Content uploaded by Ola Helenius
Author content
All content in this area was uploaded by Ola Helenius on Jun 16, 2022
Content may be subject to copyright.
Trends in Neuroscience and Education 28 (2022) 100180
Available online 10 June 2022
2211-9493/© 2022 The Author(s). Published by Elsevier GmbH. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/).
Research paper
Proactive cognitive control, mathematical cognition and functional activity
in the frontal and parietal cortex in primary school children: An fNIRS study
Simon Skau
a
,
b
,
*
, Ola Helenius
b
,
c
, Kristoffer Sundberg
b
, Lina Bunketorp-K¨
all
a
,
Hans-Georg Kuhn
a
a
Institute of Neuroscience and Physiology, Sahlgrenska Academy, University of Gothenburg, Gothenburg, Sweden
b
Department of Pedagogical, Curricular and Professional Studies, Faculty of Education, University of Gothenburg, Gothenburg, Sweden
c
National Center for Mathematics Education, University of Gothenburg, Gothenburg, Sweden
ABSTRACT
Understanding how children acquire mathematical abilities is fundamental to planning mathematical schooling. This study focuses on the relationships between
mathematical cognition, cognition in general and neural foundation in 8 to 9-year-old children. We used additive mathematics tests, cognitive tests determining the
tendency for proactive and reactive problem solving and functional near-infrared spectroscopy (fNIRS) for functional brain imaging. The ability to engage in pro-
active control had a stronger association with mathematical performance than other cognitive abilities, such as processing speed, sustained attention and pattern
recognition. The fNIRS method identied differences between proactive and reactive control, i.e., the more proactive the children were, the greater the increase in
oxygenated hemoglobin in the left lateral prefrontal cortex during reactive beneciary situations. During a text-based task involving additive reasoning, increased
activity in the dorsal medial prefrontal cortex was detected compared to a similar task with supportive spatial-geometric information.
1. Introduction
Proper understanding of how children acquire mathematical abilities
is fundamental for planning mathematical schooling. A major constitu-
ent of such understanding concerns the relationship between cognitive
abilities and the corresponding neural correlates. An important question
is to what extent the development of mathematical skills and compe-
tences, such as the ability to denote and manipulate numbers arith-
metically, mainly relies on general cognitive abilities [1], domain
specic cognitive abilities that primarily affect the learning of arith-
metic [2] or a mix of abilities that might include specic but
non-mathematical abilities such as abilities associated with language
processing [3].
In this paper we will investigate the relationship between general
cognitive ability, proactive cognitive control, mathematical cognition
and functional activity in the frontal and parietal cortex in children aged
8-9 years old.
Different cognitive control functions such as working memory, in-
hibition, and cognitive exibility have been linked to mathematical
performance [4]. However, most studies of cognitive control are only
designed to test reactive and not proactive cognitive control [5,6]. Ac-
cording to the dual mechanism of control theory (DMC), cognitive
control can be used in a proactive (preparatory) or in a reactive
(stimulus-driven) manner [6]. Proactive cognitive control is crucial to
keeping attention on the essentials of a situation and to prepare for
handling future information, for example applying tools a teacher
explained in a previous assignment.
Children begin to engage in proactive behavior around the age of 5 to
6, but it is not until the age of 8 that children begin to use proactive
control more reliably [7]. The tendency to engage in proactive control
increases with age up to adulthood [8]; hence adults tend to be more
proactive than children [6]. However, studies have shown that the
ability to be proactive decreases towards the onset of adolescence [9]. In
recent studies, the ability to use proactive control was associated with
increased mathematical performance in 6 to 11-year-old children [10,
11].
In adults, a recent meta-analysis has shown that the right medial
frontal gyrus is involved during the reactive but not the proactive mode
and the right inferior frontal gyrus is involved during the proactive but
not the reactive mode [12]. However, only a handful of imaging studies
investigating proactive control in children have been conducted so far.
Moreover, the different age groups (ranging from 5 to 15 years),
different aims and experimental designs of previous studies make it
difcult to draw generalized conclusions. For example, Kamijo and
Masaki found that children with greater physical tness (at 10 years of
age) were more proactive and showed increased activity in the posterior
* Corresponding author.
E-mail address: simon.skau@gu.se (S. Skau).
Contents lists available at ScienceDirect
Trends in Neuroscience and Education
journal homepage: www.elsevier.com/locate/tine
https://doi.org/10.1016/j.tine.2022.100180
Received 12 October 2021; Received in revised form 14 May 2022; Accepted 9 June 2022
Trends in Neuroscience and Education 28 (2022) 100180
2
parietal cortex (PPC) during reactive tasks than children with lower
tness [13]. In contrast, Strang and Pollak found increased activity in
the inferior frontal gyrus, right inferior parietal cortex, bilateral thal-
amus and insula in 10 and 15-year-olds, when being proactive [14].
However, the involvement of these structures was tied to reward con-
ditions. Even though the information about proactive and reactive
control is difcult to differentiate from the tness of the children and
reward conditions, a general trend of dynamic involvement of PPC
during proactive and reactive control can be supported [7,13–15]. More
studies on children are needed to dene the stage of development during
which the prefrontal cortex is involved in differentiating proactive from
reactive control.
For mathematical cognition, a meta-analysis of functional magnetic
resonance imaging (fMRI) studies found that children between 9 and 14
years of age involve the right inferior parietal lobule, inferior parietal
sulcus, claustrum, and insula when performing numerical tasks. Simi-
larly, for a calculation task, they also involved the right cingulate gyrus,
bilateral medial frontal gyrus, right precuneus, left claustrum and left
insula [16]. Most studies of both mathematical cognition and proactive
control have been performed using fMRI or electroencephalography
(EEG). For fMRI-based techniques, the limiting environment of the MR
scanner creates experimental restrictions. This raises the question of
ecological validity towards the mathematical tasks in school and
everyday life [16] and since the scanner environment is not
child-friendly due to the loud noise and space limitations, most studies
have been performed in adults [17]. Therefore, limitations regarding
development of mathematical cognition in children exist [18]. In light of
these issues, researchers have argued for the use of functional
near-infrared spectroscopy (fNIRS) in the study of mathematical
cognition [17]. fNIRS is used to detect oxygenated (oxy-Hb) and deox-
ygenated hemoglobin (deoxy-Hb) in a specic brain location, which are
surrogate measures for neuronal activity. Thus, fNIRS and fMRI are
sensitive to the same physiological process. However, while fNIRS has
lower spatial resolution, it provides better temporal resolution [19].
fNIRS is a non-invasive, safe, accessible, quiet and portable brain ac-
tivity monitoring system and compared to EEG and fMRI it is more
robust against motion artifacts. This makes fNIRS well suited for
assessing in children the neural substrates for mathematical cognition
and cognitive control in general [17,20,21].
This exploratory study aims to investigate three relationships: (i) the
relationship between proactive control and mathematical cognition, (ii)
the relationship between proactive control and brain activation and (iii)
the relationship between brain activation and mathematical cognition in
different situations involving children between 8 to 9 years of age. As a
measure of proactive/reactive control, we used a modied version of the
AX-Continuous Performance Test (AX-CPT) (see Fig. 1A and method
section) [10,22–24]. We wanted (i) to investigate whether proactive
control was associated more with mathematical performance than pre-
viously established constructs such as pattern recognition, sustained
attention, and processing speed [3,25,26] and (ii) to perform a con-
ceptual replication of previous fMRI imaging studies of proactive and
reactive control with children with fNIRS. In addition, we wanted to
investigate if fNIRS can reveal neural activation differences during
mathematical tasks, where only context of the presentation differs. We
developed three mathematical tests centered around different ways of
performing addition and subtraction that could be used with fNIRS. The
rst test, additive situations, examined the ability to transform mathe-
matical situations into arithmetic language, without the need to perform
any calculations (Fig. 1B). The second and third tests investigated ad-
ditive reasoning, when it is text-embedded or comes with geometric support
(Fig. 1C-D).
