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Br J Dev Psychol . 2022;40:438–452 .
wileyon linel ibrary.com/journ al/bjdp
Receive d: 8 July 2021

Accepted : 25 March 2022
DOI: 10.1111/bjdp .1241 2
ARTICLE
Executive functions, math anxiety and math
performance in middle school students
MarijaŽivković1  Sandra Pellizzoni1  Irene Cristina Mammarella2 
Maria Chiara Passolunghi1
This is an open access article u nder the t erms of the Creative Commons Attribution NonCom mercial NoDerivs License, wh ich permits use
and distribut ion in any mediu m, provided the or iginal work is properly cited, t he use is non commercia l and no mod ific ations or a daptat ions
are made.
© 2022 T he Authors. Brit ish Journal of Developmental Psycholog y published by John W iley & Sons Ltd on beh alf of British Psychologic al Society.
1Depar tment of L ife Scie nces, Ga etano K anizsa
Psycholog y Unit, Un iversity of Trieste , Trieste,
Italy
2Department of Development and Social
Psycholog y, Univers ity of Padova , Padova, Italy
Correspondence
Sandra Pell izzon i, Depa rtment of Life Sc ience,
Gaetano Kanizsa Psychology Unit, Un iversit y of
Trie ste, Trie ste, Ita ly.
Email: spell izzoni@units.it
Abstract
Previous studies mainly investigated working memory
(WM) and math anxiety (M A) leaving almost unexplored
other aspects of executive functions (EFs) in middle school
period. Filling the gap in the literature, the aims of this
study were: (1) to better examine the relationship between
MA and math performance, (2) to better examine the re
lationship between EFs and math performance and (3) to
investigate the interplay between EFs and MA on math per
formances. This study confirmed a significant and negative
relationship between MA and math performance, indicates
a significant and positive relationship between visuospatial
WM and math performance, shifting and math performance
and highlight a scarcely investigated indirect inf luence of
MA through the measure of shifting on math performance.
Our findings shed further light on the mediating role of
EFs between M A and math performance and underline
some future perspectives.
KE YWOR DS
executive functions, math anxiety, math performance, middle school
students
[Correction added on 13 May 2022, after first online publicat ion: CRUICA RE fundi ng state ment has been added.]

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BACKGROUND
Given the relevance of math skills at both individual and social levels, knowing which factors are cru
cial to mathematical acquisition and possibly understanding how they interact, is a salient topic for our
society. The literature indicated that domain general precursors like intelligence (Giofrè et al., 2 014),
executive functions (EFs) (Passolunghi & Siegel, 2001, 2004) and emotional factors (Ashcraft & Kirk,
2001) modulate math achievement. For decades, cognitive factors were studied separately from emo
tional factors. In the last 20 years, researchers have tried to propose a convergent model of the complex
interplay between cognitive and emotional factors behind math acquisition (Ashcraft & Kirk, 2001;
Ramirez et al., 2013). These studies have mainly investigated working memory (WM) and maths anxiety
(MA), but leaving almost unexplored other aspects of EFs such as inhibition and shifting.
Furthermore, studies extensively assessed primary school children (Mammarella et al., 2015), sec
ondary school students (Passolunghi et al., 2 016 ) or adults (Ashcraft & Kirk, 2001), while middle school
students are understudied (but see Trezise & Reeve, 2014, for exceptions). Studies showed a decline in
motivation and performance for many students as they move from primary to the middle school en
vironment (Midgley et al., 1989), and the literature showed that the academic developmental needs of
middle school students are different from those of elementary and high school students (Eccles et al.,
1993). The middle school period is a period of changes when teachers have higher expectations and a
grading system with more pressure on performance, the period when students need to invest more time
in studying (Midgley et al., 1995). Various changes bring difficulties for students, and unsurprisingly
students in this period showed less motivation (Lepper et al., 2005), a decline in grades ( Blackwell et al.,
2007) and an increase in negative attitudes towards school (Anderman & Midgley, 1998).
To fill this gap, the aims of our study are (1) to better examine the relationship between MA and
math performance, (2) to better examine the relationship between EFs and math performance and (3)
to investigate the interplay between EFs (VWM, VSWM, inhibition and shifting) and MA on math
performance in the middle school students.
