CodePen - Strohmaier et al
Frontline Learning Research Vol.8 No. 1 (2020) 16
- 32
ISSN 2295-3159
A comparison of self-reports and electrodermal activity as
indicators of mathematics state anxiety. An application of the
control-value theory
Anselm R. Strohmaiera, Anja
Schiepe-Tiskab & Kristina M. Reiss a b
aHeinz Nixdorf Chair of
Mathematics Education, TUM School of Education, Technical
University of Munich, Munich, Germany
bCentre for International Student Assessment, Technical
University of Munich, Munich, Germany
Article received 11 November 2018 / revised 13
December 2019/ accepted 24 January 2020 / available online 19
February
Abstract
Abstract: In the present study with 86
undergraduate students, we related trait Mathematics Anxiety
(MA) with two indicators of state anxiety: self-reported state
anxiety and electrodermal activity (EDA). Extending existing
research, we included appraisals of control and perceived value
in hierarchical multiple regression analyses in accordance with
the control-value theory of achievement emotions (Pekrun, 2006).
Results showed that trait MA predicted self-reported state
anxiety, while no additional variance was explained by including
control and value. In contrast, we found no significant relation
between trait MA and physiological state anxiety, but a
significant, negative three-way interaction effect with control
and value. Regression coefficients indicated that trait MA
predicted physiological state anxiety, but only in the presence
of negative perceived control and positive perceived value.
Thus, our results support the control-value theory for
physiological state anxiety, but not for self-reports. They
emphasize the need to distinguish between trait and state MA,
the advantages of adopting the control-value theory, and the
benefits of using EDA recording as a supplemental assessment
method for state anxiety.
Keywords: mathematics anxiety,
electrodermal activity, galvanic skin response, control-value
theory, state anxiety.
Info corresponding author anselm.strohmaier@tum.de
DOI 10.14786/flr.v8i1.427
1. Introduction
Mathematics Anxiety (MA) has a substantial impact on many
students’ academic and personal lives. It influences achievement
in mathematics tests and classes (Hembree, 1990; Ma, 1999;
Namkung, Peng, & Lin, 2019). Moreover, students with high MA
avoid mathematics in everyday life as well as in career and
academic choices (Dowker, Sarkar, & Looi, 2016; Ma, 1999). MA
is common across countries, cultures, and ages (Dowker et al.,
2016; Lee, 2009). In the 2012 study of the Programme for
International Student Assessment (PISA), 30% of students reported
that they felt helpless when doing a mathematic problem (OECD,
2013b). At the same time, MA is a problem of increasing relevance.
On average across OECD countries, MA increased significantly from
PISA 2003 to PISA 2012 (OECD, 2013b). Thus, for educational
research, it is important to understand how MA affects students
when doing mathematics. Research has elaborated the distinction
between (momentary) state anxiety (MAstate) and (habitual) trait
Mathematics Anxiety (MAtrait), assessed through separate
self-reports, but the findings left their relationship ambiguous
(Goetz, Bieg, Lüdtke, Pekrun, & Hall, 2013). Hence, merely
assessing MAtrait cannot exhaustively explain how MA affects
mathematical activities momentarily. Then again, directly
assessing MAstate provides a challenge, because self-reports of
state emotions might be unreliable (Pekrun & Bühner, 2014).
Among other physiological measures, electrodermal activity (EDA;
also referred to as galvanic skin response; GSR) had sporadically
been used as an indicator for MAstate in the 1980s, but its
relationship with self-reports of MAstate or to MAtrait remained
unclear. In this paper, we addressed this research gap by
combining two novel approaches. First, we included and compared
both self-reports and EDA as measures of MAstate. Second, we used
the control-value theory of achievement emotions (Pekrun, 2006) as
a framework to test their relation to MAtrait. Accordingly, we
included appraisals of control and perceived value as moderators
of the relation between MAtrait and MAstate.
1.2 Mathematics Anxiety
MA “involves feelings of tension and anxiety that interfere with
the manipulation of numbers and the solving of mathematical
problems in a wide variety of ordinary life and academic
situations” (Richardson & Suinn, 1972, p. 551). MA has an
adverse effect on cognitive resources, independent of actual
abilities (Ashcraft, 2007; Ashcraft & Kirk, 2001; Maloney et
al., 2013). Ashcraft and Kirk (2001) found that in a mental
addition task, undergraduates with high MA showed a smaller
working memory capacity that led to an increase in reaction time
and errors. This first finding started an intensive line of
research, largely confirming direct effects of MA on performance
(for overviews, see Dowker et al., 2016; Suárez-Pellicioni,
Núñez-Peña, & Colomé, 2016). This influence is not limited to
working memory capacity. For example, Maloney, Ansari, and
Fugelsang (2011) found that high MA students suffer from low-level
numerical deficits, like a less precise representation of
numerical magnitude. Although most studies refer to MA as a
unidimensional construct, a number of studies reported evidence
that it consists of more than one factor, most prominently a
cognitive component (“worry”) and an affective component
(“emotionality”; e.g., Ho et al., 2000; Lukowski et al., 2016;
Wigfield & Meece, 1988). These studies typically analyzed the
factorial structure of questionnaires and related the dimensions
to cognitive outcomes like mathematical achievement (e.g.,
Ashcraft & Ridley, 2005; Lukowski et al., 2016).
