Abstract
Problem-solving competency is important not only in many careers but also in everyday life. Successful problem solvers regulate their cognitive processes and emotions. Our research aimed to study the impact of gamified problem sheets designed in Seppo on self-regulated learning skills. The intervention was carried out with second-year students in the specialization of Primary and Preschool Pedagogy. The research tool was a self-regulated problem-solving scale that was used as a pre- and posttest. In the experimental group, gamification lasted for 6 weeks. The game had 3 levels and the players could choose exercises from any level they wished. The results show that the gamified task sheet helped students to stay motivated and made problem-solving more enjoyable, but decreased some of their self-regulated processes, such as checking the correctness of the solution or searching for more solutions. This decrease could be explained by some psychological theories, the game elements, and the rules of the Seppo gamified problem sheets used in the intervention. On the basis of the conclusions, the role of some gamification aspects in developing different self-regulated processes can be identified, and the importance of a careful design of gamified problem sheets is highlighted.
1 Introduction
Problem-solving skills are important in everyday life and most careers. Mathematics is one of the most important subjects for developing problem-solving skills (Pehkonen, Näveri, & Laine, 2013; Pimta et al., 2009). Therefore, while teaching this subject, the emphasis should be placed not only on the content but also on developing the students’ learning and thinking skills. The problem-based approach is one of the most advantageous strategies that develop thinking skills, such as critical thinking (Ennis, 2011), logical thinking and analytical reasoning (Kuhn & Dean, 2004), as well as decision-making (Dinçer & Dinçer, 2016). At the same time, the problem-solving approach develops self-regulation processes, such as goal setting (Bandura, 1991; Zimmerman, 2022), self-monitoring (Zimmerman, 2002), emotional self-control, and resilience (Eisenberg, Spinrad, & Eggum, 2014). The capacity for self-regulated learning (SRL) is essential for primary school students to effectively engage in the learning of mathematics (Astuti & Wangid, 2018). There is some correlation between self-regulated skills and problem-solving skills (Zsoldos-Marchiș, 2014a). The SRL ability of primary school students in mathematics is moderate, with a more pronounced proficiency in the SRL performance phase (Astuti & Wangid, 2018; Zsoldos-Marchiș, 2014a).
Teachers possessing advanced SRL abilities place greater importance on SRL and consequently incorporate these skills more frequently into their instructional practices (Hamman, 1998). Furthermore, they are more likely to integrate metacognition into their teaching practices, driven by an increased sense of self-efficacy in fostering this cognitive process (Karlen, Hirt, Jud, Rosenthal, & Eberli, 2023). Pre-service and in-service primary school teachers use some SRL processes during problem-solving, but there is room for improvement (Marchiș, 2011; Zsoldos-Marchiș, 2014b). Thus, fostering self-regulation skills in pre-service teachers during problem-solving is crucial, considering their future role as mathematics educators.
Gamification can contribute to the development of SRL competence, especially in the case of students with low self-regulation skills (Li, Xia, Chu, & Yang, 2022). In this study, gamification was selected as a tool to integrate mathematics problems and questions related to self-regulation processes. This approach not only motivates students for active participation but also enhances the enjoyment of problem-solving activities. The research presented in this article builds upon a prior experiment that investigated the efficacy of gamification in fostering the development of self-regulation during problem-solving (Egri, Opriș, & Zsoldos-Marchis, 2022). In that previous research, gamified problem sheets were designed in Seppo and given to Primary and Preschool Pedagogy specialization students during an undergraduate mathematics course. The course was offered online due to the Covid-19 pandemic using a Zoom video conference. When playing in Seppo, the students worked in groups of four to solve the problems. To facilitate collaboration between group members, breakout rooms were created in Zoom, a separate room for each group. One student from each group logged into the Seppo platform with the name of the group. The results showed a slight decrease in students’ self-regulation processes. Teamwork could have had an influence on the results from more points of view. First, it was difficult to ensure the active participation of each team member in problem-solving. Second, the groups were frequently changed due to absent students. On the basis of the results of this experiment, the need for a new experiment was outlined.
The research presented in this article further developed the ideas from the first experiment and a new intervention was designed using gamified problem sheets. In this case, the students worked individually. Another novelty of the game was the possibility of a flexible change between levels. The students were allowed to choose problems from different levels, not conditioned by acquiring some number of points. At the higher levels, tasks are worth more points, so it was possible to achieve the score required to complete the seminar activity by solving fewer tasks. The idea was that the selection of the level from which to solve a problem also needs some self-regulatory skills, for example, self-efficacy. Gamification was used during a Mathematics course which did not cover any topics related to teaching mathematics. Gamified problem sheets were used with the aim of developing pre-service primary school teachers’ self-regulation skills in addition to their problem-solving competency.
2 Theoretical Background
2.1 Self-Regulation During Problem Solving
Self-regulation is a key concept for successful academic learning. It is defined as the control of performance, cognition, and the observation of effects (Efklides, Niemivirta, & Yamauchi, 2002). Students can be described as self-regulated if they take an active role in managing and directing their learning experiences (Zimmerman, 1994); for example, they are aware of their strengths and weaknesses, be able to motivate themselves to engage in, and improve their learning. Self-regulation is a fundamental component of mathematical competence, too, so it is important to emphasize it when teaching mathematical problem-solving (De Corte, Mason, Depaepe, & Verschaffel, 2011). As Pape and Smith (2002) pointed out, “problem solving is perhaps the area of mathematics in which self-regulation is most apparent” (p. 95). The use of self-regulation strategies makes the problem-solving process more effective; thus, mathematics instruction should incorporate the development of self-regulated strategies (Fadlelmula, 2010). During the problem-solving process students must develop solution plans and apply them to test their correctness, they must argue about their ideas and evaluate those of others, which helps develop their reasoning skills (Van de Walle, Karp, & Bay-Williams, 2004). Cognitive abilities, such as good concentration, effective memory, meaningful perceptions, and logical and critical thinking, also play an important role in problem-solving (De Corte, Verschaffel, & Eynde, 2000). Therefore, there are more self-regulation processes that are important for successful problem-solving, such as self-control, self-efficacy, self-reaction, and self-regulation of motivation.