Executive functions and mathematics achievement
Diamond (2013) described EFs as: ‘skills essential for mental and physical health; success in school and
life; and cognitive, social, and psychological development’. Diamond (2013) agreed that three compo
nents of EFs exist: WM and inhibitory control distinguishing them from cognitive flexibility (the third),
which ‘builds on the other two and comes in much later in development’.
The study demonstrated the i mportance of EFs to the development of mathematical skills and showed
that children with poor EFs could experience difficulties in various areas of mathematics (Viterbori
et al., 2 017 ). Further evidence demonstrates relations among EF skills and achievement through late
childhood and early adolescence (e.g. St Clair Thompson & Gathercole, 2006). Usai et al. (2018) longi
tudinally investigated EF profiles in 5 year old children and their later math achievement. They showed
that children with weak WM shifting profiles (performed equally with typical EF profile groups in
arithmetic and math problems tasks in Grade 1) showed difficulties as a group of children with a general
deficit in EFs in Grade 3. Viterbori et al. (2015) longitudinally analysed whether EF measured during
preschool predicts math achievement in primary school. The results showed that the WM flexibility
component measured in the preschool period predicts math achievement in Grade 3. WM flexibility
predicted math scores at Grade 1 and Grade 3. The WM flexibility component in Grade 3 predicted
problem solving and arithmetical facts. The study of Orbach et al. (2020) showed the negative influence
of state MA on math performance through core EFs (inhibition, cognitive flexibility, WM capacity, a
global measure of core EFs) in the sample of fourth and fifth grade students.
Considering the impact of different EF components on math achievement, WM extensively studied
mathematical achievement and abilities, revealing its involvement in performing arithmetical opera
tions, especially in the mental calculation (Passolunghi & Siegel, 2001, 2004). Various studies found that
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children who performed poorly in WM tasks did not reach the expected levels of math performance
(Gathercole & Pickering, 2000; Geary et al., 2004; Passolunghi & Mammarella, 2010, 2012). The study
of Trezise and Reeve (2014 ) with 14 year old girls showed an association between high worry, low WM
and poor algebra results, also between low worry, high WM and high results on algebra tasks but with
out the impact of high worry with moderate WM. The previous literature showed the inf luence of ver
bal WM (V WM) and visuospatial WM (VSWM) on math performance in different ages. According to
some researchers, VWM has a more significant role in math achievement than VSWM (Friso Van den
Bos et al., 2013). On the other hand, a comprehensive study with a large sample of typical 9 year olds
with extensive battery measures showed the predictive role of VSWM, but not VWM on mathematical
achievement (Szűcs et al., 2013). The study by Giofrè et al. (2018) on middle school students (in sixth to
eighth grades) confirmed that VSWM predicts math performance and VW M predicts reading abilities.
The different role of WM components on math achievement is explained not only by the different tasks
used to measure math abilities (De Smedt et al., 2009), but also with the differences in the age of the
participants (Cragg et al., 2017 ). Given the crucial role of WM in the learning process, it is essential to
investigate the architecture of this function in more detail, especially as regards the complex interplay
with other EFs.
While WM is extensively studied, other EF components such as inhibition and shifting have
been much less investigated or indicate contradictory results (Blair & Razza, 2007; Yeniad et al.,
2013). The relationship between inhibition and mathematical performance in preschool and school
children has emerged in various studies (Usai et al., 2018). Bull and Scerif (2001) reported that the
main difficulty for primary school children lies in inhibiting a strategy already learned and switch
ing to a new one. St Clair Thompson and Gathercole (2006) partially confirmed the existence of
several differences between EFs finding an important role of WM in English and math and the
important role of inhibition in English, math and science. Their study did not show results related
to the shifting process in middle school students. On the other hand, Cragg et al. (2017 ) investi
gated the role of EFs in factual knowledge, procedural skills, conceptual understanding and overall
math achievement in a sample with the age range between 8 and 25 years. They found a significant
relationship between VWM, VSWM and overall math achievement, but did not find a significant
relationship between inhibition, shifting and overall math achievement. The explanation for their
results found in the evidence that inhibition and shifting account for less variance in math perfor
mance (Friso van den Bos et al., 2013), but suggested that inhibition and shifting can contribute a
unique variance to math achievement when they are studied independently from measures of WM
(Lee & Bull, 2016).
Statement of contribution
What is already known on this subject
1. Previous studies have mainly investigated working memory and math anxiety, but leaving
almost unexplored other aspects of executive functions.
