Exploring determinants of engagement with voluntary mathematics assignments in economics education: a correlational study

Abstract

This article uses data collections from a German university to explore determinants influencing students’ engagement with voluntary weekly mathematics homework assignments tailored for economics. Demographical, social and affective variables were collected from approximately 800 students across several years. Unlike engineering or pure mathematics disciplines in Germany, where homework assignments are often mandatory, homework in economics remains optional. The study aims to provide an exploratory insight into which students opt to tackle these voluntary tasks. For this purpose, the collected data were clustered and analyzed using regression analyses. It was found, among other things, that demographic variables such as gender and age influence the decision to engage in voluntary exercise tasks, but, for example, prior knowledge in mathematics inhibits motivation for optional task. The compulsory nature of homework assignments in other subjects made them unsuitable for comparison due to a lack of heterogeneity. Therefore, this research contributes to the Mathematics for Economists research, underscoring economics students’ unique dynamics and decision-making processes.

1 Introduction

In Germany, almost anyone wishing to study economics must inevitably attend a mathematics course in the early study period and successfully pass an examination. Although the range and weighting of math-related lectures vary from university to university, this discipline is present in most cases (Voßkamp, 2017). This is also highly sensible, as mathematics and economics are closely intertwined, with mathematics aiding in making theoretical statements clearer (Wulwick, 1990) and promoting the standardization and scientificity of economic operations (Yu, 2023).

Given the academic and theoretical importance of mathematics within economics, it can be assumed that students aiming to successfully complete an economics degree assign mathematics an equally significant role and are aware that mathematics is the key to many economic applications (Mearman et al., 2014). However, some students also fear that their mathematical background is insufficient and that they are inadequately prepared for mathematical content, as mathematics is perceived as (too) difficult and (too) abstract (Mearman et al., 2014). The increasing heterogeneity in students’ prior knowledge plays a significant role, as broad knowledge from feeder schools is assumed as a foundation in many first-semester courses. But in reality, the numbers for first-semester events are not only comprised of students with a general university entrance qualification (Dörmann et al., 2019). Rather, they also include students with an educational qualification that does not necessarily include the completion of a secondary school education, thereby quickly and often ruthlessly revealing knowledge gaps, particularly in the field of mathematics and statistics (Laging & Voßkamp, 2017; Wolf, 2018; Büchele, 2020a; Büchele & Feudel, 2023). This is not only challenging for students but also for the organizers of (mathematics-related) lectures, who now need to create opportunities to ensure long-term success for the students (Dörmann et al., 2019).

One of these opportunities, in addition to meanwhile well-investigated preparatory courses, bridging courses, tutorials, and math help centers (see, e. g. Büchele, 2020a, Büchele, 2020b, Büchele & Schürmann, 2023), can be the voluntary submission of homework sheets or assessments, which are worked on weekly and tailored to the lecture content. A special feature, compared to pure mathematics or engineering programs, is that in Germany, in the field of economics, there is usually no obligation to participate or solve these weekly assignments, for example, to be admitted to the examination performance, but rather students can and must decide independently whether to accept this offer (Laging & Voßkamp, 2016). The purpose of these optional homework assignments is to provide students with feedback on their understanding of the learning content, but above all to provide an opportunity for application. Furthermore, corrections of errors by tutors can help and provide opportunities for improvement, so that students are informed about their respective learning status at any time and not just after completing the exam. The goal seems promising, but only a few students take advantage of this opportunity (Johannessen & Tovmo, 2022). Why? It is reasonable to assume that the decision-making process regarding the completion and/or submission of optional homework assignments is influenced by many factors. Certainly, factors at a meta-level such as time capacity and local residency may play a role. However, personal and individual factors brought by the students also come into play. These certainly include commitment and motivation, work and learning behaviour, as well as previous experiences and the assessment of the impact on learning success (Laging & Voßkamp, 2016; Laging & Voßkamp, 2017).

Our study aims to provide an exploratory insight into which students exactly decide to engage with these voluntary tasks. To do this, we derive possible individual influencing factors from (mathematics) didactic theories that play a role in the decision to submit voluntary homework assignments. Subsequently, we analyze these variables for their theoretical relationship with the voluntary completion of assignments. In the empirical part of our study, we use data collected from a German university, where demographical, social, and learning theoretical variables of approximately 800 students have been collected over several years to filter out the variables that are particularly associated with the solving of voluntary homework assignments.