As problem solving and SRL are complex competencies, their development requires active and strategic participation from the learners (Cleary & Zimmerman, 2004). Gamification might be a method which fosters active participation (Zsoldos-Marchis, 2020) and could contribute to the development of some self-regulatory skills (Li et al., 2022; Li et al., 2023).
Motivation is also important for a self-regulated learner. Intrinsic motivation refers to the internal drive and desire to engage in an activity for its own sake, being characterized by genuine interest, enjoyment, and satisfaction felt when engaging in the activity (Deci, Koestner, & Ryan, 1999; Deci & Ryan, 1985; Ryan & Deci, 2000). Extrinsic motivation refers to the drive to engage in an activity primarily to attain external rewards or avoid punishments, rather than to derive inherent satisfaction or interest from the activity itself. It involves performing a task to obtain tangible or social rewards or to evade negative consequences (Deci & Ryan, 1985; Ryan & Deci, 2000). Motivation and self-regulation are closely linked, as self-regulation processes help individuals align their behavior with their motivational goals. Individuals who are highly motivated tend to engage in effective self-regulatory strategies to monitor and adjust their behavior, while self-regulatory skills contribute to the maintenance and enhancement of motivation (Zimmerman, 2000).
2.2 Gamification
Gamification is “the use of game design elements in non-game contexts” (Deterding, Dixon, Khaled, & Nacke, 2011, p. 10). The use of gamification is justified by increased learning efficiency, promoting motivation (Carrillo, García, Laguna, Magán, & Moreno, 2019; Zsoldos-Marchis, 2020), and engagement in learning (De Byl, 2012; Laskowski & Badurowicz, 2014; Zsoldos-Marchis, 2020). “Gamification is about rethinking motivation in a world where we are more often connected digitally than physically. It is about building motivation into a digitally engaged world.” (Burke, 2014, p. 135).
Research shows that gamification does not always have the expected benefits. Buckley and Doyle (2014) found that gamification could increase different types of motivation. In her review study, Dahlstrøm (2017) has shown that gamification could have neutral, positive, and negative effects on intrinsic motivation. In her opinion, based on the previous articles, the reason for the varied results is the dependence on implementation and contextual factors, such as the age, personality, and experience of the user with games, or whether the use of the gamified system took place voluntarily or not. Another factor influencing motivation is the duration of the gamification; Hanus and Fox (2015) have shown that students’ motivation decreased with long-term application. In many cases, the reward elements of gamification increase external motivation instead of internal motivation (Deci, Koestner, & Ryan, 2001; Zsoldos-Marchis, 2020). Torrado Cespón and Díaz Lage (2022) support Dahlstrøm’s findings, investigating the problem of motivation in terms of online teaching practice. They affirm that extrinsic motivation could work, but it depends on the actual reward, which should be sufficiently attractive to students.
Gamification incorporates some aspects of self-regulation (Hassan, Xi, Gurkan, Koivisto, & Hamari, 2020), such as goal setting (assured by the story), monitoring progress (ensured by progress bars, badges, and point-systems), and encouraging perseverance (provided by feedback elements: leaderboards, performance graphs, or feedback given for each task). Gamification promotes goal setting and planning, as games often provide players with clear goals and objectives, encouraging them to plan their actions and strategize to achieve those goals. This goal-directed behavior fosters self-regulation skills, as individuals learn to prioritize tasks, manage their time effectively, and persist in the face of challenges (Przybylski, Rigby, & Ryan, 2010). Gamification provides immediate feedback, which can promote self-regulation by providing individuals with information about their progress and performance, which develops a sense of self-awareness and self-reflection (Hamari, Koivisto, & Sarsa, 2014).
There are several learning management systems that apply gamification strategies or play elements to the learning experience, like Schoology, Moodle; or special online gamification platforms that can be utilized in education, e.g. ClassCraft, EdApp, Kahoot! In this study, the Seppo gamification platform was selected to be used in the intervention. This selection is for several reasons. Seppo (seppo.io platform) provides an intuitive and user-friendly interface in which it is easy to create and customize game-based learning experiences. It is possible to freely use any picture as the map of the game, thus it can be adapted to any frame story. The map could also be a real map on which GPS locations can be given, enhancing the connection of learning with the real world. The tasks could also be given with QR codes promoting the use of smartphones for learning purposes. Seppo provides educators with valuable data and analytics on student performance and progress. The platform generates comprehensive reports that allow teachers to track individual and group achievements, identify areas of improvement, and personalize instruction based on student needs.
3 Methodology
This research was conducted in the first semester of the 2021/2022 university year during the mathematics discipline for students in primary and primary school pedagogy specialization. The interview was conducted half a year after the intervention was completed.
3.1 Scope and Research Questions
The purpose of this research is to study the impact of gamification on self-regulation skills of pre-service preschool and primary school teachers. For this purpose, gamified mathematics problem sheets in Seppo were used.
The research tried to answer the following questions:
What is the influence of gamified problem-sheets in Seppo on students’ motivation?
How does the use of gamified problem-sheets in Seppo affect the usefulness perception of problem-solving?
What is the influence of gamified problem-sheets in Seppo on students’ self-efficacy?
How does the use of gamified problem-sheets in Seppo affect students’ self-control?
3.2 Participants
Participants in this study were second-year students with a specialisation in primary and preschool pedagogy from Transylvania (Romania). In the research, there were 118 students, 82 in the experimental group, and 36 in the control group. Nine students from the experimental group participated in the interview.
