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93
Sitnikova, M. A. et al. (2023). The Neural Correlates of Exact Calculation in Word and Numerical Formats in Low And High Math
Performers: A fNIRS Study, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),
11(1), 93-114.
Introduction
People use two cognitive systems to understand and operate numbers - non-symbolic system,
primarily relying on magnitude estimation without symbols (e.g., Arabic numerals), and symbolic system,
based on processing of numbers in symbolic form (Ansari, 2008; Feigenson, Dehaene and Spelke, 2004;
Waring and Penner-Wilger, 2017). Development of numerical cognition is a gradual process that started
from the nonsymbolic or approximate number system. Approximate number system is an innate cognitive
system that supports the estimation of the magnitude without relying on language or symbols. However,
the role of symbolic representations of quantity and basic arithmetic skills increases with age (Artemenko,
2021). Basic arithmetic skills are of great importance in everyday life, in STEM education, and in many
sciences that involve math: in physics, chemistry, technology and engineering, in various IT applications.
Better understanding the underlying brain mechanisms of simple and complex exact calculations is
important for numerical cognition and gives an insight into the relation between different brain areas
within a network associated within the approximate number system and exact symbolic representation
system. In practice, this knowledge can be used in the future in order to improve a person’s numerical
skills, eliminate problems associated with their lack (decrease in arithmetic and mathematical literacy,
dyscalculia). It has been shown that all these shortcomings can have negative consequences for both
the economy and society as a whole (Butterworth, Varma and Laurillard, 2011). Therefore, the practical
The Neural Correlates of Exact Calculation in Word and Numerical
Formats in Low And High Math Performers: A fNIRS Study
Maria A. Sitnikova
1,2*
, Julia A. Marakshina
2
, Timofey V. Adamovich
2
, Grigory O. Pronin
1
, Rustam G. Asadullaev
1
1
Research and Project Centre for Cognitive Neuroscience and Neurotechnologies, Belgorod National Research University,
Belgorod, Russia, e-mail: furmanchuk@bsu.edu.ru, bonessx504@gmail.com, asadullaev@bsu.edu.ru
2
Psychological Institute of Russian Academy of Education, Moscow, Russia,
e-mail: retalika@yandex.ru, tadamovich11@gmail.com
Abstract: The representation format of math problems can manifest dissimilarly in people with varying levels of math
performance. The aim of this study was to investigate the neurocognitive underpinnings of two-digit exact calculation tasks in
different formats: numerical and word. Fifty-three students were divided into groups with high and low levels of math performance
based on their ability to solve math problems. They were asked to calculate addition problems with two-digit numbers and to
read math problems that did not require calculations. Brain activation was recorded using functional near-infrared spectroscopy
(fNIRS). General linear model (GLM) analysis revealed that reading math problems without calculation led to increased activation
in the inferior temporal and fusiform gyri in a group of high-level performers, while a group of low-level performers demonstrated
increased activation in Broca’s area and the inferior frontal gyrus in the same experimental condition, as well as during solving
arithmetic problems in a word format of the exact calculation task. Analysis after bootstrapping revealed similar activation patterns
in both groups. Both domain-specic and domain-general regions of the frontal and parietal brain areas were involved in the
calculations. Right and left hemisphere activation was found both in low and high math performers. Comparing experimental
conditions with resting state revealed signicant activation in Broca’s area in all conditions in a group of high-level performers
and in a word format of arithmetic problems in a group of low-level performers. Thus, the observed brain patterns suggest the
involvement of complex sentence comprehension, especially in high-performing students. These results could be used in future
to improve educational practice for students with varying levels of math competence.
Keywords: exact calculation, addition, numerical format, word format, math competence, fNIRS.
Original scientic paper
Received: November, 22.2022.
Revised: March, 11.2023.
Accepted: March, 19.2023.
UDK:
159.953.5-057.87:511.1
10.23947/2334-8496-2023-11-1-93-114
© 2023 by the authors. This article is an open access article distributed under the terms and conditions of the
Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
*
Corresponding author: furmanchuk@bsu.edu.ru
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Sitnikova, M. A. et al. (2023). The Neural Correlates of Exact Calculation in Word and Numerical Formats in Low And High Math
Performers: A fNIRS Study, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),
11(1), 93-114.
signicance of the results is substantiated by public demand.
Previous studies at the behavioral level aim to investigate the development of numerical abilities
based on both approximate non-symbolic and exact symbolic representations from infancy to adult-hood.
Experimental evidence shows that infants as young as six months old can differentiate between two
arrays of dots as consisting of a different number of objects (Xu and Spelke, 2000). By the age of eighteen
months, toddlers can distinguish the order of numbers and choose the larger array of dots, indicating
their understanding of relative quantity (Brannon, 2002). At the age of three, children can accurately
estimate the number, a concept known as cardinality. In elementary school, children learn about numbers
as a representation of numerical values in a non-symbolic format, which is followed by the development
of an exact symbolic representation system (Ansari and Karmiloff-Smith, 2002). The symbolic system
allows for the processing of discrete numbers and is considered the foundation for math skills such as
counting, estimation, addition, subtraction, and other precise numerical calculations (Ansari, 2008; Mundy
and Gilmore, 2009; Waring and Penner-Wilger, 2017). Calculations are studied immediately after digits at
the same stage of numerical cognition, indicating the importance of the symbolic system (Von Aster and
Shalev, 2007; Vanbinst et al., 2016; Schneider et al., 2017).
Reviews on neurophysiological mechanisms associated with exact calculations, indicate the
predominant role of the fronto-parietal network in numerical processing, the role of which changes with
age (Moeller et al., 2015; Nieder et al., 2016; Clark et al., 2017; Peters and Smedt, 2018; Vogel and Smedt,
2021). Intraparietal sulcus and precuneus in the parietal region, the frontal cortex (e.g., superior and
medial frontal gyri), the claustrum, the insula and cingulate are the main structures involved in numerical
cognition (Arsalidou and Taylor, 2011). Additionally, inferior temporal and fusiform gyri are associated with
processing the numerical shapes and symbols, necessary for calculations with Arabic digits (Piazza and
Eger, 2016). Exact calculations are associated with dorsolateral prefrontal cortex, ventrolateral prefrontal
cortex, posterior superior parietal lobe, intraparietal sulcus, supramarginal gyrus, angular gyrus, fusiform
gyrus, and hippocampus (Vogel and Smedt, 2021). Activation in the frontal cortex overlaps with areas
implicated in language processing (Broca’s area), working memory and cognitive control (Stuss and
Knight, 2013; Devlin, Matthews and Rushworth, 2003; Fadiga and Craighero, 2006; Gentilucci et al, 2006;
Barbey, Koenigs and Grafman, 2013).