2 Theoretical background

In our data, we have collected numerous pieces of information about students, allowing us to draw conclusions about their personal backgrounds, educational biography, and current attitudes. We now aim to relate this information as variables to the completion of voluntary homework assignments. Our considerations are initially broad, but it quickly becomes clear that without motivation and personal engagement, engaging in voluntary homework assignments is not possible. For this reason, we will first examine motivation. Subsequently, we will explore general motives for voluntary work and identify groups of individuals who stand out in the realm of voluntary activities. Concerning educational offerings and activities, we will examine the sociocultural perspective and incorporate learning theories into our considerations.

2.1 Derivation of individual influencing factors from (mathematics) didactic theories

When dealing with motivation, an engagement with self-determination theory, developed by Edward L. Deci und Richard M. Ryan, is inevitable (Deci & Ryan, 2002).

Accordingly, someone is considered motivated if they seek to achieve something and pursue a specific purpose with their behaviour. A central aspect of self-determination theory is the distinction between intrinsic and extrinsic motivation. Intrinsic motivation refers to engagement in an activity due to its inherent value or the joy it provides. This may occur when one finds something interesting, exciting, or enjoyable. Extrinsic motivation relies on external rewards or punishments. Passing an exam can be cited as a rewarding example (Deci & Ryan, 1993; Deci & Ryan, 2000).

In the context of learning, it can be assumed that sustainable and qualified learning, in conjunction with the necessary actions, can primarily be achieved through engagement stemming from individual selves. For this reason, intrinsic learning motivation based on a genuine interest in the subject matter represents an important determinant of learning behaviour. However, the incentive to pass an examination as an extrinsic determinant must also be considered, as it can lead to voluntary work without genuine intrinsic motivation behind it (Deci & Ryan, 1993).

However, the question raised here is not whether there are motives for voluntary work, as numerous studies attest to this fact (Wuthnow, 1991), but rather who has which motives. Especially in voluntary work, it is observed that individuals align their behaviour based on whether it appears promising to them and whether investing effort for the desired outcome is worthwhile by carefully weighing the pros and cons (Wilson & Musick, 1999). The motive of advantage or success seems obvious. The question then remains about the individuals who predominantly engage in voluntary tasks. An explanatory model distinguishes between ‘exogenous’ and ‘endogenous’ personality factors. Exogenous factors include age, sex, and ethnicity, representing unchangeable characteristics of a person. It has been demonstrated that voluntary participation is directly influenced by these exogenous factors (Wilson & Musick, 1999; Klöckner, 2015). An attempt to explain this may be based on perhaps typical gender-specific characteristics but also on involvement in social structures. Regarding age, younger individuals appear to be more motivated to demonstrate performance, qualify, or further educate themselves (Klöckner, 2015). The endogenous main factor for voluntary work is named as the socio-economic and -cultural status.

Additionally educational biographical conditions also influence learners’ performance and motivation. These include the course of one’s own educational background (e. g. type of school), the type and location of school education and experiences within school and vocational education. Associated with this is the access to resources and educational opportunities, which is essential. If individuals have access to books, teaching materials, online resources, and qualified teachers, they are more willing to actively engage in learning activities (Relikowski, 2012; UNESCO, 2020). Considering these socio-cultural variables is crucial for understanding and promoting individuals’ engagement and motivation for learning activities. This perspective shows that learning and the willingness to engage with learning subjects are not only individual decisions but are strongly influenced by social and cultural factors.

Concerning an educational frame, learning is considered an active process in which the learner actively participates in the construction of knowledge and meaning (Glasersfeld, 2003). This not only influences individual perception but also behaviour in specific contexts (Eichler & Erens, 2015). Emotions also play an important role in action because action is closely related to engagement, so that one’s own identity is shaped and expanded through participation in activities. Whether this process is stimulated and students recognize what is important to them is controlled through emotions (Op’t Eynde et al. 2006). Thus, individual beliefs, attitudes, and emotions can be attributed with a guiding function for action, influencing the perception of a learning subject and learning behaviour in university processes (Manderfeld, 2020).