2. Negative inf luence of math anxiety on math performance in young children and adults.
What the present study adds
1. Better examination of relation between math anxiety and math performance in middle
school students.
2. Better examination of relation between executive functions and math performance in middle
school students.
3. The interplay between executive functions (working memory, inhibition and shifting) and
math anxiety on math performances.

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As a third aspect in the Diamond model, the shifting component seems to be relevant in math per
formance. Cragg and Nation (2009) conducted two experiments with children in different age groups
and showed that younger children (5 – 8 years old) had greater difficulty inhibiting unrelated informa
tion than older children (9– 11 years old). A meta analysis conducted by Yeniad et al. (2013) highlighted
the predictive role of shifting in performance in mathematics and reading across developmental ages.
They showed an association between shifting and math performance and found that children with a
greater capacity for shifting achieved better results in mathematics. They also provided a precise struc
ture for classifying shifting tasks by the level of complexity. The previously mentioned meta analysis
also showed the variety of tasks used to measure shifting and the different scoring methods involved
(reaction time, accuracy, efficiency or combined scores). The shifting role was implicit in some studies
and explicit in others.
Previous studies showed contradictory results, a paucity of studies on middle school students and
needs for more developmentally sensitive measures, especially for shifting. Heterogeneity in the shift
ing tasks causes heterogeneity in the results obtained in previous studies because different shifting
tasks used different dependent variables (Yeniad et al., 2013). On the other hand, the predictability of
WM measures across development makes these measures more stable compared with the measures for
shifting (Ahmed et al., 2019). However, to the best of our knowledge, no studies have yet examined
the mediating role of different EFs (VWM, VSWM, inhibition and shifting) in a sample of middle
school students, leaving the influence of EFs on math achievement in this developmental period almost
unexplored.
Mathematics anxiety and math performance
Cognitive aspects shape math performance, but an emotional component could also have a specific role
in math performance ( Mammarella et al., 2019). Ashcraft (2002) defined MA as ‘a feeling of tension,
apprehension, or fear that interferes with math performance’ and showed that individuals with more
severe MA avoid situations in which they need to perform mathematical tasks. Such avoidant behaviour
can give rise to less competence, exposure and practice, leaving students more anxious and mathemati
cally less well prepared. Studies have shown a negative correlation between math achievement and MA
(Ashcraft, 2002) and a lower quality of math learning in individuals experiencing MA (Dowker et al.,
2016). Feeling anxious about math related situations is a pretty stable phenomenon already in second
grade by the end of secondary school. Ma and Xu (2004) examined the development of anxiety about
math related situations from seventh to twelfth grades. They found that MA remained relatively stable
from Grade 8 onwards (1 year stability coefficients were slightly below 0.60).
Six meta analyses have examined the relationship between MA and maths performance (Barroso
et al., 2020; Caviola et al., 2021; Hembree, 1990; Ma, 1999; Namkung et al., 2019; Zhang et al., 2019) and
confirmed a negative inf luence of MA on math performance. The fundamental aspect that came to light
was that cognitive and emotional problems underlying math difficulties could be mainly considered
dissociable (Devine et al., 2018).
Anxiety and executive functions
Connections between EFs and anxiety have been examined, particularly through the relationship
between WM and anxiety (Beilock & Carr, 2005; Eysenck & Calvo, 1992; Mammarella et al., 2015;
Passolunghi et al., 2020; Pellizzoni et al., 2019, 2020). Stressful situations and negative feelings
(such as anxiety) can interfere with success in mathematical performance (Caviola et al., 2 0 17 ).
Attentional control theory (ACT), developed by Eysenck et al. (2007), describes anxiety as a dis
rupter of our ability to control our attention, which means that we are more readily distracted while
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performing a task. ACT thus suggests that anxiety reduces our cognitive capacity and impairs our
efficiency, regardless of whether the stimuli prompt are internal (worrying thoughts) or external
(tasks). According to this theory, anxiety influences WM and interferes with effective performance,
particularly in complex tasks. Studies on adults assessing the joint influence of WM and MA on
math performance generated contrasting results, and the literature offers different approaches.
Ashcraft and Kirk (2001) suggested that individuals with a greater WM capacity have more cognitive
resources and can simultaneously manage anxiety related thoughts and solve math tasks. Beilock
and Carr (2005) took another view, claiming that individuals with a greater WM capacity are more
susceptible to performance deficits as a result of WM disruptions (what they called a ‘choking under
pressure’ effect).
