Practical Insights and Contemporary Environment of Productive Struggle

The K-12 education system is becoming increasingly agile with its ability to enhance the learning experience for young students. However, despite the constant refinement of pedagogy, many years of research on the study of classroom ecology, and detailed analyses of the student community, the challenge to raise math based competencies is becoming increasingly elusive for educators and K-12 school administrators. As a result of this growing and complex problem, my topic is anchored in the innovative and cutting edge approach to introduce gamification as a tool and pillar to resolve the difficulties that both educators and students run into when productive struggle is put into practice. More importantly, recovering mathematical scores and learning skills is vital to the education infrastructure of the US and needs to be immediately addressed now or we can expect to further overload our already overworked educators and risk underpreparing students for their desired STEM fields (Dunlosky 2013; Boaler 2016; Deslauriers et al., 2019).

In a concerted effort to strengthen the educational pipeline for young students interested in science, technology, engineering, and mathematics subjects (STEM) we must be able to encourage innovative and dynamic strategies to help students craft a healthy approach to how they interact with each other, learn the material, and how they perceive the role of the teacher. Productive struggle should be seriously considered as classroom praxis in math-based classes to best address the recent decrease in mathematics scores among K-12 students across the country in virtually every region of the United States (National Center for Education Statistics, 2022).

Data shows that mathematics scores have dropped post-pandemic, additionally, the learning of STEM related courses involves the process of trial and error that is usually introduced initially through early math courses (Deslauriers et al., 2019; Kapur, 2008; Warshauer, 2015). Accordingly, a deeper understanding of the learning process that students go through would help educators better assist their pupils in designing individualized pathways for successful learning. This helps educators create successful ecologies that promote a team environment and collaborative process.

The main dimensions of this topic include addressing the scalability of productive struggle to become a much more viable option in public schools with larger class sizes, to provide improved layers of guidance for the instructors who want to employ a productive struggle approach, goal-setting, and to address the emotional difficulties that students struggle with when working through a productive struggle ecology. The theoretical framework of productive struggle stems from the concept of goal setting, this grassroots concept is applied multi-dimensionally throughout the process of working through almost any problem with a wide variety of courses where the goal is to learn a specific subject matter. Productive struggle creates several smaller goals for students to achieve on the way to the larger goal, it is possible to think of the smaller goals as educational checkpoints to achieve a much larger objective.

Gamification would be relatively easy to implement due to the nature of educational checkpoints and bigger achievements as part of the larger productive struggle framework, students can obtain a true sense of achievement by being rewarded with active feedback and a reward system (Hussein et al., 2022; Bainbridge et al., 2022). The ability to employ gamification as a supplementary tool for educational goals and learning in a wide breadth of fields within K-12 education. In short, gamification is a concept borrowed from traditional video games where participants are actively working towards completing an objective to make progress in a video game; people who play video games can level up, save their progress, play at their own pace, they get rewarded with accolades or improved in-game gear for making further progress, checkpoints exist as well in-case a specific point in the game is too difficult, and the gratification for completing a game incentivizes participants to continue to stay engaged (Sailer and Homner, 2020). One of the most common educational technologies that employs gamification is something called 'kahoot' which is a very popular online platform for educators to use when they want to engage their students in a friendly competition where bragging rights might be at stake or maybe a real life reward for students who rank highly at the end of a kahoot assessment.

A deep dive of K-12 math-class research and gamification in education literature through google scholar, the EBSCO Academic Ultimate Search through the University of Illinois Urbana-Champaign, the lecture from Dr. George Reese on productive struggle, the K-12 education research database, and the teachings of Vygotsky who is a central and foundational figure in education concepts.

Theoretical Framework of Productive Struggle

Productive struggle draws on the work of educational psychologists such as Edwin Locke, Lev Vygotsky, and Jean Piaget. Dr. Edwin Locke for his goal-setting theory which argues that people are typically driven to meet an objective that is intentionally designed for them either through internal or external agents (Locke et al., 1981), Dr. Jean Piaget for his constructivist approach which suggests that young individuals are able to learn more from the world by engaging in challengs and exploration than by passively learning such as sitting in a lecture listening to the teacher (1976), and Dr. Lev Vygotsky for his indirect and instrumental contributions to productive struggle via his theoretical groundwork with the zone-of-proximal development theory.

