Is there more than one path to success in math? Patterns and predictors of students’ motivation and achievement in online math courses

Assorted Electronics on table

By Stephanie Wormington
Center for the Advanced Study of Teaching and Learning, University of Virginia
Email: [email protected]

Consider two students in an online Geometry course. Both students enjoy math, see themselves as math people, and want to learn as much as possible. One student also wants to show her teacher she’s the best student in class, while the other isn’t concerned with what his teacher thinks of him. Which student is likely to perform better, persevere through challenging assignments, or pursue math in the future? More importantly, how can a Geometry instructor facilitate both students’ learning?

Supporting students’ motivation is a key concern for educators and researchers alike. Many instructors struggle to teach in a way that engages all students. Researchers have spent decades measuring motivation and documenting its link to students’ thoughts, feelings, and behavior in school (Linnenbrink-Garcia & Patall, 2016). While these findings could inform classroom practice, there is a disconnect between how researchers study motivation and what actual motivation looks like (Linnenbrink-Garcia, Patall, & Pekrun, 2016). Specifically, motivation, as it exists in the classroom, is often much more complex than it is when it’s presented in academic studies. Students have many (and often multiple) reasons for trying hard in school. However, research often considers how one type of motivation, like interest, independently relates to one type of outcome, like grades. As a result, teachers are left to translate findings about single types of motivation into practices for supporting students who hold multiple and varied reasons for learning. This translational challenge is even more pronounced for online instructors since motivation research has almost exclusively been conducted in face-to-face classrooms.

For my dissertation, I wanted to learn more about online learners’ motivation and overall experience. With online courses becoming increasingly popular within both K-12 and higher education, it’s critical for motivation researchers to expand into virtual classrooms. Because motivation tends to drastically decline in math and adolescence (Otis, Grouzet, & Pelletier, 2005), I was particularly interested in working with high school math students. As someone who struggled her way through an online Calculus AB class back in high school, I also had some personal reasons for wanting to understand the online experience better. Given their focus on motivation as a tool to support online learners, Michigan Virtual School was the perfect organization to partner with for this work.

How Do You Study Motivation?

This study builds on six years of research with my advisor, Lisa Linnenbrink-Garcia, examining motivation in samples from late childhood to college and educational settings from science to social studies. The basic premise of this work is simple: to better capture student motivation, we need to consider how many different types of motivation combine to impact a student’s success. By doing so, we can also provide educators with clearer guidelines on effectively supporting students. Our approach involves two steps:

Step 1: Measure students’ motivation comprehensively but succinctly.

From striving to making honor roll to pursuing a long-held interest in math, students have many reasons for trying hard in school. Consequently, there are scores of available measures that tap into slightly different types of motivation. Our goal was to identify a handful of measures that captured students’ motivation broadly and answered two fundamental motivational questions: “Can I do this?” and “Do I want to do this, and why?” Based on those criteria, we asked students about three types of motivation:

  • Perceived Competence: whether a student believes she can be successful (“Do I think I can do well in Calculus?”)
  • Value: whether a student considers something interesting, enjoyable, useful, or important (“Do I think Calculus is useful and worthwhile?”)
  • Achievement Goals: whether a student wants to develop or demonstrate his or her competence. Achievement goals include mastery (“Do I want to develop my skills and knowledge in Calculus?”), performance-approach (“Do I want to show others I’m smart in Calculus?”) and performance-avoidance goals (“Do I want to avoid showing others I’m dumb in Calculus?”)
Step 2: Identify common patterns of motivation.

If students can have several reasons for trying hard in school, what is the best combination to have? We use a statistical approach known as person-oriented analyses to identify common patterns of motivation – or motivational profiles – and see which profiles relate to the greatest engagement and achievement. This differs from some motivation research, which focuses on one type of motivation at a time and how it relates to learning.

