In a theoretical framework of how cognitive load might be conceptualized in the context of problem solving, Paas and van Merriënboer (1994) distinguished between causal and assessment factors of cognitive load. Causal factors include learner characteristics (e.g., prior knowledge, cognitive capabilities, motivation, and affect) as well as task environment (e.g., task complexity, time pressure). In a more recent revision of the framework, the dimension of task environment in the causal factors has been subdivided into learning task and the physical learning environment (Choi et al., 2014). Furthermore, two- and three-way-interactions illustrate the fact that each causal dimension may affect cognitive load depending on characteristics of the other dimensions. For example, the amount of cognitive load a learner invests to solve a given task might depend on task complexity, the specific context or goal (e.g., just for fun vs. high stakes test), and the learner's interest related to the given problem. In terms of assessment factors, the authors distinguished between a task-relevant cognitive load dimension of mental load, a person-relevant cognitive load dimension of mental effort and task performance (Paas and van Merriënboer, 1994). Mental load is based on characteristics of the task, representing the cognitive capacity needed to process a task. In contrast, mental effort reflects an individual’s invested cognitive capacity while working on a task. Assessments of mental effort are thought to provide information about the amount of controlled processing a person is engaged in (Paas and van Merriënboer, 1994).

Some of the assessment factors are hypothesized to be affected by the causal factors during problem solving. In particular Paas and van Merriënboer (1994) conceptualized mental load as independent from person characteristics and, thus, as being constant for a given task (e.g., in terms of cognitive capacity necessary to process the number of elements in a given task). Whereas mental effort and task performance are affected by all three causal dimension factors. Sweller et al. (2011) propose mental load and mental effort as being two different but, in most cases, positively correlated constructs, with the former being the hypothetically required and the latter being the occurring cognitive resources in relation to the learning task. However, the relationship between mental load and mental effort, as well as the relationship between mental load, mental effort, and task performance, might not necessarily be positive. For example, both high or low mental load could result in rather low mental effort due to the moderating role of person characteristics such as motivational variables and persons may reach the same number of correct answers on a test but need to work with different amounts of mental effort (Paas et al., 2003). Relatedly, Moreno (2010) suggested conceptualizing cognitive load within a cognitive-affective theory of learning and emphasizes ‘that cognitive capacity is a parameter that students bring to the learning task whereas motivation determines the actual amount of cognitive resources invested in the learning task’ (p. 137).

This framework provides a powerful tool for researchers as it allows to further investigate cognitive load by narrowing down into its constituent dimensions and provides venues for further research. For example, relating measures of mental effort and task performance allows to investigate the cognitive capacity needed for reaching a specific level of performance (Paas and van Merriënboer, 1994). Further research questions that can be derived from the framework are related to the specific relationships between learner characteristics, such as emotion and motivation, and individual’s invested mental effort (Moreno, 2010; Hawthorne et al., 2019; Skuballa et al., 2019).

The present study focuses on this framework of cognitive load (Figure 1) and is, therefore, related to the assessment and causal factors of cognitive load, assuming that the actual cognitive capacity that needs to be investigated to process a given task (i.e., mental load) is necessarily intertwined with the causal factors such as learner characteristics (especially relatively stable characteristics such as prior knowledge) and, thus, is likely to vary between individuals. Thus, it focuses on the associations between the assessment factors and causal factors, in particular the learner characteristic aspects in terms of motivation and affect. Furthermore, we examined the level of convergence between cognitive load measures obtained via objective and subjective approaches. Below we first elaborate on recent research on subjective and objective measures of assessment factors of cognitive load, then we review literature on learner characteristic related variables including self-concept, interest, and perceived stress as causal factors of cognitive load.

Subjective measures of cognitive load ask respondents to self-report the amount of cognitive load after working on a task (Sweller et al., 2011) and this has been the primary approach in research practice (e.g., Paas 1992; Nehring et al., 2012). One basic assumption of subjective measures is that individuals are aware and can quantify and report on their cognitive load (Solhjoo et al., 2019). One of the first scales that have been proposed for subjective measurement of cognitive load was developed by Paas (1992), who introduced a single-item nine-point mental effort rating scale. This scale asks respondents to rate their invested mental effort, ranging from “very, very low mental effort” to “very, very high mental effort”.

