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S H O R T R E P O R T Open Access
Mathematics anxiety among STEM and
social sciences students: the roles of
mathematics self-efficacy, and deep and
surface approach to learning
Dmitri Rozgonjuk
1,2*
, Tiina Kraav
2
, Kristel Mikkor
2
, Kerli Orav-Puurand
2
and Karin Täht
2,3
Abstract
Background: Although mathematics anxiety and self-efficacy are relatively well-researched, there are several
uninvestigated terrains. In particular, there is little research on how mathematics anxiety and mathematics self-
efficacy are associated with deep (more comprehensive) and surface (more superficial) approaches to learning
among STEM and social sciences students. The aim of the current work was to provide insights into this domain.
Results: Bivariate correlation analysis revealed that mathematics anxiety had a very high negative correlation with
mathematics self-efficacy. However, while mathematics anxiety correlated positively with surface approach to
learning in the STEM student sample, this association was not statistically significant in the social sciences student
sample. Controlled for age and gender, regression analysis showed that lower mathematics self-efficacy and female
gender predicted higher mathematics anxiety, while only mathematics self-efficacy predicted mathematics anxiety
in the social sciences student sample. Interestingly, approaches to learning were not statistically significant
predictors in multivariate analyses when mathematics self-efficacy was included.
Conclusions: The results suggest that mathematics self-efficacy plays a large role in mathematics anxiety. Therefore,
one potential takeaway from the results of the current study is that perhaps improving students’mathematics self-
efficacy could also be helpful in reducing mathematics anxiety. Since the current study was cross-sectional, it could
also be that reducing students’mathematics anxiety could be helpful in boosting their mathematics self-efficacy.
Future studies should aim to clarify the causal link in this relationship.
Keywords: Mathematics anxiety, Mathematics self-efficacy, Approaches to learning, STEM, Social sciences
Introduction
One could argue that mathematics is an important com-
ponent in science, technology, engineering, and math-
ematics (STEM) education, since most domains rely on
applying mathematical thinking. Research on teaching
and learning mathematics has received a lot of attention
over the years, as mathematical knowledge is a crucial
factor for students’successful future careers (Claessens
& Engel, 2013; Konvalina, Wileman, & Stephens, 1983).
As mathematics is commonly perceived to be difficult
(Fritz, Haase, & Räsänen, 2019), it has been proposed
that instead of instructing the content and practices of
mathematics, the main focus should be on students’ex-
perience of the discipline and providing mathematical
sense-making (Li & Schoenfeld, 2019). Research in ter-
tiary mathematics education is also a growing field as
the role of mathematics in learning other disciplines is
widely acknowledged.
© The Author(s). 2020 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License,
which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give
appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if
changes were made. The images or other third party material in this article are included in the article's Creative Commons
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licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain
permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licens es/by/4.0/.
* Correspondence: dmroz@ut.ee
1
Department of Molecular Psychology, Institute of Psychology and
Education, Ulm University, Helmholtzstraße 8/1, 89081 Ulm, Germany
2
Institute of Mathematics and Statistics, University of Tartu, Tartu, Estonia
Full list of author information is available at the end of the article
International Journal of
STEM Education
Rozgonjuk et al. International Journal of STEM Education (2020) 7:46
https://doi.org/10.1186/s40594-020-00246-z
Little research has investigated the relationships be-
tween mathematics anxiety, mathematics self-efficacy,
and approaches to learning in the context of mathemat-
ics education among STEM and social sciences students.
Do students with higher mathematics anxiety also have
a more superficial approach to learning? Or does math-
ematics self-efficacy also contribute to a more thoughtful
and integrative learning process? Are there significant
differences in mathematics self-efficacy, mathematics
anxiety, and approaches to learning between STEM and
social sciences students? Thus far, these questions have
not received a lot of attention in the academic literature.
Therefore, the main aim of this study is to provide some
insights into the relationships between mathematics anx-
iety, mathematics self-efficacy, and approaches to learn-
ing, and the potential differences in those variables
between STEM and social sciences students. While sev-
eral associations have been investigated in earlier works
(see below), this is the first study where the relationships
between all these variables are compared among STEM
and social sciences students.
Literature overview
Mathematics anxiety has been described as experiencing
feelings of panic and helplessness when asked to solve a
mathematical task or problem (Tobias & Weissbrod,
1980). Psychological as well as physiological symptoms
may appear when feeling anxious about mathematics
(Chang & Beilock, 2016). Mathematics anxiety is known
as a common problem in K-12 as well as tertiary educa-
tion (Ashcraft & Moore, 2009; Luttenberger, Wimmer,
& Paechter, 2018; Yamani, Almala, Elbedour, Woodson,
& Reed, 2018) and, therefore, has received considerable
attention as a researched topic among educational scien-
tists (Dowker, Sarkar, & Looi, 2016; Hoffman, 2010; Jan-
sen et al., 2013). For instance, in the Programme for
International Student Assessment (PISA) 2012, across
the 34 participating Organisation for Economic Co-
operation and Development (OECD) countries, 59% of
the 15-year-old students reported that they often worry
that math classes will be difficult for them and 31% re-
ported they get very nervous doing math problems
(OECD, 2013b).