To illustrate, let’s return to the example of two Geometry students. Both students reported high competency beliefs, mastery goals, and value, but they differed in their performance goals. Even though they look similar on some types of motivation, we’d consider these students separately because they have different overall patterns of motivation. We can then compare students from different profiles on exam grades or other learning outcomes to understand who is most likely to be successful.

What Motivates Online Math Students?

In Fall 2015, students in 17 Algebra I, Algebra II, Geometry, and Calculus classes at MVS were invited to participate in this study. More than 200 students, about 61% of all students enrolled in those courses, told us about their perceived competence, value, and achievement goals in math at the beginning of the semester; a subset of students also told us about their motivation and engagement at the middle and end of the semester.

There were four groups of students with distinct motivational profiles. For students who responded more than once, we also considered whether they stayed in the same profile or switched to a different one over time.

  • Highly Motivated by Any Means: about 1/4 of students reported high motivation overall; they felt competent in math, valued the subject, and wanted to both develop and demonstrate their competence. Most students switched to a different profile by mid-semester, suggesting it may be difficult to maintain high levels of motivation over time.
  • Intrinsically Motivated and Confident: another 1/3 of students also felt competent in and valued math, but weren’t concerned with demonstrating their competence to others. This profile was by far the most stable from beginning to mid-semester, suggesting that students who come into a course with these beliefs tend to maintain them over time.
  • Average All Motivation: a separate 1/3 of students reported average competence, value, and achievement goals in math. This profile was somewhat stable, with half the students maintaining average motivation and a half switching to a different profile by mid-semester.
  • Amotivated: the final 1/10 of students reported lower-than-average competence, value, and goals in math. Though most students switched into a different profile by mid-semester, students from other profiles also tended to shift into this profile over time.

Our prior research in face-to-face classrooms has consistently identified students who are Highly Motivated by Any Means, Intrinsically Motivated and Confident, and Amotivated, suggesting that online students’ motivation may be similar to students in traditional classes. However, a fourth common Performance-Focused profile – consisting of students with high-performance goals but low competence, value, and mastery goals – was noticeably absent. This could be due to differences in how students show others they’re smart in face-to-face versus online contexts (e.g., raising their hand to answer questions), or it may be simply an anomaly of this study.

Which Students Are Most Successful?

Which motivational profile leads to the greatest success? We compared profiles on outcomes like exam grades across the semester, pictured below.

Achievement table

Students in the Highly Motivated by Any Means, Intrinsically Motivated and Confident, and Average All Motivation profiles had equally high exam scores throughout the semester. They also reported similar engagement and self-regulation, with Average All Motivation students somewhat less engaged. Findings suggest that there are multiple pathways to math success rather than an ideal motivational combination; as long as students feel relatively competent, value math, and want to get better, they are likely to do well.

Conversely, Amotivated students earned exam scores 15-25 points lower than their classmates and held more negative self-perceptions. After receiving feedback on each exam, we asked all students to report on how successful they were, why they did or didn’t do well, and how they felt. Even when controlling for actual exam scores, Amotivated students reported feeling much less successful than students in other profiles. They were less likely to attribute their performance to internal and controllable factors (like effort or strategy use), suggesting that they may feel little agency to change. Consistent with findings from our other studies, the Amotivated profile represents a small but particularly at-risk group of students.

While these findings are sobering, knowing how Amotivated students respond to failure may provide a clue for how to best support them. For instance, Amotivated students may need help reframing failure positively and taking ownership of their math learning. Educational researchers have developed approaches targeting students’ reactions to failure, such as attribution retraining (where students learn to ascribe failure to controllable causes rather than uncontrollable forces; Perry et al., 2014) and growth mindset interventions (where students learn to view failure as opportunities for growth and believe that they can improve through effort; Paunesku et al., 2015). These interventions could also help buffer students who might shift into an Amotivated profile over time by helping them interpret failure in a way that helps them maintain their math motivation. Math students in other profiles also have unique strengths and challenges in the virtual classroom that can be supported differently. Ultimately, studies like this can help us think through how to tailor supports to students’ unique needs by implementing interventions based on profile, allocating resources toward at-risk students, or customizing classroom activities to fit students’ needs. By measuring motivation broadly and acknowledging individual differences, we may provide better support for all online students’ learning.