According to the research pioneered by Vygotsky (1978; 1986), there has been an optimal method identified where students should be receiving an adequate amount of challenge and support. Too much support can result in what is referred to as crutches, where students are not directly benefiting from doing the work themselves, if their personal efforts are being overshadowed by the support, in this case being the educators . The students are not going through the problem-solving steps that would help them accomplish what is being asked of them to encourage the determination of how to apply their learned skill set to similar or further mathematics subsets. On the contrary, less support would exacerbate the difficulty of the challenge students are working on. When the challenge is coming across as too difficult and students do not have a stable and consistent form of support, the likelihood of giving up and feeling negatively towards the challenge can occur. Additionally, students may be less likely to re-engage in working towards attaining the skillset or meeting set goals.

Vygotsky and Piaget are seen as the main writers of the initial research for productive struggle (Devries, 2000; Kapur 2008). They paved the foundation for researchers, educators, practitioners, and educational psychologists to continue expanding on the gaps in literature and suggestions of the predecessors. Organizations, foundations or agencies that may be funding educational programs or institutions may also be interested in direct findings or relevant research that would aid in the establishment of those programs. Additionally, the organizations or agencies could also be advocates of the continuation of research.

Meanwhile, Dr. Locke makes motivation a central variable in his goal setting theory. In some sense, goal setting also occurs with some of the guidelines that Piaget and Vygotsky created in discussing the psychological process of learning for young students. Locke argues that motivation is crucial to help individuals meet their goals, in planning to meet those goals, several psychological processes begin to take shape such as understanding the complexity of the task, making a commitment to complete the task, and being open to feedback in the middle of meeting their goal (Locke et al., 1981). This complex psychological process is integral to understanding productive struggle because students will not engage productive struggle if motivation is low, as a result, they will not be motivated to make a commitment to meet the goal required of the struggle.

Productive struggle is challenged by the belief that it can only work in specific settings. Since productive struggle requires actual effort from students, it can be possible that there are students that refuse to place effort into the act of achieving the set goals. It can be argued that productive struggle is not as effective in institutions located in lower SES areas. Therefore, there may be an increase in the number of students that are either not sufficiently challenged or the amount of difficulty is perceived higher, where students disengage or prefer to not attempt to meet educational goals (Nachtigal et al., 2022); Bainbridge et al., 2022). In this case it is predicted that for productive struggle to be efficient, it would require additional tools; productive struggle coupled with gamification would create a bridge between challenges.

Ultimately, further theoretical consideration and exploration is merited to provide a specific understanding for each step of the process. Productive struggle as a theoretical framework is riddled with ambiguity, much of it is left up for interpretation, and little to no guidelines are provided for teachers who must guide a student out of the mental frustration that they might sometimes find themselves in (Nachtigall et al., 2022; Kapur, 2008). More importantly, student motivation needs to be prioritized as an area of further study because the productive struggle model operates on the assumption that pupils are motivated to learn or motivated to go through the trial-and-error process that is required for learning mathematics, computational skills, and almost all other subjects (Nachtigall et al., 2022; Kapur, 2008)). To achieve a next level understanding of productive struggle, educational psychologists interested in this area of education should feel obligated to review contemporary research on gamification of productive struggle because of the theoretical underpinnings and its potential to cure many of the problems posed by productive struggle.

The Potential of eRebuild as an Educational Tool to Strengthen the Theoretical Concepts of Productive Struggle: Lessons Learned from Rural and Urban Students

The educational practice example, as applied in a specific learning educational practice, is a primary research study that I read about titled "Using mathematizing supports for applied problem solving in a game-based learning environment" written by Ke et al. (2024). Their study is "a naturalistic observation case study and a mixed method case study to investigate middle school students' usage of mathematizing supports in relation to their math problem-solving performance" (Ke et al., 2024, p. 468), this is essentially a study that aims to cover some of the questions and theoretical applications that I discuss as part of my written project. As a result, the following educational practice applications sections revolves around the research and findings uncovered through the work of Ke et al. One purpose of their research was to identify the types of supports that students interacted with the most when attempting to solve math problems in a computerized problem solving environment, additionally, they also wanted to know how often students used the in-game support which act as scaffolds to help build their confidence with mathematics and how they engaged with the mathematizing process. More importantly, the main purpose of their research is centered on how a game-based learning environment can revolutionize how middle school aged students learn mathematics and how the current field of mathematical research can be revolutionized with this new pattern of math learning behavior.

