This work addresses the question of how to estimate mathematical anxiety from psycho-physiological data in real-time applicable to primary school pupils. Besides establishing machine learning and statistical learning architecture, the intrusion of wearable sensors and the feasibility of test dataset collection are considered. From the psychological aspect, the framework of mathematical anxiety estimation was established within the CoolKids program. It provides an established and verified program of helping pupils with mathematical anxiety and the instruments to estimate mathematical anxiety without technology. As such it also provides the measurement scenario. Measurement and estimation system architecture and an early-stage research design are given only.
Mathematics anxiety (MA) is described as “a feeling of tension and anxiety that interferes with
the manipulation of numbers and the solving of mathematical problems in a wide variety of
ordinary life and academic situations.” [
According to Luttenberger [
An important finding is that the research showed mathematical anxiety is not necessarily
linked to lower mathematical abilities and can be caused by numerous other factors as pointed
out by Mammarella et. al. [
MA framework is a complex one and it interacts with environment-related and person-related
variables. According to Luttenberger [
In this paper, the first step of the mathematical anxiety (MA) measurement and estimation system is given. We present the study design including the measurement procedure and mathematical anxiety ground truth determination. A reliable feasibility study is one of the main goals including sensor intrusion measurement.
A primary interest of this study is to estimate mathematical anxiety (MA) from real-time
measurement and to obtain ground truth values best available today. Therefore, models of
mathematical anxiety are the first to be examined. There are several models of mathematical
anxiety studied, among them, MA as a personality construct, MA as a cognitive construct, MA
as a sociocultural construct, and MA as a neuro-biological construct as indicated by Mammarella
et. al. [
The Cool Kids Anxiety Management Program has been developed, designed, and established by
Ron Rapee and his colleagues at Macquarie University. It is been running and further developed
since 1993, [
The theoretical basis of the Cool Kids Anxiety Program is derived from Cognitive Behavioural Therapy (CBT), with a focus on teaching practical skills. There are a number of research and scientific studies evaluating the eficiency of the program available. The development of the program followed these studies. Past studies showed that the majority of attendees of the program show significant improvement. There were indications of improvements in terms of an increase in school attendance, academic achievement, confidence, and decreases in worry, shyness, and fear. The many aspect verifications of the program are crucial for our research since it assures the best available ground truth values of MA entered into statistical analysis and machine learning procedures.
Slovenian language versions of procedures materials and instruments were developed and
made available by a consortium of four child and adolescent mental health centers (SCOMS
Ljubljana and Maribor and Community Health Centres Ljubljana and Velenje), through funding
by the Ministry of Health of Republic of Slovenia while obtaining Cool Kids license [
Since MA may be afected by any aspect of cognitive processing, we examined promising studies from a wider area of processes such as fatigue, afect, and emotion.
Physiological signals were used to estimate users’ fatigue [
To the best of our knowledge, no study on MA estimation from psycho-physiological sensors is available. However, there were studies on the association of psycho-physiological signals to MA such as heart rate (HR) and electro-dermal activity (EDA), see [16][17][17]. Only low efect-size associations were found indicating the automatic estimation of MA from these signals is a dificult task.
Since sensors applicable to a given measurement scenario is a major design-deciding factor, we present psycho-psychological signals grouped by sensors primarily selected in this research. According to the previous studies’ results, see Subsec. 3.4, we selected three sensors briefly described below. 2.4.1. Empatica E4 The Empatica E4 bracelet [18] is a state-of-the-art sensor for the real-time measurement of wrist psycho-psychological signals. Among others, it covers skin electro-dermal activity (EDA), heart rate, accelerometer, gyroscope, and others. It is important to point out 200 Hz sampling rate allows for algorithmically separating EDA signal into a phasic and a tonic signal component.
Tobii pro glasses 3 [19] supports eye tracking, pupil diameter measurement, head acceleration, and other measurements. The intrusiveness of eye-tracking glasses was reduced considerably by a novel design. The calibration procedure is not required for each individual measurement. Also, it allows selecting lenses with a selected diopter. The Samling rate of eye tracking can be set to 50 or 100 .
Edge computing camera R50 [20] was selected to track the pupil’s skeleton in real-time. The OAK-D baseboard has three on-board cameras which implement stereo and RGB vision, piped directly into the OAK SoM for depth and AI processing. The data is then output to a host via USB 3.1 Gen1 (Type-C).