However, subjective measurement of cognitive load ‘has become highly problematic’ (Kirschner et al., 2011, p. 104). Krell (2015) summarized several reasons for this:

In response to such criticisms, new subjective measures of cognitive load have been proposed. For example, some authors (Klepsch et al., 2017; Leppink et al., 2013) developed instruments to assess three dimensions of cognitive load: intrinsic load, extraneous load, and germane load (cf. Paas et al., 2003). These dimensions reflect the cognitive capacity caused by the complexity of a problem (intrinsic cognitive load), the design of learning material (extraneous cognitive load), and the effort invested to solve a given task (germane cognitive load). Hence, related to the framework used in the present study (Figure 1), germane and extraneous cognitive load are related to ME, whereas intrinsic cognitive load is related to mental load (Choi et al., 2014). For both instruments, validity evidence based on various sources (e.g., internal structure, test content) have been provided (cf. AERA et al., 2014) and the authors conclude that their instrument is useful, feasible, and reliable (Klepsch et al., 2017) or that it could be used for research purposes in various knowledge domains (Leppink et al., 2013), respectively.

Related to the framework of cognitive load, which is used in the present study (Figure 1), Krell (2015, 2017) proposed the Students’ Mental Load and Mental Effort in Biology Education-Questionnaire (“StuMMBE-Q”). This instrument was designed to measure students’ mental load and mental effort on 12 rating scale items. Besides its development in the context of student assessment in biology education, it has been widely applied in various other contexts (e.g., Nebel et al., 2016; Knigge et al., 2019). Evidence for the valid interpretation of the ratings as indicators for students’ mental load and mental effort have been provided based on test content, internal structure, and relation to other variables (AERA et al., 2014). For example, psychometric analyses confirmed a two-dimensional data structure, representing measures of mental load and mental effort (Krell, 2015). Furthermore, students’ self-reported mental load and mental effort significantly increased with increasing task-complexity (Krell, 2017). In preceding studies using the StuMMBE-Q, students’ task performance was significantly negatively correlated with their self-reported mental load but not associated with their self-reported mental effort (Krell, 2015, 2017).

In sum, subjective measurement has been the primary approach in assessment of cognitive load. However, this approach is subject to influence from causal factors, in particular individual differences such as prior knowledge, interest and motivation. Thus, subjectively perceived cognitive load might not accurately reflect the characteristics and demands of the learning task. Objective measures, on the other hand, may provide more accurate reflection on task complexity presented to the learner.

Besides the measurement of cognitive load via self-reports on questionnaires (e.g., Paas, 1992; Leppink et al., 2013; Krell, 2017), other approaches suggest or use more objective, physiological measures as indicators for respondents’ cognitive load (cf. Sweller et al., 2011); such as eye movements (Ikehara and Crosby, 2005; Zu et al., 2019), degree of pupil dilation (Huh et al., 2019), or physiological stress parameters such as heart rate and cortisol secretion (Veltman and Gaillard, 1993; Kennedy and Scholey, 2000; Cranford et al., 2014). Previous research has attempted to triangulate both objective and subjective cognitive load measures (Kahneman and Peavler., 1969; Antonenko et al., 2010; Zu et al., 2019). Physiological measures have also been proposed as sources for validity evidence for self-reports, if positive correlations between both measures can be shown (e.g., Solhjoo et al., 2019). However, some studies were able to show such positive relations (e.g. Solhjoo et al., 2019), while others found differences between self-reports and physiological measures, suggesting that both might assess separate aspects of cognitive load (e.g., Zheng and Cooke, 2012 for pupillometric measures).