Ke et al. attempt to curate and forge a new answer to the difficulties, challenges, and mental roadblocks that middle school aged children have faced for decades when trying to work through math problems and learning mathematics referred to as 'Mathematizing' by the authors (Ke et al., 2024). The authors also cite several other studies that have quantified the specific areas of most difficulty for young math learners from different age groups, almost all of the studies that Ke et al. cited found that students face the most difficulty with "comprehending a task…executing horizontal mathematization… [and] schematizing for horizontal mathematization" (2024, p. 469). For example, through their literature review, Ke et al. found that about "38% and 48%" of students had difficulty with comprehending a mathematical task and applying the task as mathematical problem (Cai et al., 2022; Pan et al., 2022). This alone demonstrates the need for an education tool, such as the proposed game-based learning environment to help solve this significantly worrying statistic. Although the authors do not necessarily focus on students from low resourced communities, I am confident they would find a much more worrying statistic due to the scarce educational resources found in under-resourced communities. Additionally, Ke et al. references the framework of Kant and Sarikaya (2021) to say that three primary cognitive processes that occur with students engaging in the mathematization process are: schematizing, formalizing, and axiomatizing. As a result, Ke et al. makes a research focused attempt to help alleviate the problems while strengthening the main domains of mathematizing for middle school students by implementing a game-based learning environment with built in scaffolds and supports that were easy to refer to and easy to track.

The authors state that "few studies examined how mathematization processes are activated or supported during game-based problem solving" (Ke et al., 2024, p. 473), as a result, they were hoping to achieve a game based learning model that is innovative, helpful for students in providing a clearer pathway for mathematization success, and one that further contributes to the scarce literature available in this area of research. Consequently, the researchers were hoping to learn how effective their game-based learning environment was for student participants, which in-game scaffolds were utilized the most as well as which ones were used the least, and if their digital environment was generalizable to a higher number of students so that successful mathematization can be achieved by all students. Based on their results, they were also hoping to learn how they can improve their digital environment so that it can be updated with further quality of life improvements to make it a more viable educational tool.

Two different studies took place, however, the what remains the same because the student participants from both studies were all subject to the digital game-based learning environment called eRebuild which is like Minecraft. In eRebuild, students work to solve math problems in a computerized digital environment where they have access to a large digital landscape that has specific tasks for students to accomplish such as painting a specific square footage, in this example, students would have to first find the solution of how much paint they would need to buy from the 'store' based on their calculations for how much square footage they need to paint. Another example is having to place water barrels in a specific distance from an in-game object and identify a problem that would ask them to concurrently find the distance of the water barrels from each other to avoid the barrels from being too close to each other. Along the way, they can earn achievements referred to as 'badges' which they can use to incentivize their motivation to complete a task, but it also allows the researchers to track how many badges each student is learning along the way and how fast they earn those badges. eRebuild helps student visualize their work and actively helps them mentalize their progress, this is in stark contrast to pen-and-paper math problems where a student might be asked to understand how many pineapples Jane Doe can buy at the grocery store with x amount of money; in eRebuild they are creating their own virtual landscape which allows them to become immersed in their work through the visual process that occurs.

The participants in study one is a smaller cohort composed of a total of nine middle school students "aged 11-13 years, including 4 girls, and differing in math performance level as reported by their teachers, were purposively sampled from an urban charter school in a southeast state" (Ke et al., 2024, p. 476-477). The participants from study 2 were composed of a higher number of participants for a total of 123 middle-school students who were recruited from two different school environments, 45 of the students were from an urban public school and 78 students were from a rural public school with 44% of the total number of students identifying as girls.

