that were more difficult or impossible to assess with behavioural measures (Superkar, 2013).

**Numerical and mathematical processing analysis in neuroscience research**

The field of neuroscience has enriched the field of mathematical cognition thanks to the development of neuroimaging research focusing on the study of underlying brain areas associated with specific mental activities. A variety of neuroimaging techniques (Grabner et al. 2010a, b) enable researchers to acquire high-quality information on temporal and spatial brain activity associated with mathematical processing in individuals with different capabilities. One of these techniques, called event-related brain potentials, is based on electrophysiological recordings of a reflection of electrical activity of the brain associated with cognitive processes in real time (Neville et al. 1993), offering high temporal resolution images over the course of problem solving. Another major technique, functional magnetic resonance imaging (fMRI), enables the detection of differences in processing, thereby potentially leading to a more comprehensive understanding of the underlying processes and brain structures involved.

**Localisation of brain activation associated with mathematical processing**

Numerical processing involves several interrelated mechanisms including memorisation, arithmetic principles, comprehension and arithmetic facts retrieval (Kaufmann et al., 2013). The Triple-Code Mode of numerical cognition, a multi-route model (Dehaene, 1992 ; Dehaene & Cohen, 1995), postulates the existence of three representational codes for numbers : abstract magnitude (Dehaene & Cohen, 1995), verbal number words and Arabic digits representations (Dehaene & Cohen, 1995). This model emphasises the role of the parietal cortex in arithmetic and number processing. Dehaene et al. (2003) identified three regions of the parietal cortex linked to number processing, namely intraparietal sulcus (IPS) found to be involved in calculations; posterior superior parietal lobule (PSPL) linked to the visuospatial and attention aspects of number processing (Dehaene et al. 2003); and angular gyrus (AG) found to be involved in the verbal processing of numbers and arithmetic fact retrieval (Grabner et al. 2009). Moreover, the parietal cortex has been found to also be associated with word-problem solving (Newman et al. 2011), geometry proof generation (Anderson et al. 2011) and algebraic equations (Sohn et al. 2004). Other neurocognitive studies have linked the frontal cortex to attention-control processes and working memory (Badre 2008, Gruber and Von Cramon 2003), while the left-lateralised cortical network has been found to be activated by more advanced mathematical problem solving such as integral calculation (Krueger et al. 2008). Additionally, neuroscientific research also focused on mathematical problem solving associated with different representations of mathematical objects and found that different representations of functions, as verbal or equation for example, are connected to different cognitive processes (Sohn et al. 2004), with each representation mode imposing different attention demands, and the symbolic representation being more demanding.

**Structural and functional characteristics of brain activation reflect individual differences**

One of the main interests of neuroscientific research is to understand differences in individual mathematical abilities in order to help children to overcome mathematical difficulties. In fact, poor mathematics capability is observed in some children and can be due to different factors, such as sociocultural (poor instruction), environmental or physiological math disability (inherent weakness in mathematical cognition leading to developmental dyscalculia, for example). Some studies investigate the effect of emotional factors on mathematical learning. Kucian et al. (2018) examined the relationship between math anxiety and changes in brain structure in children with and without mathematical disabilities and found that math anxiety not only hamper children in arithmetic development, but is also associated with altered brain structure in areas related to fear processing (amygdala). This emphasises the impact of emotional factors in mathematical learning and encourages teachers to consider math anxiety to prevent detrimental long-term consequences on school achievement. Harada et al. (2013) investigated the effect of social influence, more specifically perceived social power, on mathematics performance and found that heightening a person’s sense of social power (enhancement) can increase their performance by reducing cognitive interference during calculation. Chen et al. (2018) studied the neurocognitive mechanisms by which a positive attitude towards math (ATM) influences math learning and skills. This study found that ATM was associated with increased engagement of the hippocampal learning-memory system and higher math achievement.

Neuroimaging studies not only demonstrate the neural basis of mathematical difficulties and disabilities (Butterworth et al. 2011), but also demonstrate connections between brain activity and intelligence. According to some studies, intelligence is associated with the reciprocity of several brain regions within a widespread brain network (Colom et al. 2010; Desco et al. 2011). Some studies focused on the relationship between intelligence and the area of induced brain activity during cognitive task performance (Jausovec and Jausovec 2000). These studies have led to the formulation of the neural efficiency hypothesis of intelligence, which states that “brighter individuals display lower (more efficient) brain activation while performing easy to moderate difficult cognitive tasks” (Neubauer and Fink 2009). However, while performing difficult and challenging tasks, intelligent individuals will exhibit higher brain activity (Neubauer and Fink 2009).

Taken together, these studies demonstrate that neuroscientific discoveries can contribute to mathematics education by helping us to better understand the underlying cognitive processes involved in mathematical performance, and the neural basis of success and difficulties in mathematics learning, problem solving and reasoning. Thus, collaboration between mathematics educators and neuroscientists would be crucial to allow implementation of neuroscientific findings in educational practice.

### Dr. Christine Marques

Department of Neurobiology,

Massachusetts General Hospital,

HARVARD UNIVERSITY

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Newman, S. D., Willoughby, G., & Pruce, B. (2011). The effect of problem structure on problem-solving: An fMRI study of word versus number problems. Brain Research, 1410, 77-88.

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Sohn, M.H., Goode, A., Koedinger, K.R., Stenger, V.A., Carter, C.S. & Anderson, J.R. (2004) Behavioral equivalence does not necessarily imply neural equivalence: Evidence in mathematical problem solving. Nature Neuroscience, 7(11), 1193–1194.

Supekar, K., Swigart, A. G., Tenison, C., Jolles, D. D., Rosenberg-Lee, M., Fuchs, L., & Menon, V. (2013). Neural predictors of individual differences in response to math tutoring in primary-grade school children. Proceedings of the National Academy of Sciences, 110, 8230-8235.

Krueger F, Spampinato MV, Pardini M, Pajevic S, Wood JN, Weiss GH, Landgraf S, Grafman J. (2008). Integral calculus problem solving: an fMRI investigation. Neuroreport, 19: 1095–9.

Kucian et al. (2018) Neurostructural correlate of math anxiety in the brain of children. Translational Psychiatry, 8:273

Neubauer, A. C., & Fink, A. (2009). Intelligence and neural efficiency. Neuroscience and Biobehavioral Reviews, 33(7), 1004–1023.

Neville, H. J., Coffey, S. A., Holcomb, P. J., & Tallal, P. (1993). The neurobiology of sensory and language processing in language-impaired children. Journal of Cognitive Neuroscience, 5(2), 235–253.

Newman, S. D., Willoughby, G., & Pruce, B. (2011). The effect of problem structure on problem-solving: An fMRI study of word versus number problems. Brain Research, 1410, 77-88.

Siegler, R. S. (1987). The perils of averaging data over strategies: An example from children’s addition. Journal of Experimental Psychology: General, 116(3), 250-264.

Sohn, M.H., Goode, A., Koedinger, K.R., Stenger, V.A., Carter, C.S. & Anderson, J.R. (2004) Behavioral equivalence does not necessarily imply neural equivalence: Evidence in mathematical problem solving. Nature Neuroscience, 7(11), 1193–1194.

Supekar, K., Swigart, A. G., Tenison, C., Jolles, D. D., Rosenberg-Lee, M., Fuchs, L., & Menon, V. (2013). Neural predictors of individual differences in response to math tutoring in primary-grade school children. Proceedings of the National Academy of Sciences, 110, 8230-8235.

Parabéns és fantástica!

Parabéns Cris!