2.2 Summary and clustering of influencing variables on the completion of voluntary homework assignments

We now aim to identify variables based on our general theoretical considerations regarding the motives for voluntary work in the educational context, specifically focusing on the completion of voluntary homework assignments within the framework of economic studies. From the considerations above, four main areas have emerged for us: demographical background, educational background and prior knowledge, basic needs (in context of self-determination theory) such as autonomy and perceived competence and engagement variables. Additionally, we intend to include affective variables such as self-awareness, emotion and attitude in our analysis. Categorizing these areas makes sense to us, as it allows for a comprehensive analysis of potential influencing factors from various perspectives.

2.2.1 Demographical basics

The influence of demographical variables can be derived from considerations regarding individuals who are generally predisposed to voluntary activities and from those concerning sociocultural structures. Here, we will examine the variables of age and gender more closely.

Considering the age of learners quickly reveals that various dimensions of learning and motivation are implicated. Studies across different educational contexts have shown that learners’ age can influence their motivation, engagement and approach to voluntary tasks.

Research suggests that older students in higher education tend to be more engaged in their studies than their younger counterparts (Covas & Veiga, 2021). This may be due to the different reasons for entering university, with older students often having a richer understanding of the meaning and relevance of their studies (McCune et al., 2010). In summary, learners’ age is an important factor in participating in voluntary exercise tasks. Older learners may be more inclined to engage in these tasks due to their experience and maturity.

Gender differences can also influence motivation, engagement and approach to such tasks in educational contexts. A study by Tatum et al. (2013) found that classes taught by women elicited more voluntary contributions. However, as the proportion of male students increased, both voluntary contributions and praise from instructors decreased. This suggests that both the gender of the instructors and the learners can influence participation in voluntary exercise tasks (Tatum et al., 2013).

Renaud et al. (2006) found that women participate more in voluntary further education activities than men and that the engagement of managers is higher than that of non-managers. This finding may indicate that gender differences also exist in academic contexts, with women being more inclined to engage in voluntary exercise tasks.

In summary, learners’ gender is an important factor in participating in voluntary exercise tasks. Gender-specific differences in motivation, engagement and approaches to learning tasks can impact how and why male and female students choose to participate in such tasks.

2.2.2 Educational background and prior knowledge

The relationship between the educational background and the associated prior knowledge of students and their participation in voluntary exercise tasks is an important aspect of mathematics education. The socio-economic and -cultural perspective has supported this.

Educational backgrounds thus already influence the motivation and engagement of learners and therefore their willingness to engage in these tasks. Additionally, a positive educational background generates substantial prior knowledge. We understand prior knowledge as knowledge acquired through attendance at educational institutions prior to the study of economics. Prior knowledge is thus directly related to the educational background of the students. Therefore, students’ prior knowledge can also be considered a significant factor for success in completing homework assignments. Students with a solid background in mathematics may feel more encouraged to work on voluntary exercises as they feel more competent and have the necessary confidence to successfully solve the tasks. In contrast, students with less prior knowledge or weaker mathematical skills may hesitate to participate voluntarily in additional exercises as they may have less confidence in their abilities and experience higher anxiety about failure (Schneider & Preckel, 2017b).

Research has also shown that prior knowledge has a significant impact on learning performance. In a study by Schneider & Preckel (2017a), it was found that students’ academic self-concept and prior knowledge influence their performance in mathematics. This study suggests that students who are confident in their mathematical abilities and have a solid foundation of prior knowledge are more inclined to take on challenges such as voluntary exercise tasks (Schneider & Preckel, 2017a).

Another aspect is that prior knowledge can influence how students interact with learning materials and exercise tasks. A study by Hailikari et al. (2008) shows that students with different levels of prior knowledge also employ different learning strategies. Those with more extensive prior knowledge tend to pursue deeper learning strategies, which could in turn increase their willingness to engage with complex and challenging exercise tasks (Hailikari et al., 2008).

Here, we specify the educational background of the students and describe our variables as type of feeder school and type of school leaving certificate. To make prior knowledge measurable, we formulate the variables highest previous educational qualification grade and last grade in mathematics in this context.

2.2.3 Motivation and engagement

We consider motivation, as described by Deci & Ryan, as the framework for our considerations for variables like motivation itself but also for basic needs like autonomy and competence experiences.