1.3 Trait and state Mathematics Anxiety
While there are a large number of studies on MA, very few of
them differentiate between MAstate and MAtrait (Goetz, Bieg,
Lüdtke, Pekrun, & Hall, 2013; Goldin, 2014). However, this
distinction arguably is important when focusing on the effects of
MA during mathematical activities. Self-reports of MAtrait refer
to multiple, generalized mathematical situations (Bieg, Goetz,
Wolter, & Hall, 2015). In contrast, MAstate refers to the
specific, current situation. Therefore, reports of MAtrait might
be a good predictor for long-term effects of MA on learning or
career and course choices (Dowker et al., 2016) but do not
necessarily accurately predict MAstate during specific
mathematical activities like tests or classes. When investigating
the effects of MA during such activities, directly addressing
MAstate seems to be more appropriate.
Studies investigating the role of emotions in mathematics and of
MA in particular predominantly focus on trait emotions rather than
state emotions (Goetz et al, 2013; Goldin, 2014). Accordingly, an
extensive number of findings have been gathered on effects,
individual differences, and precursors of MAtrait (Dowker et al.,
2016). In contrast, there are fewer studies on MAstate, often
using qualitative analyses (Goldin, 2014). Yet, specific
mechanisms explaining the impact of MAstate have rarely been
reported for mathematics (Dowker, 2016).
The relationship between MAstate and MAtrait is ambiguous. On
the one hand, a number of studies indicate a strong positive
relation. For high MAtrait students, MAstate is considered a key
explanation for a lower working memory capacity (Ashcraft &
Moore, 2009; Beilock, 2008). In his meta-analysis, Hembree (1990)
reports a mean correlation of r = .42 between MAtrait and state
anxiety. However, state anxiety was not necessarily assessed
during specific mathematical activities in the four reported
studies (e.g. Plake & Parker, 1982). On the other hand, some
studies indicate that there is a notable discrepancy between
MAtrait and MAstate. Goetz et al. (2013) found that girls
systematically report higher levels of MAtrait, but that this
difference is not present in reports of MAstate during mathematics
tests or classes. This difference between reports of MAtrait and
MAstate is largely explained by individual beliefs and perceptions
of competence (Bieg et al., 2015; Goetz et al., 2013). Another
reason for differences between MAtrait and MAstate might be that
MA negatively affects achievement in mathematics through long-term
avoidance behavior, but not during mathematical activities per se
(Dowker et al., 2016): To avoid aversive consequences, MAstate can
even enhance motivation momentarily and lead to an increase in
effort and strategy use during mathematics tests (Eysenck &
Calvo, 1992; Eysenck, Derakshan, Santos, & Calvo, 2007). This
indicates that MAtrait does not necessarily induce MAstate.
In general, state anxiety can have various cognitive and
motivational-affective effects on learning and performance.
Zeidner (2014) lists 15 specific deficits in information
processing during learning caused by anxiety, which are likely to
be transferable to MAstate. This includes cognitive deficits in
areas like information encoding, information storage and
processing, and information retrieval and production. Moreover,
state anxiety is associated with physiological reactions. However,
this has not been described for MAstate in particular, but only
for state anxiety in general. Per definition, state anxiety is a
“transitory emotional state consisting of feelings of
apprehension, nervousness, and physiological sequelae such as an
increased heart rate or respiration” (Wiedemann, 2015, p. 808).
Among other aspects, state anxiety is thus characterized by
increased arousal and activation of the autonomic nervous system
(Steimer, 2002; Wiedemann, 2015). Accordingly, state anxiety does
not only cause cognitive deficits, but also a physiological
reaction.
In sum, existing studies mostly focus on MAtrait, while its
relation to MAstate is left ambiguous. Thus, to better understand
how MA affects learning not only over a longer period of time but
also momentarily, additional research is needed. This refers both
to the question of the relation between MAtrait and MAstate, as
well as to the mechanisms and precursors of MAstate in particular.
In the following, we propose a theoretical framework for
investigating these questions.
1.4 The control-value theory
The control-value theory of achievement emotions (Pekrun, 2006)
characterizes predictors of achievement emotions, including state
anxiety. It states that appraisals of control and the perceived
subjective value of an achievement situation are the most proximal
predictors of achievement emotions. A low appraisal of control and
a simultaneous high perceived value of the task are key
determinants of state anxiety. In contrast, trait emotions,
environmental factors, or former achievement are considered distal
factors and are assumed to have a mostly indirect effect on state
emotions. According to the control-value theory, MAtrait should
therefore predict MAstate mostly indirectly, in association with
low appraisals of control and a high subjective value. Several
empirical studies support aspects of the control-value theory in
mathematics (e.g., Niculescu, Tempelaar, Dailey-Hebert, Segers,
& Gijselaers, 2015). Frenzel, Pekrun, and Goetz (2007) found
that MAtrait is associated with a pattern of low competence
beliefs paired with high achievement values in mathematics.
Extending the scope, research about attitudes and beliefs about
competence in mathematics offers plenty of evidence supporting the
control-value theory for other mathematical achievement emotions
(for an overview, see Goldin et al., 2016). However, to our
knowledge, no study implemented both MAtrait and MAstate as well
as appraisals of control and perceived value in one model.