Based on the Biopsychosocial Model of Challenge and Threat (Blascovich and Mendes, 2000; Blascovich, 2008) individuals can perceive performance tasks as 'challenge' or 'threat', depending on how they assess task demands and their own resources. 'Challenge' occurs when resources exceed demands (comparable with low mental load) and 'threat' if demands exceed resources (comparable with high mental load). In this model, the individual relevance of the performance goal is also important, as task engagement (comparable to mental effort) is necessary for challenge and threat states (Blascovich and Mendes, 2000). Challenge and threat states are marked by different cardiovascular patterns. Challenge states are indexed by increases in heart rate, dilation of arteries and increased blood pump, whereas threat states result in little or small increase in heart rate, constriction, and less bloodstream (Seery, 2011; Seery, 2013).

Besides the measurement of the heart rate itself (heart rate, e.g., Solhjoo et al., 2019), some heart rate variability measures were also used in educational and psychological research, including the ratio between high frequency and low frequency components (LF/HF ratio, e.g., Minkley et al., 2018), and the time-related root mean square of successive differences (RMSSD, e.g., Minkley et al., 2018). If a person is confronted with a complex problem or task, where demands exceed their resources, the RMSSD typically decreases (e.g., Malik et al., 1996), as it represents parasympathetic activity which in turn characterizes relaxation (Laborde et al., 2017). In contrast the LF/HF ratio as well as the heart rate increases (e.g., Malik et al., 1996; Isowa et al., 2006). Both parameters basically represent (at least the proportion of; LF/HF ratio) sympathetic activity, which in turn increases under stress (Laborde et al., 2017).

Thus, it is plausible to assume a relationship between subjective measures and heart rate- or hormone- based objective measures of cognitive load, which is rarely investigated yet. One study of the authors found a significant positive correlation between self-reported mental load (i.e., perceived task complexity) and perceived stress but no or rather small correlations between self-reported mental load and physiological stress responses (cortisol concentration, heart rate variability; Minkley et al., 2018). Veltman and Gaillard (1993) report similar findings and conclude that cortisol concentration might not be a valid indicator for mental activity and that heart rate variability might indicate cognitive load only in high demanding tasks. The study of Kennedy and Scholey (2000) points in a similar direction: Although a correlation between heart rate and demanding (mental arithmetic, word retrieval) vs. non demanding (control) tasks could be observed, this correlation was not present when the mental arithmetic tasks were further differentiated regarding their difficulty (serial subtraction of three vs. seven). In contrast, Cranford et al. (2014) observed a higher heart rate in chemical tasks designed to achieve high cognitive load compared to the heart rate in low cognitive load tasks. Unfortunately, the authors did not assess any self-report measure of cognitive load from their participants. However, a recent study by Solhjoo et al. (2019) found positive correlations between self-report measures of cognitive load and heart rate variability for a small sample of ten medical students. In contrast, Woody et al. (2018) found no association between cognitive load and cortisol concentration or heart rate. Hence, it is still vague regarding to what extent and under which circumstances objective measurements capture cognitive load and to what extent they converge with subjective measures of cognitive load.

As shown in Figure 1, in the theoretical framework proposed by Paas and van Merriënboer (1994), causal factors of cognitive load consist of both task characteristics and learner characteristics. To date much research of causal factors have focused on varying task characteristics such as worked example vs problem solving. Although there has been research on the roles of learner characteristics in terms of learner prior knowledge (Kalyuga et al., 2003) and age (van Gerven et al., 2002) on cognitive load, less is known about motivation and emotion and how they affect cognitive load. The related cognitive theory of multimedia learning (Moreno, 2010) also suggested that learner’s motivational and affective factors play an important role in the cognitive processes that are captured by the germane cognitive load, which in part is reflected by the learner’s invested mental effort. Motivated learners are more likely to be engaged during the learning process, thus their cognitive resources are more likely directed at schema constructions important for knowledge acquisition. In a similar way, empirical research also confirmed that factors such as learner’s emotion, enjoyment, or stress, can influence available working memory resources (Plass and Kalyuga, 2019) thus affecting the learner’s experienced cognitive load, whereas other constructs such as academic self-concept are less studied in the current context but may also affect cognitive load (Seufert, 2020). In the present study, we look specifically at constructs representing interest, stress related emotion, and academic self-concept of ability (ASCA) and how they may relate to cognitive load measurements. Below we review relevant literature in these motivational (interest and ASCA) and affective (emotion - stress) causal factors and how they affect or could theoretically affect cognitive load. Additionally, to account for the relevance of objective and subjective differentiation of cognitive load measures in the present study, we also review a relatively small pool of literature that studied the relationships between motivation, emotion and objectively measured cognitive load.