In doing so, both intrinsic and extrinsic motivation must be taken into account. Extrinsic motivation becomes particularly evident when students are primarily motivated by the desire to pass an exam and thus feel motivated to complete voluntary practice tasks. However, since we clearly focus on voluntariness (in contrast to other disciplines where practice tasks are mandatory), we primarily want to focus our considerations on intrinsic motivation.

Individuals who are intrinsically motivated to complete these types of voluntary tasks find joy and fulfillment in the activity itself. They feel motivated by the exploration, learning and mastery without the need for external incentives (Deci & Ryan, 2000).

However, in order to build and strengthen intrinsic motivation sustainably, we define students’ autonomy and competence experiences as variables in the context of basic needs in relation to the completion of voluntary practice tasks. Fulfilling these basic needs is crucial for a person’s psychological well-being. When individuals feel they can act autonomously and competent, they are more willing to face challenges, pursue personal goals and engage in their activities (Deci & Ryan, 2000).

Studies have also shown that motivation influences students’ willingness to dedicate themselves to voluntary tasks (Büchele, 2021). For example, Ntoumanis (2001) emphasizes that perceived competence and intrinsic motivation are important factors in compulsory physical education classes, affecting the completion of voluntary practice tasks. These results suggest that when students feel competent and intrinsically motivated, they are more willing to engage in voluntary tasks (Ntoumanis, 2001). It becomes evident that learners’ motivation is a key factor in participating in voluntary practice tasks. Strengthening intrinsic motivation promotes students’ willingness to engage in these tasks.

2.2.4 Affective variables (self-awareness, emotion, attitude)

Also affective variables like self-awareness, emotion and attitude are influenced by the motivation explained above. But also from the socio-economic perspective and the idea of identity development, we derive this variable in our category of affective variables.

In the literature, many definitions can be found for self-awareness, but here we identify self-awareness as self-consciousness or self-reflection. It refers to a person’s ability to be aware of their own thoughts, emotions, motivations, strengths, weaknesses, actions and behaviours. It is an important component of emotional intelligence and enables a person to understand, control and potentially adjust their behaviour to promote personal growth and success (London et al., 2023). Self-efficacy and self-concept are closely related to this, as self-awareness enables a person to develop and expand their self-efficacy and self-concept.

Here, we define self-efficacy as the belief in one’s own abilities to successfully accomplish specific tasks and self-concept as the perception and evaluation of one’s own abilities and competencies. Both are key factors influencing students’ learning behaviour and performance (Chemers et al., 2001).

Lee & Stankov (2018) identify self-efficacy and educational aspirations as important predictors of individual achievement success in mathematics. Their research findings suggest that students with high self-efficacy expectations are more likely to take on challenges, such as voluntarily tackling math exercises.

It can be concluded that self-awareness, self-efficacy and self-concept are crucial factors influencing students’ willingness and ability to engage with voluntary exercises. Strengthening these psychological constructs may effectively promote students’ active participation in voluntary math exercises.

Further affective variables such as emotions and interests can also significantly influence motivation to engage in voluntary exercises. This includes emotions, as emotional states like joy, (math) anxiety or satisfaction can influence students’ behaviour and thought processes, ultimately deciding whether voluntary offers are accepted or not. Negative emotions such as frustration or boredom, however, can decrease motivation and lead to lower engagement (Pekrun et al., 2002). Additionally, individual interests influence motivation, as people tend to invest more energy and time in tasks that align with their personal interests and passions (Deci & Ryan, 2000).

3 Method

3.1 Sample and data

Data were collected from 787 students enrolled in economics and related degree programs at a medium-sized German university. The data collection spanned multiple semesters, specifically the winter terms of 2012, 2013, 2014, 2015, 2016 and 2019. The distribution of participants across these semesters was as follows: 168 students from the winter semester of 2012, 108 from the winter semester of 2013, 165 from the winter semester of 2014, 140 from the winter semester of 2015, 138 from the winter semester of 2016 and 68 from the winter semester of 2019. The data were collected in the lecture ‘Mathematics for Economists.’ At the beginning of the relevant lecture session (week 1 and week 10), students were asked to complete a questionnaire and take a skills test. Participation in the questionnaire and test was voluntary and completely anonymous. Typically, these tests reach about 80% of the relevant students throughout the semester. During these semesters, an entry test was conducted in the first session of the ‘Mathematics for Economics’ course. This entry test comprised a non-standardized mathematical performance test and a questionnaire gathering educational biographical, social and affective variables. A midterm test with a similar questionnaire was also administered midway through the semester in the same course (see Büchele & Schürmann, 2023 for performance tests). The cohort of 787 students represents those for whom test information was available at both testing points. While the initial questionnaire primarily collected demographical data, the subsequent questionnaire was expanded to include questions regarding student learning behaviour. All tests, questionnaires and the matching process between the two test points were conducted anonymously. The tests and questionnaires are validated instruments, as referenced in Laging & Voßkamp (2017) and Laging (2021).