The role of brain structures depends on the specicity of operations such as addition, subtraction,
multiplication and division, as well as task characteristics such as format (numerical and word problems)
(Obersteiner et al., 2010; Dresler et al., 2009), complexity of arithmetic problems (simple or complex no-
carry or no-borrow or carry and borrow, respectively) (Artemenko et al. 2018a), age (Peters and Smedt,
2018; Vogel and De Smedt, 2021), and level of math performance (Meiri et al., 2012; Artemenko et al.
2018b). Studies have shown that arithmetic operations such as addition and subtraction are determined
by the necessity of carry/borrow effects and processing of magnitude, with carry and borrow operations
increasing the difculty of such problems (Klein et al., 2010). The carry means a digit that is transferred
from units to tens if the sum of units is more than ten when addition is performed. The borrow means
a digit that is transferred from tens to units, if minuend is less than subtrahend when subtraction is
performed. The activation of both frontal and parietal regions, including the left inferior frontal gyrus,
bilateral middle frontal gyrus, superior frontal gyrus, and left intraparietal sulcus, accompanies carry and
borrow effects (Artemenko et al. 2018b). The two-digit calculations require greater working memory load
for processing magnitude information and visual identication, with Broca’s area, inferior frontal gyrus and
left fusiform gyrus being among the neural correlates of complex addition and subtraction, associated with
phonological processing, verbal working memory, and visual identication of digits (Dahaene and Cohen,
1995; Pollack and Ashby, 2018).
Recent studies have discussed the role of interconnected areas associated with arithmetic
calculations, including the prefrontal, posterior parietal, occipito-temporal, and hippocampal areas, in
children compared to adults. (Peters and Smedt, 2018). Mental calculation based on the manipulation
of numerical symbols develops with age, and structures associated with symbolic numerical processing
may also become more prominent as children grow older. The dynamics is supposed to be inuenced by
an increase in mathematical competencies; thereby, math skills can inuence neural changes in the brain
networks involved in the math performance. Thus, Soltanlou et. all (2018) state that the development of
psychophysiological mechanisms for the calculations occurs in accordance with the fron-to-parietal shift,
known as a shift in brain activation during calculations from frontal structures, in particular precentral
premotor and motor areas in children, to parietal regions in adults, reecting a shift from a labor-intensive
procedural to more automatic strategies between ages 8 and 19 (Rivera et al., 2005; Kaufmann et al.,
2006; Kucian et al., 2008; Artemenko et al., 2018b).
Individuals may develop mathematical competencies differently, and their level of performance
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Sitnikova, M. A. et al. (2023). The Neural Correlates of Exact Calculation in Word and Numerical Formats in Low And High Math
Performers: A fNIRS Study, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),
11(1), 93-114.
in math may reect different neural representations of numerical skills. Some researchers have found
differences in activation dependent on math ability in the intraparietal sulcus (Park et al. 2012; Prado et
al. 2011). As reported by Artemenko et. all (2018a), some researchers found activation differences in the
left angular gyrus (Grabner et al. 2007, 2011; Menon et al., 2000). These differences in activation may
be associated with increased or decreased angular gyrus activation depending on processing efciency
or experience/training (Amalric and Dehaene 2016; Grabner et al. 2007, 2011). Additionally, low math
performers have shown higher activation in the dorsolateral prefrontal cortex during error processing
(Ansari et al., 2011). The intraparietal sulcus, right dorsolateral prefrontal cortex, and left angular gyrus
may be inuenced by math ability during single-digit arithmetic in multiple ways (Artemenko et al. 2018a),
but the underlying process remains unknown. Furthermore, adults with high mathematical abilities
demonstrate higher activation in frontal regions during calculations accompanied by carry and borrow
effects, which contradicts the fronto-parietal shift (Artemenko et al. 2018a).
Overall, exact calculation, whether it involves complex or simple math problems, rely on parietal
brain areas (intraparietal gyrus, angular gyrus, supramarginal gyrus), which represent domain-specic
processes, occipital (inferior temporal gyrus and fusiform gyrus) and frontal areas (interior frontal gyrus
and middle frontal gyrus), which represent domain-general processes. There are various mechanisms
involved in arithmetic processing and mental calculation, which can be attributed to either domain-general
processes that are related to cognitive processing in general or domain-specic processes that are
specically linked to mathematical performance (Gilmore et al., 2018). Number magnitude processing,
which is associated with domain-specic processes, is located in the intraparietal sulcus (IPS) (Artemenko,
2021). Among domain-general processes that play an important role in calculation are working memory,
which is represented in left inferior frontal gyrus (IFG) and bilateral middle frontal gyrus (MFG, and fact
retrieval, which is represented in supramarginal gyrus (SMG) and angular gyrus (AG).
According to the most inuential model of numerical cognition (Triple-Code Model) there are
three representative codes for number: analogue non-symbolic representations of quantity (in particular,
the ability to estimate the number of objects without counting), verbal-phonological representations
of quantity (words denoting Arabic numbers, and oral counting), and visual representations of Arabic
numbers (Dahaene and Cohen, 1995; Dehaene et al., 1999). Each of these representations is provided
by functionally separate brain mechanisms (Lavander-Ferreira, 2020). Numerical representations of
number activate the lower parietal regions of both hemispheres, while tasks with numerical codes (Arabic
numbers) activate the fusiform gyrus of both hemispheres. Finally, the semantic designations of the
number, represented by verbal information, cause activity in the left perisylvian areas and the left angular
gyrus. However, most studies investigate only one specic representations, rather than all three at the
same time. Moreover, the Triple-Code Model does not explain how the brain performs calculations for math
word problems. Monti, Parsons and Osherson (2012) demonstrated the role of different areas of the brain
in syntactic tasks and algebraic operations. Fuchs et al. (2006) showed the importance of arithmetic word
problems as a cognitive predictor of arithmetic calculations in the Assessment of Math Fact Fluency test
of the Math Battery, which incorporates two subtests: Addition Fact Fluency and Subtraction Fact Fluency.
Differences in brain activation patterns are found in the calculation or simple reading of two-digit addition
problems involving a numerical or text format (Richter et al., 2009). In another study (Dresler et al., 2009),
higher average oxygenation is demonstrated in the parietal and posterior frontal regions for calculation
compared to reading in word problems in primary and secondary school students. Comprehension skills
inuence arithmetic word problem performance. Thus, it is shown that even for successful word problem
solvers, performance decreases if the text of the word problem is semantically complex (Boonen et al.,
2016). Daroczy et al. (2015) consider some components of word problem difculty, such as the linguistic
complexity of the problem text itself, the numerical complexity of the arithmetic problem, and the relation
between the linguistic and numerical complexity of a problem. Moreover, two factors complicate the
solution of word problems: linguistic and numerical complexity (Verschaffel, Greer and De Corte, 2000).
