Abstract
Self-regulated learning has been shown to have a positive and long-lasting impact on students’ academic development, employability and career progression. Emotions, motivation and metacognition play an important role in students’ ability to monitor and regulate their learning, particularly when studying and engaging with Science, Technology, Engineering and Mathematics content. In this study, we investigated motivational, emotional and cognitive factors involved in self-regulated learning and their role in mathematics learning. Specifically, we analysed the impact of mathematics anxiety and self-regulated learning on mathematical literacy using the Australian subset of Programme for International Student Assessment 2012. Mathematics anxiety is a barrier to mathematical learning and is thought to hinder students’ engagement and the efficiency of their metacognitive processes. Using structural equation modelling, we showed that instrumental motivation and self-concept affect mathematics anxiety, which in turn negatively impacts mathematical literacy by affecting perseverance and self-efficacy. We consider the practical implications of our results and discuss how interventions to reduce students’ mathematics anxiety will allow for the development and/or improvement of self-regulated learning skills in mathematics.
Keywords
Introduction
Self-regulated learning (SRL) is central to learning, problem solving, reasoning and understanding complex topics (Panadero, 2017). Emotions, motivation and metacognition play an important role in students’ ability to monitor and regulate their learning, particularly when studying and engaging with Science, Technology, Engineering and Mathematics (STEM) content (Azevedo et al., 2017; Efklides, 2011). The aim of this study is to examine the relationship between self-regulatory processes and mathematical learning by investigating motivation, emotion and cognitive strategies and their impact on mathematical literacy using the Programme for International Student Assessment (PISA) 2012 data.
Most of the literature on mathematics anxiety (MA) has shown that it negatively impacts mathematics literacy by affecting cognitive processes, for example by interfering with working memory processes (e.g. Ashcraft & Kirk, 2001), but there are very few comprehensive studies linking MA and metacognition or SRL in the secondary school context (Efklides, 2011; Morsanyi et al., 2019). Investigating these relationships can offer new insights into how students with high levels of MA initially assess a mathematics task, how they monitor their progress and how much they are going to persevere when solving a mathematics problem (Morsanyi et al., 2019). Understanding the interplay of these processes can help design targeted educational interventions. This is particularly important because MA leads to local avoidance (e.g. rushing through mathematics questions) and global avoidance of mathematics (e.g. not choosing mathematics-oriented university courses and avoiding careers that involve mathematics). By avoiding mathematics and mathematics-related professions, the future career and earning opportunities of students can become severely limited (Beilock & Maloney, 2015).
With technological progress, the demand for STEM workers has been increasing in Australia. A recent study published by the Australian Department of Jobs and Small Business showed that between 2013 and 2018, employment in STEM jobs grew by 16.5%, which is 1.6 times higher than the growth rate in non-STEM occupations (Department of Jobs and Small Business, 2019). However, the number of students studying intermediate and advanced mathematics in senior secondary school has remained consistently low in Australia (Hine, 2019). There is evidence that motivational beliefs specific to mathematics are a crucial filter in decision-making regarding STEM-related careers (Watt et al., 2017). Therefore, there is a need to ensure students are engaged with mathematics throughout senior secondary school to promote interest in the pursuit of mathematics-related tertiary degrees and careers.
SRL
SRL refers to the ability of students to understand, track and control their own learning, and can be defined as ‘self-generated thoughts, feelings, and actions that are planned and cyclically adapted to the attainment of personal goals’ (Zimmerman, 2000, p. 14). It involves students’ ability to monitor and regulate their metacognition, motivation, self-beliefs and emotions (Azevedo et al., 2017; Panadero, 2017). It is a multifaceted active and constructive process, which allows students to adapt their approaches and strategies to learning (Pintrich, 2000; Winne, 1997). SRL skills help students become autonomous and independent learners, and therefore are important for life-long learning. SRL has been an important topic of research in educational psychology in the last 30 years and has led to the development of numerous theoretical and conceptual models (Lodge et al., 2019; Panadero, 2017; Winne, 1997; Zimmerman, 2000).