Mathematics anxiety can be caused by several different
factors. For instance, unpleasant teaching and assess-
ment strategies for students, like time testing (Ashcraft
& Moore, 2009) and assigning mathematics as punish-
ment (Oberlin, 1982), that are still widely in use in all
school levels, may influence the spread of mathematics
anxiety. Although mathematics anxiety may have been
appearing relatively early in life, it has been shown that
there are possibilities to reduce mathematics anxiety in
all levels of schooling (Hembree, 1990). As appropriate
mathematics-related instruction and teacher’s
enthusiasm toward mathematics are important in the
development of mathematics anxiety of students (Jack-
son & Leffingwell, 1999), reduction of pre-service
teachers’own mathematics anxiety is crucial and it could
be helpful in reducing the students’mathematics anxiety
(Gresham, 2007; Vinson, 2001). Applying more active
learning (such as group work) may also reduce anxiety
(Cooper, Downing, & Brownell, 2018).
Mathematics anxiety has been shown to be associated
with poorer performance in mathematics (Ashcraft &
Faust, 1994; Devine, Fawcett, Szűcs, & Dowker, 2012;Fan,
Hambleton, & Zhang, 2019). In addition, it has been
shown, that mathematics anxiety also correlates with
other variables (e.g., learning behavior, self-efficacy) that
influence academic performance (Feng, Suri, & Bell, 2014;
McMullan, Jones, & Lea, 2012). For example, Paechter,
Macher, Martskvishvili, Wimmer, and Papousek (2017)
investigated psychology students and showed a correlation
between mathematics and statistics anxiety and learning
behavior. In addition, Royse and Rompf (1992) compared
social work and non-social work university students and
found that the former had higher levels of mathematics
anxiety than the latter group. Nevertheless, there are no
studies comparing STEM and social sciences students
with regard to mathematics anxiety.
Attitudes toward mathematics is another construct
that plays an important role in mathematical studies, as
well as its outcomes (Ahmed, Minnaert, Kuyper, & van
der Werf, 2012; House, 2005). Mathematics attitudes
and anxiety are often studied together; nevertheless, they
cannot be equated with each other. As Zan and Martino
(2007) describe, many studies about mathematics atti-
tudes do not provide a clear definition for the construct.
It always has an emotional dimension (positive or nega-
tive emotional disposition toward mathematics), usually
also involving conceptualization of mathematics (Dow-
ker et al., 2016), and/or mathematics-related behavior,
depending on the specific research problem. In addition,
one may argue that, to some extent, attitudes toward
mathematics also reflect mathematics self-efficacy (Yusof
& Tall, 1998). Self-efficacy could be defined as one’s be-
lief in one’s ability to succeed in specific situations. The
academic aspect of this concept is called academic self-
efficacy, and is described as an individual’s belief that
they can successfully achieve at a designated level on an
academic task (Bandura, 1997). Mathematics self-efficacy
is one’s belief about how their own action and effort
could lead to success in mathematics (Luttenberger
et al., 2018; OECD, 2013b). Higher mathematics self-
efficacy has been shown to be correlated with lower
mathematics anxiety, more positive, and less negative at-
titudes toward mathematics (Akin & Kurbanoglu, 2011).
In addition, higher mathematics anxiety is related to
more negative attitudes toward mathematics (Vinson,
Rozgonjuk et al. International Journal of STEM Education (2020) 7:46 Page 2 of 11
2001). These findings underscore the importance of
mathematics anxiety in attitudes toward mathematics, as
well as mathematics self-efficacy.
More general attitudes toward learning are also im-
portant to be considered. Marton and Säljö (1976) re-
ferred to a co-existence of intention and process of
learning and described deep and surface learning ap-
proaches. Students with a deep approach to learning
look for the meaning of the studied material and try to
relate new knowledge with prior information, whereas
students with a surface approach to learning use rote
learning and un-meaningful memorization. How stu-
dents approach to learning in higher education is an im-
portant factor when speaking about educational
outcomes (Duff, Boyle, Dunleavy, & Ferguson, 2004;
Fryer & Vermunt, 2018; Maciejewski & Merchant, 2016).
Deep approach to learning is associated with better gen-
eral academic outcomes, as well as, specifically, better
mathematical performance (Murphy, 2017; Postareff,
Parpala, & Lindblom-Ylänne, 2015). Although it is not
the sole factor influencing mathematics achievement, it
is still important to determine students’approaches to
learning mathematics, as it enables educators to analyze
and shape the students’classroom experience toward
more effective learning.