The aims of this study are to evaluate the convergence between subjective (self-reports on mental load and mental effort) and objective (heart rate measures LF/HF ratio, RMSSD and heart rate) measures of cognitive load (Leppink et al., 2013; Solhjoo et al., 2019) and to provide evidence for the assumed relationships between assessment factors of cognitive load, that is mental effort and mental load (Paas and van Merriënboer, 1994) and conceptually related causal factors in terms of positive and negative motivation and affect, that is self-concept, interest and perceived stress (cf. Moreno, 2010; Minkley et al., 2014; Minkley et al., 2018; Solhjoo et al., 2019).

The data come from three earlier studies, one of which (study 1) has been published elsewhere (Minkley et al., 2018), and which are secondarily analyzed for the purpose of this study. In each of the three studies, high school students participated in a one-day out of school learning project about molecular biology techniques with instructional and practical hands-on phases, aimed at identifying genetically modified food in the teaching and learning laboratory at Ruhr-Universität Bochum. The procedure and design of the three studies were the same and also the structure of the tasks' and the measurements. The differences between the three studies lie in the fact that the content of the tasks differed in each study, although they all dealt with topics in molecular biology (see sections “Procedure” and “Tasks”).

The participants (N = 309, from three studies; Table 2) were upper-level students with a mean age of 17.48 years (SD = 1.07; Table 1), from 22 high schools in North Rhine-Westphalia, Germany. Complete heart rate variability measurements were obtained from 227 participants. Among the 82 participants which were excluded from further analysis, some did not complete the study tasks. For those who did complete the task, there were technical errors; e.g., a lack of coupling between the measurement sensor and the storage device, which leads to the fact that the measurement data could not be read out, or too many measurement artifacts. For the latter, according to the procedure of Laborde et al. (2017), the threshold value for data being considered as artifacts, was set to 0.45 s (= very low) difference between a single heartbeat interval from the local average. That is, participants with regular fluctuations above a range of 0.45 s were excluded from the data set. To avoid possible confounding effects, 18 participants with a body mass index >30 kg/m², serious medical conditions or frequent smoking were excluded from all heart rate variability analyses (Piestrzeniewicz et al., 2008; Thayer et al., 2010). Thus, we examined heart rate variability parameters from 209 students.

In all three studies the procedure was comparable in terms of learning environment and tasks. After arrival, the students', respectively their parents' written informed consent was collected and the participants were informed about the procedure of the following studies, which were conducted in accordance with the Declaration of Helsinki and approved by the Ethics Commission of the local medical school. Thereafter all students participated in the same molecular biology project, which was not associated with the present studies. The actual study started after about one half of the molecular biology project. Before the students worked on the test tasks, they were equipped with a chest belt and moved to another room. Then each of them was placed in front of a laptop, separated from each other. The students also filled in a demographic questionnaire (sex, age) including medical information (weight, height, chronic diseases, medication intake), and two scales measuring the ASCA and interest regarding biology (Sparfeldt et al., 2004; Rost et al., 2007; Wilde et al., 2009; Minkley et al., 2014). All participants were randomly seated in front of a laptop, on which the test booklets were installed. The laptops were separated from each other, so that the participants could not see the tasks of their schoolmates. The students got 10 up to 20 min to work on the tasks (depending on the study). After completion of the tasks, the students filled in a questionnaire to self-report their mental load and mental effort during working on the tasks (Krell, 2015, 2017) and indicated their perceived stress on a Visual Analogue Scale (Luria, 1975; cf. Table 2). Heart rate variability was measured continuously via a chest belt and a storage device (Polar V800).

