Mathematics Self-Efficacy and Approaches to Learning in First-Year Engineering Mathematics

Research Paper Recommended citation: Naukkarinen, J., Kangaslampi, R., Kaarakka, T., & Ratava, J. (2025). Mathematics Self-Efficacy and Approaches to Learning in First-Year Engineering Mathematics. In Kangaslampi, R., Langie, G., Järvinen, H.-M., & Nagy, B. (Eds.), SEFI 53rd Annual Conference. European Society for Engineering Education (SEFI), Tampere, Finland. DOI: 10.5281/zenodo.17631255. This Conference Paper is brought to you for open access by the 53rd Annual Conference of the European Society for Engineering Education (SEFI) at Tampere University in Tampere, Finland. This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License. MATHEMATICS SELF-EFFICACY AND APPROACHES TO LEARNING IN FIRST-YEAR ENGINEERING MATHEMATICS J. Naukkarinen a, 1 , R. Kangaslampi b, T. Kaarakka c, J. Ratava d, a LUT University, Lappeenranta, Finland, 0000-0001-6029-5515 b Tampere University, Tampere, Finland, 0000-0002-9059-8047 c Tampere University, Tampere, Finland, 0000-0002-3824-8939 d LUT University, Lappeenranta, Finland, 0000-0002-8816-6165 Conference Key Areas: Teaching mathematics and physics in engineering education; Diversity, equity and inclusion in our universities and in our teaching Keywords: Self-efficacy, approaches to learning, engineering mathematics, firstyear students ABSTRACT This study explores the relationship between self-efficacy and learning approaches among first-year engineering students in two Finnish research-intensive universities. It investigates how mathematics self-efficacy and approaches to learning (deep, surface, and organised) differ between students in international programs and Finnish programs, as well as between women and men. It also examines how approaches to learning affect students' self-efficacy, considering gender and program differences. The research was conducted in the context of a first-year engineering mathematics courses, with a total of 901 participants. The findings suggest that demographic differences in self-efficacy exist, but these differences are mediated by the approaches to learning. The study highlights the importance of 1 Corresponding Author J. Naukkarinen johanna.nauk[email protected] teaching practices that support deep and organised approaches to learning to enhance students' self-efficacy and achievement in mathematics. 1 INTRODUCTION The ways in which students study and learn have been of interest to researchers and educators since the 1960's, and the topic has been viewed from many different angles. Among the early findings was the distinction between rote and meaningful learning by Ausubel and deep and surface approaches to learning by Marton and Säljö. Since then, at least six different study strategy inventories encompassing slightly different dimensions have been developed. No common view of the correct number of dimensions has emerged. Still, based on the conceptual analysis of the instruments, it has been suggested that at least three dimensions are needed to cover the variance found in studying. (Entwistle & McCune, 2004.) In contemporary research, deep and surface approaches to learning are often accompanied by a third approach called a strategic approach or organised effort to studying (e.g. Herrmann et al., 2017; Rämö et al., 2023). It refers to how systematic the students are in their studies and how they manage their time and effort. The research on the relationship between approaches to learning and academic achievement is substantial, yet the results are not unanimous. However, much of the research has noted a positive correlation between deep approach and academic achievement, a positive correlation between organised approach and academic achievement, and a negative correlation between surface approach and academic achievement (Richardson et al., 2012). Albert Bandura’s self-efficacy theory suggests that “expectations of personal mastery affect both initiation and persistence of coping behavior” (Bandura, 1977, p. 193). The stronger the individual’s perceived self-efficacy is, the more active the efforts to achieve a particular outcome become. According to the theory, the major sources of efficiency expectations are performance accomplishments (personal successes), vicarious experience (observing others), verbal persuasion (feedback), and emotional arousal (positive/negative experiences). (Ibid.) Self-efficacy is a commonly used concept also in research on mathematics education, where a lot of attention has been directed to its magnitude (Street et al., 2024). It has been studied as an outcome, a predictor, and a mediating variable (ibid.), which illustrates well the complicated relationship between self-efficacy and other factors related to learning mathematics. Studies on self-efficacy as a predictor of mathematics achievement suggest that self-efficacy correlates positively with