Most studies investigated only the relationship between M A and WM, without considering the role
of other EF constructs. The studies were also conducted on primary school children (Ramirez et al.,
2013; Vukovic et al., 2013) or adults (Beilock & Carr, 2005), leaving the years of early adolescence
almost unexplored. Based on the ACT proposed by Eysenck and Calvo (1992), which postulates that
anxiety decreases attentional control and increases attention to threat related stimuli, Hopko et al.
(1998) indicated that math anxious individuals show a deficient in the inhibition mechanism through
which WM resources are consumed by task irrelevant distracters. These data were more recently
confirmed by different studies that underline how math anxiety (MA) impairs the inhibition control
system with specific effects on math abilities (Mammarella et al., 2 017; Van den Bussche et al., 2020).
This study could be the first attempt to assess the influence of different EFs and emotional aspect
(MA) on math performance and to observe how they will connect in the middle school period.
The present study
In the present study, we examined the role of EFs (V WM, VSWM, inhibition and shifting) and MA
on math performance in middle school students, and we tried to reach the following aims: (1) to better
examine the relationship between MA and math performance; (2) to further examine the relationship
between EFs and math performance, often left unexplored during the middle school period and (3) to
investigate, for the first time, the interplay between EFs (VWM, VSWM, inhibition and shifting) and
MA on math performance.
To achieve our aims, we hypothesized that:
1. MA would have a significant and negative relationship with math performance, referring spe
cifically to middle school students (Barroso et al., 2020),
2. Different EF components would correlate positively with math performance in middle school stu
dents (e.g. WM, inhibition and shifting; Giofrè et al., 2018; Trezise & Reeve, 2014; Usai et al., 2 018).
With respect to WM, some studies have shown the relative contributions of memory components
to general mathematics learning in secondary school students (Giofrè et al., 2018). In line with this
research, we hypothesized a specific correlation with VSWM, but not with VWM during this school
period.
3. The relation between MA and math performance will mediate through cognitive factors (VSWM, in
hibition and shifting) in middle school students (Cragg et al., 2017; Giofrè et al., 2 018; Justicia Galiano
et al., 2 017 ).
Figure 1 shows the theoretical model based on the variables included in our study.
To reach these aims, students were assessed in two phases: during the first phase at the beginning of
the school year, cognitive (V WM, VSWM, inhibition and shifting) and emotional factors (MA) were
tested. Then, 7 months later, their maths abilities were tested in the second phase.

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METHOD
Participants
The research was carried out at four different middle schools in northeastern Italy. The study enrolled
105 middle school students (48 males and 57 females; Mage = 12.62, SD = 0.67, age range from 11 to
14 years old), two of whom did not participate in the final assessment. None of the students were diag
nosed with learning disabilities (the information that we got from the teachers). The final sample thus
included 103 participants, all Caucasian. The sample's SES was primarily middle class, judging from
the school records. The student's parents and the school's principals signed a written informed consent
form following the Declaration of Helsinki. This study was conducted following the ethical guidelines
of the Italian Association of Psychology and the ethical code of the Italian Register of Professional
Psychologists. Emotional factor (15 min) and math abilities (45 min) were assessed in a collective way;
cognitive factors were assessed individually in the quiet room at school, each student for this assessment
needed around 30 min.
Measures
Cognitive factors
Verbal working memory. The Letters and Numbers Sequencing subtest of the WISC IV test battery (Wechsler
Intelligence Scale for Children, 2003) measures verbal WM, an individual's ability to retain and
manipulate verbal information in their memory. After the examiner read a string of letters or numbers
in random order, participants need to repeat them in alphabetical or numerical order. There were three
pairs of strings (of letters and numbers) of increasing length, from two letters and two numbers to
four letters and four numbers. The total raw score for the test is obtained by awarding 1 point for each
correct answer and 0 for each wrong answer. The sum of the raw scores was converted into a scaled
score using a specific conversion table.
Visuospatial working memory. A computerized version of the Dot Matrix subtest (adapted from Miyake
et al., 2001) was used. This task measures the ability to simultaneously process visuospatial information
FIGUR E 1 Theoretical model
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and to maintain information in the visuospatial store. The task required the participant to verify a
matrix equation while simultaneously remembering the location of the X in a 5 × 5 matrix. Each
trial contains a set of matrix equations followed by a 5 × 5 matrix containing one X. Participants had
4500 ms to verify the sum of two segments correctly or not described by a third presented pattern.
