1. Capiz State University Pontevedra Campus, Capiz, Philippines.

*             Correspondence: rcdaliva@capsu.edu.ph

Keywords: mathematics instruction, teaching strategy, innovation, contextualization, involvement

1. INTRODUCTION

Mathematics is a crucial subject that students must master, as it provides the foundation for many other fields of study. However, for many students, learning math can be challenging, boring, and intimidating. The traditional methods of teaching mathematics, such as lectures and rote memorization, may not be engaging enough for students leading them to perform poorly in the subject [1]; hence, educators need to find innovative and effective ways to make learning math more fun and engaging [2]. Gamification is a relatively new approach that has been gaining popularity in education [3]. An author [4] defined gamification as the process of using game elements in a non-game context. This can be achieved with or without the use of technology. The highly engaging nature of gamification is one of the reasons why there is a growing interest in it in worldwide education [5]. Gamification is the new approach rising in educational setting that has a primary goal of motivating students to learn and excel in class. This approach involves the use of game elements, such as avatars, progress maps, levels, missions, points, badges, leader boards, points, and rewards, that pushes students to become competitive and goal-oriented leading them to participate in class, which are something that need to be seen, especially, in “boring and hard” math class where students are performing poorly.  Studies have repeatedly shown that driven and actively participating learners outperform the less motivated ones in the classroom [6,7,8]. An author [9] asserted that gamification has many advantages over traditional learning approaches, including increasing learner motivation levels, improving knowledge retention, and better learner engagement through social mechanisms like badges, points, or leaderboards. It also provides students with a sense of achievement and reward. While several studies have revealed a favorable effect of gamification on students’ performance, other studies have found conflicting results [10,11]. These contradictory findings are attributable to poor game design, which closely correlates with the identified unfavorable outcomes [12]. An author [13] asserted that gamification can motivate students if designed and implemented properly as failure to do so may only make the learning process fun but with no gained learnings. The mentioned inconclusive evidences of the assumed educational benefits of gamification indicate that they have yet to be scientifically proven; thus, a more comprehensive understanding is needed which can be achieved by conducting rigorous and systematic empirical research across diverse gamification applications and learning environments. This study established a practical, methodical framework for implementing gamification strategies to maximize their effectiveness in various educational contexts. The motivation for this exploration of the emerging approach, gamification, came from the achievement gap in mathematics among high school learners in the Philippines as revealed in the international assessments, such as the 2018 Programmed for International Student Assessment (PISA) (Organization for Economic Cooperation and Development [27] , 2019 Trends in International Mathematics and Science Study (TIMSS) , and in the most recent, 2022 PISA [27], where the country ranked at the bottom among the participating countries. These low rankings, however, have been one of the undying problems faced by the country. Hence, a continuous search for effective teaching methods is needed to address this issue. Therefore, the foremost intention of this study is to investigate the effects of gamification on the learners’ performance and engagement in mathematics. This study aimed to investigate the effects of gamification on performance and engagement in mathematics of Grade 10 students. This study was anchored on different theories related to performance and learning engagement. These theories served as the bases for conceptualizing this study. Goal-Setting Theory by Edwin Locke in 1960 has been used to describe how to drive individuals to perform better at work by creating and monitoring goals. Since gamification is fundamentally a goal-oriented activity geared at encouraging motivation, it stands to reason that these two methods would complement each other quite well and help us build more motivational experiences [14]. It was assumed in this study that learners must drive themselves to experience and explore, discover, and solve mathematical issues using gamification. Flow theory is discovered by Mihaly Csikszentmihalyi in 1970s, it is one of the most important psychological effects of gamification and games had been identified as a condition of optimal experience characterized by being totally focused and engaged in an activity. It is often assumed to have nine dimensions: challenge-skill-balance, clear goals, control, (instant) feedback, autotelic experience, loss of self-consciousness, temporal transformation, concentration, and integrating action-awareness. There are currently few research exploring flow, particularly in the setting of gamification [15]; thus, limited knowledge as to which elements of flow would be particularly emergent in the context of flow. Therefore, it was assumed in this study that learners would actively participate in the math instruction, drawing on their own experiences and existing knowledge to explore and discover their mathematics skills. Constructivism theory by [16] believes that learning is an active process in which students develop new ideas and concepts based on prior information. The learner selects and transforms information, hypothesizes, and makes decisions based on a cognitive framework. Cognitive structure gives meaning and organization to experiences, allowing the individual to go beyond the information provided. Constructivism is based on learners’ ability to formulate concepts operationally through inquiry, reasoning, and abstraction [17]. Hence, in this study, it was assumed that the participant would be able to express notions properly and coherently during the conversation process. this study classified the gamification, a teaching-learning strategy, as the independent variable. Meanwhile, learners’ performance and engagement in mathematics were classified as the dependent variables. The students’ mathematical performance and engagement were assumed to be dependent on the gamification as the teaching strategy. This study investigated the effects of gamification on the performance and engagement in mathematics of the Grade 10 students.