1.5 Assessing mathematics state anxiety
To assess MAstate, research has mostly focused on qualitative
research (see Goldin, 2014, for an overview). These approaches
included retrospective interviews and videotaping, but the
reliability of these methods has been questioned (Goldin, 2014).
Using a more quantitative approach, Goetz et al. (2013) proposed
short self-reports that could be used both for measuring anxiety
during tests as well as during classes. The advantage of
self-reports is that they can be used conveniently for
experience-sampling and might be more reliable than observations.
However, self-reports about achievement emotions might disrupt the
current activity (Goldin, 2014). Moreover, it is questionable if
self-reports can reflect an accurate evaluation of current
emotions. In general, self-reports can only cover aspects of
emotions that a person is aware of, depend on the use of language,
and are subject to systematic biases, e.g. social desirability
(Pekrun & Bühner, 2014).
Consequently, other researchers have attempted to use
physiological measures to directly investigate MA in performance
situations (Dowker et al., 2016; Hannula, 2016), predominantly
using neuropsychological methods (e.g., Lyons & Beilock, 2012;
Pletzer, Kronbichler, Nuerk, & Kerschbaum, 2015). These
studies revealed that MA activates brain areas linked to fear
processing, disgust and pain processing, but they did not
distinguish between MAtrait and MAstate (Artemenko, Daroczy,
Nuerk, 2015; Suárez-Pellicioni et al., 2016).
State anxiety in general is associated with arousal and stress
and with physiological reactions due to the activation of the
autonomic nervous system. This leads to an increased heart rate
and respiration, among other physiological reactions (Steimer,
2002; Wiedemann, 2015). This also holds for state anxiety in the
context of education (Zeidner, 2014). Therefore, these specific
physiological reactions can be assumed to be an indicator for
MAstate. Some studies have assessed heart rate or cortisol
secretion to monitor stress levels during mathematical tests (Dew,
Galassi, & Galassi, 1984; Faust 1992, as cited in Ashcraft,
2002; Mattarella-Micke, Mateo, Kozak, Foster, & Beilock, 2011;
Pletzer, Wood, Moeller, Nuerk, & Kerschbaum, 2010; Sarkar,
Dowker, & Cohen Kadosh, 2014). These studies produced mixed
results. Mattarella-Micke et al. (2011) showed that cortisol
secretion can be associated with high performance (for low MA
students) or with low performance (for high MA students), probably
associated with a working memory overload. In contrast, Pletzer et
al. (2010) did not find a correlation between cortisol secretion
and reports of MA, but used self-reports of MAtrait, not MAstate.
A relation between heart rate and state anxiety has been shown in
various fields (e.g. Kantor, Endler, Heslegrave, & Kocovski,
2001), but has rarely been used in mathematics. Faust (as cited in
Ashcraft, 2002) reported changes in heart rate when a highly
math-anxious group performed mathematics tests of increasing
difficulty. In contrast, Dew, Galassi, and Galassi (1984) found no
substantial relation between heart rate and MAtrait or MAstate.
In addition to heart rate, Dew, Galassi, and Galassi (1984)
observed physiological arousal during a timed mathematics test
assessing participants’ EDA. EDA are fluctuations in skin
conductance due to an increase in sweat gland activity. Since
sweat gland activity is associated with the autonomic nervous
system activity, EDA is an established method to assess
physiological reactions to arousal, concerns, or stress (Boucsein,
2012; Naveteur & Freixa i Baqué, 1987; Nikula, 1991). In his
overview of the method, Boucsein (2012) extensively reviewed
applications and correlates of various measures of EDA. He
concludes that EDA “can be regarded as a valid indicator for the
strength of – mostly negative – emotions, for observing the course
of psychological stress, and for objectively determining coping
efficacy” (p. 521). Therefore, EDA can indicate state anxiety by
detecting associated physiological reactions (Boucsein, 2012).
EDA has recently been used to observe emotions during
educational processes like self-regulated and multimedia learning
(Dindar et al., 2019; Mudrick, Taub, Azevedo, Price, & Lester,
2017) and reading (Meer, Breznitz, & Katzir, 2016). Dew et al.
(1984) used various measures of EDA and different scales to assess
MAtrait and MAstate, but found no relation between EDA and
MAstate, and only a small relation between EDA and MAstate for one
of their measures of EDA. As a possible explanation, they
acknowledge that the challenge of comparing cognitively
experienced anxiety and physiologically experienced anxiety might
need a larger sample than their 31 students. Moreover, their study
design did not include a baseline measure, which is generally
advisable for data quality (Boucsein, 2012) and could indicate if
EDA is indeed influenced by a mathematical test context. Thus,
while their theoretical assumptions seem well-founded, the authors
argue that their data was not sufficient for a meaningful
interpretation (Dew et al., 1984).
In conclusion, MAstate has been assessed through qualitative
methods, self-reports, and physiological measures. Physiological
reactions are a vital aspect of anxiety in general and arguably of
MAstate in particular, but previous research has not provided
clear results concerning the relation between self-reports and
physiological measures of MAstate, or the relation between MAstate
and MAtrait in general.