3.3 Instrument
3.3.1 Self-Regulation Problem-Solving Scale
The scale to measure self-regulation during problem-solving contains 46 closed questions compiled based on scales in the literature (Banks, 2014; Blackweir, 2016; Fehr, 1953; Jacobse & Harskamp, 2012; Lim & Chapman, 2013; Marchis, 2010, 2012, 2013; Nicolaidou & Philippou, 2004; Tanner & Jones, 2003; Wong & Chen, 2012; Zsoldos-Marchiș, 2016). The questions are statements measured on a five-level Likert scale.
These affirmations were grouped into eight categories based on scales from the literature. Check/self-control, confidence/self-efficacy, multiple solutions, feelings/self-reaction, value/usefulness of mathematical problem solving, extrinsic goal orientation, intrinsic goal orientation, and self-regulation of motivation. The time required to complete the online questionnaire was between 20 and 30 min.
The results were qualitatively analyzed with descriptive statistics (means, standard deviations) and comparison of means.
3.3.2 Interview Guide
The interview served as a means to gather information for a more in-depth exploration of students’ responses to the self-regulation problem-solving scale, aiming to provide insights and explanations for certain results observed in the experiment. A semi-structured interview was used. Some questions, such as those presented below, were premeditated:
Do you believe it was beneficial to have the option to choose between levels in the game? If so, what criteria influenced your choices?
To what extent did the game motivate you to solve the problems, and did you find it more motivating than a traditional worksheet?
Which was more decisive for you: internal or external motivation? Additionally, how motivated were you to earn points?
Did you find it necessary to push yourself to persevere while solving the problems? Did you need to exert more or less effort compared to a traditional worksheet? Moreover, did the frame story contribute to helping you stay motivated?
In addition to premeditated questions common to all interviewed students, some particular questions were formulated for each student based on their pre- and posttest results on the self-regulated problem-solving scale. For example, the student with decreased self-efficacy was asked for explanations; the student with decreased intrinsic motivation and increased extrinsic motivation was asked for explanations, etc. The interviews were recorded, transcribed, and subjected to qualitative analysis.
3.4 Intervention
The experimental group had a six-week intervention, a two-hour seminar each week during which a gamified problem sheet designed on the Seppo platform (Figure 1) was assigned to the students.
The map for the gamified problem sheets.
The Seppo game had a story from the fairy tale world and three scenes, each scene associated with a difficulty level. Students could freely go from one scene to another. The problems given in the game were associated with the material taught during the mathematics course (i.e., logical problems, problems with sets, natural and rational numbers, proportions, equations and systems of equations, and geometry). Most of the problems were formulated as word problems whose text was correlated with the story of the game.
Questions referring to self-regulation were attached to each problem, for example:
Could you solve the problem with a different method? If so, which method is more adequate for this problem?
How did you feel during problem-solving?
Have you checked whether the solution is correct?
Did you find this problem difficult?
The game incorporated 4 of the 5 motivational elements identified by Huang and Hew (2018) based on self-determination and flow theories.
Goals – The main goal was formulated in terms of points necessary to collect in each seminar. As the gamers had access to the leaderboard, obtaining a higher place could also be a goal formulated for themselves (Landers, Bauer, & Callan, 2017).
Access – Players can freely choose the level and order of the problems they solve.
Feedback – The solutions to the problems were asked in closed questions (multiple choice, checkbox, matching pairs, filling in) so that students got immediate automatic feedback on the correctness of their solution. The questions related to self-regulation processes were not scored; their purpose was to make students monitor and control the problem-solving process. For some problems, full solutions were required to upload as a picture of their handwritten calculations, but these were not scored, and only helped the lecturer see students’ difficulties.
Challenges – The game used a leaderboard that offered the feeling of competition.
Collaboration was not implemented in this game, as the students played individually. This decision was made based on the results of the previous experiment using teamwork (Egri et al., 2022).
Students must earn a minimum of 12 points for each seminar. The maximum number of points that could have been earned in a seminar was between 27 and 32.
4 Results
4.1 Results Based on the Self-Regulated Problem-Solving Scale
The scale contains affirmations measured on a five-level Likert scale from 1 (this affirmation doesn’t characterize me at all) to 5 (this affirmation totally characterizes me). The results of the negative affirmations were reversed, and the means for each category were calculated for each student both on pretest and posttest. Then, the differences between the means by categories obtained in the posttest and pretest were calculated. As the Shapiro–Wilk test showed deviation from normality the Mann–Whitney test was used to compare the results obtained for the experimental and control group. The statistical results are shown in Table 1.
Comparison of the differences between pretest and posttest means for the experimental and control group for each category
| Category | Experimental group | Control group | p | W | ||
|---|---|---|---|---|---|---|
| Mean | SD | Mean | SD | |||
| Check/self-control | −0.17 | 0.69 | 0.13 | 0.54 | 0.020 | 1872.50 |
| Confidence/self-efficacy | −0.10 | 0.53 | −0.11 | 0.54 | 0.986 | 1472.50 |
| Multiple solutions | −0.24 | 0.64 | −0.04 | 0.84 | 0.441 | 1607.50 |
| Feelings/self-reaction | −0.07 | 0.52 | −0.05 | 0.47 | 0.493 | 1593.50 |
| Value/usefulness of mathematical problem-solving | −0.19 | 0.72 | −0.04 | 0.82 | 0.586 | 1568.00 |
| Extrinsic goal orientation | 0.13 | 0.66 | 0.23 | 0.76 | 0.625 | 1559.50 |
| Intrinsic goal orientation | −0.04 | 0.61 | 0.01 | 0.96 | 0.974 | 1482.00 |
| Self-regulation of motivation | −0.09 | 0.74 | 0.30 | 0.76 | 0.013 | 1901.50 |
There are significant differences in the case of self-control and regulation of motivation. In both cases, the means decreased from pretest to posttest in the case of the experimental group and decreased in the case of the control group.
A Multivariate Analysis of Variance was conducted to compare the posttest–pretest differences between the experimental and control groups, with the objective of examining whether the intervention had a statistically significant effect. The Wilks test revealed no significant effect, as Wilks’ Lambda = 0.914, F(1,116) = 1.286, and p = 0.258.