However, most researchers do not consider these factors together in their study.
The problem of exact calculations has been examined in various studies. However, tasks that
require different formats, such as reading or basic calculation have not been thoroughly investigated.
Studying the neural mechanisms of different formats of exact calculation tasks might help to provide
evidence for or against the Triple-code model. Recent studies provide arguments against Triple-code
model. For example, Skagenholt et al. (2018) examined all three modes of representative codes for
number simultaneously to identify the neural correlates of number processing in adults (N=46) using fMRI.
The analysis of the task-control condition contrast revealed task-dependent activity, which can be seen as
partial support for the Triple-Code model, but also revealed a complex distributed fron-to-parietal network
involved in all numerical codes. The results show that the Triple-Code Model correctly predicts the existence
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Sitnikova, M. A. et al. (2023). The Neural Correlates of Exact Calculation in Word and Numerical Formats in Low And High Math
Performers: A fNIRS Study, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),
11(1), 93-114.
of some functionally dissociated neural substrates, but needs to be up-dated to consider the interactions
with attentional processes. Contrasts corresponding to differences in task complexity revealed specic
neural correlates of the numerical distance effect (i.e., numbers that are close together are more difcult
to distinguish than numbers that are farther apart). The connectivity analysis demonstrated overlapping of
neural correlates in all tasks, conrming the notion of a fron-to-parietal number processing network. Thus,
the authors offer arguments in favor of revising the Triple-Code Model.
The comparison of the brain mechanisms involved in numerical or word format calculations is
promising for educational neuroscience (Dresler et al., 2009). Arithmetic math problems with numerals
embedded in text that describe everyday situations are common in school curricula. However, math
problems with numbers written in words (for example, “forty-seven plus twenty-one is…”) are not typical
in education. Problems of this type are thought to be related to alternative mechanisms of numeral
manipulation. Research in this area may be useful in nding effective ways of teaching mathematics,
especially for children with math difculties who have problems processing numerical symbols. It is
important to understand the neural correlates of math problem calculations in various formats, paying
special attention to individual differences, particularly, math performance.
The aim of the present study is to measure brain activation in frontal and parietal regions reected
in oxygenation changes measured by fNIRS and to estimate the differences in neurocognitive foundations
of exact calculation problems (addition) in numerical or word formats in non-overlearned conditions (two-
digit numbers) in young adults who vary in level of math competencies. This study addresses the brain
mechanisms of exact calculation problems represented both in traditional format for educational system
(problems with numerals in Arabic notation) as well as atypical format (problems with numerals written in
words). Thus, we consider the inuence of linguistic complexity on solving word problems. In addition, we
focus on processing math problems in various formats by students with different levels of mathematical
ability. The results obtained will contribute to a better understanding of the nature of domain-specic
or domain-general processes in the brain that accompany exact calculations, and can be applied in
educational neuroscience, for example, for develop new types of math problems.
The hypotheses of the present study are:
H1 - Tasks in word and numerical formats of exact calculation can cause activation in different
areas of the brain, since these two formats of presenting arithmetical problems differ in the amount of
cognitive effort needed and in the brain processes involved in calculation.
H2 - Brain activation during solving exact calculation in a word format might involve “language”
areas, such as Broca’s area, and occipital (ITG, and fusiform gyrus) and frontal areas (IFG and MFG) that
represent domain-general processes.
H3 – Individual differences based on levels of math competencies are expected to be observed.
Materials and Methods
Participants and Procedure
Sixty-ve adults were recruited through a university mailing list to participate in the study. All subjects
were native Russian speakers, have normal or corrected-to-normal vision and do not have any history of
neurological or mental disorders. Some participants were excluded from the sample due to noisy NIRS
data (n=7), technical difculties (n=2), and very poor behavioral results (n=3). For the present analysis,
the remaining subjects were divided into groups according to their performance in solving addition and
subtraction problems in word and numerical formats. We calculated error rates of 53 participants in 100
addition and subtraction problems with and without carry procedure in a word format and 100 addition and
subtraction problems with and without borrow procedure in a numerical format. Participants, who correctly
solved more than 70 % of math problems in a word format and more than 85% of math problems in a
numerical format formed the group with high level of math competencies (n=19). Those who solved less
than 50 % of math problems in a word format and less than 65% of math problems in a numerical format
formed the group with low level of math competencies (n=17). Participants from both groups signicantly
differed in solving math problems (see Table 1). The nal sample consists of 36 subjects aged 18-25 (M =
19,5, SD = 1,877, 41 females). Participants provided an informed consent to participate in the study and
received a monetary reward for their time and effort. The study was approved by the Ethics Commission
of Psychological Institute of Russian Academy of Education, 2020/11-3.
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Sitnikova, M. A. et al. (2023). The Neural Correlates of Exact Calculation in Word and Numerical Formats in Low And High Math
Performers: A fNIRS Study, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),
11(1), 93-114.
Materials
The experiment consisted of 225 arithmetic problems presented on the computer screen. There
were addition and subtraction exact calculation problems and some math problems for reading only. In the
present study only addition tasks that included 50 problems in a numerical format with Arabic numerals (for
example, 45+23=), and 50 problems in a word format with numerals written in Russian (for example, fty-
six plus seventy-one is) of different complexity levels: with and without carry procedure were analyzed. 25
tasks were presented as a math problem without calculation embedded in text (for example, Ann had 15
owers and Teddy brought her 32 owers more. How many owers did Teddy bring to Ann?).
Addition and subtraction tasks were represented by two-digit numbers in both operands with a
two-digit solution not exceeded 100 in each task. The main selection criteria for two-digit addition and
subtraction tasks were to induce computational efforts, but not guessing or retrieving results from
declarative memory (Kong et al., 2005) since when using the recall strategy, arithmetic skills are not
involved and, and other parts of the brain were activated (Ischebeck et al., 2006; Zago et al., 2001). Pure
decades (e.g., 20), as well as tie numbers (e.g., 44) were not used in exact calculation tasks, since they
were much easier to solve (for a similar procedure see (Dresler et al., 2009; Klein et al., 2009; Artemenko
et al., 2018b). In two-digit mathematical problems in a word format, a simple logico-mathematical scheme
to compute the quantities in the problem based on the assumption that the word problem is only numerical
was applied.