3.2 Variables

Table 1 provides an overview of the variables included in the study. It reports mean values or proportions for binary variables, standard deviations, ranges and Cronbach’s Alpha values for the available scales. All variables and scales have been previously validated in studies (refer to Laging & Voßkamp, 2017, Laging, 2021). Furthermore, explanations and item examples for the used scales are provided in Table A1. The completion of voluntary weekly homework assignments serves as the dependent variable in our setting. It was queried in the midterm test. Students were asked to indicate on a scale from 1 to 6 how many of the weekly homework assignments they typically completed, revealing a high average completion rate of 5.06.

Mathematics performance:

The entry test score and midterm test score reflect the students’ mathematical performance at the beginning and middle of the semester, respectively. Overall, students performed relatively poorly on both tests, with average scores of 8.49 (entry test) and 11.89 (midterm test) out of a possible 30 points. Both tests, consisting of various tasks, are comparable in content and difficulty level, primarily covering mathematical topics from the school curriculum. This is relevant in the first weeks of the semester, as much content is reviewed. Thus, the test also captures the lecture content of the ‘Mathematics for Economics’ course up to approximately the middle of the semester.

Social variables:

• Sex is a binary variable, with 48.7% of the participants being female.

• The year of study variable captures how long students have been in their program. The average was 1.17 years, with a standard deviation of 0.465, ranging from 1 to 3 years.

• The education gap variable measures the time in years between a student’s high school graduation and the start of university studies. The mean gap was 1.742 years, with a standard deviation of 2.117, ranging from 0 to 24 years.

• Language issue is a binary variable indicating whether students experience difficulties with the German language. 3.8% of the students reported such difficulties.

Educational and demographical variables:

• The preparation course participation variable indicates whether a student participated in a preparatory course before starting their studies. 62% of students had participated in such a course.

• The lecture already attended variable indicates whether a student had previously attended the ‘Mathematics for Economists’ course in a prior semester. 11.1% of students had attended the course before.

• The study program variable distinguishes between students enrolled in economics and those in related programs. 77.8% of students were enrolled in economics, while 22.2% were in related programs such as economics education.

• The entrance qualification variable indicates whether a student has a standard university entrance qualification (‘Abitur’). 69.3% of students had this qualification. Regarding the entrance qualification, it is important to note that the university in question admits students with a standard university entrance qualification (‘Abitur’) or a vocational qualification (‘Fachabitur’). Students with a ‘Fachabitur’ typically have significantly less mathematical background (see Laging & Voßkamp, 2017).

• The high school GPA variable records the average grade a student received in high school, with higher values indicating better performance. The mean GPA was 2.555, with a standard deviation of 0.546, ranging from 1.2 to 4.0.

• The high school math grade variable records the average grade a student received in high school math courses. The mean grade was 2.530, with a standard deviation of 0.883, ranging from 1 to 5.

Motivational variables:

• Perceived competence is measured on a scale from 1 to 6. The mean score was 3.601, with a standard deviation of 0.825, and a Cronbach’s Alpha of 0.81, indicating good reliability.

• Perceived autonomy is measured on a scale from 1 to 6. The mean score was 4.189, with a standard deviation of 0.812, and a Cronbach’s Alpha of 0.79, indicating good reliability.

• Perceived relatedness is measured on a scale from 1 to 6. The mean score was 4.501, with a standard deviation of 0.920, and a Cronbach’s Alpha of 0.89, indicating good reliability.

• Math interest is measured on a scale from 1 to 6. The mean score was 3.456, with a standard deviation of 1.257, and a Cronbach’s Alpha of 0.95, indicating excellent reliability.