Wilcoxon signed-rank test was used to compare the pretest and posttest results of the experimental group by categories. The statistical results are presented in Table 2. The means for self-control during problem-solving, searching for multiple solutions, and perception of the usefulness of mathematical problem-solving significantly decreased.
Comparison of the results of the pretest and posttest of the experimental group
| Category | Pretest | Posttest | p | W | ||
|---|---|---|---|---|---|---|
| Mean | MD | Mean | MD | |||
| Check/self-control | 3.70 | 0.75 | 3.52 | 0.79 | 0.048 | 1844.50 |
| Confidence/Self-efficacy | 3.16 | 0.81 | 3.06 | 0.77 | 0.052 | 1930.50 |
| Multiple Solutions | 3.05 | 0.88 | 2.81 | 0.84 | 0.003 | 1800.00 |
| Feelings/self-reaction | 3.39 | 0.72 | 3.31 | 0.68 | 0.115 | 1902.50 |
| Value/usefulness of mathematical problem-solving | 4.52 | 0.55 | 4.32 | 0.75 | 0.013 | 1173.00 |
| Extrinsic goal orientation | 2.55 | 0.76 | 2.68 | 0.81 | 0.225 | 1036.00 |
| Intrinsic goal orientation | 3.66 | 0.88 | 3.62 | 0.85 | 0.326 | 1334.00 |
| Self-regulation of motivation | 3.59 | 0.87 | 3.49 | 0.87 | 0.451 | 1488.00 |
4.2 Results of the Interviews
Semi-structured interviews were conducted to obtain in-depth information and explanations for the statistical data of the self-regulated problem-solving scale. The students were anonymized by the labels S1, S2, …, S9. The transcripts were qualitatively analyzed using the MAXQDA program and codes and sub-codes were identified. The following main codes were identified: level, goal, and motivation. In addition to the identified codes and subcodes, the content of the responses underwent analysis. This process involved discerning explanations for quantitative data and uncovering reasons behind students’ behaviors while engaging with the gamified problem sheet.
4.2.1 Navigating Between the Levels of the Game
The gamified problem sheets deviate from traditional gamification as players have the freedom to switch between levels without the obligation to complete them sequentially. They can opt for any level without having to fulfill the prerequisites of the previous ones. Therefore, students’ responses regarding this free choice of levels were analyzed. All the students found that the levels and free switching between levels were a good idea.
As regards students’ strategies to choose the level they start at, six students started with the lowest level and went on to a higher level. Students S3 and S6 started with the easy levels as they were confident, they could solve the problems on those levels:
S3: I believed I could certainly solve the problems in the easy levels, and once I experienced success with those, I progressed to more challenging levels.
S6: I consistently chose the easiest problems, solving them first. This provided me with the momentum to believe that tackling a more difficult one would undoubtedly succeed.
Only student S4 attempted to begin with the highest levels, perhaps to obtain more points faster. But finally, she also used the easy-to-difficult approach.
S4: At times, I attempted to begin with the challenging problems and then tackle the easier ones. However, I soon realized that the reverse approach worked better.
There were three students, who switched between levels using different reasoning for choosing a level. Students S1 and S6 adapted the level they started with their difficulty perception of the topic.
S6: I would begin with an intermediate task if I felt the topic was familiar to me. I hesitated to opt for a difficult task right away. When facing a challenging topic, I would start with the easiest tasks.
Student S7 jumped between levels trying to find those problems that are easier for her.
The free choice of the levels gave students a sense of control, as formulated by student S4:
S4 The free choice between levels gave me the sense that there was a strategic decision-making opportunity.
4.2.2 Adapting to the goal of earning 12 points
It is also interesting to see how the students adapted to the goal of obtaining 12 points. Students typically approach problem sheets by attempting to solve every problem, and seven students applied the same strategy in the game.
S7: If I reached 12 points, I continued solving; it wasn’t a matter of considering it done once I achieved that score. I kept working on it.
However, the game presented an extensive number of problems, exceeding the manageable scope of a two-hour seminar. Consequently, students attempting to solve all the problems experienced frustration due to the time constraints, finding it challenging to cover the entire set within the allotted time.
4.2.3 Motivation During the Game
The motivation code was the richest. A hierarchical code-subcodes model was used to visualize the subcodes of the motivation code with their frequencies (Figure 2). Aggregate frequencies were used for parent codes.
Hierarchical code-subcodes model for the motivation code.
For seven students, the gamified problem sheet was more motivating than a traditional problem sheet. Only student S1 stated that the game did not give her extra motivation.
Half of the students think their motivation was more extrinsic, as they were motivated by points (4 students) and leaderboard (one student), but also by the story (seven students), design of the game board (two students), and instant feedback (two students). The answer given by student S6 highlighted the importance of the aesthetic and the story for motivating students.
S6: The graphics of the entire experience were visually stunning, driving and motivating me to tackle one task after another. The aesthetic appeal of tracking when and how each task was completed was particularly satisfying. I found great motivation and was impressed by the coherence of all the tasks being related to a single topic, which allowed me to approach them with a sense of calm.
Student S7 also highlighted the motivating character of the immediate feedback given by the game beside the frame story.
S7: The story frame added a positive dynamic to the game, preventing it from becoming monotonous. Immediate feedback upon solving a task was particularly engaging, and I appreciated the creativity of the self-regulating questions.
The other half of the students stated that they were intrinsically motivated to focus on finding the correct solutions (one student), feeling success (one student), and self-validation (one student). Student S9 provided a detailed explanation of her intrinsic motivation.
S9: I believe my internal motivation was heightened as I sought to prove to myself that I could successfully complete the tasks. My motivation stemmed not from the points but from the awareness that I was enhancing my skills and capabilities during the assignment.