About the Author

Stephanie Wormington is a research assistant professor in the Center for Advanced Study of Teaching and Learning at the University of Virginia. Her research considers how and why motivation changes across development and how to foster lasting, resilient mindsets in education, employment, and extracurricular contexts. She is co-PI on two grants examining how motivation transfers across different life domains and developing and testing customized social-psychological interventions that promote positive motivational transfer. Stephanie is also interested in peer influences on motivation, particularly during adolescence. You can email Stephanie at [email protected].


Linnenbrink-Garcia, L., & Patall, E. A. (2016). Motivation. In E. Anderman & L. Corno (Eds.), Handbook of educational psychology, 3rd edition (pp. 91-103). New York: Taylor & Francis.
Linnenbrink-Garcia, L., Patall, E. A., & Pekrun, R. (2016). Adaptive motivation and emotion in education: Research and principles for instructional design. Policy Insights from the Behavioral and Brain Sciences, 3, 228-236.

Otis, N., Grouzet, F. M. E., & Pelletier, L. G. (2005). Latent motivational change in an academic setting: A 3-year longitudinal study. Journal of Educational Psychology, 97, 170-183.

Paunesku, D., Walton, G. M., Romero, C., Smith, E. N., Yeager, D. S., & Dweck, C. S. (2015). Mind-Set Interventions Are a Scalable Treatment for Academic Underachievement. Psychological Science, 26, 784–793.

Perry, R. P., Chipperfield, J. G., Hladkyj, S., Pekrun, R., & Hamm, J. M. (2014). Attribution- Based Treatment Interventions in Some Achievement Settings. Motivational Interventions, 1-35.

For more details on this study, see:

Wormington, S. V. (2016). Smooth sailing or choppy waters? Patterns and predictors of motivation in on-line mathematics courses (Doctoral dissertation). Retrieved from Proquest.

For more information on the other person-oriented work referenced in this article, see: Linnenbrink-Garcia, L., & Wormington, S. V. (in revision).

Linnenbrink-Garcia, L., & Wormington, S. V. (in revision). Complexity of motivation in schooling: Key challenges and potential solutions. British Journal of Educational Psychology.

Linnenbrink-Garcia, L., & Wormington, S. V. (under review). An integrative perspective for studying motivation in relation to engagement and learning. Chapter to appear in K. A. Renninger and S. E. Hidi (Eds.), The Cambridge Handbook on Motivation and Learning.

Linnenbrink-Garcia, L., Wormington, S. V., Snyder, K. E., Riggsbee, J., Perez, T., Ben-Eliyahu, A., & Hill, N. E. (in revision). Everyone is not the same: An examination of integrative motivational profiles among college and upper elementary students. Journal of Educational Psychology.

Wormington, S. V., Barger, M. M., & Linnenbrink-Garcia, L. (2014). One size fits all? Longitudinal, profile-centered examinations of adolescents’ motivation in mathematics and social studies. Paper presented at the annual American Educational Research Association, San Francisco, CA.

Wormington, S. V., & Linnenbrink-Garcia, L. (2016). A new look at multiple goal pursuit: The promise of a person-centered approach. Educational Psychology Review, 1-39. doi:10.1007/s10648-016-9358-2

Michigan Virtual Learning Research Institute

Michigan Virtual Learning Research Institute

The Michigan Virtual Learning Research Institute (MVLRI) is a non-biased organization that exists to expand Michigan’s ability to support new learning models, engage in active research to inform new policies in online and blended learning, and strengthen the state’s infrastructures for sharing best practices. MVLRI works with all online learning environments to develop the best practices for the industry as a whole.

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