2. MATERIALS AND METHODS

This study was conducted using a quasi-experimental design, specifically the matching-only pretest-posttest control group design to determine the effects of gamification on Grade 10 students’ performance and engagement in mathematics. Quasi-experimental research design investigates the cause-and-effect relationship between an intervention and an outcome for a target population without randomly assigning subjects to a group [18]. The study used matching only as a technique where subjects in the experimental group were mechanically matched to those in the control group on certain variables which does not necessarily give assurance that subjects of both groups are equivalent of each other. In this study, the experimental and control groups were mechanically paired using their average grades in the first and second grading in mathematics subject. Only those who had equal average grades were paired and included in this study. This study was conducted in one of the secondary schools in Capiz under the K-12 Curriculum of DepEd during the third quarter of the school. A purposive sampling technique was used in selecting the participants of experimental and control groups. However, random sampling technique, specifically the lottery method, was used to assign the two Grade 10 sections as experimental and control groups. The average of their 1^st and 2^nd quarter grades in mathematics was used as basis in mechanically matching the participants in the two groups. There were 22 pairs of participants with matching average of grades. The pre-determined samples were not informed that they will undergo the intervention to ensure the validity of the result. The participants of the study were the 44 Grade 10 students coming from two regular class sections in one of the secondary schools in Capiz. Specifically, there were 22 pairs of participants with matching average of grades from each section. Since they were minors, the legal consent was obtained from their guardians/parents through consent form. This study utilized three instruments for the pre-intervention stage, treatment stage, and post-intervention stage. The first instrument was a self-made module that covered the following topics: Permutations and Combinations. This module included the integration of gamification for the whole duration of the teaching and learning process of the topics involved. This was used during the treatment stage of the experimental group as the introduced intervention of the researcher who conducted the classroom instructions while the prepared DepEd learning module was used by the same researcher during the conventional instruction of the control group. The second instrument was a self-made 35-item multiple-choice test that measured the participants’ knowledge about the concept of Permutation and Combination. This was used to determine the mathematics performance of the participants before and after the intervention. The third instrument was 30-item modified checklists by [18] with a 5-point Likert scale (5 stands for strongly agree, 4 for agree, 3 for undecided/neutral, 2 for disagree, and 1 for strongly disagree) to evaluate the participants’ mathematical engagement for both experimental and control groups. The items in the checklist were divided into three categories of engagement namely the cognitive engagement (10 items); the behavioral engagement (10 items); and the affective engagement (10 items). Permission to conduct the study was obtained from the research adviser and the dean of the College of Education, Arts and Sciences. Following this, the formally requested permission from the principals of three secondary schools in Capiz to conduct a pilot test of the instruments. The schedule for administering the draft instruments during the pilot test was coordinated with the school personnel. Due to the reliability of all instruments, no revisions were necessary following the pilot test. This process ensured that the study could proceed smoothly and accurately, adhering to ethical and procedural standards. Overall, the cooperation of all involved parties facilitated the successful conduct of the study. After pilot testing, a letter is sent to addressed to the principal of one of the secondary schools in Capiz for the conduct of the study in the school. The final draft of the instruments for pre-intervention was then administered personally to the participants to ensure the completeness of information and the originality of the answers. To ensure balanced groups and generalizable results, the pre-intervention instruments included a section collecting demographic data like names (or codes), sections, and first and second-quarter math grades. The average of their grades was then used for mechanical matching. After the intervention, the post-test and checklists were administered to the participants. The results were tallied and encoded and were compared to the pre-intervention results. The comparison between them were also analyzed.

Table 01: Interpretation Scheme for the Pre-test and Post-test Scores of the Participants

Level of Proficiency	Equivalent Numerical Value	Description
Advanced (A)	90% and above	The student at this level exceeds the core requirement in terms of knowledge, skills and core understandings, and can transfer them automatically and flexibly authentic performance tasks.
Proficient (P)	85% – 89%	The student at this level has developed the fundamental knowledge and skills and core understandings and can transfer them independently through authentic performance.
Approaching Proficiency (AP)	80% – 84%	The student at this level has developed the fundamental knowledge and skills and core understanding and, with little guidance from the teacher and/or with some assistance from peers, can transfer these understandings through authentic performance.
Developing (D)	75% – 79%	The student at this level possesses the minimum knowledge and skills and core understandings but needs help throughout the performance of authentic tasks.
Beginning (B)	74% and below	The student at this level struggles with his/her understanding: prerequisite and fundamental knowledge and/or skills have not been acquired or developed adequately to aid understanding.