The type of motivation of some students changed during the intervention. Student S3 reported the change in her motivation from extrinsic driven by point to intrinsic.
S3: I think that my internal motivation has grown stronger. Initially, I was still focused on chasing points, but that changed over time. If we were to play this game live now, I believe the reactions of others would provide additional motivation.
As regards self-regulation of motivation, for seven students it was easier to stay motivated with the gamified problem sheet than in the case of a traditional problem sheet. Three students stated that they did not have to encourage themselves to solve the tasks, the game helped them stay motivated.
5 Discussion and Conclusions
The results presented in the previous section are discussed along with the research questions.
5.1 The Influence of Gamified Problem-Sheets in Seppo on Students’ Motivation
It is known from previous research that academic motivation decreases during the university year (Lazowski & Hulleman, 2016). Another aspect that must be considered is that the intervention was carried out online during the Covid-19 pandemic, and research has shown that academic motivation decreased during online teaching (Zaccoletti et al., 2020). Therefore, the results regarding the motivation of the students must be interpreted in this context. The intrinsic motivation of the students did not decrease, which could be considered a positive result from the point of view of the above observations. Interviews also confirmed that a considerable number of the students were intrinsically motivated by the satisfaction of finding the solution or by trying to prove to themselves that they are capable of problem-solving. These intrinsic motivational elements are not so evident in the case of teamwork, this could be the explanation for the intrinsic motivation decrease in the previous study of Egri et al. (2022). Some students reported in interviews a decrease in motivation by the end of the semester, explained by the fact that they had more assignments to complete in different disciplines, so they did not have as much energy left for the game as at the beginning.
Gamification is reported in the literature to increase extrinsic motivation more than intrinsic motivation (Deci et al., 2001; Zsoldos-Marchis, 2020). In the present study, the extrinsic motivation of both groups increased, but in the case of the control group the increase was more pronounced and the increase in the case of the experimental group was statistically insignificant. Based on interviews, points and the leaderboard were the most important external motivational elements. The leaderboard was found to be an important motivational element also in the research of O’Donovan, Gain, and Marais (2013) and Sillaots (2014).
The interviews highlighted the fact that in the case of gamified problem sheets the game helped students to continue to try to solve the problems, they did not need as much self-encouragement for perseverance as in the regarding of a traditional problem sheet. The story and the design of the game board were those gamification elements that contributed to maintaining motivation. This explains the decrease in the mean for the self-regulation of motivation category in the case of the experimental group, while in the control group, the mean for this category increased.
5.2 The Impact of the Gamified Problem Sheet on Students’ Beliefs About the Utility of Mathematical Competencies
Students’ beliefs about the utility of mathematical competencies influence their problem-solving behavior (Schoenfeld, 1985). It is interesting to observe that the mean of the usefulness perception of the mathematical problem solving category decreased in both groups, but more in the experimental group where this decrease is statistically significant. The problems tried to cover all the topics of the mathematics course, so a significant part of them was not taken from everyday life and were not realistic. This could have affected the perception of the usefulness of mathematics in students.
5.3 The Influence of the Gamified Problem Sheet on Students’ Self-Efficacy
Students’ self-efficacy also decreased in both groups. This could be related to the perception of the utility of the problems (Siregar & Prabawanto, 2021), which also decreased, or by experimenting failures in solving some problems (Etherton, Steele-Johnson, Salvano, & Kovacs, 2020). As students could have started with problems at higher levels, they could face more failures than in a ‘traditional’ gamification in which players cannot access higher levels before completing the lower ones. The interviews show that some students are aware of their abilities, they have decided which level to start based on their competencies regarding the mathematical topic of the game, but others have just randomly chosen the level and problems to be solved.
The experimental group was less open to searching for multiple solutions in the posttest, their mean for this category decreased significantly, whereas, in the case of the control group, the mean did not change. This can be explained by the fact that students from the experimental group tried to solve as many problems as possible in a limited time (2 hours) and not only to fulfil the goal of the game earning the required 12 points.
5.4 The Influence of the Gamified Problem Sheet on Students’ Self-Control
Self-control during problem-solving exhibited a significant decrease in the experimental group, while conversely, it showed an increase in the control group, indicating significant differences between the two groups. Again, the rule of obtaining at least 12 points could have contributed to this result. As the game gave immediate feedback and automatically scored each solution, the students submitted the solution and went to the next problem without staying to check the solution. They were not stressed to correctly solve each problem; an incorrect solution did not influence their performance. Self-control capacity could be depleted due to a change in motivation (Inzlicht, Schmeichel, & Macrae, 2014). Depletion occurs not because students become less able to self-control, but because their willingness for self-control decreases (Masicampo, Martin, & Anderson, 2014). Self-control could also decrease due to fatigue, when excessively required (Masicampo et al., 2014). During the intervention, some problems contained extra questions related to self-control, such as checking the correctness of the solution or analyzing the solving method, so that students must exercise self-control time to time, but these questions were not frequently asked.
6 Conclusions and Limitations of the Research
In summary, the incorporation of gamification into the problem sheet improved student motivation and made problem-solving more enjoyable. However, it also resulted in a decrease in specific self-regulated processes during problem-solving, such as comprehensive checking of solution correctness, exploration of multiple solutions for a given problem, and overall self-efficacy. This decrease could be explained by some psychological theories, but also by the game elements and rules of the Seppo gamified problem sheets used in the intervention. The results show the role of some gamification aspects in developing different self-regulated processes and highlight the importance of careful design when planning gamified problem sheets.
This research had several limitations. First, the duration of the intervention could have been longer. The duration of the intervention was set to 6 weeks to avoid the negative effects of long gamification (Hanus & Fox, 2015) and to be easily integrated into the “Mathematics for preschool and primary school” course offered for second-year students. Second, the research instrument that assesses the self-regulation of students during problem-solving based on self-reported measures, which may be subject to biases or inaccuracies. Self-regulated assessments are usually self-reported measures, as they ask about feelings and thoughts that are difficult to observe. Additionally, self-report inventories can be completed quickly, and the data obtained can be statistically analyzed in various ways. To gain a more comprehensive understanding of students’ self-regulation, semi-structured interviews were additionally employed. These interviews, in addition to premeditated questions, also contain questions related to the students’ responses to the self-regulated problem-solving scale to find out their explanations of the changes in their responses from the pretest to the posttest.