1.6 The present research
So far, we have discussed that the relation between MAstate and
MAtrait is not yet fully understood. In performance situations,
MAstate might be stronger related to processes influencing
mathematical thinking, like a reduction of working memory
capacity. Therefore, taking into account MAstate seems important
when analyzing effects of MA, but it can be assessed in different
ways. While self-reports of MAstate are easy to obtain, they might
suffer from systematic biases. As an alternative, some studies
used physiological measures of stress and arousal instead of
self-reports to assess MAstate in mathematical performance
situations. Yet, these studies did either not address both MAstate
and MAtrait or, in the case of Dew et al. (1984), did not show
clear results. Moreover, no study did yet include appraisals of
control or value to describe the relation between MAstate and
MAtrait in accordance with the control-value theory. We consider
this a considerable gap in research on MA. We assume that the
approach by Dew and colleagues (1984) to use EDA as an indicator
for MAstate is more promising today, because the possibilities to
record and analyze EDA have greatly improved. Particularly, the
innovations in EDA recording offer better possibilities in
observing the association between EDA and MAtrait, since they
allow to assess MAstate more reliable and in an authentic
environment. At the same time, using the control-value theory
offers a better theoretical framework for the correlation between
MAstate and individual antecedents. It has been supported by a
number of studies using self-reports and other methods to assess
state anxiety, but to our knowledge, the control-value theory has
not yet been utilized to analyze precursors of EDA.
1.7 Hypotheses
In the present study, we investigated the relation of MAtrait
with two indicators for MAstate, the physiological measure EDA and
self-reported state anxiety. We assessed MAstate both in a
baseline context (a relaxation exercise) and a mathematics test.
First, we assumed that the mathematics test would lead to an
increase in both measures (hypothesis 1) and thus indicate that
anxiety is successfully induced by the mathematics test. Second,
we assumed that there is a relation between self-reported MAstate
and EDA (hypothesis 2). Moreover, we anticipated that our findings
would replicate the direct association between self-reported
MAstate and MAtrait (Goetz et al., 2013; hypothesis 3a). We
expected to find a similar relation between EDA and MAtrait, since
EDA should reveal physiological arousal, which in turn is an
indicator of MAstate (hypothesis 3b). According to the
control-value theory, appraisals of control and subjective value
were included as predictors. We expected that this would confirm
the relation between these appraisals and both measures of MAstate
(hypotheses 4a and 4b). Finally, the relation between MAstate and
MAtrait should be higher when students report low control and high
perceived value. Thus, we expected a negative three-way
interaction between MAtrait, appraisals of control, and perceived
value, on both measures of MAstate, respectively (hypotheses 5a
and b).
2. Method
2.1 Sample and procedure
95 undergraduate students participated in the study. They gave
written informed consent before participation. The study was
conducted according to the Ethical Principles of Psychologists and
Code of Conduct of the American Psychological Association from
2017. An ethics approval was not required by institutional
guidelines or national regulations, in line with the guidelines of
the German Research Foundation. Due to technical difficulties, 5
participants had to be excluded from the sample. Additionally, we
excluded 4 students because of deviations of more than 3 SD in one
of the assessed measures. The remaining participants were 86
undergraduate students (53 female) from programs other than
mathematics, ranging from engineering to nutritional science.
Mathematics students were not recruited as participants to avoid a
bias in their beliefs and attitudes towards mathematics, as well
as in their mathematical skills. The mean age was 23.2 years (SD =
4.07). Participants were recruited on campus and were paid 15 EUR
for participation. During recruitment and before the experiment
any indication of a mathematical content of the study was avoided.
The study was described as a study investigating EDA during
various tasks.
The individual sessions of the experiment took place in an
office at the university containing only two tables, two chairs,
and a closed closet. At the beginning of the experiment, the
experimenter made participants familiar with the wristband
assessing EDA. She then put the device on the wrist of the
participant’s non-dominant hand and fitted it comfortably. After
recording had started, participants were presented a 5-minute
relaxation exercise via headphones. The exercise facilitated
relaxation through breathing exercises, accompanied by an audio
track that included sounds from nature to help promote a relaxing
environment for the participant.
When the participant removed the headphones after the exercise,
the experimenter immediately presented the first questionnaire
assessing state-anxiety. After the participant finished the
questionnaire, a first mathematical test was presented. The
participant was asked to read the instruction carefully and then
wait for the signal to start. All participants had 10 minutes to
solve the test and received a short notice after 8 minutes. After
the test, the participant answered the second state-questionnaire.
The procedure was repeated for a second mathematics test. At the
end of the experiment, trait and demographic data were assessed.
2.2 Mathematics tests
Both mathematics tests consisted of six items. Eleven items were
taken from a pool of released items from the PISA-Study (OECD,
2013a); one item was adopted from the Trends in International
Mathematics and Science Study (TIMSS, International Association
for the Evaluation of Educational Achievement [IEA], 2013). Since
research suggests that anxiety might have a larger influence for
cognitively demanding tasks (Ching, 2017; Faust, Ashcraft, &
Fleck, 1996), we composed both tests to be fairly difficult. The
overall solution rate of 42% (SD = 21%) suggests that the tests
were appropriately demanding.
The items covered a broad range of mathematical problems,
ranging from geometry to statistics. They were based on the
concept of mathematical literacy and therefore covered
mathematical competencies beyond mere factual knowledge. The tasks
required knowledge that all students should have achieved by the
end of their compulsory education. For an overall achievement
score, we coded each item according to the coding instructions
from PISA and TIMSS (0 = incorrect, 0.5 = partially correct, 1 =
correct; OECD, 2013a; IEA, 2013) and calculated a sum score for
all 12 items.