Immediately after matrix addition, a 5 × 5 matrix with an X in a cell was displayed for 1500 ms on the
screen. After, participant had to recall the appearance of X in the 5 × 5 matrix by clicking in the empty
5 × 5 matrix. The result presents the proportion of correct answers of participant.
Inhibition
The NEPSY II Inhibition test (Korkman et al., 2007) comprises two different trials (shapes and arrows)
and three conditions: Naming, Inhibition and Switching. With the condition Inhibition, participants
were presented with a series of black and white shapes (circles and squares) or black and white arrows
pointing in a given direction and had to say the opposite shape or direction as quickly as they can.
Response time, number of errors, number of self corrections, the sum of errors and the number of self
corrections recorded for each condition. The final score presents the sum of response time and sum of
errors converted into a scaled score using a specific conversion table.
Shift ing
The NEPSY II Inhibition test (Korkman et al., 2007; Switching condition). Participants are asked to
state the opposite shape if it is white and the correct shape if it is black, the same with arrows (white
arrow opposite direction, black arrow correct direction) and as quickly as possible. Before both condi
tions, participants did the example first. Response time, number of errors, number of self corrections,
the sum of errors and the number of self corrections recorded for each condition. The same as for
Inhibition, the final score presents the sum of response time and sum of errors converted into a scaled
score using a specific conversion table.
Emotional factors
Mathematics anxiety. The Abbreviated Math Anxiety Scale (AM AS, Hopko et al., 2003) is a self report
questionnaire containing nine items adapted to middle school students. The questionnaire uses a 5 point
Likert scale on which participants indicated how much anxiety they would feel in a given situation that
involves mathematics (1 = little anxiety, 5 = great anxiety). The total score was the sum of all scores for
each item, with a higher score corresponding to more severe MA.
Mathematical ability. The AC M T 3 (Cornoldi et al., 2020) tests of mathematical calculation and problem
solving skil ls from 6 to 14 years old. T his test exami nes different aspects of mathematical learn ing, written
and oral calculus skills, the ability to understand and produce numbers, arithmetical reasoning skills,
speed of calculation and problem solving skills. For this study, we used five subscales (Approximate
calculation, Fluency, Matrix, Inferences and Written calculation). The reason for choosing this battery
was that five subscales could be assessed in a collective way. Approximate calculation, participants were
shown an arithmetical operation and chose from a set of numbers closest to the correct result. They
were allowed one and a half minutes to complete 15 exercises. For Fluency, participants saw the same
series of operations and provided the correct answers as quickly as possible. They had three sheets, one
of the additions (20 exercises), one of the subtractions (20 exercises) and one of the multiplications (20
exercises). For each sheet, they had 1 min to complete the task. The matrix subscale is a mathematical
reasoning task. A series of numbers were presented in 2 × 2 or 2 × 3 matrices in which a number was
missing. Children had to choose which number was missing for each matrix. Students had two and
a half minutes to complete the task. The Inferences subscale included three different exercises where
students needed to use mathematical reasoning to solve them. The first type of exercise used symbols
instead of numbers. In the second exercise, computational operation is missing and students needed to
add it. In the last, the third exercise, there are two operations: one complete, while in the other the result
is missing. Students were required to complete the calculation using the second operation as an aid. The

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total time available for the subscale was 2 min, 1 min for the first type of the exercise and 1 min for the
second and the third types of the exercise. For the subscale Written calculation, they had eight different
operations (two additions, t wo subtractions, two multiplications and two divisions) to be solved in
5 min. The tasks were presented in a paper and pencil format. Each correct answer scored one point,
and the wrong answers scored zero. The sum of raw scores of all subscales was used as a final score.
The order of the sessions and the tasks (emotional, cognitive and math performance) were the same
for every participant.
RESULTS
Analytic strategies
SPSS IBM 21 was used to obtain the descriptive and correlation analyses between all measures. We con
ducted a bivariate correlation analysis using Pearson r between math calculation, EFs (VWM, VSWM,
Inhibition and Shifting) and MA for the whole sample. In addition, path analyses were done with the
lavaan package (Rosseel, 2012) for R (R Core Team, 2019) to explore our third hypothesis the descrip
tive statistics of all tasks are reported in Table 1.