-
Funding information: This work was not supported by any funding.
-
Author contributions: The authors have equal contributions.
-
Conflict of interest: The authors state no conflict of interest.
References
Astuti, A. D., & Wangid, M. N. (2018). Self-regulated learning ability of elementary school students in learning mathematics. Journal of Physics: Conference Series, 1108, 012120. doi: 10.1088/1742-6596/1108/1/012120.Search in Google Scholar
Bandura, A. (1991). Social cognitive theory of self-regulation. Organizational Behavior and Human Decision Processes, 50(2), 248–287.10.1016/0749-5978(91)90022-LSearch in Google Scholar
Banks, A. D. (2014). Effects of embedded study-skills instruction on high school students’ attitudes toward mathematics. (Doctoral dissertation). Walden University, Minneapolis, Minnesota. https://scholarworks.waldenu.edu/dissertations/50.Search in Google Scholar
Blackweir, J. (2016). Attitudes towards mathematics: Development and validation of an online, semantically differentiated, visual analogue scale. (Master’s thesis). The University of Western Australia Perth, Australia.Search in Google Scholar
Buckley, P., & Doyle, E. (2014). Gamification and student motivation. Interactive Learning Environments, 24(6), 1162–1175. doi: 10.1080/10494820.2014.964263.Search in Google Scholar
Burke, B. (2014). Gamify: How gamification motivates people to do extraordinary things. Brookline, MA: Bibliomotion.Search in Google Scholar
Carrillo, D. L., García, A. C., Laguna, T. R., Magán, G. R., & Moreno, J. A. (2019). Using gamification in a teaching innovation project at the University of Alcalá: A new approach to experimental science practices. Electronic Journal of e-Learning, 17(2), 93–106. doi: 10.34190/jel.17.2.03.Search in Google Scholar
Cleary, T. J., & Zimmerman, B. J. (2004). Self-regulation empowerment program: A school-based program to enhance self-regulated and self-motivated cycles of student learning. Psychology in the Schools, 41(5), 537–550. doi: 10.1002/pits.10177.Search in Google Scholar
Dahlstrøm, C. (2017). Impacts of gamification on intrinsic motivation. https://www.ntnu.edu/documents/139799/1279149990/04+Article+Final_camildah_fors%C3%B8k_2017-12-06-13-53-55_TPD4505.Camilla.Dahlstr%C3%B8m.pdf. Search in Google Scholar
De Byl, P. (2012). Can digital natives level-up in a gamified curriculum? In M. Brown, M. Hartnett, & T. Stewart (Eds.), Future challenges, sustainable futures. Proceedings Ascilite 2012 (pp. 256–266).10.14742/apubs.2012.1579Search in Google Scholar
Deci, E. L., Koestner, R., & Ryan, R. M. (1999). A meta-analytic review of experiments examining the effects of extrinsic rewards on intrinsic motivation. Psychological Bulletin, 125(6), 627–668. doi: 10.1037/0033-2909.125.6.627.Search in Google Scholar
Deci, E. L., Koestner, R., & Ryan, R. M. (2001). Extrinsic rewards and intrinsic motivation in education: Reconsidered once again. Review of Educational Research, 71(1), 1–27.10.3102/00346543071001001Search in Google Scholar
Deci, E. L., & Ryan, R. M. (1985). Intrinsic motivation and self-determination in human behavior. Perspectives on Motivation, 2, 37–61.10.1007/978-1-4899-2271-7Search in Google Scholar
De Corte, E., Mason, L., Depaepe, F., & Verschaffel, L. (2011). Self-regulation of mathematical knowledge and skills. In B. J. Zimmerman & D. H. Schunk (Eds.), Handbook of self-regulation of learning and performance (pp. 155–172). New York, NY: Routledge/Taylor & Francis Group.Search in Google Scholar
De Corte, E., Verschaffel, L., & Eynde, P. O. (2000). Self-regulation: A characteristic and a goal of mathematics education. In M. Boekaerts, P. R. Pintrich, & M. Zeidner (Eds.), Handbook of self-regulation (pp. 687–726). Cambridge, Massachusetts: Academic Press. doi: 10.1016/b978-012109890-2/50050-0.Search in Google Scholar
Deterding, S., Dixon, D., Khaled, R., & Nacke, L. (2011). From game design elements to gamefulness: Defining ‘Gamification’. Proceedings of the 15th international academic Mindtrek conference: Envisioning future media environments (pp. 9–15).10.1145/2181037.2181040Search in Google Scholar
Dinçer, H., & Dinçer, N. (2016). The effect of problem solving approaches in engineering education on development of decision making skills. Procedia - Social and Behavioral Sciences, 217, 232–239. doi: 10.1016/j.sbspro.2016.02.083.Search in Google Scholar
Efklides, A., Niemivirta, M., & Yamauchi, H. (2002). Introduction: Some issues on self-regulation to consider. Psychologia, 45(4), 207–210. doi: 10.2117/psysoc.2002.207.Search in Google Scholar
Egri, E., Opriș, E.-T., & Zsoldos-Marchis, I. (2022). Experimenting gamification for developing self-regulation skills during mathematical problem solving. INTED2022 proceedings (pp. 10155–10162). doi: 10.21125/inted.2022.2671.Search in Google Scholar
Eisenberg, N., Spinrad, T. L., & Eggum, N. D. (2014). Emotion-related self-regulation and its relation to children’s maladjustment. Annual Review of Clinical Psychology, 10, 1–27.Search in Google Scholar
Ennis, R. H. (2011). Critical thinking: Reflection and perspective - Part I. Inquiry: Critical Thinking Across the Disciplines, 26(1), 4–18.10.5840/inquiryctnews20112613Search in Google Scholar