2.3 Study measures
We assessed MAtrait using the ANXMAT-Scale developed for the
PISA-studies (five items, e.g. “I feel helpless when doing a
mathematics problem”, α = .87; OECD, 2005).
Participants answered on a 4-point Likert scale from 1, strongly
disagree to 4, strongly agree. We assessed self-reported MAstate
twice during the experiment according to Goetz et al., 2013,
asking if participants felt anxious in the previous situation (1,
definitely not to 4, definitely). Appraisals of control and
perceived values were assessed after both tests and were
task-specific. For appraisals of control, we used two items
accounting for the controllability and probability of outcomes
(e.g. “I think my competence in this area is …”, α
= .78) on a 7-point Likert-scale (1, low to 9, high; Engeser &
Rheinberg, 2008; Pekrun & Perry, 2014). Appraisals of
perceived value were assessed with the four-item cognitive
preferences-scale by Kehr, Von Rosenstiel, and Bles (1997) on a
7-point Likert-scale (e.g. “It is important to me to solve the
exercises”; 1, not at all to 9, very much; α =
.85).
For EDA data collection during the relaxation exercise and the
tests, we used an Empatica E4 wristband. The wristband is worn
like a watch and measures skin conductance with two stainless
steel electrodes at the inner wrist. The exosomatic non-invasive
sensor applies a very small, non-perceptible alternating current
with a peak value of 100 μ A at 1V with an 8Hz
frequency. The 4 Hz signal is recorded on an integrated flash
memory.
2.4 EDA data analyses
EDA signals consist of two components. The tonic signal is
influenced by medium-term factors like room temperature or
physiological characteristics of the individual. It provides a
level of skin conductance that is rather stable within some
seconds. Even though the tonic signal can be an indicator for
stress or anxiety, the phasic component of the signal is suited
better to compare EDA between individuals and is commonly used as
an indicator for state anxiety (Boucsein, 2012). Phasic components
of the EDA signal are usually called responses, since they reflect
a short peak in the signal. Responses can be specific responses to
a stimulation, for example a bursting balloon. However, there are
phasic responses that are not associated to any specific external
stimulation, hence nonspecific. The frequency of these nonspecific
responses in skin conductance is associated with stress and
anxiety and is one of the most common measures for EDA (Boucsein,
2012). The phasic and the tonic components of an EDA signal
overlap and need to be decomposed for analyses.
Data processing was carried out using MATLAB (V9.2.0) and the
MATLAB-based software Ledalab (V3.4.9). The software applies
Continuous Decomposition Analysis to extract the phasic signal
(Benedek & Kaernbach, 2010). After the extraction, any peak in
the phasic signal bigger than .01 μ S is counted
as a response (Boucsein, 2012). For both phases of the experiment
(relaxation and test), the number of events is then summed up and
divided by the duration of the phase in minutes. The result is the
frequency of nonspecific skin conductance responses per minute
(SCR.freq). SCR.freq served as the measure for physiological
MAstate.
2.5 Analyses
For hypothesis 1, we conducted a repeated measures ANOVA to test
for differences in state anxiety during the relaxation and the
test. To assess the relation between the two measures of MAstate
and their relation to MAtrait (hypothesis 2 and 3), we calculated
the correlations controlling for gender, achievement, and the
respective baseline measures (see Sect. 3.1). For hypotheses 4 and
5, we adopted a 5-step hierarchical multiple regression model for
both measures of MAstate as outcome variables (self-reported and
physiological MAstate). All predictors except gender were
z-standardized before the analyses. In step 1, we included the
control variables as predictors. In step 2, we additionally
included MAtrait. In accordance with the control-value theory,
step 3 included appraisals of control and subjective value. In
step 4, we included the interaction term between control and
subjective value. Finally, step 5 included the interaction terms
between MAtrait and appraisals of control and subjective value,
respectively. Additionally, we included the three-way interaction
between MAtrait, control, and subjective value.
3. Results
3.1 Control variables
Gender differences exist between self-reports of MA (Dowker et
al., 2016). Moreover, because of physiological differences in the
sweat gland density and activity, women tend to display a weaker
EDA reactivity than men (Boucsein, 2012). Accordingly, our results
revealed significant gender differences, with females showing
weaker EDA, t(84) = 2.93, p = .004, reporting higher MAtrait,
t(84) = -2.38, p = .020, and lower control, t(84) = 2.37, p =
.020. No significant gender differences were found regarding
self-reports of MAstate, t(84) = -0.49, p = .626, and perceived
value t(84) = 0.02, p = .984. Because of this general influence of
gender, we included gender as a control variable in all following
analyses.
In addition, achievement is associated both with trait anxiety
(Ma, 1999) and with physiological reaction (Mattarella-Micke et
al., 2011). In our data, we similarly found a significant relation
between the test score and reports of MAtrait, r(86) = -.28, p =
.008, self-reports of MAstate, r(86) = -.31, p = .004, and
control, r(86) = .51, p = .000, respectively, but no significant
relation between the test score and EDA, r(86) = .15, p = .177,
and perceived value, r(86) = .07, p = .518, respectively. Since
our analyses focused on the interplay of MAtrait and MAstate,
irrespective of achievement, we also controlled for the test score
in the following analyses. For both measures of MAstate
(self-reports and EDA), we used the data from the relaxation
exercise as respective baseline measures.