• Learning goal orientation is measured on a scale from 1 to 6. The mean score was 3.415, with a standard deviation of 0.923, and a Cronbach’s Alpha of 0.88, indicating good reliability.

Affective variables:

• Math self-efficacy is measured on a scale from 1 to 6. The mean score was 2.768, with a standard deviation of 0.820.

• Test anxiety is measured on a scale from 1 to 6. The mean score was 3.920, with a standard deviation of 1.348, and a Cronbach’s Alpha of 0.89, indicating good reliability.

• The perceived benefit of math variable measures how beneficial students perceive math to be. The mean score was 4.283, with a standard deviation of 0.773, and a Cronbach’s Alpha of 0.88, indicating good reliability.

• Math self-concept is measured on a scale from 1 to 6. The mean score was 3.400, with a standard deviation of 0.944, and a Cronbach’s Alpha of 0.88, indicating good reliability.

• Lecture attendance is measured on a scale from 1 to 6. The mean score was 5.675, with a standard deviation of 0.698.

• Tutorial attendance is measured on a scale from 1 to 6. The mean score was 5.078, with a standard deviation of 1.525.

3.3 Empirical strategy

The empirical strategy of this article supports the exploratory approach to identifying determinants influencing the completion of voluntary homework assignments in Mathematics for Economists. Building upon the theoretical factors presented in Section 2.2, a ordinary least squares (OLSs) regression model is estimated. In this model, the completion of weekly homework assignments serves as the dependent variable and the other variables as independent variables. This approach allows for the illustration of correlations between the independent and dependent variables, controlling for interdependencies among the independent variables.

4 Results

The findings reported in Table 2 focus on variables that demonstrate significant correlations, illustrating an exploration of the determinants affecting voluntary weekly assignment completion. It’s essential to acknowledge from the outset that these relationships are correlative rather than indicative of causation, providing insights into associations rather than direct effects.

The main findings of our analysis reveal several key insights. Demographical variables such as gender and proxies for age (e.g., education gap) show a positive correlation with the completion of weekly assignments. Specifically, women and older students demonstrate higher levels of engagement. Additionally, preparation course participation and secondary school GPA are positively correlated with assignment completion, indicating the importance of prior academic preparation. Interestingly, students with stronger math-specific backgrounds (indicated by the entry test score) are less likely to complete voluntary assignments, possibly due to their confidence in existing skills.

Motivational factors, including perceived competence and autonomy, are strong predictors of engagement. Students who feel competent and autonomous are more likely to complete assignments, emphasizing the role of intrinsic motivation. Furthermore, attendance in lectures and tutorials significantly influences assignment completion, indicating that active participation in these structured academic activities fosters greater engagement. Affective variables, such as math self-efficacy and test anxiety, also play a role. Higher self-efficacy correlates positively with assignment completion, while anxiety has a mixed impact. Additionally, promoting active engagement through lectures and tutorials enhances assignment completion rates. It is also crucial to acknowledge the role of self-efficacy and anxiety in shaping student behaviour and provide appropriate resources to support students’ emotional well-being.

Furthermore, the relationships between specific mathematical preparedness and broader academic readiness come to light. While higher mathematical skills, as measured by entry test performance, are negatively correlated with assignment completion, a solid general academic background (indicated by secondary school GPA) correlate positively. This dichotomy underscores the intricate dynamics between specific skills and overall preparedness in influencing academic engagement.

An aspect yet to be addressed in our study, which takes the analysis a step further, concerns the significance of (voluntary) exercise tasks for students’ performance. To explore this, an additional OLSs regression is estimated, with the midterm test score now serving as the dependent variable. Independent variables include all those described in Table 2. Table 3 presents an overview of the correlations, reporting only variables that demonstrate significant correlations.

The entry test performance, and thus prior knowledge, unsurprisingly emerges as the strongest predictor of mathematical performance in the midterm test. However, the completion of weekly homework assignments also displays a solid correlation, on the same level as other significant predictors such as entry qualification, secondary school GPA, or math self-concept. Considering these correlations with students’ mathematical performance, the completion of voluntary exercise tasks stands out as an important predictor. Given our sample, students already show a high rate of completion (5.06 on a scale of 1–6). However, it’s critical to acknowledge that the sample is selected (see limitations), implying that this high completion rate may not apply to all students.

