The Influence of Gamification on High School Students’ Motivation in Geometry Lessons

Abstract

The primary aim of this study is to introduce a didactic programme that incorporates gamification in geometry classes for high school students. The purpose of this programme is to boost students’ motivation towards learning. In the present educational scenario, the role of information and communication technologies (ICT) is paramount. Gamification has the potential to enhance the learning process by integrating game elements into non-game environments. This approach is deemed necessary as emotional factors in teaching may not lead to meaningful learning and improved academic performance. The research methodology employed a mixed approach and a pre-experimental design with pre- and post-test measurements. The sample comprised 45 10th grade students from a subsidised private high school in the Biobío Region of Chile. The study took 10 months and evaluated the factors of motivation, academic achievement, and lexical availability. Results showed a 23% increment in students’ knowledge, as proven by pre- and post-tests. The findings suggest an improvement in students’ perception regarding geometry and a significant improvement in academic performance. Furthermore, it has been confirmed that there is a noteworthy correlation between the group’s overall motivation and their academic performance, supporting gamification as an effective pedagogical strategy.

1. Introduction

The stigma of mathematics among students is that it is seen as a boring and tedious subject [1]. In addition, it is perceived as a hard, rigorous and formal subject. This view leads to rejection and creates a climate of demotivation among students which, if not eradicated, will affect the expected learning [2]. In this scenario, the teacher’s task is to find ways to motivate students towards sustainable learning practices, to interest them both in the class and in the content to be developed, to keep their attention, and to show them how fascinating and important maths is.

In this context, the teacher has to adapt and develop learning strategies to improve the level of participation and sustain students’ engagement [3]. An attractive proposal is offered by Gil et al. [4] who define gamification as “the use of game mechanics in non-game environments, which has proven to be a learning methodology that offers a great opportunity to work on aspects such as motivation, effort, loyalty, and cooperation within the school environment” (p. 74). Although the literature suggests that there may be drawbacks to the use of gamification in terms of a potential reduction in intrinsic motivation, increased anxiety, and short-lived motivational effects [5], gamification in education is flourishing due to global access to internet-connected devices.

The aim of this study was to evaluate the impact of the implementation of a gamified geometry learning unit on high school students from a subsidised, private educational institution in the Biobío region, Chile. The motivation for this endeavour is linked to the pressures imposed by the demands of the educational system, which often make teachers lose focus on the importance of aspects such as student motivation and its direct influence on learning. Hence the importance of implementing new methodologies that contribute to improving students’ disposition towards skills development. In order to analyse the formative process, a questionnaire on motivation towards the learning process was used, whose validation in Chile was also part of this research project. Also, a lexical availability test and a knowledge test were applied. Thus, the present study was conducted guided by the following research question: what is the impact of gamification on student motivation and academic performance in geometry lessons?

2. Background

2.1. Motivation

Motivation is the driving force behind goal-oriented behaviours and refers to the set of reasons that influence human actions. When individuals are motivated, their behaviour is vigorous, directed, and sustained [6]. These ideas, examined by [6,7] support the relationship between goals, behaviour, and motivation, in terms of their behavioural significance, by indicating that motivation is linked to what encourages and directs individuals to engage in a particular activity. Among the traditional conceptualisation of motivation, intrinsic and extrinsic types stand out. Intrinsic motivation comprises the internal interest of the individual, whereas extrinsic or external motivation entails physical benefits that do not arise from the student but from other people or environmental circumstances [8,9]. According to Legault [8], extrinsic motivation “is fundamentally contingent upon the attainment of an outcome that is separable from the action itself” (p. 2416).

Following this instrumental approach, Borah [9] suggests that the motivation to learn is linked to the “interest and diligence that students apply to their academic work”. Additionally, variables that impact motivation are the presentation of tasks, their content, opportunities for student interaction with peers, assessment, outcomes, teacher feedback, and instructional materials. Regarding the latter, Fadda et al. [10] posits that instructional materials, especially digital games, promote motivation as they create positive attitudes towards mathematics. In this regard, Schukajlow et al. [11] supports the idea that motivation and affect can directly impact students through the educational environment or the inappropriate use of affection by those around them.