 

Table 02: Scale for Interpreting Students’ Level of Engagement

Score	Range of Means	Verbal Interpretation	Description
5	4.50 – 5.00	Extremely Engaged	Students show exceptional depth of understanding, interest, and proficiency in mathematical concepts. They constantly exhibit initiative and exemplary behavior by going above and beyond in terms of participation, focus, and effort. They demonstrate extraordinary enthusiasm, passion, and satisfaction along with high confidence, perseverance, and intrinsic desire when engaged in mathematical tasks.
4	3.50 – 4.49	Very Engaged	Students at the level show a high level of interest and proficiency in understanding mathematical concepts. They actively participate, show persistent effort and focus, and listen attentively with a desire to solve problems. They always display positive attitudes, confidence and enthusiasm with optimism and perseverance when engaged in mathematical tasks.
3	2.50 – 3.49	Moderately Engaged	Students display consistent interest and proficiency in understanding mathematical concepts. They consistently participate, show persistent effort and focus, and listen attentively during instruction and tasks. They display positive attitudes and confidence with enthusiasm when engaged in mathematical tasks.
2	1.50 – 2.49	Engaged	At this level, students show interest and understanding in mathematical concepts. They actively participate and listen attentively with consistent effort during instruction and tasks. They display positive attitude with confidence when engaged in mathematical tasks.

3. RESULTS AND DISCUSSION

The pre-test performance in mathematics of experimental and control groups is shown in Table 03. Result revealed that the performance of the experimental group in mathematics was at the beginning level (M = 10.09, MPS = 28.83, SD = 2.07). This suggests that the students in the experimental group have not yet obtained the necessary foundational knowledge and abilities about the topics at hand, particularly in the Permutation and Combination. The students’ struggle to grasp complex mathematical concepts might stem from their limited opportunity to delve deeply into these topics, which is understandable given that these subjects have not been thoroughly introduced to them yet. Similarly, the control group’s performance in mathematics was at the beginning level (M = 9.32, MPS = 26.62, SD = 2.40). This means that students in the control group also struggled with their understanding of the topics involved, particularly Permutation and Combination. The data suggest a significant challenge for both the control and experimental groups in comprehending the concepts of Permutation and Combination. This points towards a gap in their foundational mathematical understanding. Several factors could contribute to this gap. The students simply may have not been exposed to the necessary prerequisite concepts before tackling these more complex topics. For instance, Permutation and Combination might not have been formally introduced to them yet. This lack of prior instruction or exposure to the underlying mathematical ideas could be a key reason behind the observed difficulties. Addressing this gap in foundational knowledge is absolutely crucial. By solidifying their understanding of these essential concepts, the students can progress through their educational journey with a strong base upon which to build their mathematical knowledge. The results of the study align with the findings of [19]. Both the experimental and control groups exhibited pre-test performance levels that fall below average. This is further supported by the pre-test scores, where neither group demonstrated strong proficiency in the topic being measured. These pre-test results indicate that both groups entered the study with similar levels of knowledge or skill regarding the topic. This supports the findings of the study by [20] which also showed no significant difference between the students in experimental and control groups in terms of their academic success which suggests a comparable distribution of student performance across both groups.

Table 03: Pre-test Performance in Mathematics of the Participants in the Experimental and Control Groups

Groups	N	MPS	SD	Verbal Interpretation
Experimental Group	22	28.83	2.07	Beginning
Control Group	22	26.62	2.40	Beginning

Note. Interpretation is based on the scale: 74% and below (Beginning), 75% – 79% (Developing), 80% – 84% (Approaching Proficiency), 85% – 89% (Proficient), and 90% and above (Advanced)

Table 04: Difference in the Pre-test Performance in Mathematics of the Participants in the Experimental and Control Groups

Groups	N	Md	Mean rank	U	p-value
Experimental Group	22	10.00	24.07	207.50	.412
Control Group	22	9.50	20.93

On the other hand, results revealed that control group was very engaged in mathematics (M = 3.78, SD = 0.44). This means that the students show a high level of interest and proficiency in understanding mathematical concepts. They actively participate, show persistent effort and focus, and listen attentively with a desire to solve problems. They always display positive attitudes, confidence and enthusiasm with optimism and perseverance when engaged in mathematical tasks. This suggests that students assigned to the control group are likely to exhibit improved performance in mathematics and maintain their interest in the subject even beyond the classroom environment. Additionally, they may develop a stronger sense of confidence in their mathematical abilities, which could motivate them to tackle more complex mathematical problems and challenges with greater enthusiasm and determination.

Table 05: Engagement in Mathematics of the Participants in the Experimental and Control Groups Before the Intervention as a Whole

Group	N	M	SD	Verbal Interpretation
Experimental Group	22	3.48	0.74	Moderately Engaged
Control Group	22	3.78	0.44	Very Engaged

Note. Interpretation is based on the scale: 4.50 – 5.00 (Extremely Engaged), 3.50 – 4.49 (Very Engaged), 2.50 – 3.49 (Moderately Engaged), 1.50 – 2.49 (Engaged), 1.00 – 1.49 (Somewhat Engaged)

Table 06: Cognitive Engagement in Mathematics of the Participants in the Experimental Group Before the Intervention