5 Discussion

Incorporating the theoretical insights from Section 2 into our discussion of the empirical findings reported in Table 2 provides a comprehensive framework for understanding the determinants of voluntary weekly assignment completion. Drawing from mathematics didactic theories and the principles of self-determination theory (Deci & Ryan, 2002), we analyze how the theoretical constructs manifest in the empirical data, noting where the results align or diverge from theoretical expectations and integrating relevant sources to deepen our discussion.

5.1 Discussion of results

The significance of demographical variables such as gender in influencing voluntary engagement with academic tasks is well-documented in the literature (Renaud et al., 2006; Tatum et al., 2013). The empirical correlation between sex and assignment completion echoes these theoretical discussions, affirming the role of gender-specific characteristics and societal structures in shaping educational behaviours.

The positive correlations of preparation course participation and secondary school GPA with assignment completion highlight the empirical relevance of constructivist learning theories (Glaserfeld, 2003; Hailikari et al., 2008; Schneider & Preckel, 2017a), supporting the idea that a solid foundation of prior knowledge facilitates active engagement in learning processes. However, an intriguing divergence emerges when considering math-specific prior knowledge. Empirically, we find that math-specific prior knowledge is negatively correlated with the completion of voluntary homework assignments. This counterintuitive finding could be attributed to the possibility that students with stronger math-specific backgrounds may perceive less need for the practice provided by these assignments. Their confidence in their math skills might lead them to engage less with these voluntary tasks, believing they already possess the necessary competencies to succeed without the additional practice.

The significant correlation of perceived competence with higher assignment completion rates in the empirical data underscores the critical role of (intrinsic) motivation in academic engagement, aligning with the self-determination theory’s (Deci & Ryan, 2000; Gaspard, 2023) emphasis on the need for individuals to feel competent and autonomous in their learning endeavours.

The correlation of affective variables with the homework completion is highlighted in discussions on self-efficacy, self-concept and emotional states (Chemers et al., 2001; Pekrun et al., 2002; Lee & Stankov, 2018). The empirical findings, particularly the strong correlation between self-efficacy and assignment completion, resonate with the theoretical assertion that students’ beliefs in their capabilities and their emotional responses to academic tasks significantly influence their engagement.

The findings of this study align with and extend existing literature. For instance, the positive correlation between gender and homework completion. Downey & Vogt Yuan (2005) identified that girls generally outperform boys in academic metrics, including homework completion rates, largely due to social and behavioural skills. This study further refines this understanding by demonstrating the consistency and robustness of this gender effect across multiple models. Additionally, Trautwein & Lüdtke (2008) found that gender differences in homework effort were domain-specific, aligning with this study’s observation that these differences might be more pronounced in certain subjects.

Moreover, the role of motivational factors strongly influencing homework completion aligns with the findings of Hoover-Dempsey et al. (2001), who emphasized that supportive parental involvement might enhance student autonomy and motivation, thereby improving homework outcomes. This study extends these insights by quantifying the impact of perceived competence and autonomy on voluntary assignments, underscoring their importance. Further, the negative correlation between entry test scores and homework completion suggests that students with strong math backgrounds might rely on their existing skills, which is not extensively covered in previous literature. Trautwein & Lüdtke (2007) also noted that students’ homework effort is significantly influenced by conscientiousness and perceived homework quality, which this study corroborates by highlighting how lecture and tutorial attendance foster greater engagement.

5.2 Recommendations for teaching mathematics for economists

In light of the findings from our analysis and the theoretical frameworks discussed, this section proposes recommendations for the design of university-level mathematics for Economists courses, particularly concerning the role of voluntary versus mandatory homework assignments. These recommendations aim to enhance student engagement and performance based on insights derived from our study and relevant literature on educational motivation and behaviour.