Little research has been done in the domain of ap-
proaches to learning in relation to mathematics anxiety
and self-efficacy in tertiary education. Anxiety in general
is associated with higher surface and lower deep ap-
proach to learning (Marton & Säljö, 1984). In one study,
surface approach to learning has been found to correlate
with mathematics anxiety (Bessant, 1995). It has also
been demonstrated that students with positive attitudes
toward mathematics tend to use more deep and less sur-
face approach when learning mathematics (Alkhateeb &
Hammoudi, 2006; Gorero & Balila, 2016). Another com-
mon finding in educational research is that students
who have higher self-efficacy adopt more deep approach
to learning (Papinczak, Young, Groves, & Haynes, 2008;
Phan, 2011; Prat-Sala & Redford, 2010).
There are not many studies investigating the role of
deep and surface approaches to learning in mathematics
anxiety. Although a study by Bessant (1995) showed that
mathematics students scored lower on mathematics anx-
iety measure than psychology/sociology students, the re-
lations between mathematics anxiety and approaches to
learning in STEM and social sciences students is a
largely unexplored area.
Conceptual framework
Several studies have aimed to explain the potential
causes for mathematics anxiety. It has been proposed
that the origins of mathematics anxiety could be catego-
rized into three groups (Baloglu & Kocak, 2006):
situational, dispositional, and environmental factors.
Situational factors are direct stimuli related to feelings of
anxiety in relation to mathematics. Dispositional factors
include individual characteristics, such as personality
traits; for instance, it has been shown that people with
higher trait neuroticism (the tendency to experience
negative effect; McCrae & Costa, 2003) worry more and
tend to be more anxious in general (Costa & McCrae,
1985), although this typically decreases with age (Mõttus
& Rozgonjuk, 2019). Finally, environmental factors in-
clude prior perceptions, attitudes, and experiences that
may have affected the individual (Baloglu & Kocak,
2006).
In the current work, mathematics self-efficacy as well
as approaches to learning could be conceptualized as en-
vironmental factors that could potentially affect the de-
velopment of mathematics anxiety. Furthermore,
students’age, gender, and the curricula could be consid-
ered as environmental factors potentially affecting math-
ematics anxiety (Baloglu & Kocak, 2006).
Aims and hypotheses
The general aim of this study is to investigate how math-
ematics anxiety and self-efficacy, as well as approaches
to learning (deep and surface), are related to each other.
Furthermore, these relationships are also compared
across STEM and social sciences student samples. Based
on the previous literature, we have posed some hypoth-
eses that are rather confirmatory of previous findings.
Based on the previous literature, we hypothesize the
following:
H1: Mathematics anxiety and mathematics self-efficacy
are negatively correlated.
Previously it has been demonstrated that mathematics
anxiety and self-efficacy are inversely associated (Akin &
Kurbanoglu, 2011; Vinson, 2001).
H2: Mathematics anxiety is positively correlated with
surface approach to learning and negatively with deep
approach to learning. Even though one study found
that mathematics anxiety correlates positively with
surface approach to learning (Bessant, 1995), it would
also be natural to assume that deep approach to
learning is negatively associated with mathematics
anxiety, since typically surface and deep approaches to
learning are inversely correlated (Rozgonjuk, Saal, &
Täht, 2018).
H3: Mathematics self-efficacy is positively associated
with deep and negatively with surface approach to
learning. It has previously been shown that high self-
efficacy, in general, is associated with more deep and
less surface approach to learning (Chou & Liang, 2012;
Rozgonjuk et al. International Journal of STEM Education (2020) 7:46 Page 3 of 11
Papinczak et al., 2008). Therefore, it would be logical to
assume that also in the context of mathematics, these
constructs would be correlated.
H4: STEM students have less mathematics anxiety than
social sciences students. Previously, Bessant (1995) have
demonstrated that mathematics students had lower
scores on mathematics anxiety measure than
psychology/sociology students. However, our study
goes beyond comparing only mathematics students,
and includes students from other disciplines (e.g.,
biology) as well, forming a more heterogeneous STEM
student group.
H5: Approaches to learning and mathematics self-
efficacy predict mathematics anxiety when age and gen-
der are controlled for. Based on previous research and
hypotheses mentioned above, there is evidence to
believe that the associations between approaches to
learning, mathematics self-efficacy, and mathematics
anxiety would hold also when covariates are included.
There is relatively little research in this domain and
knowing the associations between these variables may
help educators to improve and adjust their teaching
strategies to potentially improve the learning process.
The results of this study aim to outline the important
predictors of mathematics anxiety, and, therefore, ex-
pand the existing research in this field of study, and in-
fluence future teaching strategies. The results of this
work could be helpful for the teacher/lecturer when he/
she aims toward reducing mathematics anxiety by, e.g.,
using teaching strategies that could enhance deeper (and
less surface) approach to learning, increase mathematics
self-efficacy, or both.
Material and methods
Sample and procedure
The study participants were students who either took an
introductory calculus course (dealing with more elabor-
ate topics than in secondary education) for university
students or an introductory statistical modeling course
at a major Estonian university. Importantly, these
courses were mandatory in order to complete the stu-
dent’s curriculum and, in most cases, were prerequisite
courses for other courses in the curriculum. While most
of the students in the introductory calculus course were
STEM curricula students, mainly psychology and polit-
ical sciences majors were enrolled in the statistical mod-
eling course. However, because it is possible to take
these courses as electives as well, students with various
backgrounds could participate in these courses. This
means that, theoretically, both student groups could en-
roll in either the calculus or statistical modeling course.