Fig. 1. The test done during fNIRS. A) The modied AX-CPT test with an example of the serial stimulus presentation with the arrow indicating the order of pre-
sentation. Subjects press right or left to indicate the correct response to the stimuli presented in the squares. The designations AX (“dog” probe followed by “cat”
stimulus), BY (“no dog” probe followed by “no cat” stimulus), AY (“dog” probe followed by “no cat” stimulus) and BX (“no dog” probe followed by “cat” stimulus)
indicate the four probe types that can be generated from image pairs (see Method section for further information). B) Example of the Additive situations task. C)
Example of the Additive reasoning with geometric support task. D) example of Additive reasoning text-based task.
S. Skau et al.
Trends in Neuroscience and Education 28 (2022) 100180
3
2. Materials and methods
The present study is part of the larger Gothenburg AMBLE project
(Arena for Mind, Brain, Learning and Environment) which integrates
research from developmental psychology, neuroscience and educational
science.
2.1. Participants
Participants were recruited from the second grade in two Swedish
primary schools located in two different cities. Parents gave their writ-
ten informed consent before the study began and the participants were
told that they could withdraw at any time. In total, 53 children from the
two schools participated in the study (21 from a school in Uppland and
32 from a school in V¨
astra G¨
otaland). The cohort consisted of 30 boys,
23 girls and a mean age of 8.5 years with a standard deviation of 4
months, with an age range between 8.1 and 9.3 years of age. Based on
self-reports, 46 of the children were right-handed, and seven were left-
handed. The study was approved by the Gothenburg Regional Com-
mittee of the Swedish Ethical Review Authority (reference number: 839-
17).
2.2. Experimental design
The study was conducted during the 2019 spring term and consisted
of one individual session per child conducted by a researcher and one
whole-class session two weeks later conducted by their teacher. For the
individual session, all tests, including the fNIRS recordings, were per-
formed in a separate room near the children’s classroom. The data was
collected with the participant seated in a chair at a table with a computer
screen. All participants performed the tasks in the same order, starting
with the pen and paper tasks, Symbol Search [27] and Digit Symbol
Coding [27], followed by a reaction time test. After the reaction time
task, the fNIRS cap (EASYCAP GmbH, Germany), with the fNIRS optodes
and detectors attached was carefully placed on the participant’s head.
Participants performed a modied version of the AX-Continuous Per-
formance Test, followed by the additive situation test and
geometric/text-based test (Fig. 1). The procedure took between 50-60
min in total, including preparations and trial runs for all tasks.
2.3. Measures
Symbol Search and Digit Symbol Coding are subtests within the Pro-
cessing Speed Index in Wechsler Intelligence Scale for Children fourth
edition (WISC-IV) [28]. In both tests, the subject was asked to process as
many symbols as possible during 2 min. The raw score was dened as
the number of correctly processed symbols.
Reaction time: the participants were asked to press the space key as
fast as possible on a computer whenever they heard a sound with a 5-sec-
ond interval.
Modied version of AX-Continuous Performance Test (AX-CPT). The
test involved cues called A and B and targets X and Y. We used a child-
adapted version of a setup we used on adults in a previous study [29]
using pictures of animals instead of letters. The participant was pre-
sented with one picture of an animal at a time on the computer screen.
The participant was instructed to respond with the left hand on a
keyboard whenever a picture of a cat (X) preceded by a picture of a dog
was shown (A) and to respond with the right hand on the keyboard for
all other combinations of cue-target pairs, also referred to as probes
(Fig. 1) [30]. Each stimulus (picture of an animal) had two functions; it
served as the target item for the current trial and represented the cue for
the upcoming trial, which results in four different kinds of trials: AX
(dog→cat), AY (dog→no cat), BX (no dog→ cat) and BY (no dog→no
cat), only the rst (AX: dog followed by cat) trial required a left-hand
response (Fig. 1A). The trials can be categorized as; AX, target trials;
AY, situation benetting from reactive control (or reactive trials for
short); BX, situation benetting from proactive control (or proactive trials
for short); BY, control trials [29]. The following list of animals were used:
dog, cat, elephant, camel, giraffe, shark, buttery, rat. We used three
different pictures of dogs and two different pictures of cats. The trials
were semi-randomized and generated 22 AX, 18 AY, 22 BX and 34 BY
trials.
Participants were asked to answer as fast and correct as possible and
had 4,000 ms to respond before the picture on the screen disappeared.
The time span between response and the next stimulus jittered between
5 and 7 s, with a mean of 6 s. During this time, participants were asked to
focus on a plus sign on the screen. A 30-second break was given after half
of the 96 trials. Raw scores were recorded as reaction time, errors, and
omissions.
From the response time data, we calculated the proactive behavioral
index (PBI) according to the formula below. This has previously been
applied in similar contexts [22–24]:
PBI =(AY −BX
AY +BX)
A positive PBI value indicates more proactive tendency and a nega-
tive value more reactive tendency. We also calculated the d’ context
index, which is based on the proportion of accuracy scores for AX and BX
trials. The proportion of correct AX trials is subtracted by the proportion
of errors on BX trials. 100% accuracy on AX trials was replaced with
(2
−(1/N)
; N =AX trials), and 100% accuracy for BX trials was replaced
with (1-2
−(1/N)
; N =BX trials), to get an unbiased estimation [15]. A
higher d’ context value indicates a higher sensitivity to contextual cues
[15].
2.4. Response time adjustment
In order to adjust the response time based on the error rate, the linear
integrated speed-accuracy score (LISAS) [31] was calculated.
LISAS =RTi+(SRT
SPE)×PEi
Where RTi is the participant’s mean response time in condition i, PEi
is the participant’s proportion of errors in condition i; SRT is the par-
ticipant’s overall RT standard deviation; and SPE is the participant’s
overall PE standard deviation. Weighting the PE with the RT and PE
standard deviation ratio is done to achieve a similar weight of the two
components, RT and PE.
2.5. Mathematical test for fNIRS imaging
Additive situations. The author, O.H., developed the test based on
Vergnaud’s theoretical analysis of the psychology of the addition and
subtraction operations [32]. The children were asked to listen to a
description of an additive situation involving two numbers. They were
then asked to choose the arithmetic expressions that described the sit-
uation out of four possible choices presented on the computer screen
(see Fig. 1B). Each arithmetic expression was highlighted with a specic
color and presented at different sites on the screen. The participants
responded by pressing a colored button on a gamepad corresponding to
the specic color of the arithmetic expression, and was located on the
same side on the gamepad as on the screen. There were a total of 17
trials. Each question was verbally presented and, within a few seconds,
repeated once more. The participant had 25 s to answer before the trial
ended and there was 4 to 6 s between the end of a trial and the beginning
of the next. All participants performed the trials in the same order. The
number of correct answers was recorded as a raw score.