In this section, we provide an outline of the measurement and mathematical anxiety estimation operation procedure and PC-based application including selected psycho-physiological sensors.
System requirements were derived from research goals and research questions mainly directed toward the feasibility of automatic mathematical anxiety estimation: 1. Measurement device (to which sensors are connected) might not be the same as the device presenting estimation results in real-time; 2. Near-real-time measurement and anxiety estimation, delays under 1 second are acceptable; 3. Psycho-physiological sensor connection - there is no applicable standard for sensor connection and a specific solution for each sensor must be provided; 4. Reliability and end-to-end delay: reliability is of crucial importance and will be regularly verified (see Sec. 3.1.3). End-to-end delay (measurement, processing, MA estimation) is not critical, a delay of 1 sec. is acceptable.
Considering also ethical (including GDPR) requirements we decided the architecture system architecture is based on a client-server architecture built around node.js run-time environment [21] and real-time database InfluxDB [ 22]. Specifically: 1. Client/server architecture based on node.js run-time environment; 2. User interface must support 1. real-time interaction of a session supervisor, 2. real-time visualization of measured signals to monitor sensor ”burn-in” period (for instance, the bracelet for EDA must get to the right temperature), and to make sure the measurement system is operating properly; 3. Measurement device is Windows PC as it allows the simplest development environment; 4. Measured signals database: we selected the real-time database InfluxDB meeting all requirements; 5. Candidate sensors are given in Subsection 2.4.
The resulting architecture is given in Fig 1
The outline of the operation is the following: First, we run a script that starts up the sensors. Data from sensors has to be collected and sent to the server database. This is done with the help of a python program that turns on the sensors and triggers the sensors to start measuring. It also sends data to the server database. Values that are sent represent sensor measurements and are written in JSON format. Next, the database receives the JSON strings that contain sensor measurements. It stores them in a table that contains a timestamp to maintain the necessary relations between diferent sources. This information is later used to calculate which values pertain to the measured event. Afterward, the server’s main assignment is to maintain a connection between the back-end and front-end. It receives client input which determines the state of the data-gathering process. Based on client input and values from the database it calculates the level of anxiety. Calculated data is then forwarded to the client side where it is presented. The connection between the client and server side is a two-way connection. Its job is to maintain a connection between the two parts. It forwards the state of the data-gathering process from the client side and forwards calculation results from the server side. Note that client is responsible for taking user input that defines the state of the data-gathering process and forwarding it to the server side. It also presents calculated results from the server side.
Reliability verification will be implemented in terms of 1. Regular arrival data points from sensors: are sensors fully functional? 2. Missing data points from sensors: is the proportion of missing values low enough? 3. Correctness of machine-learning algorithms for MA estimation: do we receive correct
MA estimation results? According to our experience with similar systems, the wireless connections (WIFi and Bluetooth) of sensors to the measurement device is the main source of reliability issues. Reliability will be verified during the usage of the system regularly once per month.
End-to-end delay will be measured on three diferent test persons through automatic analysis of system log files. In the verification mode, the system will be logging the following events: data point arrivals from sensors, each estimation of MA and user interface refresh. All events will be time-stamped.
The measurement scenario is taken from the Cool Kids format. As an established and verified program, our goal was to modify it as little as possible. The time frame is given by carefully designed and structured ten sessions each pupil attends. Sessions are one-to-one and supervised by certificated psychologists.
We plan to measure two out of ten sessions as identified by the field experts. The session
will be upgraded by a standard explanation of the study purpose to the participants and their
parents and sensor mounting. The online measurements and MA estimation results are not
planned to be shown to the participants. For a fair comparison of results, the rest of the Cool
Kids [
To label our measured data on real subjects with estimated mathematical anxiety we also lean on
Cool Kids program [
During the process of the session, the participant’s (pupil’s) mathematical anxiety is measured several times using a single-dimensional 10-level anxiety level scale as a pupil self-report. The participant estimates and reports her anxiety by looking at the graphical representation of the scale attached to the wall.
The number of Likert scale levels of MA as a ground truth will be determined according to the distribution of obtained values on the 10-level scale. The starting point is a 10-level scale.