3.2 Main analyses
3.2.1 Descriptive results
Table 1 provides the means and standard deviations for MAtrait
and appraisals of control and perceived value. Additionally, mean
scores and standard deviations for both measures of MAstate during
the relaxation exercise and the test are included. For both
measures, MAstate was significantly higher during the test
compared to the relaxation exercise, confirming hypothesis 1.
While physiological MAstate increased from 15.43 events per minute
to 20.04 events per minute (F(85) = 10.53, p = .002, 2 = .10),
self-reported anxiety increased from 1.37 to 1.62 (F(85) = 17.23,
p < .001, 2 = .17).
Table 1
Descriptive statistics and differences between MAstate in
relaxation exercise and tests
Note. The unit for physiological state Mathematics Anxiety
is SCR.freq [1/min].
**p < .01 ***p < .001.
3.2.2 Correlations
Table 2 provides correlations between all measures. All
correlations were controlled for gender and test score and for the
respective MAstate baseline during the relaxation exercise.
Contrary to hypothesis 2, no significant correlation was observed
between the two measures of MAstate (r = .06, p = .63). MAtrait
showed a moderate and significant correlation with self-reported
MAstate (r = .34, p = .002), but not with physiological MAstate (r
= .08, p = .48), which supports hypothesis 3a, but not 3b.
Including appraisals of control and perceived values, MAtrait
correlated moderately and significantly with control and value (r
= -.38, p < .001; r = .24, p = .029). A significant, moderate
correlation emerged between appraisals of control and
self-reported MAstate (r = -.29, p = .008), but not physiological
MAstate (r = .05, p = .65). In contrast, appraisals of the
perceived value were significantly related to physiological
MAstate (r = .29, p = .007), but not to self-reported MAstate (r =
.16, p = .15). Appraisals of control and perceived value showed no
significant relation (r = -.01, p = .95).
Table 2
Correlations between measures of anxiety and appraisals of
control and perceived value
Note. Correlations of the two measures of state
Mathematics Anxiety are controlled for their respective baseline.
All correlations are controlled for gender and test score. n = 86.
*p < .05 **p < .01 ***p < .001.
3.2.3 Hierarchical multiple regression
Results of the hierarchical multiple regressions are reported in
Table 3. It displays only the predictors added in each step. For
the full hierarchical models, see Appendix A.1. For the two
regressions, we used the two measures of MAstate as outcome
measures respectively. Inclusion of the control variables
explained 58% of the variance in physiological MAstate during the
test (p < .001), and 24% of the variance in self-reported
MAstate (p < .001).
For self-reported MAstate, step 2 revealed a significant
relation between MAtrait and self-reported MAstate ( β
= 0.32, p = .002) that explained additional 9% of the variance in
self-reported MAstate (p = .002). Step 3 did not confirm a
relation between appraisals of control or perceived value and
self-reported MAstate ( β = -0.20, p = .090;
β = 0.09, p = .37). Step 4 did not reveal an
interaction effect of control x value ( β = -0.00,
p = .98), and step 5 revealed no three-way interaction effect of
MAtrait x control x value ( β = -0.15, p = .20).
Similarly, the interaction effects MAtrait x control and MA x
value were not significant ( β = -0.06, p = .59;
β = -0.23, p = .053). These findings do not support
hypothesis 4a or 5a. Overall, the predictors explained 39% of the
variance in self-reported MAstate (p < .001).
We conducted the same hierarchical multiple regression for
physiological MAstate. Contrary to self-reported MAstate, step 2
did not reveal a significant relation with MAtrait ( β
= 0.06, p = .48). In step 3, adding appraisals of control and
perceived value increased the R2 significantly by 4% (p = .033).
In this step, perceived value had a significant positive relation
with physiological MAstate ( β = 0.19, p = .009),
while no relation was found for control ( β =
-0.04, p = .65). Again, step 4 did not reveal an interaction of
the control and value on MAstate ( β = 0.04, p =
.65). Contrary to self-reported MAstate, step 5 revealed a
negative three-way interaction effect of MAtrait x control x value
( β = -0.23, p = .008), while the interaction
effects MAtrait x control and MAtrait x value were not significant
( β = -0.06, p = .44; β = -0.01, p
= .96). These effects explained an additional 4% of the variance
in physiological MAstate (p = .041). The three-way interaction
effect is displayed in Figure 1 (right). For comparison, Figure 1
(left) displays the non-significant interaction for self-reported
MAstate. Because there was no significant direct relation between
MAtrait and physiological MAstate, the slopes are less steep in
Figure 1 (right) than for self-reported MAstate. However, it
illustrates that the slope of MAtrait on physiological MAstate
increases for students appraising low control and high perceived
value at the same time. These results support hypothesis 5b, but
not hypothesis 4b. Overall, the predictors explained 66% of the
variance in physiological MAstate (p < .001).
Table 3
Hierarchical multiple regression analyses for physiological
MAstate and self-reported MAstate
Figure 1. Relation between MAtrait and MAstate in
dependence of control and perceived value.
4. Discussion
4.1 Measures of state anxiety in mathematics tests
In line with hypothesis 1, we found significant differences
between the relaxation exercise and the test for both measures of
MAstate. This implies that the mathematics test induced anxiety
compared to the relaxation exercise. However, descriptive analyses
showed that self-reports of MAstate were relatively low in our
study. This might be due to the fact that the experiment was a
low-stakes test for the participants. We would assume that our
result might emerge even stronger in a high-stakes test situation.
