Introduction
Persistence, or grit, is the ability of leaners to continue engaging in learning tasks until they master the relevant skills (Cloninger et al.,
1993; Duckworth et al.,
2007). Recent studies have reported that persistence is correlated with academic performance (Poropat,
2009), creativity (Prabhu et al.,
2008), and long-term personal goals, such as studying later in life and future earnings (Datu et al.,
2017; Duckworth et al.,
2007). Educational psychology suggests that students who persist in their learning endeavors, embracing challenges as opportunities for growth, tend to achieve higher levels of skill proficiency (Dweck,
2006). This correlation is particularly evident in formative assessments, where persistent students demonstrate deeper engagement and higher rates of skill mastery (Black & Wiliam,
1998). Moreover, empirical studies underscore the importance of fostering persistence, as it enables learners to overcome obstacles and adaptively engage with complex material (Bandura et al.,
1999). However, persistence may not always lead to successful outcomes. If a learner repeatedly attempts a task without achieving success, their subsequent efforts can become unproductive, resulting in a phenomenon known as wheel-spinning. Wheel-spinning refers to a behavior where students spend excessive time attempting to answer a question or solve a problem without making substantial progress (Beck & Gong,
2013). This behavior can hinder their learning process and impede their ability to move forward effectively. Wheel-spinning behavior indicates that learners continue to reattempt a task even when they recognize their inability to complete it. Beck et al. (
2014) investigated whether affective factors influenced wheel-spinning and identified a correlation between this behavior and gaming the system (e.g., guessing). Unproductive persistence may result in spending prolonged time and exhaustive effort on the challenges, thus leading to inefficient learning. Unlike wheel-spinning, in which learners persist unproductively, non-persistence refers to discontinuing a task without achieving the required mastery level. In addition to hindering the administration of effective interventions by learning systems, a lack of persistence prevents learners from fully mastering their current skills and makes it difficult for them to acquire new skills (Botelho et al.,
2015).
In the context of a learning task, students can exhibit one of three persistence states: productive persistence, wheel-spinning, or non-persistence. In educational contexts, it is essential to differentiate between productive persistence and wheel-spinning behavior to optimize learning outcomes. Productive persistence refers to a learner's consistent and effective effort, marked by resilience and adaptive strategies, leading to meaningful skill development and mastery (Zimmerman,
2002). In contrast, wheel-spinning is characterized by continuous effort without significant progress, often due to ineffective learning strategies or lack of appropriate support (Beck & Gong,
2013). This distinction is crucial as it guides educators in tailoring their interventions; while productive persistence should be encouraged, wheel-spinning requires a shift in approach or additional support to overcome learning stagnation. The ability to identify these behaviors is key for educators, as it impacts not only the efficacy of instructional strategies but also students' motivation and confidence (Pintrich,
2003). Effective identification and response to these behaviors can lead to improved educational outcomes, making it a vital aspect of teaching and learning. Recent studies have aimed to predict students' non-persistence and wheel-spinning behaviors at an early stage in a learning task (Beck & Gong,
2013; Wang et al.,
2020). These studies have explored methods to identify and anticipate when students might exhibit these unproductive or disengaged behaviors, allowing educators to intervene and provide timely support. Persistence propensity represents the tendency of learners to exhibit persistent behavior during the learning process. Research studies have emphasized the value of modeling persistence propensity for predicting student engagement and success in educational contexts (Credé & Phillips,
2011). These models provide insights into the role of motivation, self-regulation, and task characteristics in shaping individuals' persistence (Pintrich,
2003; Wolters,
2003). By considering these factors, educators can design interventions that promote adaptive persistence behaviors and cultivate a growth mindset, leading to improved learning outcomes and academic performance (Duckworth et al.,
2007; Dweck,
2006). Such modeling efforts contribute to creating supportive learning environments that empower students to persist and overcome challenges, ultimately enhancing their educational experiences and long-term success.