achievement among 15-year-old students (Hiller et al., 2022) as well as university undergraduate students (Zakariya, 2021). Even though both approaches to learning and self-efficacy in learning mathematics have been studied extensively, studies of their reciprocal relationship are rare. Lahdenperä et al. (2019) compared students’ approaches to learning and selfefficacy in two pedagogically different undergraduate mathematics courses. They discovered that students with a deep approach to learning had significantly higher mathematics self-efficacy than students with a surface approach to learning in both of the studied contexts. They did not, however, make any assumptions about the relational mechanisms of the two concepts, as their interest lay in the effects of the different pedagogical arrangements. Kulcsár (2020) focused on the relationship between mathematics self-efficacy, learning approaches and mathematics achievement in bachelor-level engineering students and found statistically significant correlations but also did not elaborate on the nature of the relationship between selfefficacy and learning approaches. In contrast to the aforementioned research, Zakariya et al. (2022) explicitly aimed to explain the causal relationship between self-efficacy and approaches to learning in engineering mathematics courses. They argued that the causality arises from selfefficacy regulating decisional processes, and thus affecting learning approaches. They found support for their hypothesis through structural equation modelling. An argument for the opposite direction of the causality could be presented based on the mediation of academic achievement, whereby approaches to learning affect mathematics learning, which strengthens the mathematics self-efficacy via accomplishments, feedback and emotions. It is also plausible that the relationship between self-efficacy and approaches to learning is bidirectional with the potential for a positive cycle in which a deep approach to learning strengthens self-efficacy, which in turn directs the learner towards further search for meaning, or to a negative cycle in which a surface approach to learning weakens self-efficacy, which then directs learning even more towards rote learning and memorisation. How the organised approach to learning fits this picture and relates to self-efficacy remains to be understood. Undoubtedly, both self-efficacy and approaches to learning are influenced by many additional factors. A meta-analysis of gender differences in academic self-efficacy suggests that males have higher mathematics self-efficacy, with the gender difference increasing with age (Huang, 2013). A large study of middle school students found that Asian countries demonstrate low and Western countries have high math self-efficacy regardless of their level of proficiency (Lee, 2009). Similar findings can also be found among university students (Han et al., 2015). Research on cultural or gender differences in approaches to learning mathematics is less common. Rämö et al. (2023) discovered that among first-year engineering mathematics students, gender was not associated with deep approaches to learning. However, surface and organised learning was higher for female students, although the gender difference was only statistically significant at one of the five points at which it was measured. In contrast, Tossavainen et al. (2021) suggest that Nordic male engineering students have more instrumental interests in mathematics (interested in results and usefulness) and female students have more intrinsic mathematical interests (enjoy learning and mathematical thinking), the latter of which is commonly associated with deep learning and the prior with organised or surface learning. Unfortunately, we could not locate any previous research on cultural differences in approaches to learning mathematics. This study aims to shed some light on mathematics self-efficacy and how first-year engineering students approach learning (deep, surface and organised approach) in a Finnish research-intensive university and examine the possible cultural and gender differences in the respective concepts. Our research questions are: 1. How do the mathematics self-efficacy and the approaches to learning differ between a. Students in international programs and Finnish programs? b. Women and men students? 2. How is the students' mathematics self-efficacy affected by their approaches to learning (deep, surface, and organised approach), whether they are men or women, and whether they are in a Finnish or international program? 