Although the terms metacognition and SRL have been used interchangeably in the literature (Panadero, 2017), most contemporary models consider metacognition as one of the key elements of SRL (Efklides, 2011; Winne, 2017). In their conceptual framework, Chauhan and Singh (2014) define metacognition as the processes by which learners plan, monitor, control, evaluate and adapt their behaviour to solve a task. Metacognition has been shown to be a strong predictor of academic achievement, particularly in mathematics (Desoete & Veenman, 2006; Schneider & Artelt, 2010). The active management of motivation is also crucial to SRL (Efklides, 2011; Wolters, 2003). Instrumental (also known as ‘extrinsic’) motivation plays an important role in initiating and sustaining SRL (Boekaerts, 2010; Pintrich, 1999). If students attach value to a task and see a task as useful to achieve future goals, they are more likely to use cognitive and metacognitive learning strategies to solve that task, which leads to a greater likelihood of task success (Ahmed, 2017; Berger & Karabenick, 2011; Zimmerman, 2000). In this way, motivation can be considered as a driver of SRL. Cleary and Zimmerman (2012) differentiate the SRL process in terms of ‘will’ – the impact of stable, motivational beliefs that are established before participating in a task – and ‘skill’ – the learner’s ability to regulate their learning and engagement on-task.
Emotions are central to how efficiently students can regulate their own learning and also influence motivation (Efklides, 2011). Positive emotions can provide students with the necessary resources to control their focus and commitment towards achieving their learning goals (Efklides et al., 2017). Negative emotions, such as anxiety, are associated with avoidance motivation and result in superficial learning strategies (Pekrun, 2013). If students face a challenge or a difficult situation that induces negative emotions, their initial motivation may not be sufficient to ensure that they follow through and complete the learning task successfully. Therefore, they must be able to regulate their emotions to ensure that they are committed to finding a solution, persevere and develop the strategies they need to succeed.
In our study, the concept of SRL was operationalised by using the indicator of perseverance in the PISA 2012 assessment (OECD, 2013). Perseverance is a construct that depends on SRL skills and has strong metacognitive, motivational and emotional components (Burleson, 2013; Star, 2015). When learners decide to give up or persevere with a strategy, change to a new approach and recognise if they are making progress, they heavily rely on their SRL skills. Empirical studies have shown that students who display high levels of SRL are more perseverant and persistent in their learning than students with low levels of SRL (Wolters & Hussain, 2015; Zimmerman & Schunk, 2008).
MA and SRL
MA, the experience of fear and nervousness when participating in mathematical tasks, is widely studied for its negative impact on mathematics learning (Richardson & Suinn, 1972). Higher levels of MA have been linked to negative attitudes about mathematics and lower levels of mathematics interest, value, self-concept and confidence in abilities (Dowker et al., 2016; Suárez-Pellicioni et al., 2016). According to the control-value theory of achievement emotions (Pekrun, 2006), the experience of emotion in achievement settings is determined by two types of appraisals: those relating to control (e.g. expectations for success, confidence or self-concept beliefs) and those relating to value (e.g. the level of importance ascribed to a task or subject). The theory posits that the antecedents of anxiety are poorer control appraisals combined with higher levels of value. This pattern of lower control and higher value beliefs has been studied in research and linked to higher levels of self-reported MA (Frenzel et al., 2007; Lauermann et al., 2017). However, the relationship between value and anxiety in mathematics is complex. For instance, Luo et al. (2016) found a negative correlation between utility value (the perceived usefulness of mathematics for future aspirations and life) and MA but the association between the two became positive once self-efficacy was controlled for. Self-efficacy – beliefs in one’s own abilities in relation to completing specific tasks (Muenks et al., 2018) – could be considered as a form of control appraisal outlined in the control-value theory.
Much of the research on MA has focussed on investigating its negative impact on performance and learning. Some researchers use the state-MA/trait-MA model to distinguish between (i) the mechanisms that lead MA to impair performance (state MA or on-task MA) from (ii) the impact of MA on long-term decisions to avoid study and career pathways involving mathematics (trait MA; Buckley et al., 2016). Studies have demonstrated that state MA can compromise an individual’s performance on a mathematics task by disrupting working memory processes (e.g. Ashcraft & Kirk, 2001; Beilock et al., 2004). This process is thought to occur when the individual ruminates on intrusive and negative worries regarding their mathematics performance, which then leads to compromised working memory capacity (Ramirez et al., 2018). Given that self-regulation has been conceptualised as an interrelated set of processes involving control, evaluation and adaptation, and the experience of state MA has been linked to overloaded working memory and reduced control of cognitive processes, understanding the interplay between MA and SRL is crucial for initiatives targeted at improving mathematics learning.