Procedure
The recent study is a part of a larger experiment. The duration of this part of the experiment was
30 minutes. The measurement was conducted individually with each participant seated comfortably in
front of the computer screen. Each session began with an introduction to the NIRS measurement and the
experimental procedure.
During fNIRS measurement, participants were instructed to perform exact calculation tasks in two
different modalities (types): in a numerical format (condition 1), and in a word format (condition 2), as well
as to read without calculating the arithmetic problems embedded in text (condition 3). The experiment was
in a block design, with a total number of 25 blocks, with an inter-block-interval of 20 s for a short rest. There
were three conditions in the experiment: (1) addition exact calculation problems in a numerical format (10
blocks); (2) addition exact calculation problems in a word format (10 blocks); (3) reading condition (5
blocks). Each measurement started with an fNIRS resting state recording for 3 minutes. The number of
trials was limited and equal for all participants. The sequence of the blocks within each condition and
conditions themselves was randomized. Before each condition there were detailed instructions presented
on the screen, and 3 training trials. No feedback was given to participants.
The trial started with a xation cross, presented for 0.5 – 0.8 s in a randomized order to prevent
adaptation to it, and was followed by the arithmetic task for 4.5 s. After that, an empty screen with a grey
block to insert the answer appeared for 2.5 s. The sequence of a trial is shown in Fig. 1. If no answers were
presented within the given time, the next trial appeared on the screen. The participant had an opportunity
to correct the answer if a mistake was made within the limited time of 2.5 s. In our study we applied a
written production paradigm as the most typical format of giving the solution for the math problem in the
education system. In a written production paradigm, adults had to type in the solution to the math problem
with the help of numerical keyboard as quickly and accurately as possible.
Figure 1. Scheme of a trial
Participants were instructed to read the problems silently and choose one out of two numbers in a
reading condition, or calculate mentally in exact calculation conditions. The participants could either wait
until the time for presenting the stimulus nished or press the spacebar as soon as they had calculated
the problem or completely read it and chosen the answer, respectively.
The exact calculation and reading only problems were presented horizontally in white against a
dark grey background at the center of the computer screen using the free software package PsychoPy
(Peirce, 2007).
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Sitnikova, M. A. et al. (2023). The Neural Correlates of Exact Calculation in Word and Numerical Formats in Low And High Math
Performers: A fNIRS Study, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),
11(1), 93-114.
fNIRS data acquisition
fNIRS recordings were acquired using the mobile near-infrared spectroscopy device NIRSport Model
88 (NIRx Medical Technologies, LLC, NY, the USA) with eight light- emitters and eight photodetectors.
A probeset of 14 channels, with an interoptode distance of 30 mm, was integrated into an elastic cap to
cover the frontal and parietal brain regions of both hemispheres (see Fig.2). All optodes were positioned
according to the 10-20 system (Jasper 1958), with the center in P3 and P4 positions in the parietal region,
and in F1 and F2 in the frontal regions. Two near-infrared laser beams with wave-lengths of 760 and
850 nm were emitted, and the sampling rate was 7.8125 Hz. The correspondence of fNIRS channels to
the underlying cortical areas was estimated using the fNIRS optode’s location decider (fOLD), software
(Zimeo Morais, Balardin and Sato, 2018), which utilizes the Automated Anatomical Labeling 2 (AAL2)
atlas (Tzourio-Mazoyer et al. 2002; Rolls, Joliot and Tzourio-Mazoyer, 2015) for probing arrangement.
In our study, we dened 4 regions of interest (ROIs) that included parietal and frontal regions known
from previous studies to be related to exact calculation and reading arithmetic problems. In the parietal
brain area, ROIs were formed in the left hemisphere by channels S1-D1 (left angular gyrus, intraparietal
sulcus, Wernicke), S1-D2, and S2-D1 (left supramarginal gyrus), S2-D2 (left middle temporal gyrus), S2-
D3 (left inferior temporal gyrus, fusiform gyrus); and in the right hemisphere by channels S3-D4 and S3-
D5 (right angular gyrus, intraparietal sulcus), S4-D4 (right supramarginal gyrus), and S4-D5 (right middle
temporal gyrus). In the frontal brain, area ROIs were formed in the left hemisphere by channels S5-D6
(Broca’s area, left inferior frontal gyrus), S5-D7 and S6-D7 (left middle frontal gyrus); and in the right
hemisphere by channels S7-D8 and S8-D8 (right middle frontal gyrus) (channels can be found at Fig.2).
Figure 2. Probeset used for the fNIRS measurements indicating optode positions (red - source,
green - detector) and channels that are formed by source-detector pair (violet lines)
Behavioral analysis
The results of the participants were analyzed for task performance (accuracy score) and reaction
time (response time, RT). The accuracy score was calculated as the number of correct answers divided
by the total number of trials. Response time (RT) was dened as the time from when grey box for inserting
the answer appeared until the time when the actual answer was given or the space bar was pressed (see
Table 1).
The estimation of accuracy score and response time differences by group and task type was
performed by a two-factor repeated measures ANOVA with partial eta-squared as the effect size measure.
Post-hoc comparisons were conducted using pairwise repeated measures t-test with Tukey correction.
The analysis was performed in R 4.1.2 and Jamovi 2.2.3.
Statistical analysis of NIRS data
fNIRS data was preprocessed and analyzed using a custom script based on free software packages
MNE-fNIRS (Esch et al, 2019; Luke et al., 2020). MNE provides complete data analysis pipelines and
toolboxes in Python for fNIRS data processing.
During fNIRs data preprocessing, the raw intensity values were rst converted to optical density.
At this stage, the coupling quality between the scalp and optodes was quantied using the scalp coupling
index (SCI index, for detailed description see Pollonini et al., 2014). The SCI index helps to detect a strong
cardiac oscillation in fNIRS raw signals, which is undesirable for measuring evoked cortical hemodynamic
responses (Themelis et al., 2004). By applying this method to raw data of all participants, we scanned all
channels to nd out the presence of synchronous signals in the frequency range of cardiac signals across
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Sitnikova, M. A. et al. (2023). The Neural Correlates of Exact Calculation in Word and Numerical Formats in Low And High Math
Performers: A fNIRS Study, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),
11(1), 93-114.
both photodetected signals. Channels with SCI below 0.6 were marked as bad channels and eliminated
from any further analysis. Remaining noisy channels in ltered data were interpolated using the mean of the
surrounding channels (nearest method). To remove motion artifacts from the analyzed data, the temporal
derivative distribution repair lter (TDDR) was applied (Fishburn et al., 2019). According to recent studies,
the TDDR lter shows better results when applied to the optical density of fNIRS data before calculating
the relative concentration changes of hemoglobin (Fishburn et al., 2019). Next, the relative concentration
changes of oxygenated (O2Hb) and deoxygenated hemoglobin (HHb) were estimated for every channel
using the modied Beer-Lambert law. However, in this study, we focused on the parameter O2Hb as
several researchers regarded this hemoglobin chromophore more sensitive to changes in cerebral blood
ow (Hoshi, Kobayashi and Tamura, 2001; Dresler et al., 2009). Finally, we applied a 0.02-0.2 Hz band-
pass lter to the data to remove heart rate oscillations as well as slow drifts.