2 METHODOLOGY The study was conducted in the context of a first-year engineering mathematics course at two research-intensive universities in Finland in the autumn of 2023. The total number of participants was 901, including 616 males and 270 females (with 15 unspecified). Of these, 793 students were enrolled in Finnish engineering programs at either of the two participating universities, while 108 were in international engineering programs where the language of instruction was English. At LUT University, data was collected from students in the departments of Energy Technology, Mechanical Engineering, Electrical Engineering, and Sustainability Science within the LUT School of Energy Systems. At Tampere University, participants came from all Bachelor of Science programs in engineering. The data on international study programs used in this article was collected from four Bachelor of Science programs at LUT University: Energy Engineering, Electrical Engineering, and Mechanical Engineering (implemented in cooperation with Hebei University of Technology in China), and Technology and Engineering Science program (implemented by LUT). Students’ self-assessments of their self-efficacy and approaches to learning were conducted through online tests on the Moodle platform. Students gave a written consent to participate, and were informed about their right to withdraw from the study at any time without the need to give a reason. Research permission was obtained from both universities involved in the study. The study adhered to the ethical principles of the Finnish National Board on Research Integrity. As the participants were adults who gave informed consent and were not in any physical or mental danger, no ethical review was required (TENK 2019). Participants completed the survey at the beginning of their first engineering mathematics course in August and September 2023. The questionnaire consisted of Likert-scale statements on approaches to learning and self-efficacy (Parpala & and Lindblom-Ylänne, 2012; Zimmerman & Kitsantas, 2007). Responses were collected, anonymised, and combined for analysis. The responses were converted into numerical values ranging from 1 to 5, with 1 corresponding to "totally disagree" and 5 to "totally agree." Subsequently, average scores were calculated for deep approach, surface approach, organised approach (each based on four statements), and self-efficacy (based on eight statements). The statistical significance of differences between groups was tested with Welch twosample t-test and the effect sizes were tested using Cohen’s d. The relationship between self-efficacy, gender, program, and the three approaches to learning was examined using multiple linear regression analyses. All statistical analyses were performed using R Studio. 3 RESULTS The means and standard deviations for the three different approaches to learning and self-efficacy for all the student groups studied are presented in Table 1. They show that students generally had relatively high deep approaches and relatively low surface approaches to learning, with organised approach to learning and selfefficacy somewhere in between them. Table 1. The approaches to learning and self-efficacy of different respondents N Deep M(SD) Surface M(SD) Organised M(SD) Self-efficacy M(SD) All 901 4.06 (.55) 2.65 (.71) 3.70 (.76) 3.68 (.53) International programs 108 4.24 (.69) 2.69 (.93) 4.09 (.77) 3.84 (.55) Finnish programs 793 4.04 (.53) 2.65 (.67) 3.65 (.74) 3.66 (.53) Women 270 4.11 (.52) 2.75 (.71) 3.92 (.70) 3.77 (.53) Men 616 4.04 (.57) 2.61 (.70) 3.62 (.75) 3.65 (.53) We observed differences in the mean values for self-efficacy and approaches to learning between students in the international program and in the Finnish program, see Table 2. By the Welch two-sample t-test, the mean value of self-efficacy was significantly higher for the students of the international program (M=3.84) compared to the Finnish program (M=3.66), t(134.65)=3.14, p=0.002, with a small-to-medium effect size by Cohen’s d (d=0.37). Also, the mean values of deep approach to learning (international M=4.24, Finnish M=4.03, t(124.33)=2.90, p=0.004) and organised learning (international M=4.09, Finnish M=3.65, t(134.9)=5.61, p<.001) were higher for the students in the international program. The effect size was medium for organised learning (d=0.60) and small for self-efficacy (d=0.33). No difference was observed in the surface approach to learning values between the groups (international M=2.69, Finnish M=2.65, t(122.57)=0.50, p=0.617). Table 2. Differences in approaches to learning and self-efficacy between students in international and Finnish degree programs Variable Mean (International) Mean (Finnish) t p-value Cohen's d Deep Approach 4.24 4.04 2.91 0.004 0.37 Surface Approach 2.69 2.65 0.50 0.617 0.07 Organised Learning 4.09 3.65 5.61 <0.001 0.60 Self-Efficacy 3.84 3.66 3.14 0.002 0.33 Differences were also observed between women and men, see Table 3. By the Welch two-sample t-test, the mean value of self-efficacy was significantly higher for women (M=3.77) compared to men (M=3.65), with t(514.97)=3.25, p=0.001, but the effect size by Cohen’s d was small (d=0.32). For the approaches to learning, there were differences in the mean