In each of the three studies, participants completed several tasks that had the same structure and differed only slightly in content, but all related to molecular structures and phenomena covered in biology classes (e.g., DNA structure, diffusion). In order to achieve a test design that is as close to school reality as possible, we have checked the tasks for alignment with the course content and the biology curriculum in high school. In each task, there was a representation of a molecular structure or process. The task complexity was varied by considering different cognitive demands in all three studies. In the simpler tasks (about one half) the participants had to recognize and select the correct name or a true statement about a depicted molecular structure or process from several answering options (i.e., single-best answer format). In the more complex tasks, the participants had to explain or compare the depicted molecular structure or process in a short written text (i.e., constructed response format). The tasks also differed regarding the types of representation (one half of the tasks included purely symbolic representations, the other half combined symbolic–textual representations; Minkley et al., 2018). The distribution between simple and complex tasks as well as the type of representation was systematically distributed in all three studies. The tasks have been discussed in several rounds by the first and the last author of this article to evaluate their content validity. In the present study, however, task complexity is not a focus, given the abundance of prior research.

The instruments used in the present investigation are comparable across the studies included. Table 2 lists the assessments in the three studies. Further explanations are provided in the text below. All assessed data have been z-standardized for further analyses.

The StuMMBE-Q instrument was applied in the present study to achieve indicators for the students’ mental load and mental effort (Krell, 2015, 2017). For both dimensions of cognitive load, that is mental load (e.g., "The tasks were challenging.") and mental effort (e.g., "I have tried hard to answer the tasks correctly."), six rating scale items for self-reporting are included in the StuMMBE-Q. For each item, a seven-point rating scale ranging from ‘not at all’ (=1) to ‘totally’ (=7) was provided. Measures for mental load and mental effort have been computed by calculating the mean score of the six respective items. For the total sample, mean scores are M _{Mental load} = 4.09 (SD = 1.19) and M _{Mental effort} = 4.39 (SD = 1.09), respectively. The internal consistency of the questionnaire is satisfying, with Cronbach’s alpha for mental load = 0.85 and for mental effort = 0.81.

In order to assess students’ biology-specific ASCA in study 1 and 2, we used a modification (Minkley et al., 2014) of the DISC-Grid (Rost et al., 2007). There, the participants have to rate eight items (e.g., “For me it is easy to solve biology problems.” or “I have a good feeling when thinking about my achievements concerning biology.”) on a 6-point rating scale, ranging from 1 (“does not apply to me at all”) to 6 (“fully applies to me”). Measures of ASCA have been computed by calculating the sum score of the eight items. The mean score is M _ASCA = 32.34 (SD = 9.74). The internal consistency of the questionnaire is excellent, with Cronbach’s alpha for ASCA = 0.92.

In study 1, the students' interest regarding biology was assessed by rating 8 items on a 6-point rating scale ranging from “does not apply to me at all” (=1) to “fully applies to me” (=6) (e.g., “I am interested in Biology.” or “I enjoy working on tasks in biology.”) adapted from Sparfeldt et al. (2004). In study 2, three items with a 7-point rating scale ranging from “does not apply to me at all” (=1) to “fully applies to me” (=7) have been used to assess the same construct based on Wilde et al. (2009) (e.g.,” Biology lessons are interesting.” or “I enjoy biology lessons.”). Measures of interest have been computed by calculating the mean score of the items. For the total sample, mean scores are M _Interest = 3.89 (SD = 1.04) for study 1 and M _Interest = 5.29 (SD = 1.26) for study 2, respectively. The internal consistency of the questionnaire is excellent, with Cronbach’s alpha = 0.91 (for study 1) and = 0.91 (for study 2).

The perceived stress was assessed using a Visual Analogue Scale (Luria, 1975) in all three studies. The Visual Analogue Scale consists of a 100mm-long line, with the label ‘no stress’ on the left end and ‘maximum stress’ on the right end. The participants placed a cross on this line at that point which expresses how stressed they felt at that moment. Afterward the distance between the left end of the line and the participants' cross was measured; therefore, the possible score range is from 0 to 100. For the total sample, the mean score is M _Stress = 29.84 (SD = 21.82).