Etherton, K., Steele-Johnson, D., Salvano, K., & Kovacs, N. (2020). Resilience effects on student performance and well-being: The role of self-efficacy, self-set goals, and anxiety. The Journal of General Psychology, 149(3):279–298. doi: 10.1080/00221309.2020.1835800.Search in Google Scholar
Fadlelmula, F. K. (2010). Mathematical problem solving and self-regulated learning. The International Journal of Learning: Annual Review, 17(3), 363–372. doi: 10.18848/1447-9494/cgp/v17i03.Search in Google Scholar
Fehr, H. F. (1953). The learning of mathematics: Its theory and practice. (21st Yearbook of the National Council of Teachers of Mathematics). Washington, DC: National Council of Teachers of Mathematics.Search in Google Scholar
Hamari, J., Koivisto, J., & Sarsa, H. (2014). Does gamification work? A literature review of empirical studies on gamification. Proceedings of the annual hawaii international conference on system sciences (pp. 3025–3034). IEEE Computer Society.10.1109/HICSS.2014.377Search in Google Scholar
Hamman, D. (1998). Preservice teachers’ value for learning-strategy instruction. The Journal of Experimental Education, 66(3), 209–221.10.1080/00220979809604405Search in Google Scholar
Hanus, M. D., & Fox, J. (2015). Assessing the effects of gamification in the classroom: A longitudinal study on intrinsic motivation, social comparison, satisfaction, effort, and academic performance. Computers & Education, 80, 152–161. doi: 10.1016/j.compedu.2014.08.019.Search in Google Scholar
Hassan, L., Xi, N., Gurkan, B., Koivisto, J., & Hamari, J. (2020). Gameful self-regulation: A study on how gamified self-tracking features evoke gameful experiences. Proceedings of the annual hawaii international conference on system sciences (pp. 1103–1112). doi: 10.24251/hicss.2020.138.Search in Google Scholar
Huang, B., & Hew, K. F. (2018). Implementing a theory-driven gamification model in higher education flipped courses: Effects on out-of-class activity completion and quality of artifacts. Computers & Education, 125, 254–272. doi: 10.1016/j.compedu.2018.06.018.Search in Google Scholar
Inzlicht, M., Schmeichel, B. J., & Macrae, C. N. (2014). Why self-control seems (but may not be) limited. Trends in Cognitive Sciences, 18(3), 127–133. doi: 10.1016/j.tics.2013.12.009.Search in Google Scholar
Jacobse, A. E., & Harskamp, E. G. (2012). Towards efficient measurement of metacognition in mathematical problem solving, Metacognition and Learning, 7(2), 133–149. doi: 10.1007/s11409-012-9088-x.Search in Google Scholar
Karlen, Y., Hirt, C. N., Jud, J., Rosenthal, A., & Eberli, T. D. (2023). Teachers as learners and agents of self-regulated learning: The importance of different teachers’ competence aspects for promoting metacognition. Teaching and Teacher Education, 125, 104055. doi: 10.1016/j.tate.2023.104055.Search in Google Scholar
Kuhn, D., & Dean, D. (2004). Metacognition: A bridge between cognitive psychology and educational practice. Theory Into Practice, 43(4):268–273. Teaching and Teacher Education, 125.10.1353/tip.2004.0047Search in Google Scholar
Landers, R. N., Bauer, K. N., & Callan, R. C. (2017). Gamification of task performance with leaderboards: A goal setting experiment. Computers in Human Behavior, 71, 508–515. doi: 10.1016/j.chb.2015.08.008.Search in Google Scholar
Laskowski, M., & Badurowicz, M. (2014). Gamification in higher education: A case study. Proceedings of the management, knowledge and learning international conference (pp. 971–975). doi: 10.13140/2.1.3311.9046.Search in Google Scholar
Lazowski, R. A., & Hulleman, C. S. (2016). Motivation interventions in education: A meta-analytic review. Review of Educational Research, 86(2), 602–640. doi: 10.3102/0034654315617832.Search in Google Scholar
Li, M., Ma, S., & Shi, Y. (2023). Examining the effectiveness of gamification as a tool promoting teaching and learning in educational settings: A meta-analysis. Frontiers in Psychology, Section Media Psychology, 14, 1253549. doi: 10.3389/fpsyg.2023.1253549.Search in Google Scholar
Li, X., Xia, Q., Chu, S. K. W., & Yang, Y. (2022). Using gamification to facilitate students’ self-regulation in e-learning: A case study on students’ L2 english learning. Sustainability, 14(12), 7008. doi: 10.3390/su14127008.Search in Google Scholar
Lim, S.Y., & Chapman, E. (2013). Development of a short form of the attitudes toward mathematics inventory. Educational Studies in Mathematics, 82(1), 145–164. doi: 10.1007/s10649-012-9414-x.Search in Google Scholar
Marchis, I. (2011). Primary school teachers’ self-regulated learning skills. Acta Didactica Napocensia, 4(4), 11–18.Search in Google Scholar
Marchis, I. (2012). Self-regulated learning and mathematical problem solving. The New Educational Review, 27(1), 195–208.Search in Google Scholar
Marchis, I. (2013). Relation between students’ attitude towards mathematics and their problem solving skills. PedActa, 3(2), 59–66.Search in Google Scholar
Masicampo, E. J., Martin, S. R., & Anderson, R. A. (2014). Understanding and overcoming self-control depletion. Social and Personality Psychology Compass, 8(11), 638–649. doi: 10.1111/spc3.12139.Search in Google Scholar
Nicolaidou, M., & Philippou, G. (2004). Attitudes towards mathematics, self-efficacy and achievement in problem solving. In M. A. Mariotti (Ed.), European research in mathematics education III (pp. 1–11). Italy: University of Pisa.Search in Google Scholar