Although various approaches and log data have been explored for modeling persistence, few studies have specifically modeled learners’ persistence propensity using psychometric models. The successful application of various psychometric models, such as item response theory (IRT), for modeling the latent abilities of students in computerized adaptive testing (Choi & McClenen,
2020; Desmarais & Baker,
2012; Melesko & Novickij,
2019) has promoted the application of relevant models in the evaluation of persistence propensity (Zhang et al.,
2021). In addition, the definition of persistence and the granularity of data for measurement may vary across learning contexts. Zhang et al. (
2021) measured item-level persistence propensity and defined the trait as the propensity to reattempt an item after an incorrect response. Thus, the modeling of persistence propensity with a different granularity of log data is essential. In the present study, an IRT model was used to evaluate the topic-level persistence propensity of high school students through formative assessments in which students were assessed on their learned topics. In addition, their wheel-spinning propensity was measured; this parameter has not been extensively studied previously. Wheel-spinning propensity indicates the tendency of students to exhibit wheel-spinning behavior in the assessments. Subsequently, we investigated the correlation between the aforementioned traits and various attempt statistics to observe whether the latent traits reflect the corresponding behaviors and explored whether two latent traits were correlated. Further, the influence of the traits on long-term academic performance was evaluated. Overall, the following research questions were addressed in the present study:
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RQ1 Can the item response theory model be used to model students’ persistence and wheel-spinning propensities?
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RQ2 What are the influences of persistence and wheel-spinning propensities on students’ academic performance?
Discussion and conclusion
We used an IRT model to evaluate students’ persistence and wheel-spinning propensities in formative assessments and investigated the correlation between the latent traits and various attempt statistics. The study contributes to the relevant literature by providing insights into the evaluation of psychometric traits (e.g., persistence and wheel-spinning propensities) that are essential to learning. Persistence propensity was correlated with frequency-related statistics (e.g., average number of attempts per topic and percentages of attempted topics and items), whereas wheel-spinning propensity was correlated with correctness-related statistics (e.g., percentages of correct response across attempts and the eventual correct response). These findings are consistent with those reported by Whitmer et al. (
2019) and Zhang et al. (
2021). Whitmer et al. (
2019) indicated that self-reported grit in a learning management system was strongly correlated with the number of attempts made during an assessment. Zhang et al. (
2021) reported that persistence was correlated with a decision to reattempt an item after providing an incorrect response. They further identified a correlation between persistence and the percentage of eventual correct responses. This indicates that wheel-spinning propensity is correlated with item-level persistence; thus, students who show a tendency to reattempt an item until responding correctly are less likely to exhibit wheel-spinning behavior on the topic. However, this correlation requires further validation. The persistence and wheel-spinning propensities were strongly correlated with the number of topics the students persisted on and that the students exhibited wheel-spinning behavior on, respectively; thus, the proposed approach reflects the likelihood of the corresponding behaviors. The present study provides an unobtrusive and practical approach for modeling individuals’ persistence and wheel-spinning propensities, which are key psychometric traits associated with long-term educational and work-related outcomes (Datu et al.,
2017; Duckworth et al.,
2007).
We found no correlation between persistence propensity and wheel-spinning propensity, which indicated that high persistence propensity may not necessarily lead to high wheel-spinning propensity. This finding suggests that non-persistence and wheel-spinning propensities may result from various factors and should be differentiated. The low correlation between the two propensities represents that both latent traits should be included when creating learner profiles. Modeling latent traits may have several advantages. First, these traits may be used in various prediction studies. Although the current effective models facilitate the early prediction of wheel-spinning and non-persistence propensities on a given task (Mu et al.,
2020; Wang et al.,
2020; Zhang et al.,
2019), the level of predictive performance decrease substantially during the next assignment (Botelho et al.,
2019). The modeling approach used in the present study may be used to predict the non-persistence and wheel-spinning behaviors for the next assignment. Thus, a researcher can estimate students’ current latent traits using only attempt data in previous tasks to predict the students’ non-persistence and wheel-spinning behaviors for the next task. Second, the estimated traits can be used to create learner profiles for personalized learning, such as learning paths or quiz recommendations. In addition, the topic properties obtained using the IRT model can be used to provide personalize interventions. For example, recommending topics with low persistence difficulty to students with low persistence propensity may prevent them from quitting.