For instance, as could be seen in Supplementary Table 1
there are some Economics students who enrolled in a
Calculus course, while all other social sciences students
were enrolled in the statistical modeling course. Stu-
dents’responses across variables of interest across cur-
ricula are depicted in Supplementary Figures 1to 4.
The data were collected during the start of both
courses, in September 2019. Students were asked to take
part in a web survey which aimed to investigate the role
of different factors in mathematics education. Participa-
tion in the study was voluntary, anonymous, and in line
with the Helsinki Declaration.
In total, there were 358 responses. However, many rows
were empty or most of the data were missing, after some
initial data cleaning, 234 rows of responses were kept. The
reason for the aforementioned “missing data”lies in the
fact that whenever a person opens the questionnaire en-
vironment, this gets logged as a response row. However, it
does not necessarily mean that a person provides any re-
sponses to the questionnaire. Therefore, as mentioned,
out of 358 rows logged, only 234 were actually partially or
fully filled in with responses. Finally, because n=3people
did not specify their major, we excluded those rows.
Therefore, the effective sample comprised 231 students
(age M = 21.39, SD = 5.12; 79 (34.2%) men, 152 (65.8%)
women). There were 147 (63.6% of total sample) STEM
students (age M = 20.55, SD = 4.51; 57 men, 90 women),
and 84 (36.4%) social sciences students (age M = 22.87,
SD = 5.78; 22 men, 62 women).
Measures
We queried about the study participants’socio-
demographic variables (e.g., age, gender, curriculum/
major), mathematics anxiety and mathematics self-
efficacy, and approaches to learning (deep and surface).
Mathematics anxiety
Mathematics anxiety was measured with the 5-item
mathematics anxiety questionnaire used in the inter-
national PISA 2012 survey (OECD, 2013a). Students
were asked to assess on a 4-point scale (1 = strongly dis-
agree to 4 = strongly agree) the extent of agreement with
the following statements: (1) I often worry that mathem-
atics classes will be difficult for me; (2) I get very tense
when I have to do mathematics homework; (3) I get very
nervous doing mathematics problems; (4) I feel helpless
when doing a mathematics problem; (5) I worry that I
will get poor grades in mathematics. The psychometric
properties of this scale in an adolescent population could
be found in OECD report (2014; Table 16.7 on page
320). As a side comment, we opted for using this meas-
ure as opposed to, e.g., the Abbreviated Mathematics
Anxiety Scale (AMAS; Hopko, Mahadevan, Bare, &
Hunt, 2003), because the PISA-study mathematics anx-
iety scale fits better with contemporary classroom where
the role of digitalization is increasing (e.g., the AMAS
Rozgonjuk et al. International Journal of STEM Education (2020) 7:46 Page 4 of 11
items include words like “book”and “blackboard,”but
not digital resources). Secondly, PISA mathematics anx-
iety scale has demonstrated good psychometric proper-
ties, it has probably been administered in a larger variety
of cultural settings (as opposed to the AMAS), and it
has been validated against mathematics aptitude test in
all these cultures (e.g., see the report by OECD (2014),
p. 320, Table 16.7, ANXMAT). Finally, in all PISA sur-
vey questionnaires, stringent quality-assurance mecha-
nisms are implemented by experts in translation,
sampling, and data collection, resulting in a high degree
of reliability and validity (OECD, 2017). Cronbach’s
alpha for the effective sample of this measure was very
good, α= 0.90.
Mathematics self-efficacy
Mathematics self-efficacy was measured with three
items, measuring the extent of agreement on a four-
point scale (1 = strongly disagree to 4 = strongly agree)
from Yusof and Tall (1998). All items from the mathem-
atics self-efficacy scale (Yusof & Tall, 1998) were trans-
lated into Estonian by the members of our mathematics
education team and were reviewed by a professional Es-
tonian philologist. The questionnaire was then translated
back into English by another translator, and the back-
translated English version was reviewed by an English-
speaking student in order to estimate the content and
the similarities between the original and the back-
translated items. The items were the following: (1) I usu-
ally understand a mathematical idea quickly; (2) I have
to work very hard to understand mathematics; (3) I can
connect mathematical ideas that I have learned. Cron-
bach’s alpha for this three-item measure was α= 0.83.
Approaches to learning
Approaches to learning were measured with the Esto-
nian adaptation of the Revised Study Process Question-
naire (Biggs, Kember, & Leung, 2001; Valk & Marandi,
2005). It is a 16-item measure (8 items for deep and 8
items for surface approach to learning) that measures
deep and surface approaches to learning on a five-point
scale (1 = do not agree at all to 5 = totally agree). Ex-
ample items for the deep approach to learning scale are
as follows: I find most new topics interesting and often
spend extra time trying to obtain more information about
them, and I learn because I want to understand the
world. Example items for the surface approach to learn-
ing scale are as follows: I see no point in learning mater-
ial which is not likely to be in the examination,andIn
case of difficult topics, learning by rote is one way to pass
an exam. The internal consistency of deep and surface
approaches to learning were acceptable, Cronbach’sα=
0.71 for both scales.