To separate and remove physiological confounds from fNIRS data, a general multivariate regression
model (general linear model, GLM) analysis (Yücel et al., 2021; Luke et al., 2021) available in the MNE-
NIRS package (Yucel et al., 2021) was applied to examine the task-specic neural activity associated with
reading, exact calculation in a numerical format, exact calculation in a word format in two experimental
groups. We modeled the expected neural response for each experimental condition using the SPM
hemodynamic response function (HRF) combined with the stimulus event times and durations. All fNIRS
signal changes unrelated to task-specic neural responses were marked as drifts, and included in the
design matrix as cosine drift regressors. We specied 5 regressors with a 1/ high pass lter cut off (in our
case 0.002 Hz). For every group three contrasts, such as (1) reading versus addition exact calculation
in a numerical format; (2) reading versus addition exact calculation in a word format; (3) addition exact
calculation in a numerical format versus addition exact calculation in a word format) based on beta-values
were calculated.
Additionally, to test if there were task-specic neural activation compared to a non-task baseline
activation we compared all three task-related contrasts with resting-state derived contrast. Resting-state
was used in our study as a baseline marker of brain activity. Resting state may be considered as a brain
activity without work load or any purposeful cognitive process activated and assumed as a ‘baseline’ for
any comparison with task specic activity (Hurlburt et al., 2015), however this view sometimes argues
(Morcom and Fletcher, 2007). In our study 3 minutes resting state with closed eyes was used as a new
condition with activity unrelated to math or reading. Comparison of three experimental conditions with
resting state allowed tracing of changes specic related to calculation and reading in general. Resting
state with close eyes was analyzed.
Bootstrapping (random sampling with replacement) with 200 iterations for multiple comparisons
correction for every contrast in both groups was applied to reduce the risk of the type I error (false positive)
and to overcome the possible problems caused by small samples. Bootstrapping estimates properties of
estimands by sampling from an approximating distribution. In our study we applied the following scheme
for bootstrapping: rst were randomly chosen 14 subjects from the main sample (random sampling), on
the next step three contrasts were calculated 200 times (a numerical format versus a word format of the
calculation; a word format of calculation versus reading; a numerical format of the calculation versus
reading) and 200 beta values for each channel was obtained. A median value for each channel out of 200
iterations was set as a typical beta value for this channel. The signicance of each channel was dened
based on Z criterion, so that if in more than 50% of iterations the signicance was true, the channel was
marked as signicant. For analyses of statistically signicant differences between groups, the pairwise
comparisons were made using permutation Mann-Whitney test.
Results
Behavioral results
Table 1 presents the results of the participants’ task performance accuracy and response time (RT)
are presented in Table 1. The lowest accuracy and response time were observed for calculation problems
in a word format. While performing the reading task, both experimental groups showed consistent
performance, however, the accuracy was lower and response time was higher across all conditions for
low-performers.
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Sitnikova, M. A. et al. (2023). The Neural Correlates of Exact Calculation in Word and Numerical Formats in Low And High Math
Performers: A fNIRS Study, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),
11(1), 93-114.
Table 1
Mean scores and mean response time within three experimental conditions in groups of high-level
and low-level performers
Note. num – a numerical format of the exact calculation, word – a word format of exact calculation, high – group with
high level of math competencies, low - group with low level of math competencies
Table 2 presents the results of the ANOVA comparison between task format and group. The analysis
showed signicant (p < 0.01) differences in the accuracy across the three task conditions (reading,
calculation problems in a word format, calculation problems in a numerical format), as well as signicant
interaction between task format and group. Regarding response time, only the tasks showed signicant
differences, with no difference observed between high and low groups.
Table 2
Within and between subjects’ effects in task and group comparison
Table 3 presents the results of the post-hoc analysis conducted on the ANOVA results. The analysis
indicated signicant differences in the accuracy among all groups (dened by task format and group).
Regarding response time, signicant differences were observed only between the calculation task in a
word format and the other two task formats. The calculation task in a word format showed signicantly
higher response time than the other two tasks.
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Sitnikova, M. A. et al. (2023). The Neural Correlates of Exact Calculation in Word and Numerical Formats in Low And High Math
Performers: A fNIRS Study, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),
11(1), 93-114.
Table 3
Post-hoc comparison
Note. high – group with high level of math competencies, low - group with low level of math competencies
fNIRS results
We used GLM analysis and estimated the activation of brain areas for each of three experimental
conditions based on statistically signicant channel-specic effects, assessed by thresholding a test
statistic Z (Yucel et al., 2021). Individuals with high level of math competencies showed signicant neural
activation in the left angular gyrus (AG), intraparietal sulcus (IPS), and in left inferior frontal gyrus (IFG),
and deactivation in the left middle temporal gyrus, specically in a numerical format of the exact calculation
task (Fig. 3, a). In contrast, in the same condition, the group with low level of math competencies showed
no signicant activation (Fig. 3, b).
Figure 3. Activation associated with a numerical format of calculation task in (a) group with high
level of math competencies, and (b) group with low level of math competencies
Note. Numadd – addition task in a numerical format
Regarding a word format of the exact calculation task, individuals with high level of math
competencies did not demonstrate any signicant neural activation. However, individuals with low level
of math competencies showed signicant activation in the right middle frontal gyrus (MFG), right angular
gyrus (AG), and intraparietal sulcus (IPS) (Fig. 4, b).
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Sitnikova, M. A. et al. (2023). The Neural Correlates of Exact Calculation in Word and Numerical Formats in Low And High Math
Performers: A fNIRS Study, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),
11(1), 93-114.
Figure 4. Activation associated with a word format of calculation task in (a) group with high level of
math competencies, and (b) group with low level of math competencies
Note. Textadd – addition task in a word format
Regarding the reading condition (without calculation), subjects with high level of math competencies
showed increased activation in the left middle temporal gyrus and fusiform gyrus (Fig. 5. a). In contrast,
in the same experimental condition, subjects with low level of math competencies showed no signicant
activation.