Statement		M	SD	Verbal Interpretation
1	I think studying advanced mathematics is useful.	4.14	1.04	Very Engaged
2	I believe studying math helps me with problem solving in other subjects.	3.73	1.49	Very Engaged
3	I prefer to understand the concepts behind formulas over memorizing them for solving mathematical problems.	3.59	1.01	Very Engaged
4	I value understanding formulas over memorization for learning mathematics.	3.55	0.96	Very Engaged
5	I actively explore beyond classroom teachings to understand mathematics better.	3.45	0.96	Moderately Engaged
6	I think the best way to learn mathematics is to try to do drills.	3.45	1.01	Moderately Engaged
7	I can think of many ways to use mathematics outside of school.	3.23	1.41	Moderately Engaged
8	I relate the things I learn in mathematics to the things I go through in real life.	3.14	1.17	Moderately Engaged
9	I relate the things I learn in mathematics to other subjects.	2.95	1.00	Moderately Engaged
10	I experiment with varied problem-solving methods in mathematics.	2.95	1.33	Moderately Engaged
	Cognitive Engagement	3.42	0.69	Moderately Engaged

Note. Interpretation is based on the scale: 4.50 – 5.00 (Extremely Engaged), 3.50 – 4.49 (Very Engaged), 2.50 – 3.49 (Moderately Engaged), 1.50 – 2.49 (Engaged), 1.00 – 1.49 (Somewhat Engaged)

Table 07: Cognitive Engagement in Mathematics of the Participants in the Control Group Before the Intervention

Statement		M	SD	Verbal Interpretation
1	I think studying advanced mathematics is useful.	4.09	0.97	Very Engaged
2	I prefer to understand the concepts behind formulas over memorizing them for solving mathematical problems.	4.00	1.07	Very Engaged
3	I value understanding formulas over memorization for learning mathematics.	3.91	0.81	Very Engaged
4	I believe studying math helps me with problem solving in other subjects.	3.86	0.94	Very Engaged
5	I relate the things I learn in mathematics to the things I go through in real life.	3.77	1.02	Very Engaged
6	I actively explore beyond classroom teachings to understand mathematics better.	3.64	0.66	Very Engaged
7	I relate the things I learn in mathematics to other subjects.	3.59	0.73	Very Engaged
8	I think the best way to learn mathematics is to try to do drills.	3.55	1.14	Very Engaged
9	I experiment with varied problem-solving methods in mathematics.	3.55	0.86	Very Engaged
10	I can think of many ways to use mathematics outside of school.	3.45	1.06	Moderately Engaged
	Cognitive Engagement	3.74	0.48	Very Engaged

Note. Interpretation is based on the scale: 4.50 – 5.00 (Extremely Engaged), 3.50 – 4.49 (Very Engaged), 2.50 – 3.49 (Moderately Engaged), 1.50 – 2.49 (Engaged), 1.00 – 1.49 (Somewhat Engaged)

Table 08: Behavioral Engagement in Mathematics of the Participants in the Experimental Group Before the Intervention

Statement		M	SD	Verbal Interpretation
1	I focus when the mathematics teacher teaches in the classroom.	3.95	1.25	Very Engaged
2	I listen to the mathematics teachers’ instructions attentively.	3.64	1.26	Very Engaged
3	I always try my best to solve mathematical problems.	3.64	1.29	Very Engaged
4	I participate in discussions during mathematics learning.	3.50	1.26	Very Engaged
5	I am sure I will get the right answer if I keep trying to solve mathematics problems.	3.50	0.96	Very Engaged
6	I want to develop my mathematical skills through solving mathematics problem.	3.41	1.37	Moderately Engaged
7	I tackle math problems with consistent effort and effective strategies.	3.36	1.29	Moderately Engaged
8	I try to use a different method if I continue to not be able to solve the mathematics problems.	3.32	1.13	Moderately Engaged
9	I like to solve new problems in mathematics.	3.14	1.25	Moderately Engaged
10	I persistently engage in math assignments due to my love for problem-solving.	3.05	1.21	Moderately Engaged
	Behavioral Engagement	3.45	0.92	Moderately Engaged

Note. Interpretation is based on the scale: 4.50 – 5.00 (Extremely Engaged), 3.50 – 4.49 (Very Engaged), 2.50 – 3.49 (Moderately Engaged), 1.50 – 2.49 (Engaged), 1.00 – 1.49 (Somewhat Engaged)

Table 09: Behavioral Engagement in Mathematics of the Participants in the Control Group Before the Intervention

Statement		M	SD	Verbal Interpretation
1	I listen to the mathematics teachers’ instructions attentively.	4.36	0.73	Very Engaged
2	I always try my best to solve mathematical problems.	4.23	0.69	Very Engaged
3	I want to develop my mathematical skills through solving mathematics problem.	4.00	0.76	Very Engaged
4	I am sure I will get the right answer if I keep trying to solve mathematics problem.	3.91	0.92	Very Engaged
5	I focus when the mathematics teacher teachers in the classroom.	3.82	1.01	Very Engaged
6	I tackle math problems with consistent effort and effective strategies.	3.77	1.07	Very Engaged
7	I try to use a different method if I continue to not be able to solve the mathematics problem.	3.73	0.83	Very Engaged
8	I participate in discussions during mathematics learning.	3.68	0.84	Very Engaged
9	I like to solve new problems in mathematics.	3.41	0.85	Moderately Engaged
10	I persistently engage in math assignments due to my love for problem-solving	3.14	0.94	Moderately Engaged
	Behavioral Engagement	3.80	0.46	Very Engaged