Analysis
Data analysis was conducted in the R software version
3.5.3 (R Core Team, 2020). As mentioned in the “Sample
and procedure”section, we first removed the data rows
that were not valid responses (empty rows) or where
people did not specify their major (n= 3). After this pro-
cedure, there were no missing data in key variables. In-
ternal consistency statistics were calculated with the
alpha() function from the psych package (Revelle, 2018).
Since the sample sizes were not equal, Mann-Whitney U
tests to analyze the potential group differences between
STEM and social sciences students in age, math anxiety
and self-efficacy, and deep and surface approach to learn-
ing were used. Chi-square test was used to see if there are
differences in gender distribution among those student
groups.
We then computed descriptive statistics and con-
ducted Spearman correlation analysis (with pvalues ad-
justed for multiple testing with the Holm’s method),
using the rcorr.adjust() function from the RcmdrMisc
package (Fox, 2020). Finally, we computed regression
models where mathematics anxiety was treated as the
outcome variable, either surface or deep approach to
learning as the predictor, age and sex were covariates,
and we also computed additional regression models
where mathematics self-efficacy was additionally in-
cluded as a predictor variable. We ran these analyses for
the whole sample, as well as for STEM and social sci-
ences students separately.
The data as well as the analysis script are included
with this work as Supplementary Materials.
Results
Firstly, we analyzed if STEM and social sciences students
had group differences in key variables. There were no sta-
tistically significant group differences in deep and surface
approaches to learning, mathematics anxiety, as well as in
gender distribution (all ps > 0.01). However, the social sci-
ences student group was slightly older (M=22.87,SD=
5.78) than the STEM student group (M=20.55,SD=
4.51), W= 9742, p< 0.001. In addition, STEM students
(M= 8.39, SD = 1.92) had higher mathematics self-
efficacy scores than social sciences students (M=7.77,SD
=2.03),W= 5080.50, p=0.023.
Descriptive statistics and correlations for mathematics
anxiety and self-efficacy, and approaches to learning
The descriptive statistics and Spearman correlation coef-
ficients between the variables are in Table 1.
According to Table 1, mathematics anxiety was very
strongly negatively correlated to mathematics self-
efficacy across all samples. Additionally, surface learning
was positively significantly associated with mathematics
anxiety in the total and STEM student sample, but it
Rozgonjuk et al. International Journal of STEM Education (2020) 7:46 Page 5 of 11
was not significant among social sciences students. Deep
approach to learning and age were not statistically sig-
nificantly associated with mathematics anxiety.
Mathematics self-efficacy was negatively significantly
associated with surface approach to learning in total and
STEM student samples, but not in social sciences stu-
dents. Mathematics self-efficacy did not correlate with
deep approach to learning.
Surface approach to learning was negatively correlated
to deep approach to learning in total and STEM student
samples (but not in social sciences student sample) and
had a statistically significant negative correlation with
age only in social sciences student sample. Deep ap-
proach to learning did not correlate with age.
Which factors predict mathematics anxiety?
Next, we computed several regression models where
mathematics anxiety was treated as the outcome vari-
able. We computed models for three samples of stu-
dents: the full sample (N= 231), the STEM student
sample (N= 147), and the social sciences students (N=
84). For each sample of students, we computed two
models. Model 1 included age, gender, and surface and
deep approaches to learning as predictors. In model 2,
mathematics self-efficacy was added as an additional
predictor. For the full sample, we also included the stu-
dent group (STEM vs social sciences) as a predictor.
According to results in Table 2, when regression
models are computed across the full sample, female stu-
dents tend to have greater mathematics anxiety than
male students. Approaches to learning, age, and being a
STEM versus social sciences student did not predict
mathematics anxiety. Finally, including the mathematics
self-efficacy variable was negatively associated with
mathematics anxiety in this multivariate model. In
addition, it seems that mathematics self-efficacy explains
a large proportion of mathematics anxiety, as inclusion
of this variable improved the explained variance by al-
most 50% in the regression model full sample level.
However, the regression analysis results are somewhat
different when the sample is broken down into the
STEM and social sciences student group. In STEM stu-
dents, it seems higher mathematics anxiety is associated
with older age, female gender, and more surface and less
deep approach to learning. However, when mathematics
self-efficacy is included in the model, only gender and
mathematics self-efficacy effects are significant.