Figure 5. Activation associated with reading of math problem without calculation in (a) group with
high level of math competencies, and (b) group with low level of math competencies
Note. Nocalc – reading
On the second level of GLM analysis, the coefcients of neural activation in each channel within
different experimental conditions were compared between individuals in a group with high level of math
competencies, as well as between individuals in a group with low level of math competences. In the group
of individuals with high level of math competencies, signicant activation was identied in the reading
task, in comparison to a numerical format and a word format of the exact calculation tasks, in the inferior
temporal gyrus and fusiform gyrus (Tables 4 and 5).
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Sitnikova, M. A. et al. (2023). The Neural Correlates of Exact Calculation in Word and Numerical Formats in Low And High Math
Performers: A fNIRS Study, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),
11(1), 93-114.
Table 4
Beta coefcients of second level of GLM contrast “reading task versus a numerical format of
calculation” in high level performers
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Sitnikova, M. A. et al. (2023). The Neural Correlates of Exact Calculation in Word and Numerical Formats in Low And High Math
Performers: A fNIRS Study, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),
11(1), 93-114.
Table 5
Beta coefcients of second level of GLM contrast “reading task versus a word format of calculation”
in high level performers
In the group of individuals with low level of math competencies, a different pattern of signicant
neural activation was found. In the reading task, in comparison both to a numerical as well as to a word
formats of the exact calculation task, signicant activation was identied in the inferior frontal gyrus (IFG)
and middle frontal gyrus (MFG), particularly in the Broca’s area (Tables 6 and 7).
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105
Sitnikova, M. A. et al. (2023). The Neural Correlates of Exact Calculation in Word and Numerical Formats in Low And High Math
Performers: A fNIRS Study, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),
11(1), 93-114.
Table 6
Beta coefcients of second level of GLM contrast “reading task versus a numerical format of
calculation” in low level performers
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106
Sitnikova, M. A. et al. (2023). The Neural Correlates of Exact Calculation in Word and Numerical Formats in Low And High Math
Performers: A fNIRS Study, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),
11(1), 93-114.
Table 7
Beta coefcients of second level of GLM contrast “word versus a numerical format of calculation”
in low level performers
We also performed bootstrapping with 200 iterations for multiple comparisons correction for every
contrast in both groups. Consistent results were found in a group of high-level performers, with signicant
neural activation in the inferior temporal gyrus and fusiform gyrus in the reading task in comparison to the
calculation in a numerical format, but not in a word format. In the group of low-level performers, signicant
activation after bootstrapping remained in the left IFG, particularly in the Broca’s area, in a word format of
the exact calculation task in comparison to a numerical format.
Furthermore, comparison of task-specic brain activation with brain activation during a 3 minutes
resting-state revealed signicant differences in low performers during the calculation task in a word format,
with activation in the left IFG, particularly in the Broca’s area, and in the right MFG, as well as deactivation
in the angular gyrus, Wernicke’s area, and IPS. In high-performers, signicant differences were found in
the reading task in the left IFG, particularly in the Broca’s area in a word format of the exact calculation
task in the Broca’s area, as well as in the ITG and fusiform gyrus and in a numerical format of the exact
calculation task in the right AG and IPS, as well as in Broca’s area.
As the experimental groups did not follow a normal distribution, we used the Mann-Whitney test to
statistically compare neural activation between individuals with high and low levels of math competencies
in reading task and exact calculation tasks, both in numerical and word formats. To correct for multiple
comparisons, we used a post hoc permutation test with 90 iterations (Ye et al., 2009; Yucel et al., 2021).
Our analysis found statistically signicant differences in neural activation in the exact calculation tasks in
a numerical format in the right SMG and IPS (U=98, Z=6.9703, p=0.0455). We also observed marginal
differences in the left SMG (U=100, Z=6.7507, p=0.0545).
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107
Sitnikova, M. A. et al. (2023). The Neural Correlates of Exact Calculation in Word and Numerical Formats in Low And High Math
Performers: A fNIRS Study, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),
11(1), 93-114.
Discussion
We analyzed and compared fNIRS data of subjects from two groups: with low and high levels
of math competencies to detect the neural foundations of calculation of two-digits addition problems,
both with and without carry effect, in two formats: numerical and word. Additionally, we added a third
experimental condition of reading math problems without calculation to account for word processing, and
linguistic complexity of text itself, and the relation between linguistic and numerical complexity within a
math problem. Two out of three tasks/conditions in our experiment (a numerical format of calculation and
reading arithmetic tasks embedded in text) were highly corresponding to school curriculum. However,
the third one (a word format of calculation) is not typical for school mathematics tasks and could cause
additional involvement of domain-general cognitive processes to solve them. This research is in line
with studies investigating the effects of mathematical competency and math task format (numerical and
word problems) (Dresler et al., 2009; Obersteiner et al., 2010), as well as with studies that consider brain
activation and individual differences in arithmetic performance (Menon et al. 2000; Grabner et al. 2007;
Artemenko et al., 2018a). Our study revealed that young adults with high level of math competencies did
not have signicant differences in engaging frontal or parietal brain areas for solving exact calculation
problems in numerical or word formats, while individuals with low level of math competencies recruited
left frontal areas associated with language comprehension and understanding of complex sentences for
processing problems in a word format, the same as for processing the reading task.
Mental calculation and reading in high level performers
In this study, GLM analysis revealed signicant left hemisphere activation in the frontal and
parietal regions for exact calculation tasks in exact calculation task in a numerical format, and in the left
inferior temporal gyrus and left fusiform gyrus in reading tasks in individuals with a high level of math
competencies. The activation of the left angular gyrus, left inferior temporal, and left fusiform gyri could be
associated with domain-general abilities, while left IPS activation could be associated with both domain-
general and domain-specic abilities. Angular gyrus, especially in the left hemisphere, has been shown
to be associated with numerical and mathematical processing, particularly arithmetic problemsolving
(i.e., mental arithmetic) (Delazer et al. 2003; Zamarian, Ischebeck and Delazer, 2009; Seghier 2013).
It could be linked to the retrieval of numerical information from memory (Dehaene et al., 2003), but in
our studyit could not be explained solely by fact retrieval. According to the recent review (Sokolowski,
Matejko and Ansari, 2022) recent research has suggested that AG activation in high performers could
be due to the involvement in mapping numerical symbols and their meaning (symbol-referent theory), as
well as engaging bottom-up attention required when an arithmetic solution was recalled from memory.