Note. Interpretation is based on the scale: 4.50 – 5.00 (Extremely Engaged), 3.50 – 4.49 (Very Engaged), 2.50 – 3. 49 (Moderately Engaged), 1.50 – 2.49 (Engaged), 1.00 – 1.49 (Somewhat Engaged)

These results mean that students in both experimental and control groups always display positive attitude, confidence and enthusiasm with optimism and perseverance when engaged in mathematical tasks. This implies that students are more likely to grow in confidence in themselves and increase their level of self-efficacy, which increases their readiness to take on difficult mathematical tasks.

Table 10: Affective Engagement in Mathematics of the Participants in the Experimental Group Before the Intervention

Statement		M	SD	Verbal Interpretation
1	I am happy to learn mathematics.	3.91	0.81	Very Engaged
2	I enjoy learning mathematics.	3.91	0.97	Very Engaged
3	I feel happy when I get good mathematics results.	3.73	1.35	Very Engaged
4	I really like mathematics.	3.64	0.95	Very Engaged
5	I get a great deal of satisfaction out of solving a mathematical problem.	3.59	0.85	Very Engaged
6	I feel satisfaction and confidence when solving math problems.	3.59	1.05	Very Engaged
7	I love solving mathematics problems.	3.55	1.18	Very Engaged
8	I find joy in understanding math concepts.	3.41	1.47	Moderately Engaged
9	I feel a definite positive reactive towards math.	3.36	0.95	Moderately Engaged
10	I am confident when participating in math class discussion.	3.09	1.19	Moderately Engaged
	Affective Engagement	3.58	0.74	Very Engaged

Note. Interpretation is based on the scale: 4.50 – 5.00 (Extremely Engaged), 3.50 – 4.49 (Very Engaged), 2.50 – 3.49 (Moderately Engaged), 1.50 – 2.49 (Engaged), 1.00 – 1.49 (Somewhat Engaged)

Table 11: Affective Engagement in Mathematics of the Participants in the Control Group Before the Intervention

Statement		M	SD	Verbal Interpretation
1	I am happy to learn mathematics.	4.23	0.75	Very Engaged
2	I enjoy learning mathematics.	3.95	0.72	Very Engaged
3	I love solving mathematics problems.	3.91	0.92	Very Engaged
4	I feel happy when I get good mathematics results.	3.91	1.02	Very Engaged
5	I really like mathematics.	3.86	0.83	Very Engaged
6	I feel satisfaction and confidence when solving math problems.	3.86	1.13	Very Engaged
7	I find joy in understanding math concepts.	3.68	0.84	Very Engaged
8	I am confident when participating in math class discussion.	3.55	0.86	Very Engaged
9	I get a great deal of satisfaction out of solving a mathematical problem.	3.50	1.10	Very Engaged
10	I feel a definite positive reaction towards math.	3.41	1.01	Moderately Engaged
	Affective Engagement	3.79	0.62	Very Engaged

Note. Interpretation is based on the scale: 4.50 – 5.00 (Extremely Engaged), 3.50 – 4.49 (Very Engaged), 2.50 – 3.49 (Moderately Engaged), 1.50 – 2.49 (Engaged), 1.00 – 1.49 (Somewhat Engaged)

The reliability of the study findings is increased by this baseline equivalency. This supports the finding of the study by [21]. In their study, it was found that there was no significant difference between the engagement ratings of the experimental and control groups before the intervention. Generally, the post-test performance of the experimental group is at developing level, while of that control group is at beginning level. This result supports the finding of [22] and [23] who found out that the students in the experimental and control groups have improved their mathematics performance after the conduct of the study. However, the students from the experimental group who were exposed to gamification obtained a higher post-test result than the students from the control group. This indicated that students’ knowledge has increased after the gamification intervention.

Table 12: Difference in the Engagement in Mathematics of the Participants in the Experimental and Control Groups Before the Intervention

Groups	N	Md	Mean rank	U	p-value
Experimental Group	22	3.59	19.91	185.00	.181
Control Group	22	3.80	25.09

Table 13: Post-test Performance in Mathematics of the Participants in the Experimental and Control Groups

Groups	N	M	MPS	SD	Verbal Interpretation
Experimental Group	22	26.68	76.23	5.90	Developing
Control Group	22	22.55	64.43	6.65	Beginning

Note. Interpretation is based on the scale: 74% and below (Beginning), 75% – 79% (Developing), 80% – 84% (Approaching Proficiency), 85% – 89% (Proficient), and 90% and above (Advanced)

The current study’s findings align with previous research by [24], and [25]. These studies all demonstrated that gamification significantly boosted student performance in mathematics. This suggests that gamification not only fosters a strong interest and ability to grasp concepts, but also enables students to apply their understanding to real-life problems.  This study reinforces the idea that gamification can boost engagement. Similar to [26], students exposed to gamified activities were more engaged than those in a traditional setting. This highlights a positive correlation between gamified learning and student participation. Gamification could be a valuable tool for educators to create a more motivating learning environment.