Morsanyi et al. (2019) recently published a framework looking at the relationships between MA and the metacognitive processes involved in mathematical reasoning and problem solving. They propose that MA along with confidence beliefs about mathematics (i.e. self-concept) have an impact on metacognitive monitoring and control processes at multiple stages throughout the learning process. Supporting this framework, some research suggests that SRL, particularly metacognition, may mediate part of the relationship between MA and performance (Lai et al., 2015). In other words, student performance that is compromised by trait MA can be explained, in part, by poorer SRL. Other research has examined metacognition and SRL with MA as the outcome variable. Jain and Dowson (2009) found that self-efficacy mediated the relationship between SRL and MA and that less efficient SRL led to higher levels of MA by reducing students’ self-efficacy. These studies provide support for conceptualising the structure of SRL as a feedback loop operating before, during and after interacting with a task (Cleary & Zimmerman, 2012).
In this study, we used Australian PISA 2012 data to investigate the relationship between MA and SRL. The measurement of these constructs in this dataset has implications for how the sequential impact of these constructs on learning is hypothesised and tested. Trait measures of MA are appropriate when examining anxiety’s role in SRL either before a learner’s interaction with a mathematics task or more generally when measuring a learner’s stable emotional disposition. State measures, on the other hand, are designed to capture the experience and impact of MA during the task itself (Buckley et al., 2016; Suárez-Pellicioni et al., 2016). In the PISA 2012 data, trait MA was measured. Our proposal is that the PISA 2012 data allow investigation of the impact of trait motivation and emotion on SRL because it assesses students’ self-beliefs in relation to learning, namely the part of SRL that occurs before participating in a learning task or the ‘will’ component of SRL (Cleary & Zimmerman, 2012).
PISA and the proposed model
PISA is an international survey run by the Organisation for Economic Co-operation and Development (OECD) that assesses how well 15-year-old students can apply what they learn in school to real-life situations. It measures literacy in mathematics, science and reading and records a range of background information including economic, social and cultural status, gender and attitudes towards learning (OECD, 2013). It has been held every three years since 2000, and in 2012 the focus was on mathematical literacy. In this study, we used the Australian sample of PISA 2012 to investigate the relationship between MA, SRL and mathematical literacy. In PISA 2012, students’ levels of perseverance during learning were assessed and we used this as a cognitive representative of SRL in our investigation along with the following constructs: MA, instrumental motivation, mathematics self-concept, mathematics self-efficacy and mathematical literacy.
Figure 1 illustrates the hypothesised model tested in our study that focuses on the relationship between SRL and MA before task completion or the ‘will’ component of SRL (Cleary & Zimmerman, 2012). In line with the control-value theory of achievement emotions (Pekrun, 2006), self-concept and instrumental motivation represent the control and value appraisals, respectively, predicting levels of MA. The construct of instrumental motivation in PISA is similar to the construct of extrinsic motivation and utility value in the research literature (Wigfield & Cambria, 2010). Therefore, this variable can be used as representative of the value appraisal component of the control-value theory. MA is predictive of perseverance in our model as we propose that trait levels of MA will determine the level of cognitive self-regulation reported by students in the form of perseverance. The last component of the model describes perseverance predicting levels of self-efficacy, which, in turn, predicts mathematical literacy. Our rationale behind placing perseverance before self-efficacy is that self-efficacy is a task-specific measure of mathematics confidence or control and therefore is the construct closest to the sequence of SRL that occurs on-task.
Hypothesised model.
In our model we have also allowed the constructs of instrumental motivation and self-concept to be correlated to determine their combined and independent effects on MA. We also show self-concept predicting levels of self-efficacy given both of these constructs are measuring students’ control appraisals in relation to mathematics but at different levels of specificity with self-concept at the general level and self-efficacy at the task-specific level.