Traditionally, IPS is considered a core region in processing symbolic numerical information and in
calculation (Matejko and Ansari, 2017). Left hemispheric IPS activation could be associated with symbolic
arithmetic in Arabic notation (Venkatraman et al., 2005; Artemenko et al., 2020). In terms of frontal
regions, we found signicant activation in the left inferior frontal gyrus, which is a language-related region
of arithmetic processing involved in calculations and visuospatial processing (Zamarin, Ischebeck and
Delazer, 2009). Left angular gyrus, together with left inferior frontal gyrus, is thought to be involved in
exact calculation (Dehaene et al., 1999), and higher activation in the left angular gyrus is associated with
a high level of arithmetic skills (Grabner et al., 2007). Deactivation in the left middle frontal gyrus could be
associated with decreased demand for working memory load due to automatization of addition. The left
temporal gyrus, including the fusiform gyrus, is known to be involved in processing semantic information
and word recognition.
The group level of GLM, as well as the bootstrap analysis, revealed brain patterns specic to the
reading versus a numerical format of the calculation in the occipito-temporal region, particularly in the
left inferior temporal gyrus and left fusiform gyrus. These regions are involved in recognizing symbolic
objects (Pammer, Korrel and Bell, 2014; Rüsseler et al., 2018) and processing the phonology of written
characters while reading and comprehending text. The fusiform gyrus is also important for reading and
can be impaired in dyslexia. Our results suggest that high performers experienced increased workload
in reading skills, particularly in transcribing between number words, rather than in calculation skills. The
absence of specic activation for math problems in a numerical format as well as in a word format may
indicate that this group was able to perform calculations relatively easily without additional brain effort due
to the involvement of domain-general processes.
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108
Sitnikova, M. A. et al. (2023). The Neural Correlates of Exact Calculation in Word and Numerical Formats in Low And High Math
Performers: A fNIRS Study, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),
11(1), 93-114.
Mental calculation and reading in low level performers
The results of the rst level of GLM analysis in the group with low math competencies showed
signicant activation in the right hemisphere, specically in the middle frontal gyrus (MFG), angular gyrus
(AG), and intraparietal sulcus (IPS), but only in a word format of exact calculation task. The activation of
MFG and AG is related to domain-general processes, while IPS is activated during both domain-general
and domain-specic processes. In case of a word format of calculation task, angular gyrus might be
associated with reading, and interpretation of what is written, as well as arithmetic processing. Within
this group, a more workload was necessary for calculation in a word format. Thus, analysis revealed
that some patterns of activation are not specic for this format. This nding can be used as an argument
in favor of domain-general theories as opposed to domain-specic theories, particularly the Triple-code
model. Overall, the calculation-induced increased activation in the parietal regions is consistent with
the results of previous studies. In research by Richter et al. (2009), participants calculated or read two-
digit addition problems either in a numerical or text format. Calculations in both formats compared to
reading task induced parietal activation. This may be partly related to the peculiarities of the tasks used
in the study. The study also found that the carry effect was shown to activate several brain regions,
including the intraparietal sulcus and the middle frontal gyrus. Previous studies demonstrated that the
carry effect induced activation in the bilateral MFG, the cingulate cortex, the left IFG and the left IPS in
tasks combining two-digit with single-digit operands (Kong et al., 2005; Klein et al., 2009; Yi-Rong et al.,
2011). Nevertheless, the carry effect and related brain activation analysis was not the aim of this study, so
this problem requires further detailed analysis. In line with aforementioned studies, problems with carry
effect used in our study in half of the trials might be a possible explanation for middle frontal gyrus that
was activated during a word format of math problems. MFG involvement can be explained in two ways.
One of them is a categorical effect that is based on the distinction of whether the carry operation has to
be applied or not (Klein et al., 2010; Verner et al., 2013). In our study participants were also constantly
required to switch between tasks with carry operation and without it. Another explanation can be related
to the working memory which supports the role of place-value integration arising during carry operation
with multi-digit numbers (Owen et al., 2005). The role of working memory in the carry effect in addition is
highlighted by a number of authors (Fürst and Hitch 2000; Imbo, Vandierendonck and De Rammelaere,
2007; Klein et al. 2010; Moeller, Klein and Nuerk, 2011a; Moeller, Klein and Nuerk, 2011b; Nuerk et al.,
2011; Caviola et al., 2012; Göbel et al., 2014). Of particular importance is working memory capacity that
can predict math performance (Peng and Fuchs, 2016; Cragg et el., 2017; Fanari,Meloni and Massidda,
2019). According to a number of authors, the phonological loop (the verbal component of working
memory) is crucial for exact calculations (Frisovan den Bos еt al., 2013). The role of working memory in
exact calculations is related to the phonological loop (the verbal component of working memory) being
crucial for encoding and processing number words, which is important for math word problems solving.
Additionally, working memory is involved in manipulating number words, such as performing arithmetic
calculations and retrieving arithmetic facts from long-term memory (Lavander-Ferreira, 2020). At the same
time, our results support ndings of other authors that conrm involvement of parietal areas in the carry
effect (Artemenko et al., 2018a). Nevertheless, carry effect and related brain activation analysis was not
the aim of this study, so this problem requires further detailed analysis.
Generally, the second level of GLM analysis and analysis after bootstrapping showed consistent
results in the low performers. GLM revealed an increased activation in tasks involving word problems (a
word format of exact calculation and reading task) in the frontal cortex, including Broca’s area, and IFG.
Although Broca’s area and inferior frontal gyrus are thought to be crucial regions for speech production,
some investigations demonstrated its involvement in comprehension of complex sentences (Grewe et
al., 2005). Our results are consistent with previous ndings that report higher activation of inferior frontal
regions in high-ambiguity sentence processing (Rodd et al., 2005): possible ambiguity is associated with
an unusual format for presenting math problems in a word format and arithmetic tasks embedded in text
that do not require solving. Analysis after bootstrapping demonstrated an increased activation in exact
calculations in a word format compared to numeric format in the Broca’s area and left inferior frontal gyrus.
Thus, the predominant role of the frontal regions in comprehension was conrmed.
Differences between young adults from groups with high and low levels of math competences
It’s worth noting that signicant activation in low performers was mostly in the same brain regions
as in high performers, however in right hemisphere, but not in left hemisphere. In the literature there were
some viewpoints that cerebral hemispheres played different roles in processing information depending on
the solution strategy applied to solve the task. Solution-irrelevant interpretations of words in the problems
might lead to rough semantic coding associated with the right hemisphere (Beeman and Bowden, 2000).
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109
Sitnikova, M. A. et al. (2023). The Neural Correlates of Exact Calculation in Word and Numerical Formats in Low And High Math
Performers: A fNIRS Study, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),
11(1), 93-114.