This study was completed during the years of the COVID-19 pandemic, as a result, all students engaged in this educational research at their school environment during school hours. Although all participants were part of the eRebuild digital sandbox, some students engaged in the research while attending school in-person and other students engaged in the research while on the zoom platform. However, the researchers do not specify which years this research took place other than to say that it was during the pandemic. Additionally, similar vagueness is expressed for the location only going as far as to say that this occurred in a southeast state of the United States.

The findings of the first study mark a promising number of results best summarized by the authors themselves by using the badges as the best marker of mathematical success: students completed "19 task trials and successfully completed 7.9 game levels/tasks on average within 1.5 hours. They also acquired 7.9 badges on average within 1.5 hours of gameplay, with the ratio of acquired badges to the completed tasks being 1" (Ke et al., 2024, p. 478). Keeping in mind that the students of this first studied varied in mathematical level, these results are successful because as noted before, each badge is an achievement indicative of successful learning outcomes with pre-determined scaffolds in-place. However, without further data, it is difficult to pinpoint exactly which mathematical concepts were learned and without mastery-based competency exams it is uncertain if their mathematical skills were retained in deeper mathematical understanding. Additionally, researchers found that students in the first study did not like the two in-game supports because they likened the in-game supports to textbooks which required a lot of reading and reading comprehension, as a result, the researchers actually found that the time that students spent using the in-game supports ranged from 30-50 seconds indicating that students saw how much reading was required and instead preferred to go back into the eRebuild sandbox to continue through with a trial-and-error process to find the solution to their problem. In sum, the digital environment enabled students to successfully learn mathematical concepts, but they did not appreciate or fully use the scaffolds at hand.

Study two was also able to yield very promising results as well, the dataset of study two is subject to descriptive statistics analysis by the authors which was not used in study one, more concretely study two data is analyzed using a paired t-test to identify if this digital learning environment was found to be statistically significant in helping participants successfully engage the mathematization process, regression analysis was also completed to further corroborate results from the paired t-tests, and unsupervised cluster analysis with game-logged data was also conducted which allowed the researchers to group students in 4 different clusters for further comparative analysis. This strong quantitative approach found that although the students in this study group also did not like the in-game scaffolds, it found that students who used the in-game scaffolds were able to achieve quicker success in solving their applied math problem. Furthermore, the results solidified the positive findings in study one, study two strongly and quantitatively corroborated the notion that most students in this second study achieved a badge/mathematical success with a specific math-based learning objective for each hour spent in eRebuild. Additionally, in this second study, students were tested post-eRebuild for verifiable mathematical knowledge and it was found that students performed well in math tests as well. 

Gamification as a Solution for the Pedagogical Gap of Productive Struggle

In conclusion, from a theoretical lens, elements of gamification implemented into a productive struggle pedagogy strongly suggests that it would be highly successful across a wide variety of schools and learning environments (Ke et al., 2024; Cai et al., 2022; Pan et al., 2022; Sailer 2020); anchored in Vygotsky centric research, empirical evidence from the work of Ke et al., and their detailed educational practice research, my findings indicate the need to further explore the intersection of gamifying productive struggle to extend its benefits to students in rural and urban under-resourced student communities. Clear guidelines can be created for teachers to better understand productive struggle in a shorter amount of time, this can be done by creating a 'teachers edition' for gamification of productive struggle. More specifically, one of the stress points for teachers is the obscure and unclear guidelines regarding the balance between crutches and scaffolds. As a result, a summer seminar course for teachers can be led one of the experienced math teachers who is motivated to help other math teachers learn the nuances of productive struggle. Additionally, once it is put into practice, the automation that comes from gamification will make it much easier for students to learn, achieve checkpoints, increase motivation to learn with the help of school specific incentives, and diffuse the frustration that might occur when a student is in-between zones of proximal developments. To create this environment, a computer lab would have to be required for students to sit in and reap the benefits of computerized gamification. Students typically have math class every day in K-12, my proposed model would require at least 3 days in a computer lab. The hope is that students will think of this as an opportunity to play games when they are learning mathematics in a gamified environment.