In contrast to our hypothesis, students’ self-reports about
MAstate and their physiological MAstate were not significantly
related. Our assumption had been that even though self-reports and
physiological measures might differ to some extent, they should
still refer to a similar MAstate and hence be related. Judging
from our results, the two measures might refer to conceptually
different aspects of MAstate. Some researchers suggest that
MAtrait is a multidimensional construct, usually differentiating
between a cognitive and an affective dimension (Lukowski et al.,
2016; Wigfield & Meece, 1988). Similarly, physiological
MAstate and self-reported MAstate as assessed in this study might
refer to different facets of MAstate. Consequently, they might not
necessarily be related. For example, EDA might be more associated
with arousal and an affective, emotional dimension of MAstate. In
contrast, self-reports might be more related to a cognitive
dimension of MAstate that is associated with worries and cognitive
resources (Ashcraft & Moore, 2009; Beilock, 2008; Liebert
& Morris, 1967). Future research could include a
multi-dimensional assessment of MA to address this possibility.
Additionally, the measures might differ because of their differing
mode of assessment (Pekrun & Bühner, 2014). Self-reports might
not be able to paint an adequate picture of achievement emotions,
especially for a highly physiological emotion like anxiety (Pekrun
& Bühner, 2014). Furthermore, self-reports of MAstate might be
subject to biases like social desirability (Pekrun & Bühner,
2014) or stereotypes (Goetz et al., 2013).
4.2 The relation between MAstate and MAtrait
In line with Goetz et al. (2013), we found a significant
relation between MAtrait and self-reported MAstate which was
within the range of previous findings reported by Hembree (1990).
Students with higher MAtrait also reported higher MAstate during a
mathematical test. However, we did not find a relation between
MAtrait and physiological MAstate. This finding is contrary to
hypothesis 3b but is in line with previous findings by Dew et al.
(1984). Dew et al. (1984) proposed two explanations. First, the
results might be viewed as questioning the construct validity of
MAtrait scales. Since these scales have been further validated
since then and worked as expected with regard to self-reported
MAstate, this explanation seems unlikely. Alternatively, since
students reporting MAstate need to evaluate their perceived
anxiety cognitively, it is assumed that they might in part refer
to generalized beliefs about mathematics. This might include the
same resources as their evaluation of MAtrait (Bieg, Goetz, &
Lipnevich, 2014; Goetz et al., 2013), or students might even refer
directly to their MAtrait when trying to evaluate MAstate. This
would increase the relation between self-reported MAstate and
MAtrait, but not between physiological MAstate and MAtrait.
4.3 The control-value theory
According to the control-value theory (Pekrun, 2006), MAstate
should primarily be determined by appraisals of control and
perceived value. These appraisals should also moderate the
relation between MAtrait and MAstate. For the two measures of
MAstate, the application of the control-value theory in the
present study produced diverging results.
Both MAtrait and self-reported MAstate were related to
appraisals of control. Nevertheless, the hierarchical multiple
regression did not produce signs that appraisals of control or
value play an important role for the relation between MAtrait and
self-reported MAstate. Rather, this relation seemed to be direct.
Hence, we did not find support for the control-value theory for
self-reported MAstate. As was proposed above, the relation between
MAtrait and self-reported MAstate might be increased by the
similar mode of assessment. The resulting direct relation could
overweight a possible indirect effect of appraisals of control and
perceived value.
In contrast, physiological MAstate showed a different pattern.
In opposition to self-reported MAstate, we did not find a direct
correlation with MAtrait. However, we found strong support for the
control-value theory in this second multiple regression analysis.
First, perceived value was related to MAstate, independent of
MAtrait. Second, including appraisals of control and perceived
value explained additional 8% of variance of physiological
MAstate, which indicates a substantial contribution to its
emergence. Third, the interplay between MAtrait, control, and
value also was observed as expected. As illustrated in Figure 1
(right), high MAtrait was related to high MAstate, but only when
students appraised their control low and their perceived value
high. This effect is in line with the control-value theory, since
MAtrait is considered a distal antecedent, whereas appraisals of
control and perceived value are considered proximal causes of
MAstate. These results further support the notion that the causal
relation between MAtrait and the two measures of MAstate might be
conceptually different.
4.4 Limitations
Using EDA comes with some immanent limitations, and only some of
them can be overcome. For example, EDA is subject to physiological
gender differences. This inhibits its practicality for inquiring
the gender gap in MA. Even when controlling for a baseline value,
differences in reactivity exist. In general, a large variance
between students’ EDA makes comparisons more difficult. In our
study, we assessed the baseline value during a relatively short
period of time. A more reliable value could be obtained through
several hours or days of baseline recordings (Boucsein, 2012). Of
course, such a study requires much more time. Lastly, even though
MA is common in students of all ages, our specific sample cannot
be overgeneralized. It needs to be verified if EDA recording can
be useful in schools and for specific groups of students, for
example high-anxiety students or younger students.
More generally, our test did not seem to induce a very strong
emotional reaction. In order to generalize our findings to
high-stakes testing which might cause more MAstate, additional
studies are needed. Moreover, we followed Goetz at al. (2013) in
using a single-item scale to assess self-reported MAstate. This
keeps the disruption of the participants at a minimum but might
result in some inaccuracies. Our results indicate that the scale
was working properly, but future studies might try to assess
MAstate at more occasions or check if the one-item scale is
appropriately precise. Similarly, a number of different
questionnaires exist to assess MA and general test anxiety.