Method
Data source and sample
The Australian PISA 2012 dataset contains responses from a nationally representative sample of 14,481 15-year-old students. Each participating student was administered one of three overlapping subsets of the PISA student questionnaire, of which one contained all items of interest for this article. Our analysis focused on the data collected from this subset (4752 students). The results presented in this article only considered students who gave valid responses for every item (4295 students – 2129 girls). Using listwise deletion was justified in this case because the sample size was large enough to retain sufficient power and there were no extra layers of measurement error added via the imputation of missing values (Cheema, 2014).
Variables
The variable names, the item wording used in PISA and the labels used in our model can be found in Appendix 1.
Instrumental motivation
PISA’s instrumental motivation is a goal-oriented drive. It can be described as the degree to which students believe mathematics is important for their future studies and careers (OECD, 2013). This construct has also been referred to as extrinsic motivation and utility value in the research literature (Wigfield & Cambria, 2010). In PISA 2012, this construct was assessed using four questions such as ‘Making an effort in mathematics is worth it because it will help me in the work that I want to do later on’.
Mathematics self-concept
PISA defines self-concept as students’ beliefs in their own mathematics abilities (OECD, 2013). PISA 2012 assessed mathematical self-concept by asking five questions, such as ‘Do you agree with the statement: I learn mathematics quickly?’.
MA
MA is defined in PISA as ‘thoughts and feelings about the self in relation to mathematics, such as feelings of helplessness and stress when dealing with mathematics’ (OECD, 2013). One of the five questions assessing MA from PISA 2012 was ‘I get very nervous doing maths problems’.
Perseverance
PISA assesses perseverance based on students’ responses about their willingness to work on difficult problems, even when they encounter problems and face adversity (OECD, 2013). In PISA 2012, perseverance was measured through five questions such as ‘When confronted with a problem, I give up easily’ or ‘When confronted with a problem, I do more than what is expected of me’. Students answered using a scale ranging from ‘this is very much like me’ to ‘this is not like me at all’.
Mathematics self-efficacy
PISA defines mathematical self-efficacy as the students’ beliefs that they can successfully solve mathematics problems (OECD, 2013). In the 2012 assessment, eight questions were asked to assess mathematical self-efficacy. Students were asked to rate their level of confidence for questions such as ‘How confident do you feel about solving an equation like 3x + 5 = 17?’.
Mathematical literacy
Mathematical literacy is defined as students’ ability to reason and apply their mathematical knowledge and skills to solve and interpret problems set in real-world contexts (OECD, 2013). To provide adequate coverage of all aspects of mathematics literacy, in PISA, test items are spread across a number of rotated forms to keep test administration times manageable for students. A model based on Item Response Theory is applied to all available information and students are assigned a random sample of five plausible values (PVs) from the posterior distribution based on the test items they actually answered and on their responses to the student questionnaire. Many studies using PISA data use only one of the five PVs as a proxy for mathematical literacy which leads to underestimation of the standard error associated with the variables being studied (Rutkowski et al., 2010). In line with the recommended use of the PISA data, our model incorporates all five PVs.
Structural equation modelling (SEM)
SEM is a popular statistical approach, commonly used in the field of educational psychology for testing relationships among observed and hypothetical constructs (or latent variables) which are not directly measured (Finch & French, 2015; Khine, 2013). Motivated by the use of SEM in some of the previous work surrounding mathematical anxiety (Jain & Dowson, 2009; Özcan & Eren Gümüş, 2019) and its ability to test causal hypothesised relationships between latent constructs, SEM was adopted in this study to examine the relationship between MA, SRL and mathematical literacy.