Interestingly, when mathematics self-efficacy is not in-
cluded as a predictor of mathematics anxiety, there are no
statistically significant predictors in the social sciences stu-
dent sample; however, once it is included in the regression
Table 1 Descriptive statistics and correlations for math anxiety and self-efficacy, approaches to learning, and age
Sample (N) M SD Min Max 1 2 3 4
Total sample (N= 231)
1. Math anxiety 11.06 3.77 5 20 1
2. Math self-efficacy 8.17 1.98 3 12 −0.769*** 1
3. SAL 19.00 4.53 9 33 0.251*** −0.210* 1
4. DAL 27.51 4.06 12 36 −0.115 0.085 −0.318*** 1
5. Age 21.39 5.12 17 51 0.128 −0.202* −0.113 0.167
STEM sample (N= 147)
1. Math anxiety 10.73 3.64 5 20 1
2. Math self-efficacy 8.39 1.92 3 12 −0.759*** 1
3. SAL 19.03 4.50 10 31 0.317*** −0.233* 1
4. DAL 27.17 4.23 12 36 −0.215 0.160 −0.351*** 1
5. Age 20.55 4.51 17 45 0.125 −0.206 −0.025 0.083
Social sciences sample (N= 84)
1. Math anxiety 11.64 3.94 5 20 1
2. Math self-efficacy 7.77 2.03 3 12 −0.802*** 1
3. SAL 18.93 4.60 9 33 0.148 −0.182 1
4. DAL 28.11 3.68 20 36 0.031 −0.005 −0.246 1
5. Age 22.87 5.78 19 51 −0.059 0.059 −0.319* 0.208
SAL surface approach to learning; DAL deep approach to learning
Pvalues are adjusted for multiple testing with the Holm’s method
*p< 0.05
**p< 0.01
***p< 0.001
Rozgonjuk et al. International Journal of STEM Education (2020) 7:46 Page 6 of 11
model, mathematics self-efficacy is statistically signifi-
cantly and negatively associated with mathematics anxiety.
Discussion
The aim of the current study was to investigate the rela-
tionships between mathematics anxiety, mathematics
self-efficacy, and approaches to learning (deep and sur-
face) among STEM and social sciences students. We had
posed several hypotheses to meet that aim.
Based on the literature (Akin & Kurbanoglu, 2011;
Vinson, 2001), we expected mathematics anxiety and
mathematics self-efficacy to have a negative association
(H1). This hypothesis found support from the data. The
very high negative correlation of r=−0.768 (across the
full sample) suggests that these variables explain each
other’s variance relatively well. These results were ex-
pected, since students who perceive that they can suc-
ceed in mathematics and who have a more positive
attitude toward this topic, should experience less anx-
iety; furthermore, as mentioned earlier, these findings
are coherent with previous research (Akin & Kurbano-
glu, 2011).
Our second hypothesis (H2) regarded the relationship
between mathematics anxiety and approaches to learn-
ing. Specifically, we expected that mathematics anxiety
correlates positively with surface approach to learning
and negatively with deep approach to learning. While
surface approach to learning should be associated with
increased and deep approach to learning with decreased
anxiety in general, a study found that only higher levels
of surface approach to learning correlated with more
mathematics anxiety (Bessant, 1995). The results of the
current study supported this hypothesis on the full and
STEM student sample level; however, surface approach
to learning did not correlate significantly with mathem-
atics anxiety in social sciences students. Furthermore,
deep approach to learning was negatively correlated with
mathematics anxiety in the STEM student sample. This
is the first study demonstrating that there are discrepan-
cies in approaches to learning in association with math-
ematics anxiety between STEM and social sciences
students. Although it is hard to explain these discrepan-
cies based on our data, it is certainly a topic that needs
to be pursued further.
According to the third hypothesis (H3), we expected
mathematics self-efficacy to be positively correlated with
deep and negatively with surface approach to learning,
in line with some previous findings (Alkhateeb & Ham-
moudi, 2006; Gorero & Balila, 2016). This hypothesis
found partial support from the data. Deep approach to
learning was not associated with mathematics self-
efficacy, while surface approach to learning had a nega-
tive correlation with mathematics self-efficacy on the full
and STEM student sample level.