Comparing these questionnaires regarding their relation to EDA,
particularly regarding cognitive and affective dimensions of these
scales, could help to explain the absent relation between
self-reported and physiological MAstate.
The relation between EDA and physiological arousal has been well
established by previous research (Boucsein, 2012). However, other
factors than MAstate might additionally influence EDA during
mathematics tests. Future research could incorporate additional
state measures that assess cognitive load or situational
motivation to further narrow down the processes associated with
EDA reactivity, and might support these findings through
qualitative data like interviews or think-aloud-protocols. Until
the validity of EDA as a measure of physiological MAstate is fully
understood, results will always require a cautious discussion of
limitations and different explanations.
The control-value theory is generalizable to various achievement
emotions, including both trait and state emotions (Pekrun, 2006).
In the current cross-sectional study, we focused on MAstate as an
outcome, and task-specific appraisals of control and perceived
value as moderators. Consequently, we considered MAtrait as a
distal predictor. However, future studies could also consider
MAtrait as an outcome itself. For analyzing effects of general
appraisals of control and perceived value towards mathematics as
predictors of MAtrait, longitudinal designs would be more
advantageous.
4.5 Conclusion
Our study combined several innovative approaches that have
emerged in research on MA within the last years. With the
distinction between MAtrait and MAstate, we differentiated between
two different facets of MA. Further, through the adoption of the
control-value theory, we compared EDA recordings and common
self-reports as a tool for observing MAstate and investigated
their unique relations to MAtrait. Overall, we found that EDA was
related to MAtrait, but that this relation only got visible when
taking appraisals of control and perceived value into account.
Students reporting high MAtrait were not necessarily more
physiologically anxious during mathematical activities. Rather, a
pattern of appraisals of low control and high perceived value
accompanied that relation. Hence, with regard to EDA, our results
were in line with the control-value theory, which on the other
hand was not supported by self-reported measures of MAstate. In
sum, our findings match the plea by Goetz at al. (2013) to
consequently distinguish between MAtrait and MAstate in research
on MA, as well as to additionally include physiological data in
assessing emotions in learning.
Furthermore, our results indicate that self-reports and
physiological measures might refer to different aspects of
MAstate. Thus, our results support theoretical considerations and
empirical findings that self-reports of MAstate should be
interpreted cautiously. Ultimately, we cannot decide if
self-reports or EDA captured actual MAstate. Rather, the two
measures both seem to be related to MAtrait, but in different
ways. Therefore, we cannot conclude that EDA can make self-reports
obsolete, but we propose that the assessment of EDA can provide
additional information about underlying affective aspects of
MAstate. Because of recent technical advances in recording and
analyses of EDA, the method seems to offer a convenient addition
to the common practice of self-reports. Furthermore, the advances
in EDA-recording offer the possibility to conduct studies in the
classroom during regular classes with hardly any disruption. We
believe that our study can be a first step into this promising
direction of in vivo research on MA.
As a next step, the relation to mathematical achievement should
be investigated. In the recent study, we used a mathematics test,
the goal of which was to trigger MA, but that was not designed to
diagnose mathematical achievement in detail. Our preliminary
results indicate that achievement might be differently associated
with self-reported and physiological MAstate, but a study that
assesses mathematical performance in more detail is needed to shed
light on this question. Additionally, achievement under conditions
of MAstate and no MAstate should be compared in a within-subject
design, since EDA shows a notable variance between subjects.
Similarly, using tests that are not mathematical could help to
distinguish how specific MAstate is linked to mathematics. At the
same time, using EDA for other domains or test anxiety in general,
possibly using the control-value theory, might be an interesting
and fruitful perspective for future research. Lastly, the relation
to working memory capacity, which has proven to be a key factor in
the effects of MA, should be taken into account. Ultimately, this
knowledge could be used to design longitudinal and intervention
studies that use EDA to observe the role of MAstate for learning
processes or create ways to decrease MAstate in mathematics tests,
possibly without necessarily tackling MAtrait.
With a number of questions remaining unanswered, our study is
merely a first step in including EDA as an indicator for MAstate.
Nevertheless, the results illustrate that self-reports only
comprise one perspective on the multi-faceted phenomenon of
Mathematics Anxiety, and that including EDA can be uniquely
insightful.
Keypoints
We did not find a correlation between EDA and measures of
state anxiety or trait Mathematics Anxiety, respectively.
Self-reported state anxiety correlated significantly with
trait anxiety independent of appraisals of control and perceived
value, which is in contrast to the control-value theory.
In line with the control-value theory, trait Mathematics
Anxiety predicted physiological state anxiety when high
perceived value and low control of the achievement situation
were reported.
Acknowledgments
We would like to thank Ashley L. Johnson and Kathrin Ebenhöh for
their contributions during data collection. This research was
funded by the Federal Ministry of Education and Research (BMBF)
and the Standing Conference of the Ministers of Education and
Cultural Affairs of the Länder in the Federal Republic of Germany
(KMK) [Grant number ZIB2016].
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Table A.1
Full hierarchical multiple regression analyses for
physiological MAstate and self-reported MAstate