The structural equation model implemented in this study was fitted to the entire dataset in two steps (Anderson & Gerbing, 1988). First, a measurement model (confirmatory factor analysis) was used to estimate the latent variables and assess the fit of the estimated factor structure (Finch & French, 2015). The correlation between each pair of these identified latent constructs was also calculated and examined in line with Cohen (1988). Second, a structural model was used to specify a regression-like path analysis and examine the hypothesised directional and non-directional nature of relationships between these variables. Kline (2016) and Simsek (2007), among others, suggest the use of comparative fit index (CFI), root mean square error of approximation (RMSEA), goodness of fit index (GFI), adjusted goodness of fit index (AGFI), standardised root mean square residual (SRMR) and Chi-Square goodness of fit as indices to assess the model fit. However, the Chi-Square goodness of fit is not always a reliable measure for assessing individual model fit (Finch & French, 2015) and hence, not reported in this study. Also, although each of these other measures have widely accepted cut-off values, Marsh et al. (2004) argue that these measures are heuristic and should be treated with caution. The entire analysis was conducted using the Lavaan package in R (Rosseel, 2012).
Results
The fit measures for the estimated measurement model indicate good fit (CFI = 0.988; RMSEA = 0.039; GFI = 0.989; AGFI = 0.988; SRMR = 0.044) suggesting that the identified factor structure is supported well by the data. Similarly, the structural model – that is the measurement model augmented with the path analysis to examine relationships between the latent variables – also indicates overall good fit to the data (CFI = 0.982; RMSEA = 0.046; GFI = 0.986; AGFI = 0.983; SRMR = 0.051).
Correlations between the identified latent variables were calculated and found to be significant at the 0.01 level. Table 1 shows the Pearson correlation coefficients of the latent variables. MA is negatively correlated with all other latent constructs while the other latent variables are positively correlated with one another. Thus, higher levels of MA are associated with lower levels of instrumental motivation, self-concept, perseverance, self-efficacy and mathematical literacy.
Correlations among the latent variables.
MA: mathematics anxiety.
Assessing the results of the path analysis, all the unstandardised factor loadings of the observed variables on the latent variables are statistically significant at the 0.01 level (see Table 2), indicating that the proposed factor structure fits the data well. Also, the standardised factor loadings are higher than 0.5, suggesting that the observed variables are closely related to their associated factors (Yong & Pearce, 2013). Furthermore, the hypothesised direct and indirect relationships between the latent variables are significant and their estimates are listed in Table 3. Assessing the structural estimates, we found a negative relationship between self-concept and MA. However, instrumental motivation predicts MA positively (see Figure 2), despite a moderate negative correlation between instrumental motivation and MA (Cohen, 1988, see Table 1). The other estimates of the path analysis are reported in Table 3.
Factor loadings.
MA: mathematics anxiety.
SEM path coefficients.
MA: mathematics anxiety; SEM: structural equation modelling.
1∼ indicates direct effects; 2∼∼ indicates indirect effects in the path analysis.
Structural equation model.
Discussion
Many studies have identified a negative relationship between MA and mathematics performance, but this relationship is complex and depends on a range of emotional, motivational and metacognitive factors (Ashcraft & Moore, 2009). In this cross-sectional study, we examined self-regulatory processes involved in mathematical learning by investigating relationships between motivation, MA, cognitive strategies and mathematical literacy as measured in the 2012 cycle of PISA with Australian students. Similar to previous research (Luo et al., 2016), our findings lend some support to the control-value theory’s conceptualisation of anxiety. Higher levels of MA were associated with lower levels of self-concept and slightly higher levels of value; however, the findings had an added layer of complexity. Instrumental motivation or value was negatively correlated with MA and only once self-concept was taken into account did the relationship between value and MA become positive. These results suggest that self-concept interacts with value and together this interaction has implications for the experience of MA. Self-concept may moderate the relationship between value and MA; however, further analysis would be needed to investigate these effects. Future studies could also examine different types of mathematics value (e.g. instrumental, intrinsic and attainment value) and their relationship with self-concept and MA.