Bivariate correlations between mathematical performance, EFs and MA are presented in Table 2.
Preliminary analyses included a test of a theoretical framework for better understanding the inf lu
ence of cognitive and emotional factors on math calculation. This theoretical model used cognitive fac
tors as mediators (V WM, VSWM, inhibition and shifting). We ran a path analysis and tested model fit
considering: the chi square (χ2), the comparative fit index (CFI), the normed fit index (NFI), the Tucker
fit index (TFI) and the root mean square error of approximation (RMSEA); the chi square difference
(Δχ2) and the Akaike information criterion (AIC) were also used to compare the fit of alternative models
(Kline, 2011). A priori power analysis (Gpower: Faul et al., 2007) indicated that a sample size of 63 would
be sufficient to detect a significant interaction effect with a power of .95 and an alpha of .05.
The statistical fit for the theoretical model was: CMIN = 13.75, df = 4, CMIN/df = 3.43, p = .008,
CFI = .883, NFI = .860, TLI = .560, RMSEA = .154, AIC = 1976.922, BIC = 2019.078. Results showed
Mathematical performance to be significantly directly predicted by VSWM (β = .18; p = .038), Shifting
(β = .29; p = .001) and negatively by MA (β = −.35; p = .000). Indirectly, significant and negative impact
on Mathematical performance had MA through measure of Shift ing ( p = .024). Analysis, also, showed sig
nificant paths between VSWM and Shift ing ( β = .31; p = .002) and between Sh ifting and MA (β = −.28;
p = .003). Also, results showed non significant path bet ween MA and Inhibition (β = −.09; p = .357), MA
and VWM (β = −.11; p = .186) and MA and VSWM (β = −.13; p = .259).
From the theoretical model we excluded all non significant paths because we wanted to see if
there will be changes in the fit indexes in a new model. Furthermore, we ran the path analysis by
testing for both direct and indirect influences to show the influence of MA on math performance
mediated by shifting. Model statistical fit was good: CMIN = 1.25, df = 1, CMIN/df = 1.25, p = .26,
TABL E 1 Descriptive statistics of the tasks used in our study
Mean (SD)Minimum Maximum Reliability
VWM (scaled scores) 11.37 (4.2 2) 123 .90
VSWM ( proport ions) 0.3 8 (.23) 0.07 0.98 .85
Inhibition (scaled scores) 10.03 (2.33) 115 .80
Shifting (scaled scores) 9.67 (2.78) 4 15 .80
MA (raw scores) 21.80 (6.36) 938 .83
Math (z score) 6.15 (4.60) −5.12 17. 25 .73
Abbreviations: MA, math an xiet y; SD, sta ndard deviat ion; VSW M, visuospat ial W M; VWM, verbal W M.
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ŽIV KOVIĆ et al .
CFI = .996, NFI = .982, TLI = .976, RMSEA = .050, AIC = 1591.879, BIC = 1615.592. Results
showed Mathematical performance to be significantly directly predicted by VSWM (β = .20; p = .018),
Shift ing ( β = .29; p = .001) and negatively by MA (β = −.40; p = .000). Indirectly, significant and
negative impact on Mathematical performance had MA through measure of Shif ting ( p = .033). Analysis
showed significant path between VSWM and Shifting (β = .32; p = .002) and between Sh if ting and MA
(β = −25; p = .006). Results concerning direct and indirect influence and percentage of explained
variance (R2) are presented in Figure 2.
DISCUSSION
Researchers have investigated the influence of cognitive and emotional factors on math performance
in adults (Ashcraft & Kirk, 2001) and, more recently, in primary school children (Ramirez et al., 2013),
mainly leaving unexplored the middle school period and the complex interplay between factors specifi
cally referring to cognitive processes. The most investigated aspects were the inf luence of WM and MA,
but rarely the influence of other EFs (e.g. inhibition and shifting) on math performance (Mammarella
et al., 2 017 ). Because of the lack of literature on the sample of middle school students, we designed the
present study to understand the importance of EFs and investigate the reciprocal role of cognitive ( WM,
inhibition and shifting) and emotional factors (MA) in mathematical performances. The goals of our
study were to analyse: (1) the relationship between MA and maths performance, (2) the relationship
between EFs and math performance and (3) the interplay between EFs (VWM, VSWM, inhibition and
shifting) and MA on math performance.