The practice and theory are connected in the body of my work because it is specific to traditionally under-resourced communities such as Chicago communities that have been historically families from socio-economic backgrounds such as some parts of the west and southern parts of Chicago, in addition to down state Illinois in rural counties. Although the theory does not necessarily address how productive struggle frameworks can help students from under-resourced areas, the practice section of my work has proven to be an effective example of how productive struggle, with elements of gamification, can be financially achievable for school districts, feasible for teachers to employ, and it would increase motivation for students to learn math.

The theory is directly and indirectly connected to the practice through the implementation of several different variables acting as virtually materialized versions of theoretical concepts. For example, the different zones of proximal development can actually be different levels in the math based video game, individualized pathways can be reflected by allowing students to go through the same lesson by picking their own in-game campaign with a variety of campaigns to choose from for individual lessons, for collaborative based learning then a 'multiplayer' approach can be adopted by allowing computers to be connected with each other via a Local Area Network (LAN), checkpoints or saving progress can serve as the concept for goal setting, and fortunately with the help of widespread use of computers, older video games such as Halo, Sims, Fortnite, Minecraft, and Mario Party can be repurposed with mathematical concepts integrated into the games. Automated in-game feedback can be provided to serve as baseline scaffolds and if further assistance is needed by the teacher, then they can add a few more individualized scaffolds depending on the student which would emphasize the unique learning pathways that might be needed for specific students.

The practice comes close to fulfilling the promise of the theory, however, with practical and financial limitations in mind it would be almost impossible to completely fulfill the promise of the theory without compromising the boundaries of the intended audience in mind. When considering theoretical applications for low resources K-12 schools, finances are critical barriers to consider that would be unwise to ignore when considering implementations. If we did try to fulfill the promise of the theory then we would have to digress back to needing fully and well-educated teachers, smaller class sizes, and students with a higher motivation to learn.

My overall interpretation of my selected topic is that it has very positive intentions and aims to address some key issues that have made it difficult for under-resourced schools to produce high performing math learners who would otherwise excel in schools with double the amount of resources and teachers. My topic might not directly impact the nationally declining math scores but it has potential to shift the tide for low resourced communities and their families to further encourage their exploration of a STEM interest.

The critics say that productive struggle is in need of further research because currently there are far too many gray areas for educators to successfully and widely implement productive struggle as a common practice. For example, the balance between crutches and scaffolds is not clear at all and is almost entirely dependent on a teacher's judgement which would require many years of teaching experience with their specific population of students (Kapur, 2008; Nachtigall et al., 2020). However, one of the more common themes for critics of productive struggle often cites the psychological ramifications of productive struggle on a student's mental walkthrough of a problem. For example, math is already a frustrating concept for students since it naturally involves trial and error, now imagine having to work through a math problem without much guidance from the instructor because they need to be careful not to provide crutches or imagine the scenario where a student is naturally hesitant about asking for help from a teacher in front of other peers because self-esteem is such a big issue for students already, how would teachers help a student through a math problem if the student does not ask for help? How is it feasible for the larger classrooms often found in urban schools? Additionally, students themselves tend to feel isolated if they must work through a math problem without much help, especially if motivation is already low. My own personal critique of productive struggle is that it assumes that students are highly motivated individuals, however, motivation to learn is sometimes lower than usual in under-resourced communities not because they don’t want to learn but rather because they are dealing with external factors and stressors that are sometimes associated with living in lower socioeconomic families.

Collectively, the ideals and purposes of the intersection of productive struggle and gamification are hard to realize but not necessarily impossibly to apply in low resourced schools. The research also agrees that there is too much gray area associated with productive struggle, however, it also says that there is a lot of potential and success with productive struggle. To move forward with the gamification of productive struggle, help is needed from the entire community and companies that live in the community to provide the financial means and resources to provide baseline technology to transform the physical space of math based classes that would allow each student to have access to a computer during their math class. Additionally, an openness to this new framework would be key because administrators would naturally want to maintain their current physical spaces and regular teacher training. This integrated concept would provide some disruptions to their summer schedules with providing a new 'productive struggle' centric training and it would mean that the students who pilot this concept in practice would have to learn how to adapt to this new style of teaching and learning. However, the research and exploration presented here poses a very strong case to begin a wider implementation of this cutting-edge theoretical combination for schools across nation, starting with our under-resourced school communities.