Our analyses examined self-regulatory processes before task participation or what Cleary and Zimmerman (2012) labelled the ‘will’ component or influence of self-beliefs on SRL. This stage of SRL was chosen as the focus of the analyses due to the characteristics of the data collected in PISA 2012. These data focus on the stable or trait motivational, emotional and cognitive characteristics that Australian students reported before their participation in the PISA 2012 mathematics problem-solving tasks. In particular, researchers have emphasised the importance of distinguishing the measurement of trait MA from state MA due to their different impacts on learning (Buckley et al., 2016; Suárez-Pellicioni et al., 2016). Our results suggest that trait MA negatively impacts students’ self-reported perseverance, that perseverance has a positive influence on reported self-efficacy which, in turn, positively impacts mathematical literacy. These findings support the framework proposed by Morsanyi et al. (2019) and their assertion that metacognitive processes such as perseverance have an impact on mathematical learning but are also shaped by MA and self-concept beliefs. A caveat to note relates to the PISA 2012 construct of perseverance, which was domain-general whereby students were asked to rate their level of agreement to statements assessing willingness to respond to challenges in general learning tasks. It is possible that students were primed to think about their tendency to persevere in mathematics specifically as they had just completed the PISA assessment, the majority of which consisted of mathematics problem-solving tasks. However, perseverance in mathematical learning was not explicitly assessed. Given research findings illustrating that motivation, emotion and SRL may operate differently depending on the domain or subject area considered particularly in STEM subjects (e.g. Boekaerts et al., 2003; Göetz et al., 2010), future research investigating the relationship between motivation, MA, mathematical learning and mathematics perseverance should be explored.
Our results support research that shows a student’s MA may be alleviated by increasing their self-concept in mathematics. Göetz et al. (2010) describe several ways in which this can be achieved. Thus, for instance, teachers could highlight what students are already able to do before attempting new challenges, emphasising to students that they should focus on past successes to track individual growth and changing the frame of references from the other to the individual, and helping students to appreciate the control they have over their achievements in mathematics. The latter approach aligns with researchers who suggest that challenging negative and maladaptive beliefs about mathematics ability is a key factor in reducing trait MA (Buckley et al., 2016).
When using PISA data, as we have, it is important to bear in mind that PISA’s focus has been on education systems rather than individual student growth, and consequently collecting longitudinal data has been outside the scope of that assessment. The cross-sectional data PISA offers are a snapshot of a single point in time and cannot show how a particular student evolves over the course of their studies. SRL has been described as a self-oriented feedback loop in which students use a dynamic cyclical process to monitor their own learning activity (Zimmerman, 2000). Longitudinal studies are required to confirm and further investigate the dynamics of the relationships identified in our model. For example, a longitudinal approach would allow researchers to ask questions such as, ‘To what extent do interventions addressing students’ MA lead to an increase in perseverance, and then improved mathematical learning?’, and ‘Do the benefits of a classroom intervention to improve SRL skills persist and do they have later implications for students’ trait MA?’.
Although self-report measures like those used in PISA have many advantages (e.g. they are easy to produce, administer and score), they also have some limitations (e.g. validity and bias issues) and do not necessarily reflect the complex nature of MA and SRL (Wolters & Won, 2017). Advanced learning technologies (e.g. intelligent tutoring systems, virtual reality, serious games) are emerging and allow researchers to use objective or external measures of emotion and metacognitive SRL processes using various multichannel online trace data (e.g. eye-tracking, log files, electrodermal bracelets; Azevedo et al., 2017). Such multichannel data allow researchers to capture actual student behaviour alongside self-reports. While these systems are still fairly novel and thus pose challenges, for example in terms of difficulties with temporal alignment of data channels or lack of appropriate analytical techniques, they represent a promising avenue for developing systems that provide intelligent individualised support in real time.
By reducing students’ MA, developing their SRL skills and encouraging them to study mathematics, Australia can build a strong STEM workforce needed for the 21st century. Our results support the widely accepted position that in order to encourage students to continue studying mathematics, the curriculum should not focus solely on content, but reinforce the importance of motivation, emotion and self-regulation in learning. One of the general capabilities included in the Australian Curriculum, self-management, is closely related to SRL and describes how students should be able to ‘effectively regulate, manage and monitor their own emotional responses, and persist in completing tasks and overcoming obstacles’ (ACARA, 2018). By developing a greater understanding of the nature of the relationship between MA and SRL processes, better educational programmes and interventions can be developed to ensure that students stay engaged in mathematics, enjoy a better learning experience and pursue mathematics-oriented careers in the future.
Footnotes
Acknowledgements
The authors would like to thank Professor Phil Winne for his comments on an early version of the model and Dr Jason Signolet for his help with data processing and his insightful comments.
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) received no financial support for the research, authorship, and/or publication of this article.