After the session, participants will again fill out a short self-report measure of MA (to be decided later between several diferent scales in consideration at the moment).
To the best of our knowledge, automatic estimation of Mathematical anxiety in real-time from psycho-physiological signals was not reported yet. However, useful algorithms were reported and described from likely related estimations including stress and attention estimation.
Literature review shows machine and statistical learning algorithms are selected and optimized according to the selected psycho-physiological signals and features extracted from them. As such, feature extraction is the main challenge of information extraction from physiological signals [23][24][25][26]. Since measuring the time dynamics of our test participants, we will pay special attention to time-local features. Signal-specific feature extraction yields the best results. Regarding EDA, decomposition to tonic and phasic components is of key importance [27]. Standard feature extraction includes the number of peaks, variability, and spectral-based features. There are specific feature extraction techniques. Observing EDA at diferent frequencies is studied in [28]. Authors of [29] focus on time and frequency domain features followed by information-based feature selection approaches including maximization of mutual information and input symmetrical relevance. Chaspari et al [30] proposed a multidimensional EDA fingerprint as a model of efective feature extraction. Authors of [ 31] focus on multi-modal feature extraction proposing 40 features designed for fear classification but applicable to other tasks.
Regarding heart signals, authors of [32] propose dimensionality reduction and salient features approach to ECG signal directly linked to feature selection and machine learning methods. Ebrahimzadeh propose lime-local features of ECG signal evaluated for sudden cardiac death [33]. Authors of [34] focus on fusion-based feature extraction of ECG signal applicable as general purpose framework. Van Gent et. al pay special attention to noisy heart rate signals [35] also providing a Python toolbox. A systematic review of deep learning-based methods is given in [36] covering 154 research papers. Machine learning techniques are usually linked to specific signals and their features [37].
Studies directed into mathematical anxiety estimation are summarised in [16]. As a framework, the human autonomous response system is described. The most reliable measurement pointed out was salivary cortisol level which is not applicable in real-time measurement. There were several studies on hart rate (HR) correlation to MA and one study [17] reported a negative correlation to the Anxiety Toward Mathematics Scale with low efect size. Other studies did not ifnd correlations. Regarding Skin conductance (as a part of Electro-dermal activity) one study found a positive correlation to the Anxiety Toward Mathematics Scale and to the Mathematics Anxiety Rating Scale [17]. No pupil diameter relations to MA were reported.
Several Python toolkit are available, we will base our work on Tsfresh [24], PySiology [25], Neurokit2 [38] and PyHeart [35].
The measured psycho-physiological signals will be reprocessed (missing values, outliers etc.), time-synchronized, and labeled by the MA ground truth. To make machine learning model evaluation possible, we will extract candidate psycho-physiological signal features and visualize them. According to the addressed research question, the following data analysis is planned. 1. Which signal features are associated with MA? A one-way ANOVA design will be applied.
Since signal features are typically not distributed normally, we will use Kruskal-Wallis ANOVA when necessary. 2. Which statistical model explains most of the MA variability? To test linear and nonlinear models, we will statistically test the null hypothesis 0 = [ 2 = 0] for each tested model. 2 stands for the Coeficient of determination. 3. Which machine learning model performs the best classification on MA classes? For practical application of MA estimation, classification of MA into predefined classes may be more efective compared to regression models (ad 2.). We will analyze the distribution of ground truth values of MA, group them into three or more classes, and evaluate ML classification algorithms using Area Under ROC measure.
The problem of real-time mathematical anxiety (MA) estimation is posed and the outline of the solution in terms of technology, procedure, and ground truth of MA determination is proposed. A plan of statistical analysis is also provided. As the research project is in an early stage, no experimental results on measurements or machine learning algorithms’ performance are presented.
Future work includes measurement application implementation and verification (currently in progress), two-phase measurement of real subjects, selection and adaptation of most efective machine learning algorithms, and the evaluation of the results. Note that the research is primarily focused on the feasibility of the automatic MA estimation using sensors. Performance in terms of reliability and end-to-end delay is scheduled first. Based on a small-scale study of ifve participants, we will select classic instruments to measure MA later utilized as machine learning test labels. Experimental results will be presented in the form of a feasibility study in terms of machine learning and measurement (sensor intrusion included).
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