values of surface approach (women M=2.75, men M=2.61), with t(507.23)=2.74, p=0.006, and organised learning (women M=3.92, men M=3.62), with t(544.77)=5.86, p<0.001. The size for the effect on the surface approach was small (d=0.20), for organised learning medium (d=0.60). No difference in the mean values for the deep approach was observed between women and men. Table 3. Differences in approaches to learning and self-efficacy between female and male students Variable Mean (women) Mean (men) t p-value Cohen's d Deep Approach 4.12 4.04 2.10 0.036 0.15 Surface Approach 2.75 2.61 2.74 0.006 0.20 Organised Learning 3.92 3.62 5.86 <0.001 0.60 Self-Efficacy 3.77 3.65 3.25 0.001 0.32 To examine the predictors of self-efficacy we conducted multiple linear regression analyses. In the initial model (Model 1), the study group (international vs. Finnish programs) and gender were included as predictors. In the extended model (Model 2), we added the three approaches to learning: deep approach, surface approach, and organised learning. In Model 1, predicting self-efficacy with the student group and gender, both group and gender were significant predictors of self-efficacy (R^2 = 0.022, F(2,883)=10.09, p<0.001). Students in the Finnish study programs scored lower on self-efficacy than international programs (β=−0.167, t=−3.093, p=0.002). Women scored higher on self-efficacy than men (β=0.125, t=3.273, p=0.001). In Model 2, where the approaches to learning were added as predictors, the effect of group and gender became nonsignificant, suggesting that their initial effects were mediated by the approaches to learning (R^2 = 0.304, F(5,880)=76.97, p<0.001). In this model: • The deep approach was positively associated with self-efficacy (β=0.258, t=9.294, p<0.001). • The surface approach was negatively associated (β=−0.141, t=−7.077, p<0.001). • Organised learning was positively associated (β=0.288, t=13.640, p<0.001). • Neither group (β=−0.002, p=0.965) nor gender (β=0.036, p=0.243) remained significant. The results indicate that while the study group and gender initially appear to influence self-efficacy, their effects are mediated through the approaches to learning. Specifically, the higher self-efficacy scores associated with the international student group and female participants are explained by their stronger adoption of a deep or organised approach to learning and lower use of a surface approach. The relationship between the measured self-efficacy and the self-efficacy predicted by approaches to learning is presented in Figure 1. Figure 1. Measured self-efficacy versus self-efficacy predicted by approaches to learning 4 DISCUSSION Our findings suggest that, in our context, there are demographic differences in the mathematics self-efficacy of undergraduate engineering students. Some of these differences, such as women’s higher self-efficacy than men’s, seem surprising in the light of previous research. However, they may not have much practical significance as self-efficacy appears to be related to approaches to learning in a way that eliminates the demographic effects. The study confirms the positive association of a deep approach to learning and the negative association of a surface approach to learning to self-efficacy that has been noted in the literature (Lahdenperä et al., 2019; Kulcsár, 2020). It also draws attention to the positive connection between selfefficacy and organised approach to learning which was the connection with the largest effect in our study, but has not received much attention in previous research. This study investigated the relationship between self-efficacy and approaches to learning under the assumption that the latter influences the former, whereas other scholars such as Zakariya et al. (2022) have taken the opposite approach. We maintain that there is a clear relationship between self-efficacy and approaches to learning clearly, but that more research is needed to fully understand its directions and mechanisms. We also suggest that complementing the often polarised conception of deep and surface approaches to learning with the organised approach to learning in these studies can greatly enhance our understanding of the phenomenon and also suggest novel practical implications for improving the teaching of and achievement in mathematics at university level. On the practical side, this study suggests that teaching practices that support deep and organised approaches to learning have great potential to increase students’ self efficacy and thus also have an impact on their achievement in mathematics. One example of such a practice is the Extreme Apprenticeship method which was noticed to elicit higher levels of deep and organised approaches to learning and lower levels of surface approach to learning than the more traditional lecture-based teaching model (Lahdenperä et al., 2019). 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