Our first hypothesis was confirmed, and results showed a significant and negative relationship be
tween MA and maths performance. The results are in line with previous studies in primary school
TABL E 2 Biva riate correlat ions bet ween all variables considered in t he sample
123456
1. VWM –
2. VSW M . 314** –
3. Inh ibition −.061 .106 –
4. Shif ting .075 .332** .348** –
5. MA −.136 −.110 −.090 −.260* * –
6. Math .188 .335** .137 .446** −.492** –
Abbreviations: MA, math an xiet y; VSW M, visuospatial WM; VW M, verbal WM .
**p ≤ .01.
FIGUR E 2 Fina l model

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students ( Vukovic et al., 2013), in middle school students (Madjar et al., 2018) and with adults (Ashkenazi
& Danan, 2017 ).
The second hypothesis of the study was partially confirmed by cognitive factors (VWM, VSWM,
inhibition and shifting) having a significant and positive relationship with math performance in middle
school students. Results showed a positive relationship between VSWM and math performance and be
tween shifting and math performance, but not a significant relationship between VWM and math per
formance. Giofrè et al. (2018) showed that VWM and VSWM could be split regarding their predictive
influence on reading and mathematics. The results of their study indicated the importance of VSWM
for math, and the importance of VWM in reading. Also, some of the previous studies can be used to ex
plain our results, for example, the studies that underline the impact on math performance by depressing
specifically VSWM resources (Soltanlou et al., 2019). The authors showed how MA primarily impacts
the visual component (e.g. Trezise & Reeve, 2018). The study with a sample of 14 year old female stu
dents (Trezise & Reeve, 2014) showed an association between high worry, low WM and poor algebra
results, also between low worry, high W M and high results in algebra tasks but without the impact of
high worry with moderate WM. On the other hand, Wong and Szücs (2013) showed that maths tasks
presented in a written format can inherently engage the visual components and had shown that format
influences strategies that participants would choose (Katz et al., 2000).
In respect to inhibition, studies on pre schoolers showed a significant relationship between inhibi
tion and math performance in preschool children (Clark et al., 2010). The study of Bull and Scerif (2001)
on primary school students who had lower mathematical abilities indicated that students had major dif
ficulties with inhibition of learned strategy and switching to a new one. Moreover, Orbach et al. (2020),
with a sample of fourth and fifth grade students, showed the negative inf luence of state MA on math
performance through core EFs (inhibition, cognitive flexibility, WM capacity, a global measure of core
EFs). Some of the studies also addressed this relationship in samples of middle school students showing
the role of inhibition of math performance (St Clair Thompson & Gathercole, 2006).
A non significant relationship between inhibition and math performance was observed in our study.
The explanation of this result could be due to the type of task proposed in the NEPSY II evaluation.
The Inhibition and Shifting tasks were based on the same type of material but with an increasing level of
WM required. While in the ‘inhibition’ test participants were presented with a series of black and white
shapes (circles and squares) or black and white arrows (pointing in a given direction) and participants
had to say as quickly as they could the opposite shape or direction, the Shifting test required participants
to state the opposite shape if it is white and the correct shape if it is black. The necessity to compare the
rule and modify the strategies according to the material, different from the first task, implies a more
challenging performance in this last assignment. In this more challenging case, a significant relation
ship between shifting and math performance was observed.
The third hypothesis has been partially confirmed, too. The indirect influence of MA through the
cognitive measures was significant just for the measure of shifting but not for VWM, VSWM and inhi
bition. In other words, our results indicated that only shifting mediated the relations between MA and
maths performance in middle school students. Previous studies investigated the mediating role of WM
in primary school (Justicia Galiano et al., 2017 ) and middle school students (Owens et al., 2012), but not
the mediating role of other EFs. Another possible explanation is related to the nature of the math tasks
used in our study. MA reducing the capacity of shifting and relying on WM decrease math performance.
Because of the negative inf luence of MA that consumes capacity for shifting, participants showed lower
results on the math tasks where they needed to shift from one strategy to another. It is important to note
that, as math tasks, we used five different tasks that involve various computational operations (addition,
subtraction, multiplication and division) and inferences that require more involvement of shifting.