Additive reasoning text-based or with geometric support. The test was
developed by author O.H. and contained 20 arithmetical tasks that can
be solved with the addition operation. Half of the tasks were formulated
in natural language (Swedish), describing an additive situation
S. Skau et al.
Trends in Neuroscience and Education 28 (2022) 100180
4
(Fig. 1D). The other half of the tasks consisted of similar additive tasks,
matched for arithmetic difculty, but were formulated with the help of a
picture involving spatial/geometric settings, such as length, distance or
movement (Fig. 1C). The two types of tasks were randomly mixed and all
participants performed the tasks in the same order. For each task, par-
ticipants were handed a sheet of paper describing/depicting the task.
The researcher read the task aloud to the participant twice with a short
pause in between. Participants had 25 s to write down the answer before
the sheet of paper was removed. 4-6 s later, the next sheet of paper with
a task was presented. The participants were informed that they could
write on the sheet of paper if they wanted to make sketches or calcu-
lations. The raw scores were dened as the number of correct answers.
2.6. Whole class-based measurements
Basic numeracy and calculations (BANUCA) [33]. The test assessed the
basic non-symbolic and symbolic number sense, subitizing and con-
ceptual subitizing, simple addition and subtraction and the ability to
identify simple number patterns. We also added ten simple multiplica-
tion questions. We used the total score (maximum score of 89 points) as
the outcome.
Additive and multiplicative reasoning (AMR) [34]. The test con-
tained a total of 17 tasks. About half of the tasks require additive
reasoning, such as “Jamal and Sara play a game. Sara is on number 11
and Jamal on number 4. How much further ahead is Sara?” (accompa-
nied by a picture of the board game with Sara’s and Jamal’s positions
shown). Half of the tasks are multiplicative such as “There are 3 rabbits
in each house, how many rabbits in total live in the 4 houses?”
(accompanied by a picture of 4 houses with the digit 3 on one of them).
Test of Visual Perceptual Skills-III (TVPS-III) [35]. Children were
presented with a gure or pattern and underneath, four more compli-
cated gures. One of the four gures contains the rst gure. Children
are asked to nd and mark that gure. The test contained 18 tasks in
total.
Working memory subtest from Lilla Duvan [36]. The test has a
dual-task format where a child is orally presented with a letter symbol
immediately followed by a straightforward yes/no question (e.g., Can
dogs bark?). The yes/no answer is given using red and green signs.
Following the answer, the task is to recall the presented letter. There
were six tasks with an increasing number of or letters (2-4) to remember.
The correct letters in the correct order yielded two points, whereas
correct letters in incorrect order yielded one point. We only used the
total score (max score is 36) as the outcome.
2.7. fNIRS data acquisition
The fNIRS measurements were performed using a continuous wave
system (NTS, Optical Imaging System, Gowerlabs Ltd., UK) [37], using
two wavelengths (780 and 850nm) to measure changes in the concen-
tration of oxygenated hemoglobin (oxy-Hb), deoxygenated hemoglobin
(deoxy-Hb) and their sum, total hemoglobin (tot-Hb). The system has 16
dual-wavelength sources and 16 detectors. The array used 43 channels
(i.e., source/detector pairs) with a source-detector distance of 30mm
and two short-separation channels with a 10-mm distance, as suggested
from previous studies [38,39]. Short separation channels are only sen-
sitive to hemodynamic activity in the scalp and skull. They are used to
regress out the scalp signal and improve the fNIRS measurement’s
specicity of hemodynamic responses [38,39]. The optode placements
were designed to encompass both the dorsolateral prefrontal cortex and
the parietal cortex (Fig. 2). The fNIRS data was acquired at a sampling
frequency of 10 Hz.
2.8. fNIRS data analysis
The fNIRS data was preprocessed using MATLAB 2018b [40] and the
MATLAB-based fNIRS-processing package HomER2 [41]. The process-
ing pipeline started with pruning the raw data. Channels were rejected if
their mean intensity was below the instrument’s noise oor (1e-3 A.U.).
Fig. 2. Layout of the fNIRS measurement. A) The cap with fNIRS optodes on a child. B) Visualization of the measurement points/channel (red dots). The region of
interest (ROI); LPPC, lateral posterior parietal cortex; MPPC, medial posterior parietal cortex; LPC, lateral parietal cortex; MPC, medial parietal cortex; DLPFC,
dorsolateral prefrontal cortex, DMPFC, dorsomedial prefrontal cortex; aDLPFC, anterior dorsolateral prefrontal cortex, aDMPFC, anterior dorsomedial prefron-
tal cortex.
S. Skau et al.
Trends in Neuroscience and Education 28 (2022) 100180
5
The raw data was then converted to optical density. A high-pass lter of
0.03 Hz was used to correct for drift and a low-pass 0.5 Hz lter to
remove pulse and respiration. The HomER2 functions hmrMotionArti-
fact and hmrMotionCorrectSpline were used to correct for motion arti-
facts. Optical density was converted to hemoglobin concentration with
hmrOD2Conc, using the default values [6.0 6.0] for the partial path-
length factors.
To calculate the hemodynamic response function (HRF), the
hmrDeconvHRF_DriftSS function in HomER2, which estimates the HRF
by applying a General Linear Model (GLM), was used. To solve the GLM,
a least-square t of a convolution model in which the HRF at each
channel and chromophore was modeled as a series of Gaussian basis
functions, with a spacing and standard deviation of 0.5 s [42]. The
model included polynomial drift regressors up to the 3rd order. The
regression time length for the three mathematical tests was -5 to 25 s and
for the AX-CPT -2 to 12 s. The short separation channel selection for
regression of each long channel was chosen based on the highest cor-
relation to the long channel.
Since the wavelengths used by the Gowers Lab NTS system (780 nm,
850 nm) are less sensitive to deoxy-Hb, only the oxy-Hb data were sta-
tistically analyzed [43,44]. For the mathematical test analysis, each
channel was analyzed individually, while for the AX-CPT, channels were
pooled together into predened regions of interests (ROIs) by averaging
the signals, see Fig. 2. For the mathematical test, the maximum peak
between 3 and 25 s after each stimulus was identied for each channel,
and two s around the peak value were averaged. For the AX-CPT, the
maximum peak between 2 and 10 s after each stimulus was identied for
each channel, and two seconds around the peak value were averaged.
2.9. Statistical analyses
Since the study is exploratory in nature, we choose a Bayes factor
(BF) analysis using the open-source program JASP version 0.10. [45].
We have applied BF
10
as the main criterion, and the interpretation of
BF
10
=3 would be that, given the data, the alternative hypothesis (H
1
) is
3 times more likely than the null hypothesis (H
0
), while BF
10
=0.3 can be
interpreted that, given the data, the H
0
is 3 times more likely than H
1
. A
BF
10
>3 can also be interpreted as the equivalent to a p-value <0.01
[46]. The H
0
is dened in this study as no difference or no association,
depending on the test. Following the praxis of Wagenmakers and col-
leagues [47], a BF
10
in one of the four categories between 3-10, 10-30,
30-100 or above 100 is interpreted as substantial, strong, very strong or
extreme evidence for H
1
, respectively.
For the rst aim of the study, we took the average proportion of
correct answers to the math tests, additive situations, additive reasoning
text-based, additive reasoning with geometric support, BANUCA, and AMR,
denoting it math performance. We then conducted a Bayes factor version
of Pearson’s correlation of math performance in relation to PBI, d’
context, reaction time, performance on the AX-CPT, Symbol Search, Digit
Symbol Coding, Lilla Duvan, and TVPS-III. For the correlations, we used
the default stretched beta prior width of 1.