Our analysis shows that motivational factors such as individual competence and perceived autonomy are strong predictors of engaging in voluntary exercises. Since these predictors are closely linked to intrinsic motivation, it is important to support students in ‘Mathematics for Economists’ courses with learning methods that fulfill the basic psychological needs described in Self-Determination Theory (Deci & Ryan, 2002). Specifically, educational environments must be structured in such a way that they promote feelings of autonomy, competence and relatedness. Since our analysis also shows that self-efficacy is positively correlated with task completion, the learning offerings should include elements such as regular and constructive feedback, strengthening problem-solving abilities and making successes visible through achievable goals. However, they should avoid exerting pressure that could reinforce or create math anxiety. Voluntary homework assignments leave room for fulfilling these attributes, however the debate between voluntary and mandatory homework assignments hinges on finding the right balance between fostering intrinsic motivation and ensuring consistent engagement across the student body (Holden & Burazin, 2023). While mandatory assignments guarantee that students engage with the material, they may not always foster deep learning or intrinsic motivation. In contrast, voluntary assignments, especially when designed with the above recommendations in mind, can motivate students to engage more deeply with the material out of genuine interest and a desire to improve their understanding and performance. The positive correlation between participation in preparatory courses and the completion of voluntary exercises, as revealed by our analysis, reinforces this assumption, especially since participation in these preparatory courses is also voluntary. The success experiences and the learning of self-organization techniques, such as goal setting and planning of learning activities (Voßkamp & Laging, 2014), can help students take control of their own learning and experience intrinsic motivation, which can then be transferred to voluntary exercises throughout the semester.

Furthermore, tutorial attendance emerged as a strong predictor of engagement with voluntary assignments, suggesting that supportive learning environments can play a crucial role in motivating student participation. Facilitating access to tutorials, study groups and other support structures can help students feel more connected and supported in their learning journey, addressing the need for relatedness and belonging. This sense of belonging could potentially simplify access to other voluntary offerings, such as completing voluntary exercises, as it can be easily integrated into existing study groups without much effort.

Another recommendation, based on the positive correlations with self-efficacy and the sense of group belonging from supportive tutors, is the integration of gamification elements into voluntary exercises, such as earning badges or recognition for completing tasks. This introduces an element of fun and competition to encourage engagement with the material (Ab Rahman et al., 2019). Students receive positive feedback on their performance (self-efficacy) and also have the opportunity to discuss shared experiences and successes or achieve goals together (supportive learning environment).

This approach can leverage the motivational impact of achieving visible milestones, encouraging continuous engagement without the need for extrinsic rewards.

5.3 Limitations

As with any study, it is important to acknowledge the limitations of our research to provide context for the interpretation of the findings and guide future research directions. The considerations outlined below highlight areas where caution should be applied in interpreting our results and suggest avenues for further investigation.

5.3.1 Correlational, not causal, interpretations

The data analyzed in this study allow for the identification of significant correlations between various factors and the completion of voluntary weekly assignments. However, it is crucial to understand that these relationships do not imply causality. The nature of our analysis does not enable us to determine whether these factors directly cause changes in students’ engagement with voluntary assignments or their academic performance. Future studies employing experimental or longitudinal designs could provide deeper insights into causal relationships.

5.3.2 Selected sample

Our research captures data from students who were still attending lectures at the midpoint of the semester, which may inherently bias our sample towards better-performing and more motivated students. This selection effect limits the generalizability of our findings to the broader student population, as those who disengage from the course before this point are not represented. Understanding the dynamics that influence the engagement and performance of this broader group remains a critical area for future research.

5.3.3 Data age and the impact of COVID-19

The data utilized in this study predate the significant shift towards digital learning prompted by the COVID-19 pandemic. The transition to online and hybrid learning environments represents a substantial change in the educational landscape, potentially affecting student engagement with voluntary exercises and overall academic performance. Investigating how digital learning modalities influence student behaviours and outcomes is a pertinent direction for future research, offering insights into the evolving nature of academic engagement in response to global challenges.

5.3.4 Lack of data on learning strategies

While our analysis incorporates a wide range of variables, data on students’ learning strategies were sporadically collected and only available for a subset of the sample. Preliminary analyses with this subset indicate that incorporating learning strategies does not significantly alter the robustness of our findings. Furthermore, high elaboration strategies correlate positively with the use of voluntary assignments, whereas memorization strategies do not show a significant correlation. These findings align with other studies (Büchele, 2023) examining the relationship between learning strategies and engagement. Despite the consistency of these results with the literature, the absence of comprehensive data on learning strategies across the entire sample represents a limitation, underscoring the need for future studies to explore the impact of different learning approaches on student engagement and performance more systematically.

References

A Appendix