We calculated the posttest scores of the students and found that the two latent traits influenced their academic performance. As expected, the students with high persistence and low wheel-spinning propensities exhibited the best performance. Although some studies have indicated a correlation between persistence and academic performance (Borghans et al.,
2008; Poropat,
2009), others have reported no apparent correlation between the two (Duckworth et al.,
2007; Zhang et al.,
2021). The inclusion of wheel-spinning propensity may affect the correlation results because persistence may not always be productive. As mentioned, students may quit after their first attempt for various reasons; they may find the topic extremely difficult or boring or believe that they understand the topic well and thus stop after achieving success on their first attempt. In the present study, some of the students might have preferred attempting the exercises in their paper-based textbook or might not have been assessment-oriented because attempting the exercises and submitting the responses on BookRoll were not mandatory. Furthermore, some students exhibited wheel-spinning behavior after persistently attempting exercises and submitting their responses on BookRoll; this suggests that although these students made effort, they could not be successful. Students who have been struggling for a long time should be stopped from persisting and restudy the knowledge instead. Previous studies have shown that wheel-spinning behavior correlates with gaming behaviors, such as random guessing (Beck et al.,
2014). Thus, further investigation of the factors contributing to persistence and wheel-spinning propensities in the current context is essential and will be our next step.
Implications
Our findings have several implications. First, the study proposed an unobtrusive and practical approach for modeling crucial traits that are otherwise difficult to evaluate. Although previous studies have attempted to predict and identify non-persistence and wheel-spinning behaviors, these approaches were unable to quantify these latent traits. Thus, our study may serve as a reference for future studies aimed at modeling persistence and wheel-spinning propensities using other types (e.g., temporal data) and granularity (e.g., item-level and topic-level) of data. The latent traits estimated in our study may be used to predict students’ quitting and wheel-spinning behaviors for future tasks. Because non-persistence and wheel-spinning propensities negatively influenced academic performance, future studies should consider using latent traits for the early identification of at-risk students. Second, our study may facilitate the modeling of persistence propensity in other contexts (e.g., persistence in reading or collaborative learning). The correlation between the persistence propensity in various contexts can be explored. Furthermore, various models may be used to assess other psychometric traits and behaviors, such as the propensity to copy answers, cheat, or procrastinate, which can be combined to create learner profiles for personalized learning. For practice, teachers may identify students who tend to quit or exhibit wheel-spinning behavior during an assessment and design appropriate interventions to help the students, such as sending warning messages. The topic properties obtained using the IRT model may also enable teachers to improve their students’ latent traits. For example, recommending topics with low persistence difficulty to students who tend to quit may encourage them to persist on a given topic. Finally, these topic properties may help teachers to improve their teaching approach. The topics on which many students quit or exhibit wheel-spinning behavior may be perceived as difficult or complex. Thus, teachers must invest extensive effort in teaching these topics and ensure the required levels of baseline knowledge in their students before permitting them to attempt exercises.
Limitations and future research
Our study has some limitations. First, attempting the exercises on all topics was not mandatory, and the number of items per topic varied, which resulted in data sparsity. Because the students selected the topics for practice, the attempted topics markedly varied across the students. Some students attempted even those topics that their teachers did not teach. The number of topics attempted by each student varied despite data preprocessing, which might have influenced the evaluation outcomes of the latent traits. For example, of two students who quit on all of their attempted topics, the student who attempted fewer topics might have had higher persistence propensity than the one who attempted more topics. Data sparsity might have also affected the evaluation outcomes of topic properties. Some topics exhibited the maximum value of wheel-spinning difficulty. This might be because only a few students attempted the aforementioned topics. Future studies are recommended to devise stricter strategies for evaluating the latent traits, such as by selecting a specific number of items and topics as the study exercise and making it mandatory for all students to attempt the exercise. Second, the definitions of persistence and wheel-spinning behaviors in the current context might have differed from those in the relevant literature. Because definitions may considerably influence evaluation outcomes, other definitions can be explored to evaluate these behaviors. In addition, we modeled persistence and wheel-spinning propensities in formative assessments. Future studies can compare the latent traits evaluated using the IRT model with the existing measures of persistence that consider both assessment and other activities through self-report or controlled experiments. It should also be noted that the findings in this study may not generalize to different classroom settings, grade levels, subjects, and geographic locations due to heterogeneity and variability in introductory high school mathematics curricula and the aptitude levels of the students enrolled in this particular course. Finally, we analyzed only the quantitative and aggregate data (i.e., the number of items attempted and the final responses of the students) on each topic. Future studies can include qualitative and other types of data, such as interview, self-reported, and temporal data to investigate key factors that influence students' tendencies to persist or exhibit wheel-spinning behavior in learning tasks.
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