Table 14: Difference in the Post-test Performance in Mathematics of the Participants in the Experimental and Control Groups

Paired Groups	N	Md	Mean Rank	U	p-value
Experimental Group	22	28.00	26.41	156.00*	.043
Control Group	22	22.50	18.59

Table 15: Engagement in Mathematics of the Participants in the Experimental and Control Groups After the Intervention

Group	N	M	SD	Verbal Interpretation
Experimental Group	22	3.95	0.51	Very Engaged
Control Group	22	3.69	0.47	Very Engaged

Note. Interpretation is based on the scale: 4.50 – 5.00 (Extremely Engaged), 3.50 – 4.49 (Very Engaged), 2.50 – 3.49 (Moderately Engaged), 1.50 – 2.49 (Engaged), 1.00 – 1.49 (Somewhat Engaged)

It is recognized that the experimental group’s cognitive engagement is higher than the control groups based on the mean rankings of the two groups’ levels of cognitive engagement. This outcome is consistent with the study by [27] where students in the treatment group demonstrated more instances of the higher cognitive engagement indicator than the students in the control group.

Table 16: Cognitive Engagement in Mathematics of the Participants in the Experimental Group After the Intervention

Statement				M		SD		Verbal Interpretation
1		I think the best way to learn mathematics is to try to do drills.		4.14		0.71		Very Engaged
2		I can think of many ways to use mathematics outside of school.		4.00		0.76		Very Engaged
3		I relate the things I learn in mathematics to other subjects.		4.00		1.07		Very Engaged
4		I value understanding formulas over memorization for learning mathematics.		3.95		0.65		Very Engaged
5		I think studying advanced mathematics is useful.		3.91		0.92		Very Engaged
6		I relate the things I learn in mathematics to the things I go through in real life.		3.91		1.15		Very Engaged
7		I actively explore beyond classroom teachings to understand mathematics better.		3.82		0.59		Very Engaged
8		I experiment with varied problem-solving methods in mathematics.		3.64		0.49		Very Engaged
9		I believe studying math helps me with problem solving in other subjects.		3.64		0.73		Very Engaged
10		I prefer to understanding the concepts behind formulas over memorizing them for solving mathematical problems.		3.59		0.73		Very Engaged
	Cognitive Engagement		3.86		0.51		Very Engaged

Note. Interpretation is based on the scale: 4.50 – 5.00 (Extremely Engaged), 3.50 – 4.49 (Very Engaged), 2.50 – 3.49 (Moderately Engaged), 1.50 – 2.49 (Engaged), 1.00 – 1.49 (Somewhat Engaged)

Table 17: Cognitive Engagement in Mathematics of the Participants in the Control Group After the Intervention

Statement		M	SD	Verbal Interpretation
1	I value understanding formulas over memorization for learning mathematics.	3.91	0.43	Very Engaged
2	I think studying advanced mathematics is useful.	3.86	0.89	Very Engaged
3	I relate the things I learn in mathematics to the things I go through in real life.	3.77	0.75	Very Engaged
4	I prefer to understanding the concepts behind formulas over memorizing them for solving mathematical problems.	3.77	0.92	Very Engaged
5	I believe studying math helps me with problem solving in other subjects.	3.77	0.75	Very Engaged
6	I think the best way to learn mathematics is to try to do drills.	3.73	0.83	Very Engaged
7	I relate the things I learn in mathematics to other subjects.	3.59	0.67	Very Engaged
8	I experiment with varied problem-solving methods in mathematics.	3.55	0.74	Very Engaged
9	I actively explore beyond classroom teachings to understand mathematics better.	3.55	0.74	Very Engaged
10	I can think of many ways to use mathematics outside of school.	3.45	0.96	Moderately Engaged
	Cognitive Engagement	3.70	0.49	Very Engaged

Note. Interpretation is based on the scale: 4.50 – 5.00 (Extremely Engaged), 3.50 – 4.49 (Very Engaged), 2.50 – 3.49 (Moderately Engaged), 1.50 – 2.49 (Engaged), 1.00 – 1.49 (Somewhat Engaged)

These results mean that students in both groups actively participate, show persistent effort and focus, and listen attentively with a desire to solve problems. The teaching methods employed might have influenced the behavioral engagement of the students in both groups, and the presented mathematics concepts may be perceived as relevant and interesting to the students, making them become interested and motivated to solve math problems. Furthermore, there might be a positive relationship between the teacher and students that encouraged them to be attentive and actively participate in class. The findings suggest that both the teaching methods used are successful in promoting student engagement, especially in terms of behavioral aspect. The analysis of mean rankings between the experimental and control groups reveals a promising trend. Students in the experimental group, who were exposed to gamification, exhibit a higher behavioral engagement compared to the control group. Aligned with research by [28] showing gamified activities promote faster task completion, higher behavioral engagement in the gamified group suggests this approach fosters a more stimulating learning environment, leading to increased student focus and participation.