O’Donovan, S., Gain, J. E., & Marais, P. (2013). A case study in the gamification of a university-level games development course. In J. McNeill, K. L. Bradshaw, P. Machanick, & M. Tsietsi (Eds.), SAICSIT (pp. 242–251). New York, NY: ACM.10.1145/2513456.2513469Search in Google Scholar
Pape, S. J., & Smith, C. (2002). Self-regulating mathematics skills. Theory Into Practice, 41(2), 93–101. doi: 10.1207/s15430421tip4102_5.Search in Google Scholar
Pehkonen, E., Näveri, L., & Laine, A. (2013). On teaching problem solving in school mathematics. Center for Educational Policy Studies Journal, 3(4), 9–23.10.26529/cepsj.220Search in Google Scholar
Pimta, S., Tayraukham, S., & Nuangchalerm, P. (2009). Factors influencing mathematic problem-solving ability of sixth grade students. Journal of Social Sciences, 5(4), 381–385.10.3844/jssp.2009.381.385Search in Google Scholar
Przybylski, A. K., Rigby, C. S., & Ryan, R. M. (2010). A motivational model of video game engagement. Review of General Psychology, 14(2), 371–392.10.1037/a0019440Search in Google Scholar
Ryan, R. M., & Deci, E. L. (2000). Intrinsic and extrinsic motivations: Classic definitions and new directions. Contemporary Educational Psychology, 25(1), 54–67.10.1006/ceps.1999.1020Search in Google Scholar
Schoenfeld, A. H. (1985). Mathematical problem-solving. New York: Academic Press.Search in Google Scholar
Sillaots, M. (2014). Gamification of higher education by the example of course of research methods. Advances in web-based learning – ICWL. Springer Lecture Notes in Computer Science, (Vol. 8613, pp. 106–115). Tallinn: Springer.10.1007/978-3-319-09635-3_11Search in Google Scholar
Siregar, R. N., & Prabawanto, S. (2021). Increasing students’ self-efficacy through a realistic mathematical education. Journal of Innovative Mathematics Learning, 4(2), 63–74. doi: 10.22460/jiml.v4i2.p63-74.Search in Google Scholar
Tanner, H., & Jones, S. (2003). Self-efficacy in mathematics and students’ use of self-regulated learning strategies during assessment events. International Group for the Psychology of Mathematics Education, 4, 275–282.Search in Google Scholar
Torrado Cespón, M., & Díaz Lage, J. M. (2022). Gamification, online learning and motivation: A quantitative and qualitative analysis in higher education. Contemporary Educational Technology, 14(4), ep381. doi: 10.30935/cedtech/12297.Search in Google Scholar
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2004). Elementary and middle school mathematics: Teaching developmentally (5th ed.), Boston: Allyn and Bacon.Search in Google Scholar
Wong, K. Y., & Chen, Q. (2012). Nature of an attitudes toward learning mathematics questionnaire. In J. Diundyal, L. P. Cheng, & S. F. Ng (Eds.), 35th annual conference of the Mathematics Education Research Group of Australasia incorporated (MERGA 2012) on “Mathematics education: Expanding horizons” (pp. 2–6). Singapore: MERGA.Search in Google Scholar
Zaccoletti, S., Camacho, A., Correia, N., Aguiar, C., Mason, L., Alves, R. A., & Daniel, J. R. (2020). Parents’ perceptions of student academic motivation during the COVID-19 lockdown: A cross-country comparison. Frontiers in Psychology, 11, 592670. doi: 10.3389/fpsyg.2020.59267.Search in Google Scholar
Zimmerman, B. J. (1994). Dimensions of academic self-regulation. In D. H. Schunk & B. J. Zimmerman (Eds.), Self-regulation of learning and performance: Issues and educational applications (pp. 3–21). Hillsdale, NJ: Lawrence Erlbaum.10.4324/9780203763353-1Search in Google Scholar
Zimmerman, B. J. (2000). Attaining self-regulation: A social cognitive perspective. In M. Boekaerts, P. R. Pintrich, & M. Zeidner (Eds.), Handbook of self-regulation (pp. 13–39). San Diego, CA.: Academic Press.Search in Google Scholar
Zimmerman, B. J. (2002). Becoming a self-regulated learner: An overview. Theory into Practice, 41(2), 64–70.10.1207/s15430421tip4102_2Search in Google Scholar
Zimmerman, B. J. (2022). From cognitive modeling to self-regulation: A social cognitive career theory perspective. In M. C. Smith (Ed.), The Oxford handbook of cognitive psychology (pp. 413–431). New York, NY: Oxford University Press.Search in Google Scholar
Zsoldos-Marchis, I. (2014a). 10–11 year old pupils’ self-regulated learning and problem-solving skills. Review of Science, Mathematics and ICT Education, 8(1), 33–42.Search in Google Scholar
Zsoldos-Marchis, I. (2014b). Self-regulation during pre-service primary school teachers’ mathematical problem solving. In L. Gómez Chova, A. López Martínez, & I. Candel Torres (Eds.), EDULEARN14 proceedings (pp. 5503–5509). IATED Academy.Search in Google Scholar
Zsoldos-Marchiș, I. (2016). Influence of cooperative problem solving on students’ control and help-seeking strategies during mathematical problem solving. Review of Science, Mathematics and ICT Education, 10(1), 5–22.Search in Google Scholar
Zsoldos-Marchis, I. (2020). Gamification of the mathematics course for pre-service preschool and Primary School Teachers. In L. Gómez Chova, A. López Martínez, & I. Candel Torres (Eds.), EDULEARN16 proceedings (pp. 6787–6794). IATED Academy. doi: 10.21125/edulearn.2020.1765.Search in Google Scholar
© 2024 the author(s), published by De Gruyter
This work is licensed under the Creative Commons Attribution 4.0 International License.