Therefore, a possible explanation is that the right hemisphere is activated in stressful situations. In our
case, for most individuals, due to their low math performance, solving exact calculation tasks in a word
format was stressful. In support of this nding, previous studies found that right dorso-lateral prefrontal
cortex (DLPFC) activation is associated with high trait anxiety (Basten, Stelzel and Fiebach, 2012). MFG
can be referred to as DLPFC. Klados et al., (2015) reported frontal changes during arithmetic calculation
that are thought to be related to the inuence of math anxiety on working memory. However, our results
demonstrated activation patterns versus deactivation shown in some other studies (Klados et al., 2015).
Nevertheless, our assumption about the effect of anxiety needs additional investigation.
Another important nding was the detected specicity in the groups of low and high performers,
which indicated differences in the mechanisms for solving the same type of tasks depending on the level
of mathematical competence. This result is consistent with the neural efciency hypothesis, according
to which individuals with higher intelligence spend less brain resources on solving cognitive tasks
(Nussbaumer et al., 2015). This is expressed in the absence of differences in activation during solving
math problems in various formats in high-level performers in our study. In low-level performers, there were
signicant differences in activation in different formats of exact addition problems solving. Between-groups
comparison showed statistically signicant differences in neural activation in exact calculation tasks in a
numerical format as well in bilateral supramarginal gyrus (SMG) and right intraparietal sulcus. The SMG
is known to be involved in complex calculation due to the high demands of visuospatial working memory
(Zago et al., 2001). Two-digit non-overlearned calculation is regarded as recruiting storage of intermediate
results in a short-term memory to successfully solve the math problem (Menon et al., 2000). Therefore,
our ndings might indicate specic activation for calculation based on the differences in performance.
Differences between task-induced activation and resting state
Comparison of brain activation during tasks and resting state also revealed a certain heterogeneity
in brain mechanisms of math abilities. In the high performing group, all three conditions were associated
with higher involvement of Broca’s area and inferior frontal gyrus, as well as some task-specic activation.
As mentioned previously, the Broca’s area and IFG could be related to understanding complex sentences.
Involvement of Broca’s area and IFG in the math processes could possibly be attributed to the reading of
the actual presented stimulus (Rogalsky, Matchin and Hickok, 2008; Klein et al., 2015). Reading numerals
written in a word format in our study and subsequent analysis of semantics, however, might be related to
two opposite processes. On the one hand, activation of speech-related areas could indicate the process
of transformation of any numerical information into semantic form followed by the calculation process. On
the other hand, it might reect the process of transformation of any symbolic information into nonsymbolic
form for the following calculations. Considering higher activation of Broca’s area in a word format of
calculation in this study, we might have weak evidence for the second process, however this evidence is
far from decisive and the rst process might be more important for math abilities, both processes might
operate simultaneously. This problem needs to be addressed additionally in future research. In the low-
performing group, only a word format of calculation task signicantly differed from resting state, with
higher activation in Broca’s area, inferior frontal gyrus and middle frontal gyrus and lower activation in
angular gyrus, Wernicke, and IPS. This pattern of activation seems to be consistent with the inter-task
comparison. We detected no signicant difference in activation between resting state, reading task and
a numerical format of the calculation task. The absence of any task-induced activity could be the result
of weak implication of executive functions (Bull and Lee, 2014). People with weak executive functions
demonstrate difculties in remembering and following instructions, inhibiting irrelevant information and
staying focused on task, as well as quickly choosing appropriate task strategies. There might be a
substantial variability in brain mechanisms related to poor performance in calculations and this variability
prevents statistically signicant difference in activation induced by resting state and tasks. Therefore, high
and low levels of performance in calculations might be attributed to different neurocognitive mechanisms.
Limitations
Our study has several limitations. Firstly, we have a relatively small sample size and have used
group comparison as the primary method of assessing the level of math competence. Secondly, we did
not fully estimate the differences between the two groups, and it may be important to use more appropriate
methods for comparing group (or individual) performance within one condition. Thirdly, our analysis was
limited to four areas of interest and did not cover the whole brain activity. Finally, we did not assess carry/
no-carry effects and compare addition from the perspective of brain activation during various conditions.
We plan to address all these limitations in future studies.
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110
Sitnikova, M. A. et al. (2023). The Neural Correlates of Exact Calculation in Word and Numerical Formats in Low And High Math
Performers: A fNIRS Study, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),
11(1), 93-114.
Conclusions
Our study aimed to measure brain activation in frontal and parietal regions using fNIRS to
investigate the neural correlates of exact calculation problems with two-digit numbers in different formats
(word versus numerical). We found that tasks in word and numerical formats activate different areas of
the brain, since these two formats of presenting arithmetical problems differ in the amount of cognitive
effort required and processes involved in calculation. Our ndings support domain-general theories
in numerical cognition, which suggest that both domain-specic skills such as magnitude processing,
and domain-general skills such as working memory, fact retrieval, and attention are involved in mental
calculation. Solving of arithmetical problems presented in a word format requires several steps, including
understanding the verbal information underlying mathematical relations, and transitioning to symbolic
mathematical expression. This processing of numerical information is more complex, and results in higher
oxygen consumption compared to solving numerical problems. We also found that the patterns of neural
activation differed between individuals with low and high levels of math competencies. Low performers
demonstrated right hemisphere activation, while high performers showed left hemisphere activation.
Right hemisphere activation in low performers when solving exact calculation tasks in a word format
might be stress-induced, as solution-irrelevant interpretations of words within a task might lead to rough
semantic coding associated with the right hemisphere. We observed increased activation in the Broca’s
area and left inferior frontal gyrus in low performers when solving problems in a word format compared
to a numerical format. In high performers, we found increased activation in the occipi-to-temporal region,
particularly in the left inferior temporal gyrus and left fusiform gyrus, when solving problems in a reading
format compared to a numerical format. In summary, our ndings demonstrate that the neural correlates
of two-digit exact calculation in numerical and word formats differ in individuals with low and high math
competencies. These results suggest that future research should consider cognitive performance when
describing neurocognitive mechanisms of calculation.
Acknowledgements
The paper is part of the project no. 22-28-02030, funded by RSF (Russia).
Conict of interests
The authors declare no conict of interest.
Author Contributions
Conceptualization, study design and stimuli preparation: M.A.S., J.A.M. and T.V.A.; software for
preprocessing and analysis: G.O.P., R.G.A.; data collection and analysis: MAS and R.G.A.; writing-
original draft preparation: M.A.S., J.A.M. and T.V.A.; writing-review and editing: M.A.S. and J.A.M. All
authors approved the nal version of the manuscript for submission.
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