The heart rate variability of the participants was measured continuously via a chest belt with an integrated ECG-sensor (V800, Polar). After the measurement, the data was transmitted to a software (Kubios) to calculate time and frequency domain measures. We calculated the root mean square of successive differences (RMSSD) as a common time domain measure of heart rate variability, reflecting vagal tone (Laborde et al., 2017), or rather parasympathetic activity (Malik et al., 1996; Hjortskov et al., 2004). Additionally, we calculated LF/HF ratio as a frequency domain measure reflecting the ratio between parasympathetic (high frequency components; 0.15–0.4 Hz) and sympathetic (low frequency components; 0.04–0.15 Hz) nervous system activity. For the total sample, mean scores are M _{Heart rate} = 90.28 (SD = 17.65), M _RMSSD = 51.64 (SD = 36.11), and M _{LF/HF ratio} = 2.63 (SD = 2.29), respectively.

To assess task performance, performance expectations were prepared for all tasks and points were awarded as follows. For the tasks in single-best answer format, respondents received a full score for the correct answer (=1) or no points if they selected a wrong answering option. For the constructed response items, scoring was done according to a predetermined scoring scheme, which also allowed for partially correct answers. This performance expectation was discussed and revised in several rounds as part of the task development (see section 2.4). To calculate a task performance score, the percentage of achieved points relative to maximum points was used; therefore, the possible score range is from 0 to 100. For the total sample, the mean score is M _Performance = 41.83 (SD = 24.03).

The Software IBM SPSS Statistics was Used for Data Analysis.

Measurements of almost all scales had skewness and kurtosis statistics between -2 and 2 (except kurtosis of LF/HF ratio = 3.55 ± 0.32), indicating approximately normal distribution (Gravetter and Wallnau, 2012).

For the analysis of the convergence of cognitive load measures via subjective and objective measures (RQ 1), correlational analyses were performed with mental load or mental effort and the objective measures (heart rate, LF/HF ratio, RMSSD).

For the analysis of how subjective and objective measures of cognitive load predict task performance (RQ 2), first a basic analysis of the correlations between mental load, mental effort, objective measures, and task performance was carried out. Subsequently, a joint test of the variables was performed in the form of a regression analysis with objective and subjective measures of cognitive load as predictor variables for task performance.

For the analysis of how students' self-concept, interest and stress perception predict their subjectively and objectively measured cognitive load (RQ 3), also basic analyses of the correlations between subjective and objective measures of cognitive load, self-concept, interest, and stress perception were carried out. Subsequently, linear regression analyses were performed with subjective and objective measures of cognitive load as dependent variables and self-concept, interest, and perceived stress as predictor variables.

For all linear regression analyses, no serious violations of assumptions could be found; the Durban-Watson-statistic is in the range of 1 and 3, indicating that there is no considerable autocorrelation, and VIF is < 10 for all items, indicating no serious multicollinearity (Field, 2009). (See regression tables for the exact values.)

Naturally, this study has several limitations. First, self-reported measures are vulnerable to several biases (e.g., social desirability, cultural background), especially in the case of measuring “interest”, where we have used different instruments. Second, we assumed, tested, and found linear relationships between some of the included variables; however, for some variables, non-linear relationships might be considered as well. For example, Paas et al. (2003) discuss a non-linear relationship between task performance and ME. Third, we did not systematically investigate the causal factors of learning task and learning environment (Choi et al., 2014) and also did not consider the two- and three-way-interactions proposed in the framework for cognitive load (Figure 1). As a minor limitation, one of the measurements (LF/HF ratio) shows kurtosis above 2, which is outside normal distribution. This could be due to sample fluctuation. Hence, future studies should investigate whether the specific relationships between person characteristics and dimensions of cognitive load, which were found in this study, might be specific for the present tasks and environment (i.e., tasks dealing with molecular structures and phenomena, presented digitally on laptops, and solved during an out-of-school experience). Also, future study could replicate the findings through other objective measures such as pupillary measures and skin conductance measures.