To the best of our knowledge, this is the first study that simultaneously investigated EFs and MA
and evaluated the mediating role of shifting in the relation between MA and maths performance in
middle school students. These data seem to reflect a change in the developmental trajectory resulting
in a specific role of shifting, during this specific developmental stage, compared to other EFs (St Clair
Thompson & Gathercole, 2006). Various studies with a sample of primary school students showed
448

ŽIV KOVIĆ et al .
a negative correlation between arithmetic ability and shifting (Bull et al., 1999; Bull & Scerif, 2001;
McLean & Hitch, 1999). Latzman et al. (2010), with a sample of male adolescents, showed that higher
levels of performance on shifting tests were related to higher math performance. Finally, we can specu
late that the influence of EFs on math performance may change in middle school students underlining
the critical role of shifting in this developmental stage (Miyake & Friedman, 2012).
Although our findings shed further light on the mediating role of EFs between MA and maths per
formance, this study also shows some limitations that should be taken into account in further research.
First, we did not measure general anxiety as a control variable of MA. The control variable will give
a clearer view how MA influences math performance. Second, task impurity is a major issue with EF
components. In our study, we used a unique task from which we derived the measures of inhibition
and shifting that can be confounding given the level of task impurity (Denckla, 1994; Miyake et al.,
2000), and we used a VWM task including numbers that can increase specific anxiety in children who
already feel diff iculties with math. It is worth noting, that in an additional analysis, we did not find
differences in terms of VWM tested on numbers and letters for students with high MA (F(1, 26) = .288,
p = .596, ηp
2 = 3.889). As a third aspect, we did not consider individual resources, such as self concept,
self efficacy, motivation and ego resilience which have been shown important to mediate the relation
between M A and maths performance (Donolato et al., 2020; Mammarella et al., 2 018).
EFs are important for developing math skills and their decrease can cause a delay in math learning
(Bull & Lee, 2014). Our study confirmed the importance of VSWM and shifting for maths performance
in middle school students and the necessity for the studies investigating WM separately from inhibition
and shifting (Cragg et al., 2 017). Whether students with low arithmetic skills are tested, difficulties in
shifting may be expected, thus future studies should longitudinally investigate the influence of shifting
on math performance. Also, it would be important to investigate the role of shifting as moderator by
considering the complexity of the math tasks, in order to understand whether the moderation effect is
influenced by the WM demands of the math task used.
Educational implications
The study has several implications for math acquisition during secondary school. First, intervention
programmes designed to increase math performance should be targeted at emotional and cognitive fac
tors at the base of this type of achievement, focusing on exercises that can promote emotional control
during tasks and awareness of how emotion and EFs could influence performance. Overall, meta
cognitive exercises may be used to increase awareness about strategies to solve math tasks (Passolunghi
et al., 2020). Second, students often report receiving less emotional support during the transition into
adolescence (Larson et al., 1996; National Research Council, 2004). Third, we deem as crucial for teach
ers to be aware of the early signs of MA and to promote intervention to train emotions, WM and EFs
that base achievement to drive students to positive school adjustment. These findings highlight the
importance of (1) raising awareness on the importance of math learning and all the factors that could
promote or hinder math acquisition and (2) providing training on effective ways to contrast MA and
ameliorate the classroom climate and equal educational opportunities for all students (Pellizzoni et al.,
2019, 2020).
To conclude, further longitudinal and experimental studies should be carried out to better determine
the direction between cognitive and emotional factors and their influence on math performance by
considering individual resources and environmental factors.
ACKNOWLEDGEMENTS
Open Access Funding provided by Universita degli Studi di Trieste within the CRUICARE Agreement.
CONFLICT OF INTER EST
All authors declare no conflict of interest.

449
EFS, M ATH ANXI ETY A ND MATH PER FORM ANCE
AUTHOR CONTRIBUTION
Marija Zivkovic: Conceptualization; Data curation; Formal analysis; Writing – original draft;
Writing – review & editing. Sandra Pellizzoni: Methodology; Writing – original draft; Writing
– review & editing. IreneCristinaMammarella: Conceptualization; Formal analysis; Writing –
review & editing. MariaChiaraPassolunghi: Conceptualization; Supervision; Writing – review
& editing.
DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available from the corresponding author upon rea
sonable request.
ORCID
Marija Živković https://orcid.org/0000000331262903
Sandra Pellizzoni https://orcid.org/0000000244240925
Irene Cristina Mammarella https://orcid.org/0000000269864793
Maria Chiara Passolunghi https://orcid.org/000000016713866X
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