For the study’s second aim, we used Pearson’s r correlation between
peak oxy-Hb concentration in each ROI for AY and BX trials, with the PBI
and d’ context.
For the third aim of the study, a Bayes factor version of paired t-test
was conducted to compare average peak oxy-Hb values for the three
different mathematical situations (additive situations, additive reasoning
with geometric support, additive reasoning text-based) for each channel. We
used a default Cauchy prior of 0.707.
3. Results
3.1. Descriptive result and evaluation of variables
Two children could not undergo fNIRS recording due to discomfort
wearing the cap and were thus excluded from the analysis. Three were
excluded from the AX-CPT analysis since they either were unable to
perform the whole AX-CPT test or had two or fewer correct responses on
the BX trials. One child did not perform Digit Symbol Coding and
Symbol Search; ve did not perform Lilla Duvan, eight did not perform
the AMR, seven did not perform BANUCA, and twelve did not perform
TVPS-III. When analyzing processing speed as measured by the Digit
Symbol Coding and Symbol Search subtests of the WISC-IV processing
speed index, the children had an average processing speed index of 103
points, corresponding to the 58-percentile compared to the age-matched
WISC-IV reference population [28]. Only one child had a processing
speed outside two standard deviations with a processing speed index of
131 points. Additional descriptive data are presented in Table 1. Based
on visual analysis of histogram and Q-Q plots (Supplementary Fig.1), the
following variables were not used in correlation with math performance:
AY error, BX error, BY error, AX omission, AY omission, BX omission, BY
omission.
3.2. Performance in the individual mathematical test
The average correct responses for the additive situation test were
61.4%, the additive reasoning with geometric support 65.6% and the ad-
ditive reasoning text-based 79.0%, indicating that the additive situations
and additive reasoning with geometric support were more difcult tasks
than the additive reasoning text-based. The associations between the three
tests and the two whole class tests of mathematics are shown in Table 2.
When we correlated the performance results for the general cognitive
tests with all mathematical tests, we nd a positive association of d’
context with additive reasoning with geometric support (with r =.47 and
BF
10
=56.0) and BANUCA test (with r =.43 and BF
10
=13.27). The
Digit Symbol Coding was positively correlated with additive reasoning
text-based (with r =.473 and BF
10
=77.75), indicating that the higher
the children’s general processing speed, the higher the number of cor-
rect answers on the additive reasoning text-based. The AMR test was
negatively associated with response time on all four probes; AX (r =-.60
and BF
10
=995.4), AY (r =-.49 and BF
10
=39), BX (r =-.51 and BF
10
=
61.9) and BY (r =-.47 and BF
10
=26), indicating that faster responses on
the AX-CPT task are associated with higher scores on the AMR test. None
of the mathematical test results were associated with the Symbol Search
test performance or the PBI (see Table 2).
To evaluate our rst aim, we calculated math performance as the
Table 1
Descriptive statistics of the behavioral variables.
N Mean SD Min Max
Age 51 104.3 3.94 97 112
Reaction time 50 305.1 59.781 211 489
Additive situations 52 10.4 2.30 4 15
Geometric support 52 6.5 2.47 1 10
Text-based 52 7.9 2.07 1 10
AMR 46 78.5 7.05 49 88
BANUCA 45 12.2 2.84 6 18
PBI 50 -0.113 0.09 -0.274 0.102
d context 50 0.698 0.18 0.182 0.924
Lilla Duvan 48 29.1 5.45 14 36
TVPS-III 41 13.7 3.02 5 18
Digit Symbol Coding 52 35.6 6.74 19 52
Symbol Search 52 20.5 3.77 12 30
AX 50 1133.7 338.2 497.7 2084.1
AY 50 1029.2 185.1 686.8 1474.3
BX 50 1316.6 332.7 667.6 2167.8
BY 50 1158.4 280.4 592.8 1711.1
AX error 50 3.940 2.94 0 12
AY error 50 0.580 0.92 0 4
BX error 50 2.620 3.18 0 17
BY error 50 1.060 2.61 0 17
AX omission 50 0.640 0.87 0 3
AY omission 50 0.260 0.63 0 3
BX omission 50 1 1.21 0 5
BY omission 50 0.680 1.26 0 6
S. Skau et al.
Trends in Neuroscience and Education 28 (2022) 100180
6
average mathematical performance on all ve tasks and correlated it
with all behavioral variables (Table 2). The overall math performance
was associated with d’ context (r=.051 and BF
10
=43.6), TVPS-III (r=.43
and BF
10
=3.68), Digit Symbol Coding (r=.39 and BF
10
=3.90), and
response time on AY (r=-.41 and BF
10
=4.88) and BX trials (r=-.56 and
BF
10
=128). PBI was not associated with average math performance
with an r=.34 and BF
10
=1.87 (for scatter plots of average math per-
formance with PBI, d’ context, and BX response time see Fig. 3, and for
scatter plots with all other behavioral variables see Supplementary
Fig. 2).
3.3. fNIRS results AX-CPT
The second aim was to associate children’s tendency to use reactive
or proactive control with functional activity in the frontal and parietal
cortex. We performed Pearson’s r correlation of both PBI and d’ context
with oxy-Hb in the predetermined ROIs for AY trials and BX trials. All
results are summarized in Table 3. There is evidence for an association
between PBI and oxy-Hb increase in the right LPPC during AY trials (r =
0.491 and BF₁₀ =9.496) indicating that with higher PBI score a larger
increase in oxy-Hb in right PPC is observed during situations beneting
from reactive control (Fig. 4A). The peak oxy-HB in left DLPFC during
BX trials with d’ context showed very strong evidence with an r =-.498 and
BF₁₀ =56.85, indicating that the higher the d’ context score, the less the
left DLPFC was involved during BX trials (Fig. 4B).
3.4. fNIRS results mathematical test
Our third aim was to evaluate if there was a functional difference in
the frontal or parietal cortex between an arithmetic math task without
calculations (additive situation), a text-based task and a task with geo-
metric support. Average oxy-Hb curves for each channel for additive
situation, additive reasoning with geometric support, and text-based, plus t-
values based on the paired t-test for each channel are visualized in Fig. 5,
and degree of freedom, t-value, BF₁₀ and Cohen’s d are shown in Sup-
plementary Table 1-3.
Both the geometric support and text-based showed higher activity in
the anterior PFC compared to additive situation. For the comparison
between additive reasoning with geometric support and additive situations,
seven of the most anterior channels showed very strong evidence or more
for higher activity during additive reasoning with geometric support than
for additive situations, with an average Cohen’s d of 0.741 ranging from
0.637 to 0.839. The posterior channel in the right DLPFC also indicated
increased activity for additive reasoning with geometric support with a BF₁₀
=10.36 and Cohen’s d of 0.622, as well as one channel in the left LPPC
with a BF₁₀ =13.35 and Cohen’s d of 0.676. For the comparison between
text-based and additive situations, all of the seven most anterior channels
showed very strong to extreme evidence for increased activity during text-
Table 2
Correlation between mathematical tests and behavioral variables.