We expected that STEM students have less mathemat-
ics anxiety than social sciences students in our fourth
hypothesis (H4). Royse and Rompf (1992) compared
groups of students who did and did not study social
Table 2 Results for regression models where age and gender, approaches to learning, and mathematics self-efficacy predict
mathematics anxiety in STEM and social sciences student samples
Dependent variable: math anxiety
Full sample STEM sample Social sciences sample
Predictors Model 1 Model 2 Model 1 Model 2 Model 1 Model 2
Intercept 5.853* (2.562) 20.756*** (1.888) 5.274 (2.865) 20.432*** (2.313) 4.993 (4.716) 21.688*** (3.206)
Age 0.086 (0.048) 0.008 (0.032) 0.147* (0.062) −0.016 (0.045) 0.007 (0.077) 0.038 (0.047)
Gender 1.407** (0.510) 1.207*** (0.335) 1.927** (0.576) 1.682*** (0.397) 0.284 (0.995) 0.271 (0.605)
SAL 0.183** (0.056) 0.037 (0.038) 0.179** (0.066) 0.053 (0.047) 0.185 (0.100) 0.013 (0.062)
DAL −0.074 (0.064) −0.036 (0.042) −0.150* (0.072) −0.065 (0.050) 0.089 (0.126) 0.018 (0.077)
Student group −0.628 (0.507) 0.104 (0.335)
Math self-efficacy −1.427*** (0.083) −1.350*** (0.107) −1.560*** (0.134)
Model statistics
N 231 231 147 147 84 84
R
2
0.116 0.622 0.183 0.615 0.046 0.652
Adjusted R
2
0.097 0.612 0.160 0.601 −0.002 0.630
Residual SE (df) 3.584 (225) 2.350 (224) 3.338 (142) 2.300 (141) 3.945 (79) 2.399 (78)
F (df) 5.927*** (5; 225) 61.352*** (6; 224) 7.968*** (4; 142) 45.044*** (5; 141) 0.961 (4; 79) 29.205*** (5; 78)
Regression coefficients are displayed (with standard errors in parentheses)
SAL surface approach to learning; DAL deep approach to learning
*p< 0.05
**p< 0.01
***p< 0.001
Rozgonjuk et al. International Journal of STEM Education (2020) 7:46 Page 7 of 11
work and found that the former had higher mathematics
anxiety. However, this was not the case in the current
study. STEM and social sciences students did not differ
from each other in group comparison analysis. There-
fore, this hypothesis did not find support from data.
These results are surprising, since one may logically
think that if a student chooses to major in a subject that
has a strong mathematics component, the student’s anx-
iety toward mathematics could be lower than among
students who choose a curriculum where the share of
mathematics may be rather small (on an undergraduate
level). Furthermore, STEM students are more likely to
have mathematics in different courses throughout their
studies as well as professionally after graduation. There-
fore, these results are certainly interesting, since they
demonstrate that STEM and social sciences students are
as much or as little anxious toward mathematics.
Finally, to understand how mathematics anxiety would
be predicted from approaches to learning and mathem-
atics self-efficacy when age and gender are controlled
for, we conducted regression models on the total, STEM,
and social sciences student samples. We hypothesized
that approaches to learning and mathematics self-
efficacy predict mathematics anxiety, also when age and
gender are controlled for (H5).The regression model re-
sults showed that among STEM student sample, older
age, female gender, higher surface, and lower deep ap-
proach to learning predicted higher mathematics anx-
iety. However, when mathematics self-efficacy was
included in the model, only female gender and lower
mathematics self-efficacy were significant predictors of
mathematics anxiety. Gender differences are somewhat
in line with research finding that female students tend to
experience more anxiety in STEM classroom settings
(Pelch, 2018). Interestingly, only lower mathematics self-
efficacy predicted higher mathematics anxiety in social
sciences student sample.
One potential takeaway from the results of this study
is that in order to lower one’s mathematics anxiety, it
could be necessary to boost one’s mathematics self-
efficacy. However, this may prove to be a rather difficult
task, since there is a potential problem of a “vicious cir-
cle:”one’s mathematics self-efficacy may be dependent
on one’s performance in mathematics, and vice versa
(Carey, Hill, Devine, & Szücs, 2016). Therefore, if a stu-
dent performs well on a mathematics task, their self-
efficacy may get a boost, consequently lowering
mathematics-related anxiety. On the other hand, if a stu-
dent performs poorly, their self-efficacy may drop,
followed by increased anxiety. Mathematics anxiety, in
turn, could further hamper one’s mathematics perform-
ance, resulting in poorer perceived self-efficacy. It would
be, therefore, necessary to further study—preferably ex-
perimentally and in a longitudinal study design—how
working with one’s mathematics self-efficacy could be
helpful against mathematics anxiety.
While we discussed the association between mathem-
atics anxiety and self-efficacy, it is nevertheless note-
worthy that approaches to learning seem to play a
significant role in mathematics anxiety among STEM
students. Somewhat coherent with previous findings,
more surface approach to learning predicted more math-
ematics anxiety (Bessant, 1995). These results suggest
that perhaps—at least among STEM students—there is a
possibility to tailor the classroom experience so that it
would promote more synthesis of study materials, and
decrease fact-based, rote-learning. STEM subjects likely
have more universal facts (e.g., equations, proofs) to be
learned, possibly promoting superficial learning. Here,
too, could be a potentially vicious circle in play: a stu-
dent who has to study materials that may seemingly be
isolated facts, could implement rote-learning. This re-
sults in superficial knowledge, which may not prove to
be useful when synthesis with other materials is needed.
In turn, this may lead to poor performance and higher
mathematics anxiety due to that. As discussed earlier,
mathematics self-efficacy also likely plays a crucial role
in this process. On the other hand, this reasoning does
not entirely explain why approaches to learning did not
predict mathematics anxiety among social sciences stu-
dents. It could be that STEM students differ in how they
perceive mathematics in general due to having to use
this more in their studies. We believe that this should
receive more attention in future research.