Table 18: Behavioral Engagement in Mathematics of the Participants in the Experimental Group After the Intervention

Statement		M	SD	Verbal Interpretation
1	I want to develop my mathematical skills through solving mathematics problem.	4.32	1.04	Very Engaged
2	I listen to the mathematics teachers’ instructions attentively.	4.32	0.65	Very Engaged
3	I participate in discussions during mathematics learning.	4.09	0.61	Very Engaged
4	I always try my best to solve mathematical problems.	4.00	0.69	Very Engaged
5	I am sure I will get the right answer if I keep trying to solve mathematics problems.	4.00	0.69	Very Engaged
6	I focus when the mathematics teacher teaches in the classroom.	4.00	0.87	Very Engaged
7	I tackle math problems with consistent effort and effective strategies.	3.95	0.58	Very Engaged
8	I persistently engage in math assignments due to my love for problem-solving.	3.82	0.66	Very Engaged
9	I like to solve new problems in mathematics.	3.73	0.88	Very Engaged
10	I try to use a different method if I continue to not be able to solve the mathematics problems.	3.68	0.78	Very Engaged
	Behavioral Engagement	3.99	0.51	Very Engaged

Note. Interpretation is based on the scale: 4.50 – 5.00 (Extremely Engaged), 3.50 – 4.49 (Very Engaged), 2.50 – 3.49 (Moderately Engaged), 1.50 – 2.49 (Engaged), 1.00 – 1.49 (Somewhat Engaged)

Table 19: Behavioral Engagement in Mathematics of the Participants in the Control Group After the Intervention

Statement		M	SD	Verbal Interpretation
1	I listen to the mathematics teachers’ instructions attentively.	4.00	0.82	Very Engaged
2	I persistently engage in math assignments due to my love for problem-solving.	3.82	0.59	Very Engaged
3	I want to develop my mathematical skills through solving mathematics problem.	3.68	1.04	Very Engaged
4	I focus when the mathematics teacher teaches in the classroom.	3.68	0.99	Very Engaged
5	I am sure I will get the right answer if I keep trying to solve mathematics problems.	3.68	0.84	Very Engaged
6	I always try my best to solve mathematical problems.	3.59	0.96	Very Engaged
7	I tackle math problems with consistent effort and effective strategies.	3.55	0.80	Very Engaged
8	I participate in discussions during mathematics learning.	3.55	0.74	Very Engaged
9	I try to use a different method if I continue to not be able to solve the mathematics problems.	3.55	0.96	Very Engaged
10	I like to solve new problems in mathematics.	3.50	0.86	Very Engaged
	Behavioral Engagement	3.66	0.52	Very Engaged

Note. Interpretation is based on the scale: 4.50 – 5.00 (Extremely Engaged), 3.50 – 4.49 (Very Engaged), 2.50 – 3.49 (Moderately Engaged), 1.50 – 2.49 (Engaged), 1.00 – 1.49 (Somewhat Engaged)

Table 20: Affective Engagement in Mathematics of the Participants in the Experimental Group After the Intervention

Statement		M	SD	Verbal Interpretation
1	I feel happy when I get good mathematics results.	4.23	0.81	Very Engaged
2	I am happy to learn mathematics.	4.18	0.96	Very Engaged
3	I enjoy learning mathematics.	4.18	0.66	Very Engaged
4	I feel a definite positive reaction towards math.	4.09	0.97	Very Engaged
5	I find joy in understanding math concepts.	4.05	0.84	Very Engaged
6	I love solving mathematics problems.	4.00	0.69	Very Engaged
7	I get a great deal of satisfaction out of solving a mathematical problem.	3.95	0.79	Very Engaged
8	I feel satisfaction and confidence when solving math problems.	3.91	0.97	Very Engaged
9	I am confident when participating in math class discussion.	3.82	0.50	Very Engaged
10	I really like mathematics.	3.64	1.00	Very Engaged
	Affective Engagement	4.00	0.62	Very Engaged

Note. Interpretation is based on the scale: 4.50 – 5.00 (Extremely Engaged), 3.50 – 4.49 (Very Engaged), 2.50 – 3.49 (Moderately Engaged), 1.50 – 2.49 (Engaged), 1.00 – 1.49 (Somewhat Engaged)

Table 21: Affective Engagement in Mathematics of the Participants in the Control Group After the Intervention

Statement		M	SD	Verbal Interpretation
1	I am happy to learn mathematics.	3.91	0.75	Very Engaged
2	I really like mathematics.	3.86	0.89	Very Engaged
3	I find joy in understanding math concepts.	3.77	1.02	Very Engaged
4	I feel happy when I get good mathematics results.	3.77	0.81	Very Engaged
5	I am confident when participating in math class discussion.	3.73	0.55	Very Engaged
6	I enjoy learning mathematics.	3.68	0.95	Very Engaged
7	I feel a definite positive reaction towards math.	3.68	0.57	Very Engaged
8	I feel satisfaction and confidence when solving math problems.	3.68	0.78	Very Engaged
9	I get a great deal of satisfaction out of solving a mathematical problem.	3.59	0.67	Very Engaged
10	I love solving mathematics problems.	3.55	1.06	Very Engaged
	Affective Engagement	3.72	0.51	Very Engaged