Math P(n=39) Additive situation (n=52) Text-based(n=52) Geometric support(n=52) BANUCA(n=46) AMR(n=45)
Variables r BF₁₀ r BF₁₀ r BF₁₀ r BF₁₀ r BF₁₀ r BF₁₀
PBI (n¼50) .34 1.87 .02 0.17 .19 0.43 .22 0.58 .08 0.21 .20 0.44
d’ context (n¼50) .51 43.6 .22 0.60 .36 4.33 .47 56.0 .43 13.27 .33 2.05
Reaction time .03 0.20 -.17 0.34 .09 0.21 -.08 0.20 .00 0.19 .23 0.57
Lilla Duvan (n¼48) .17 0.34 .00 0.18 .12 0.25 .14 0.28 .20 0.45 .30 1.35
TVPS-III (n¼41) .43 3.68 .34 1.99 .15 0.30 .37 3.03 .25 0.62 .42 4.42
DSC (n¼52) .39 3.90 .14 0.28 .47 77.7 .38 8.92 .37 4.38 .22 0.51
SS (n¼52) .33 1.68 .19 0.42 .32 2.66 .30 1.66 .29 1.17 .18 0.37
Age (n¼51) .17 0.34 .05 0.18 .06 0.19 .17 0.34 .02 0.18 .03 0.19
AX (n¼50) -.31 1.13 .08 0.21 -.37 5.83 -.29 1.36 -.22 0.52 -.60 995.4
AY (n¼50) -.41 4.88 -.09 0.21 -.19 0.43 -.18 0.37 -.06 0.20 -.49 39.0
BX (n¼50) -.56 128 -.07 0.20 -.29 1.41 -.31 1.80 -.09 0.22 -.51 61.9
BY (n¼50) -.36 2.48 -.03 0.18 -.32 2.25 -.20 0.45 -.17 0.35 -.47 26.0
AX E (n¼50) -.42 6.59 -.12 0.25 -.37 6.70 -.31 2.18 -.61 >1000 -.20 0.44
Math P — —
Additive situation .61 871 — —
Text-based .83 >1000 .21 0.56 — —
Geometric support .90 >1000 .42 18.3 .68 >1000 — —
BANUCA .72 >1000 .35 3.20 .70 >1000 .64 >1000 — —
AMR .63 >1000 .10 0.23 .59 >1000 .42 10.5 .32 1.50 — —
Numbers in bold signify a Bayes factor (BF
10
) over 3. >1000 signies a BF
10
over 1000; PBI, proactive behavioral index; DSC, Digit Symbol Coding; SS, Symbol Search;
AMR, Additive and multiplicative reasoning; BANUCA, Basic numeracy and calculations; TVPS-III, Test of Visual Perceptual Skill-III.
Fig. 3. Scatter plot for average math performance. A) PBI (proactive behavioral index), B) d’ context, and C) response time for BX trials.
S. Skau et al.
Trends in Neuroscience and Education 28 (2022) 100180
7
based situation, with an average Cohen’s d of 0.9840 ranging from 0.811
to 1.185. The four channels in DMPFC (around Fz) had an average
Cohen’s d of 0.693, ranging from 0.598 to 0.849. A channel in the DLPFC
with BF₁₀ =137 and Cohen’s d of 0.745, and two channels in the left
LPPC with BF₁₀ =39.82 and Cohen’s d of 0.781, BF₁₀ =13.61 and
Cohen’s d of 0.662.
When comparing the text-based with geometric support, one channel
showed evidence for a difference in the anterior DMPFC with a BF₁₀ =
3.696 and Cohen’s d of 0.411.
4. Discussion
The present study had three aims 1) to investigate whether the ten-
dency to engage in proactive cognitive control is more associated with
mathematical performance than processing speed, sustained attention
and pattern recognition; 2) to investigate the functional activity of
proactive control in the frontal and parietal cortex; 3) to explore the
functional difference in the frontal or parietal cortex during arithmetic
tasks, a text-based mathematical task and a mathematical task with
geometric support in 8 and 9-year-old children.
4.1. Proactive cognitive control
Cognitive control has been a reliable predictor of mathematical
performance and development of mathematical cognition [4]. The most
consistent predictor has been visual spatial working memory [48], fol-
lowed by other cognitive domains such as inhibition, cognitive exi-
bility and processing speed [4]. The ability to engage in proactive
control is dependent on the developmental trajectory as well as the in-
dividuals’ working memory capacity and uid intelligence [8,49]. Since
the default design of most cognitive control tasks emphasizes a reactive
mode or strategy [5,6], few studies of cognitive control have focused on
the ability to engage in proactive control. In a recent study, Kubota et al.
observed that proactive ability, as measured by the d’ context index,
made a unique contribution in predicting mathematical performance
over working memory, inhibition and cognitive exibility [10]. Our
result corroborates this nding, with very strong evidence for a relation
between d’ context and mathematical performance indicating a relation
between a child’s ability to focus on the cue (A or B) in the AX-CPT and
mathematical performance. There was no substantial association be-
tween PBI and mathematical performance, contrary to the ndings of
Wang et al. [11] which found that PBI explained additional variance in
mathematical performance beyond the effect of working memory.
However, in our sample there was an association between response
time on the BX trials, processing speed during a situation benetting
from proactive control, and mathematical performance. Based on the
spread of the PBI, only a handful of children had a positive value on the
PBI i.e., tendency to be more proactive, meaning that the children could
rather be viewed as engaging in a reactive mode. If two children engage
in a reactive mode and are presented with an image of a cat (in the BX
trial), the child that is faster in recalling the previous image (not a dog),
will have a faster response time on BX than a child that is slower in
recalling the previous image. That type of “quickness of short-term
Table 3
Correlation for oxy-Hb in all ROIs with PBI and d’ context.
PBI d’ context
AY BX AY BX
r BF₁₀ r BF₁₀ r BF₁₀ r BF₁₀
Left DLPFC
(n¼44)
.20 0.44 -.01 0.18 -.22 0.53 -.49 56.85
DMPFC (n¼41) .16 0.32 .01 0.19 -.13 0.27 -.41 6.11
Right DLPFC
(n¼44)
.08 0.21 -.04 0.19 -.29 1.14 -.07 0.21
Left aDLPFC
(n¼48)
-.05 0.19 -.10 0.23 -.16 0.33 -.11 0.24
aDMPFC
(n¼48)
.09 0.21 -.07 0.20 .06 0.19 -.06 0.19
Right aDLPFC
(n¼48)
-.02 0.18 .01 0.18 -.18 0.39 -.10 0.23
Left LPPC
(n¼34)
.06 0.22 -.19 0.37 .00 0.21 .11 0.25
Left MPPC
(n¼31)
.13 0.28 -.29 0.76 -.08 0.24 .01 0.22
Left LPC (n¼38) .06 0.21 -.18 0.36 -.16 0.33 -.16 0.33
Left MPC
(n¼33)
.01 0.21 -.03 0.22 -.09 0.24 -.19 0.37
Right MPPC
(n¼40)
-.05 0.20 -.15 0.30 .17 0.35 .05 0.20
Right LPPC
(n¼31)
.49 9.49 -.19 0.37 .16 0.33 -.21 0.42
Right MPC
(n¼40)
.17 0.34 -.08 0.22 .05 0.20 -.07 0.22
Right LPC
(n¼37)
.18 0.35 -.04 0.21 .07 0.22 -.09 0.23
Numbers in bold signify a Bayes factor (BF10) over 3; PBI, proactive behavioral
index; LPPC, lateral posterior parietal cortex; MPPC, medial posterior parietal
cortex; LPC, lateral parietal cortex; MPC, medial parietal cortex; DLPFC,
dorsolateral prefrontal cortex, DMPFC, dorsomedial prefrontal cortex; aDLPFC,
anterior dorsolateral prefrontal cortex, aDMPFC, anterior dorsomedial pre-
frontal cortex
Fig. 4. Scatter plot peak oxy-Hb and proactive control indices. A) x-axis is proactive behavioral index (PBI) and data points are peak oxy-Hb during AY trials in right
posterior partial cortex. B) x-axis is d’ context and data points are peak oxy-Hb during BX trials in left dorsolateral prefrontal cortex.