The main contribution of this study is providing insights
into the potential role of mathematics self-efficacy, and
deep and surface approaches to learning in mathematics
anxiety in STEM and social sciences students. All in all, it
could be inferred from this study that while surface ap-
proach to learning may be, to some extent, an important
factor possibly predicting mathematics anxiety, the role of
mathematics self-efficacy should be further studied in
combination with approaches to learning in order to
understand mathematics anxiety. It could be further hy-
pothesized that by improving mathematics self-efficacy, it
could also be helpful in reducing mathematics anxiety, as
well as surface approaches to learning. Interestingly, while
STEM and social science students differ in attitudes to-
ward mathematics (with STEM students scoring higher),
there were no differences in mathematics anxiety between
these student groups.
There are limitations that need to be mentioned.
Firstly, we used self-reports in our study. It could be
helpful to include other important variables, such as
grades and test scores, to complement the results. In
addition, methods such as experience sampling may also
provide more valid results (Lehtamo, Juuti, Inkinen, &
Lavonen, 2018). Secondly, there were significantly fewer
Rozgonjuk et al. International Journal of STEM Education (2020) 7:46 Page 8 of 11
social sciences students than STEM students in the total
sample, and social sciences students were slightly older
than STEM students. Although age was accounted for in
multivariate analyses, future studies should aim toward
equal sample sizes as well as higher similarity in other
demographic characteristics (e.g., age, gender). A third limi-
tation was the absence of controlling for students’prior
academicability(e.g.,gradepoint average, course grades,
ability test results). It could be that there are inherent differ-
ences between the past performance in mathematics-
related courses and mathematics self-efficacy and anxiety.
Future works should include variables of prior academic
ability as control variables. In addition, future works could
also collect data among STEM and social sciences students
across multiple semesters, providing more robust results.
The fourth limitation regards the use of the mathematics
anxiety scale that has been validated in a sample of adoles-
cents. Some additional measures of mathematics anxiety
designed for tertiary-education settings, such as the AMAS
(Hopko et al., 2003), could further validate the findings. Fi-
nally, future studies could also include other external fac-
tors to models predicting mathematics anxiety (Martin-
Hansen, 2018).
Conclusions
In conclusion, we found that STEM and social sciences
students do not differ largely with regard to mathematics
anxiety, while STEM students do have higher mathemat-
ics self-efficacy. It may be that surface approach to learn-
ing plays a larger role in mathematics anxiety in STEM
students than in social sciences students. This is the first
work to investigate the differences between STEM and
social sciences students in mathematics anxiety and self-
efficacy, as well as deep and surface approaches to learn-
ing. The results could be helpful for mathematics educa-
tors, as it is relevant for them to learn about and
understand the interplay between deep and surface ap-
proach to learning, mathematics anxiety and self-
efficacy, and students’curricula. It could be that improv-
ing students’mathematics self-efficacy, as well as facili-
tating more synthesis among the learned materials could
help as a remedy against mathematics anxiety. This,
however, should be investigated in future research that,
preferably, implements an experimental and longitudinal
study design.
Supplementary information
Supplementary information accompanies this paper at https://doi.org/10.
1186/s40594-020-00246-z.
Additional file 1: Supplementary Table 1 Grouping of students to social
sciences/STEM by self-reported curricula, and the distribution of students'
curricula by course taken Notes. LT_Calc1 = Calculus I (LTMS.00.003);
MT_Calc1 = Calculus I (MTMM.00.340); SH_StatM = Statistical Modeling
(SHSH.00.002). Supplementary Figure 1: Students' mathematics anxiety
summed scores plotted by curricula. Note: points are jittered on the
graph (with the geom_jitter() function). Supplementary Figure 2: Stu-
dents' mathematics self-efficacy summed scores plotted by curricula.
Note: points are jittered on the graph (with the geom_jitter() function).
Supplementary Figure 3: Students' deep approach to learning summed
scores plotted by curricula. Note: points are jittered on the graph (with
the geom_jitter() function). Supplementary Figure 4: Students' surface ap-
proach to learning summed scores plotted by curricula. Note: points are
jittered on the graph (with the geom_jitter() function). Math anxiety
study
Acknowledgements
N/A
Authors’contributions
DR designed the study, collected and analyzed the data, and wrote the first
draft; TK designed the study, collected the data, and revised the manuscript;
KOP collected the data and revised the manuscript; KM collected the data,
and revised the manuscript; KT collected the data, and revised the
manuscript. The author(s) read and approved the final manuscript.
Funding
This work did not receive funding. Open access funding provided by Projekt
DEAL.
Availability of data and materials
The data as well as analysis script are available among the supplementary
materials.
Competing interests
The authors declare that they have no competing interests.
Author details
1
Department of Molecular Psychology, Institute of Psychology and
Education, Ulm University, Helmholtzstraße 8/1, 89081 Ulm, Germany.
2
Institute of Mathematics and Statistics, University of Tartu, Tartu, Estonia.
3
Institute of Psychology, University of Tartu, Tartu, Estonia.
Received: 3 March 2020 Accepted: 9 August 2020
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