Understanding Student Problem-Solving Experiences Through Peer-Learning in a Gamified Math Environment

Purpose

Elementary students in the United States are struggling with mathematics, with only 36% of fourth graders performing at or above grade level in mathematics as of 2022 (National Center for Education Statistics [NCES], 2022). Black, Hispanic, and low-income students perform even worse, with fewer achieving proficiency (NCES, 2022). This highlights the urgent need for evidence-based instructional strategies to improve math performance and close achievement gaps. Peer-learning, where students share knowledge and ideas, is a proven strategy to address this issue (Boud, 2001). Research has shown that peer-learning improves problem-solving performance, particularly in gamified environments (Hwang & Hu, 2013; Ke & Clark, 2020). Gamification elements like challenges, rewards, and progression systems enhance student engagement and learning outcomes (Deterding et al., 2011).

Understanding students' perspectives on learning environments is critical for designing effective instruction. Student voice provides insights into the factors that impact their learning experiences and outcomes (Oerlemans, 2007). Despite the established benefits of peer-learning, there is limited research amplifying student voice to understand the cognitive, environmental, and behavioral factors that improve problem-solving. This study aims to explore how students perceive peer-learning experiences in a gamified math environment through the lens of Social Cognitive Theory (SCT).

Theoretical Framework

Social Cognitive Theory (SCT) emphasizes that learning occurs in a social context where cognitive, environmental, and behavioral factors dynamically influence each other (Bandura, 1986). In gamified problem-solving, peer interactions are vital for knowledge acquisition and skill development (King, 2002). Cognitive factors include beliefs, expectations, and knowledge; environmental factors encompass social and physical contexts; and behavioral factors involve actions and responses influenced by the other two dimensions. These reciprocal influences underscore the importance of peer-learning in shaping student attitudes, behaviors, and self-efficacy.

Methods

This qualitative study examined fourth and fifth-graders' perceptions of their learning experiences in a gamified math environment. It was part of a larger study on the effects of peer-learning on expressive communication and problem-solving. Participants were 49 students (32 females) from an urban school district in the Northeastern United States, where 40.6% of families receive government assistance, and all schools are Title I.

Students were divided into peer-learning (n=25) and non-peer-learning (n=24) groups. Peer-learning was teacher-facilitated, with teachers providing structure, prompts, and encouragement (Gillies & Khan, 2008). Non-peer-learning students worked independently, though incidental collaboration was not prohibited. Data collection spanned four months and included weekly classroom visits for interviews. The study used the First in Math (FIM) online platform, a gamified environment proven effective for low-income, high-minority populations (Columba, 2020).

Data were collected through audio-recorded, semi-structured interviews with questions such as: "Can you describe a time when you were particularly challenged by a math problem or concept?" and "How do you decide which math strategies to use?" Responses were thematically analyzed using deductive coding based on SCT (Saldaña, 2016). Two researchers independently coded the data, achieving inter-rater agreement through discussion.

Results and Discussion

Cognitive Factors

Peer-learning students demonstrated higher accuracy in using academic vocabulary compared to non-peer-learning students. For instance, a peer-learning student described their progress as, “I'm working on multiplication, division, equations, fractions, the order of operations, decimals, and integers.” This clear and accurate use of mathematical terms contrasted with non-peer-learning students, who often struggled with terminology. One student said, “If you plus like 100 times 200… but if you times it, it'll be much more complicated,” which was unclear and inaccurate.

Peer-learning students also expressed consistently positive attitudes toward math and the gamified platform, often referencing personal growth. They exhibited goal-setting behaviors, using in-game rewards like stickers and points to monitor progress. One student stated, “I was trying to hit my goal of 100,000 [stickers], but I was one-fifth of that,” demonstrating both progress monitoring and practical application of fractions. Non-peer-learning students showed mixed attitudes toward math. While some expressed enthusiasm, others reported frustration, particularly with challenging problems. Non-peer-learning students were also less likely to set goals or engage in progress monitoring.

Environmental Factors

Students in the peer-learning group frequently cited peers as a key source of support during problem-solving. One student shared, “If it's hard, I ask my friends to help me with the problem and figure it out.” Peer interactions were both cooperative and competitive, with students referencing leaderboards as motivators for setting goals like “player of the day.” They also highlighted game features such as rewards, timers, and vocabulary definitions as beneficial and engaging. In contrast, non-peer-learning students sought help exclusively from teachers or adults and did not reference peer support. They had mixed opinions about the platform’s usability and game features. Their problem-solving strategies were simpler and less detailed.