S. Skau et al.
Trends in Neuroscience and Education 28 (2022) 100180
8
memory access” or processing speed in recalling rules and recently
presented relevant information, even in a reactive mode, could be
benecial when facing a new mathematical problem. Consider a typical
task like “Nilla has 6 owers and Nicke has 5 owers, how many do they
have together?” It is not until the second part of the sentence that the
instruction for how to deal with the numbers is given. The second part of
the question could have been “…how many more owers does Nilla
have?” which would have triggered another mathematical operation.
When listening to, or reading the task, the child must wait until the end
to receive information on how to deal with the numerical information
presented earlier. It is possible that if the process of retrieving the pre-
vious information is too slow, then the child forgets or mixes up which
operation to carry out. This may explain why BX compared to the other
trial types (AX, AY and BY) has a strong association with math perfor-
mance, which needs to be investigated in future studies.
When interpreting behavioral results, the relationship between
response time (efciency) and accuracy (effectiveness) should be
considered [50]. There is usually a trade-off relationship, i.e., a fast
response time leads to lower accuracy or high accuracy leads to slower
response time. However, in this sample, there was a positive association
between response time and accuracy, violating this trade-off principle
(Supplementary Table 4). Not only did the more reactive children
respond slower on proactive trials, but they also made more errors. As
shown in the method section, the d’ context is based on the accuracy
score of AX and BX trials, whereas the PBI is based on the response time
on AY and BX trials. To see if the complementary information in both
response time and accuracy could be combined, we performed a sec-
ondary analysis where we used the LISAS adjustments to the response
time [31,51]. However, the LISAS-adjusted PBI did not correlate more
with average mathematic performance and the adjusted BX response
time had an even lower association with mathematical performance.
There are many possible explanations for why the adjusted BX and
adjusted PBI did not co-vary to the same extent as the d’ context with
mathematical performance. For example, only the more reactive chil-
dren potentially disrupted the trade-off relationship for BX trials and not
the more proactive children, which means that an adjustment would
penalize the children with slower reaction time on BX trials, making the
difference greater and less nuanced as hoped. Further investigation is
required to determine whether this is a general feature of development
or whether response time adjustments are not suitable for reactive and
proactive testing. One reason for the d’ context with mathematical per-
formance might also be that the d’ context variable taps into an aspect of
proactivity that simply is particularly useful when dealing with the type
of mathematical tasks that are so popular in mathematics tests. In the
example with Nicke and Nilla above, it would obviously be advanta-
geous to already plan ahead after seeing the rst numerical items and
prepare to process information about the mathematical operation e.g.,
addition, subtraction (or something else).
4.2. Functional imaging
The PBI scores, which indicate proactive or reactive tendencies in
behavior, are based on reaction times and our results suggest that the
less reactive (i.e., more proactive) children tend to be, the more they use
the right LPPC in reactive situations. This is in accordance with other
imaging studies with children [7,13–15]. We can conrm the usefulness
of fNIRS for studying the neural correlates of cognitive control in chil-
dren. The analysis of d´context, which is based on response accuracy,
indicates that the less a child utilizes contextual cues to solve upcoming
tasks, the more the left DLPFC is activated during BX trials. The intuition
behind the d’ context index is that, if participants have been observant of
the cues (A or B) then they should have similar accuracy score on the AX
and the BX trials. However, if participants did not pay attention to the
cues, then there should be a difference in accuracy for AX and BX trials.
These assumptions correspond well with our data, where children with
lower d´context score appear to have, on their successful BX trials, higher
Fig. 5. Peak oxy-Hb during mathematical tests. The upper row shows channel layout, from the transverse view, with paired t-value difference between additive
reasoning with geometric support (AR-G) vs additive situations (AS) (left), additive reasoning text-based (AR-T) vs. AS (middle) and AR-T vs AR-G (right). Lower row
shows average oxy-Hb curve for all channels during AS on the left, during AR-G in the middle and AR-T on the right. Black dots indicate 10/20 landmarks. White
marks are short separation channels.
S. Skau et al.
Trends in Neuroscience and Education 28 (2022) 100180
9
activity in the left DLPFC, possibly due to the added cognitive load of
remembering what the previous cue was.
4.3. Mathematical reasoning
For the third aim, both the text-based task and tasks with geometric
support evoked a larger increase of oxy-Hb in the anterior PFC and the
left parietal cortex than during the additive situations task (Fig. 5).
There was one channel, located over DMPFC, showing a substantially
larger increase in oxy-Hb for additive reasoning text-based compared to
additive reasoning with geometric support. Also, other channels in the left
latera parietal cortex and PFC showed a larger difference but were not
sufcient to reach substantial evidence (see Supplementary Table 3).
These results are in line with other fNIRS studies that found evidence
of an increase in oxy-Hb concentration in the parietal cortex for text-
embedded mathematical questions compared to numerical calcula-
tions for 9- and 10-year-olds [52,53]. Similar ndings were described in
adults [54]; although, none of the studies measured oxy-Hb in the PFC.
Overall, these results show promise for studying the difference between
different mathematical tasks with fNIRS. However, a recent review of
fNIRS and mathematical cognition in children (age 9 to 16 year of age)
found only six studies using fNIRS with some having a low number of
participants (n=8 and n=14) [17].
Literature on arithmetical development supports the participation of
a larger network involving PFC, PPC (including angular gyrus, inferior
parietal sulcus and precuneus), along with deeper brains structures not
detectable with fNIRS [16, 55]. With increased prociency and less
reliance on cognitive control, the involvement of PFC decreases and PPC
increases [55]. In order to reduce differences in the cognitive load be-
tween the mathematical tasks, all questions were read aloud twice to the
children [56]. However, several differences remain. The additive situ-
ation test involved answering by pressing a button while the additive
reasoning with geometric support and additive reasoning text-based required
written answers. Moreover, children had to solve the tasks in additive
reasoning with geometric support and text-based test, while for the additive
situation test, children were presented with alternatives, imposing
different cognitive loads. Based purely on the fNIRS data, a possible
interpretation is that even though children in second grade have learned
how to read, text-based information in a mathematical task adds to the
cognitive load. The potential answer options in additive situations and
the geometric information on the geometric support task could function
similar to gestures, which have been shown to reduce cognitive load
during mathematical tasks for 9-year-olds [57]. Additionally, according
to the gateway hypothesis [58], the rostral PFC/frontal polar area,
which in our studies showed increased activity during additive reasoning
text-based compared to additive reasoning with geometric support, is
involved when shifting from attending to external information to
attending to internal representations, as part of increased metacognitive
demand.