Note. Interpretation is based on the scale: 4.50 – 5.00 (Extremely Engaged), 3.50 – 4.49 (Very Engaged), 2.50 – 3.49 (Moderately Engaged), 1.50 – 2.49 (Engaged), 1.00 – 1.49 (Somewhat Engaged)

Furthermore, this shows the potential for gamification to improve learning experiences and outcomes in educational settings more particularly in Mathematics subject. This implies the need for a pedagogical shift toward more innovative and student-centered learning techniques that incorporate gamified elements with proper implementation and context. This finding supports the conclusions of [29] who found that gamification is an effective strategy in increasing motivation and engagement of the student. This is also in line with the findings of [30] who found a significant improvement in engagement of the students from the treatment group that considered.

Table 22: Difference in the Engagement in Mathematics of the Participants in the Experimental and Control Groups After the Intervention

Groups	N	Md	Mean rank	U	p-value
Experimental Group	22	4.02	26.41	156.00*	.043
Control Group	22	3.74	18.59

Table 23: Difference in the Pre-test and Post-test Performance in Mathematics of the Experimental Group

Variable	Ranks	N	Md	Mean Rank	Z	p-value
Pre-test	Negative Ranks	0	10.00	0.00	-4.115*	< .001
Post-test	Positive Ranks	22	28.00	11.50
	Ties	0

 

Table 24: Difference in the Pre-test and Post-test Performance in Mathematics of the Control Group

Variable	Ranks	N	Md	Mean Rank	Z	p-value
Pre-test	Negative Ranks	1	9.50	1.50	-4.060*	< .001
Post-test	Positive Ranks	21	22.50	11.98
	Ties	0

Table 25: Difference in the Engagement in Mathematics Before and After the Intervention of the Experimental Group

Variable	Ranks	N	Md	Mean Rank	Z	p-value
Pre-test	Negative Ranks	7	3.59	6.79	-2.365*	.018
Post-test	Positive Ranks	14	4.02	13.11
	Ties	0

Table 26: Difference in the Engagement in Mathematics Before and After the Intervention of the Control Group

Variable	Ranks	N	Md	Mean Rank	Z	p-value
Pre-test	Negative Ranks	14	3.80	10.39	-0.617*	.537
Post-test	Positive Ranks	8	3.74	13.44
	Ties	0

4. CONCLUSION

Before the implementation of the intervention, students in both the experimental and control groups have not yet obtained the necessary foundational knowledge and abilities about the topics at hand, particularly in Permutation and Combination. They struggle with their understanding of the topics involved.  The pre-test performance of the experimental and control groups is comparable, which rules out the possibility of having potential threat to the internal validity in terms of selection. Hence, this helps the study findings become more reliable. Before the conduct of the intervention, the students in the experimental group displayed consistent interest and proficiency in understanding mathematical concepts, while to that of control group showed a high level of interest and proficiency in understanding mathematical concepts. Behaviorally, the students in both the experimental and control groups consistently participate, show persistent effort and focus, and listen attentively during instruction and tasks but only the control group has a desire to solve problems. Both the experimental and control groups consistently exhibit a positive attitude, self-assurance, and enthusiasm along with optimism and perseverance when engaged in mathematical tasks. Despite having different engagement before the intervention was implemented, the engagement of the experimental and control groups was still comparable. This baseline equivalence rules out the threat to internal validity in terms of selection and increases the reliability of the study findings. After the intervention, the students in the experimental group possessed the minimum knowledge and skills and core understanding but still need help throughout the performance of authentic tasks. Meanwhile, the students in the control group have not yet fully obtained the necessary foundational knowledge needed to understand the topics at hand. Gamification is an effective approach than the traditional method in enhancing student performance. This highlights the importance of aligning the curriculum goals and learning objectives with engaging and interactive instructional approaches, especially gamification to ensure that students are actively involved in the learning process. Students in both the experimental and control group show a high level of interest and proficiency in understanding mathematical concepts after the implementation of the intervention. They actively participate, show persistent effort and focus, and listen attentively with a desire to solve problems. They also always display positive attitudes, confidence and enthusiasm with optimism and perseverance when engaged in mathematical tasks. Gamification successfully increases the engagement of the experimental group, which means that it is more effective than the traditional approach of teaching. This underscores the potential of gamification to enhance learning experiences and outcomes in educational settings. Both the gamification and conventional approaches have improved the performance in mathematics of the students in the experimental and control groups, which means that both approaches are effective. Only the experimental group has successfully increased their engagement in mathematics. This means that only the gamification approach is effective in increasing the engagement in mathematics of the students.

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