Behavioral Factors

Peer-learning students practiced math skills more frequently and employed more complex problem-solving strategies. One student explained their approach to division: “If you get an answer and don't know if it's correct, times it and then subtract it. If it's zero, you're correct.” This response demonstrated a clear understanding of mathematical concepts and effective problem-solving.

Non-peer-learning students exhibited simpler strategies and relied more heavily on teacher assistance. One student said, “When it gets hard, I grab my paper and do the strategies the teacher taught me.” Such responses lacked specificity and creativity.

Overall, peer-learning students demonstrated higher quality and complexity in cognitive, environmental, and behavioral responses. They were more likely to articulate clear problem-solving strategies, express positive attitudes toward math, and practice skills independently and collaboratively. Non-peer-learning students relied more heavily on external support and exhibited less engagement with the gamified environment.

Significance

This study highlights the impact of cognitive, environmental, and behavioral factors on student problem-solving in mathematics. Teacher-facilitated peer-learning enhanced students’ ability to articulate complex strategies, communicate effectively, and set meaningful goals. Peer-learning students exhibited stronger collaboration, greater willingness to seek and provide peer support, and a more positive attitude toward mathematics. These benefits were particularly evident in an underserved population, emphasizing the potential of peer-learning to address educational inequities.

Our findings suggest that practitioners should prioritize collaborative problem-solving, foster supportive communities, and leverage gamification to improve math performance. Future research should explore the long-term effects of peer-learning in gamified contexts and interventions to support collaborative problem-solving skills.

References

1. Bandura, A. (1986). Social Foundations of Thought and Action: A Social Cognitive Theory. Prentice-Hall.
2. Boud, D. (2001). Peer Learning in Higher Education: Learning from and with Each Other. Kogan Page.
3. Columba, L. (2020). Computational thinking using the first in math® online program. Mathematics Teaching-Research Journal, 12(1), 45-57.
4. Deterding, S., Dixon, D., Khaled, R., & Nacke, L. (2011). From game design elements to gamefulness: Defining "gamification." In Proceedings of the 15th International Academic MindTrek Conference: Envisioning Future Media Environments, pp. 9-15. ACM. https://doi.org/10.1145/2181037.2181040 
5. Hwang, W. Y., & Hu, S.-S. (2013). Analysis of peer-learning behaviors using multiple representations in virtual reality and their impacts on geometry problem solving. Computers & Education, 62, 308–319. https://doi.org/10.1016/j.compedu.2012.10.005 
6. Gillies, R. M., & Khan, A. (2008). The effects of teacher discourse on students’ discourse, problem-solving and reasoning during cooperative learning. International Journal of Educational Research, 47(6), 323–340. https://doi.org/10.1016/j.ijer.2008.06.001 
7. Ke, F., & M. Clark, K. (2020). Game-based multimodal representations and mathematical problem solving. International Journal of Science and Mathematics Education, 18(1), 103-122.
8. King, A. (2002). Structuring Peer Interaction to Promote High-Level Cognitive Processing. Theory Into Practice, 41(1), 33–39. https://doi.org/10.1207/s15430421tip4101_6
9. Klang, N., Karlsson, N., Kilborn, W., Eriksson, P., & Karlberg, M. (2021). Mathematical problem-solving through cooperative learning—the importance of peer acceptance and friendships. Frontiers in Education, 6, 710296.
10. National Center for Education Statistics. (2022). The Nation's Report Card: 2022 Mathematics Assessment (NCES 2023-014). U.S. Department of Education, Institute of Education Sciences. https://nces.ed.gov/nationsreportcard/
11. NCES: Condition of Education (no date). Education Demographic and Geographic Estimates. National Center for Education Statistics. Available at: https://nces.ed.gov/programs/coe/ (Accessed: March 3, 2023).
12. Oerlemans, K. (2007). Students as Stakeholders: Voices from the Antipodes. Journal of Educational Administration and History, 39(1), 17–32. https://doi.org/10.1080/00220620701194267 
13. Saldaña, J. (2016). The Coding Manual for Qualitative Researchers (3rd ed.). Sage Publications.

Table 1

Codebook

Table 2

Results Table by Learning Group and SCT Factors