However, the cognitive load interpretation does not align with the
behavioral data, where error rates of additive situations and additive
reasoning with geometric support were close to equivalent, but still higher
compared to additive reasoning text based. Error rate is usually an indi-
cator for the difculty level of a task and higher difculty might suggest
that more cognitive resources are involved to solve the tasks. More
likely, in line with fMRI studies on children, the additive situations did
not induce any calculation, but instead induced an answer based on a
sense of familiarity. Studies using fMRI have found that medial frontal
cortex and right parietal cortex, especially, inferior parietal sulcus, show
increased functional activity during calculation [16], which was not
present in the additive situations test. Our analysis did not detect any
difference for additive reasoning with geometric support and text-based
compared to additive situations in the right PPC, however such a differ-
ence was detected in the medial prefrontal cortex and left PPC, involving
the left inferior parietal sulcus. It is typical for the performance on
different mathematical tests at this age to correlate relatively highly
with each other as well as with cognitive tests [59]. However, it is worth
recognizing that the test performance for additive situations only corre-
lated with additive reasoning with geometric support and possibly with
BANUCA (see Table 2), but not with any other mathematical or cogni-
tive test leading us to the abductive conclusion that the task is not as
rmly associated with general cognitive level or general mathematical
performance as the other tests.
5. Limitations
For some brain areas, especially for the parietal cortex, there was a
relatively high loss of data due to a higher incidence of signal drop-out
and the removal of very weak signals in the preprocessing stage. The
source of the weaker signal was usually the absorption of light by hair
between the optodes and the scalp. Dense and thick hair, especially at
the top of the head, made it more challenging to gain a sufcient signal
for estimation of the hemodynamic response. Our experimental design
allowed for a few min per child to optimize the fNIRS signal, which
resulted in some loss of data.
During the fNIRS mathematical tests (additive situation, additive
reasoning with geometric support and additive reasoning text-based)
response time was not saved, which would have been valuable infor-
mation to evaluate both the hemodynamic response and how difcult
the children perceived the test to be. Since the individual test session and
the whole class sessions were not performed during the same week, for
some children we lack data on the whole class test.
Based on the function for partial pathlength factor from [60], rec-
ommended values for this age group and wavelength would be [5.6 4.6]
instead of [6.0 6.0] which were used in this study. However, since the
group is homogenous with respect to age (SD of 3.9 month and age range
of 15 months), the within group comparison should not be affected.
Due to the time constraint, digitizing the placement of the fNIRS
optodes was not done. We cannot control for variability of the placement
of the channels. This variability is not a concern for the ROI analysis,
where several channels are pooled together, but is a possible concern for
the single channel comparison. However, head size measurements were
taken before the experiment and cap sizes 50, 52, 54 or 56 were used to
t the child’s head as accurately as possible using face and head land-
marks in order to get measurements where intended.
6. Conclusion
In the present exploratory study we were able to corroborate previ-
ous studies, where the ability to engage in proactive control co-varies
with mathematical performance better than other cognitive abilities,
such as processing speed, sustained attention, and pattern recognition.
With fNIRS, we could also conceptually replicate previous studies using
other imaging modalities, showing that more proactive children have an
increased activity in posterior parietal cortex during reactive situations.
For the mathematical part we found that children tended to activate the
prefrontal cortex more during text-based mathematical tasks compared
to tasks that also had a visual geometric support. Although the fNIRS
result is in line with the hypothesis that text-based tasks involve a higher
cognitive load, the behavioral result did not support this interpretation.
Future studies are needed to evaluate whether geometrical support re-
duces the cognitive load during mathematical tasks.
Ethics
The study was approved by the Regional Ethical Review Board in
Gothenburg (reference number: 839-17).
The parents gave their written informed consent before their chil-
dren took part in the study, and the participants were told that they
could withdraw at any time.
All data were anonymous.
S. Skau et al.
Trends in Neuroscience and Education 28 (2022) 100180
10
Funding
The study was funded by grants from the Swedish Research Council
(Vetenskapsrådet 712-2014-2468, VR-MH 2019-01637) and the STENA
Foundation for Culture and Health.
Declaration of Competing Interest
The authors declare that they have no known competing nancial
interests or personal relationships that could have appeared to inuence
the work reported in this paper.
Supplementary materials
Supplementary material associated with this article can be found, in
the online version, at doi:10.1016/j.tine.2022.100180.
References
[1] D. Szucs, et al., Developmental dyscalculia is related to visuo-spatial memory and
inhibition impairment, Cortex 49 (10) (2013) 2674–2688.
[2] K. Landerl, A. Bevan, B. Butterworth, Developmental dyscalculia and basic
numerical capacities: a study of 8–9-year-old students, Cognition 93 (2) (2004)
99–125.
[3] D.C. Geary, et al., Mathematical Cognition decits in children with learning
disabilities and persistent low achievement: a ve-year prospective study, J. Educ.
Psychol. 104 (1) (2012) 206–223.
[4] H.L. St Clair-Thompson, S.E. Gathercole, Executive functions and achievements in
school: shifting, updating, inhibition, and working memory, Q. J. Exp. Psychol. 59
(4) (2006) 745–759.
[5] A.R. Aron, From reactive to proactive and selective control: developing a richer
model for stopping inappropriate responses, Biol. Psychiatry 69 (12) (2011)
e55–e68.
[6] T.S. Braver, The variable nature of cognitive control: a dual mechanisms
framework, Trends Cogn. Sci. 16 (2) (2012) 106–113.
[7] N. Chevalier, et al., Metacognitive processes in executive control development: the
case of reactive and proactive control, J. Cogn. Neurosci. 27 (6) (2015) 1125–1136.
[8] P.W. Van Gerven, et al., Switch hands! Mapping proactive and reactive cognitive
control across the life span, Dev. Psychol. 52 (6) (2016) 960–971.
[9] N.R. Polizzotto, et al., Normal development of context processing using the AXCPT
paradigm, PLoS One 13 (5) (2018), e0197812.
[10] M. Kubota, et al., Consistent use of proactive control and relation with academic
achievement in childhood, Cognition (2020) 203.
[11] C. Wang, B. Li, Y. Yao, Proactive control mediates the relationship between
working memory and math ability in early childhood, Front. Psychol. (1612)
(2021) 12.
[12] G. Gavazzi, et al., Contiguity of proactive and reactive inhibitory brain areas: a
cognitive model based on ALE meta-analyses, Brain Imaging Behav. (2020).
[13] K. Kamijo, H. Masaki, Fitness and ERP indices of cognitive control mode during
task preparation in preadolescent children, Front. Hum. Neurosci. 10 (2016) 441.
[14] N.M. Strang, S.D. Pollak, Developmental continuity in reward-related
enhancement of cognitive control, Dev. Cognitive Neurosci. 10 (2014) 34–43.
[15] S.V. Troller-Renfree, G.A. Buzzell, N.A. Fox, Changes in working memory inuence
the transition from reactive to proactive cognitive control during childhood, Dev.
Sci. 23 (6) (2020) p. n/a-n/a.
[16] M. Arsalidou, et al., Brain areas associated with numbers and calculations in
children: Meta-analyses of fMRI studies, Dev. Cogn. Neurosci. 30 (2018) 239–250.
[17] M. Soltanlou, et al., Applications of Functional Near-Infrared Spectroscopy (fNIRS)
in studying cognitive development: the case of mathematics and language, Front.
Psychol. 9 (2018) 277.
[18] D. Ansari, Neurocognitive approaches to developmental disorders of numerical and
mathematical cognition: the perils of neglecting the role of development, Learn.
Individ. Differ. 20 (2) (2010) 123–129.
[19] V. Quaresima, S. Bisconti, M. Ferrari, A brief review on the use of functional near-
infrared spectroscopy (fNIRS) for language imaging studies in human newborns
and adults, Brain Lang. 121 (2) (2012) 79–89.
[20] S. Rossi, et al., Shedding light on words and sentences: near-infrared spectroscopy
in language research, Brain Lang. 121 (2) (2012) 152–163.
[21] Y. Moriguchi, K. Hiraki, Prefrontal cortex and executive function in young
children: a review of NIRS studies, Front. Hum. Neurosci. 7 (DEC) (2013).
[22] S.G. Ryman, et al., Proactive and reactive cognitive control rely on exible use of
the ventrolateral prefrontal cortex, Hum. Brain Mapp. 40 (3) (2019) 955–966.
[23] C. Gonthier, et al., Inducing proactive control shifts in the AX-CPT, Front. Psychol.
7 (2016) 1822.
[24] T.S. Braver, et al., Flexible neural mechanisms of cognitive control within human
prefrontal cortex, Proc. Natl. Acad. Sci. 106 (18) (2009) 7351.
[25] R.L. Peterson, et al., Cognitive prediction of reading, math, and attention: shared
and unique inuences, J. Learn. Disabil. 50 (4) (2017) 408–421.
[26] J. Cui, et al., Visual form perception can be a cognitive correlate of lower level
math categories for teenagers, Front. Psychol. 8 (2017) 1336.
[27] D. Wechsler, Wechsler Adut Intelligence Scale - Fourth Edition, swedish edition,
Pearson Assessment, Stockholm, 2010.
[28] D. Wechsler, Wechsler Intelligence Scale For Children - Fourth Edition, swedish
edition, Pearson Assessment, Stockholm, 2003.
[29] S. Skau, et al., Different properties of the hemodynamic response and its relation to
trait mental fatigue and proactive cognitive control, Neuroimage: Rep. 1 (3)
(2021), 100038.
[30] C.H. Chatham, M.J. Frank, Y. Munakata, Pupillometric and behavioral markers of a
developmental shift in the temporal dynamics of cognitive control, in: Proceedings
of the National Academy of Sciences of the United States of America 106, 2009,
pp. 5529–5533.
[31] A. Vandierendonck, A comparison of methods to combine speed and accuracy
measures of performance: a rejoinder on the binning procedure, Behav. Res.
Methods 49 (2) (2017) 653–673.
[32] T.P. Carpenter, J.M. Moser, T.A. Romberg, Addition and Subtraction: A Cognitive
Perspective, L. Erlbaum Associates, Hillsdale, N.J., 1982.
[33] R¨
as¨
anen, P., BANUCA: Basic Numerical and Calculation abilities =Lukuk¨
asitteen
ja Laskutaidon Hallinnan Testi, ed. P. R¨
as¨
anen. 2005, Jyv¨
askyl¨
a: Niilo M¨
aki
Instituutti (NMI).
[34] T. Nunes, et al., The scheme of correspondence and its role in children’s
mathematics, Br. J. Educ. Psychol. 2 (7) (2010) 83–99.
[35] N.A. Martin, TVPS-3: Test of Visual Perceptual Skills, Academic Therapy
Publications, Novato, CA, 2006.
[36] U. Wolff, Lilla DUVAN: Dyslexiscreening f¨
or Årskurs 3, 5 Och 7, Hogrefe
Psykologif¨
orlaget Stockholm, 2010.
[37] N.L. Everdell, et al., A frequency multiplexed near-infrared topography system for
imaging functional activation in the brain, Rev. Sci. Instrum. 76 (9) (2005).
[38] L. Gagnon, et al., Improved recovery of the hemodynamic response in diffuse
optical imaging using short optode separations and state-space modeling,
Neuroimage 56 (3) (2011) 1362–1371.
[39] S. Brigadoi, R.J. Cooper, How short is short? Optimum source-detector distance for
short-separation channels in functional near-infrared spectroscopy,
Neurophotonics 2 (2) (2015), 025005.
[40] MATLAB, The MathWorks, Inc, Massachusetts, United States, 2014.
[41] T.J. Huppert, et al., HomER: a review of time-series analysis methods for near-
infrared spectroscopy of the brain, Appl. Opt. 48 (10) (2009) D280–D298.
[42] J.C. Ye, et al., NIRS-SPM: statistical parametric mapping for near-infrared
spectroscopy, Neuroimage 44 (2) (2009) 428–447.
[43] H. Sato, et al., A NIRS-fMRI investigation of prefrontal cortex activity during a
working memory task, Neuroimage 83 (2013) 158–173.
[44] K. Uludag, et al., Separability and cross talk: optimizing dual wavelength
combinations for near-infrared spectroscopy of the adult head, Neuroimage 22 (2)
(2004) 583–589.
[45] M. Marsman, E.-J. Wagenmakers, Bayesian benets with JASP, Eur. J. Dev.
Psychol. 14 (5) (2017) 545–555.
[46] M. Jeon, P. De Boeck, Decision qualities of Bayes factor and p value-based
hypothesis testing, Psychol. Methods 22 (2) (2017) 340–360.
[47] E.J. Wagenmakers, et al., Why psychologists must change the way they analyze
their data: the case of psi: comment on Bem (2011), J. Pers. Soc. Psychol. 100 (3)
(2011) 426–432.
[48] K. Allen, S. Higgins, J. Adams, The relationship between visuospatial working
memory and mathematical performance in school-aged children: a systematic
review, Educ. Psychol. Rev. 31 (3) (2019) 509–531.
[49] L.L. Richmond, T.S. Redick, T.S. Braver, Remembering to prepare: the benets (and
costs) of high working memory capacity, J. Exp. Psychol. Learn. Mem. Cogn. 41 (6)
(2015) 1764–1777.
[50] M.W. Eysenck, et al., Anxiety and cognitive performance: attentional control
theory, Emotion 7 (2) (2007) 336–353.
[51] A. Vandierendonck, Further tests of the utility of integrated speed-accuracy
measures in task switching, J. Cogn. 1 (1) (2018) 8.
[52] A. Obersteiner, et al., Bringing brain imaging to the school to assess arithmetic
problem solving: chances and limitations in combining educational and
neuroscientic research, ZDM 42 (6) (2010) 541–554.
[53] T. Dresler, et al., Arithmetic tasks in different formats and their inuence on
behavior and brain oxygenation as assessed with near-infrared spectroscopy
(NIRS): a study involving primary and secondary school children, J. Neural.
Transm. 116 (12) (2009) 1689–1700.
[54] M. Richter, et al., Changes in cortical blood oxygenation during arithmetical tasks
measured by near-infrared spectroscopy, J. Neural Transm. 116 (3) (2009)
267–273.
[55] L. Peters, B. De Smedt, Arithmetic in the developing brain: A review of brain
imaging studies, Dev. Cognitive Neurosci. 30 (2018) 265–279.
[56] S. Gillmor, J. Poggio, S. Embretson, Effects of reducing the cognitive load of
mathematics test items on student performance, Numeracy 8 (1) (2015).
[57] S. Goldin-Meadow, et al., Explaining math: gesturing lightens the load, Psychol.
Sci. 12 (6) (2001) 516–522.
[58] P.W. Burgess, I. Dumontheil, S.J. Gilbert, The gateway hypothesis of rostral
prefrontal cortex (area 10) function, Trends Cogn. Sci. 11 (7) (2007) 290–298.
[59] L.S. Fuchs, et al., The cognitive correlates of third-grade skill in arithmetic,
algorithmic computation, and arithmetic word problems, J. Educ. Psychol. 98 (1)
(2006) 29–43.
[60] F. Scholkmann, M. Wolf, General equation for the differential pathlength factor of
the frontal human head depending on wavelength and age, J. Biomed. Opt. 18 (10)
(2013), 105004.
S. Skau et al.