Regarding motivation and the attitude towards the teaching of mathematics, it is common to encounter students with a negative attitude towards mathematics, often due to cultural or negative experiences. Berger et al. [12] notes that this is due to how students value mathematics tasks and the extent to which they expect to succeed in them. These two elements, students’ task value and expected success can predict achievement in any given subject [13]. Also, evidence [14,15] suggests that task values are strong predictors of engagement and that a positive self-perception can make students feel competent in the task at hand. Thus, the introduction of gamification into maths classes can potentiate this, since it acknowledges emotions, fosters curiosity and imagination, and promotes a sense of completion and success [16].

2.2. Gamification

The concept of gamification employs game design components and implements them into a non-game context. Though this approach has been utilised in fields like marketing, health, and finance [17,18], it is particularly used in educational contexts to improve learning. The aim of gamification is not to utilize games outright, but rather to incorporate some of their fundamental principles or mechanics, including points or incentives, narrative, immediate feedback, and recognition, in order to enhance the learning journey [17,18,19]. Gamification functions as a pedagogical motivational tactic in the teaching and learning process. It stimulates students’ behaviour within a captivating milieu that fosters their commitment to the learning activity, as well as encourages the attainment of positive experiences that lead to substantial learning gains [17,19,20]. This strategy has been linked with the improvement of cognitive abilities, receptiveness, drive, and efficiency among students.

In mathematics, educators face the challenge of devising a teaching plan that departs from the traditional approach. Theoretical classes should not rely solely on expository and one-way communication. Instead, they should provide situations that pique learners’ interest, motivating them and steering clear of unstimulating, repetitive procedures [18]. Thus, gamification does not concentrate on game elements and mechanics, but rather on the outcome and motivation for the sustainability of learning [17,19]. It is a pedagogical method influenced by technology that provides various actions to optimize the acquisition of specific mathematical knowledge through a proposal that fosters enthusiasm and engagement [20].

2.3. Lexical Availability

Lexical availability (LD) is an area of research that aims to gather and analyse the lexicon (LD) present within a particular community, i.e., the words that immediately and naturally come to a speaker’s mind when discussing a specific topic [21]. The use of a LD is useful to understand the vocabulary adopted by a society to describe a particular field. It also helps to identify how the community comprehends a concept, highlighting any deficiencies or weaknesses in the association between the terms and the concept conveyed. To acquire the fundamental vocabulary, we analyse texts using the parameters of frequency and dispersal. The lexicon is established via surveys that motivate the informant to refresh their mental lexicon, which, as Jiménez Catalán and Dewaele [22] explain, is the aspect of grammar containing the words required by the speaker. This lexical information includes phonological, morphological, syntactic, and semantic attributes, pertaining to both meaning and conceptual structure [23]. According to Aitchison [24], words are added to and/or maintained in the mental lexicon based on their pronunciation, spelling, syntactic structure, and conceptual meaning. To obtain a comprehensive lexicon of a community, centres of interest (such as food, games, professions, etc.) have long been used as stimulants. Within a given time limit, typically two minutes per centre of interest, participants are asked to generate ordered lists of lexical units.

3. Materials and Methods

A quantitative method study was conducted, primarily using a descriptive and analytical approach, using the action research (AR) methodology. The study took place in a public school located in the Biobío Region, Chile, in 2022. To conduct this AR study, the following research question was formulated:

• What impact does the implementation of gamification have on students’ motivation in the geometry class?
• What impact does the implementation of gamification have on students’ academic achievement in the geometry class?

3.1. General Objective

To determine the impact of a didactic intervention using gamification in high school geometry classes to enhance student motivation.

Specific Objectives

To implement a gamified learning unit to teach geometry to 10th grade students.

To ascertain the participating students’ levels of motivation with a pre- and post-test.

To ascertain the participating students’ knowledge of geometry with a pre- and post-test.

To examine the relationship between global motivation scores and academic performance.

3.2. Hypotheses

The study puts forth various hypotheses:

Initially, a comparison of the marks mean at distinct time intervals will be conducted, with the following assumption:

H1. 

Students’ academic achievement improves after the gamification intervention ($\overline{x}$ post-test > $\overline{x}$ pre-test).

Also, a comparison will be conducted between the word count at different moments, with the following hypothesis:

H2. 

Students’ average word production improves after the gamification intervention ($\overline{x}$ Nº words post-test > $\overline{x}$ Nº words pre-test).

Moreover, a comparison will take place between the personal lexical availability index (LAIp) at distinct time points, holding the following hypothesis:

H3. 

Students’ personal lexical availability is higher after the gamification intervention (LAIp post-test > LAIp pre-test).

Subsequently, the overall motivation levels of the group will be compared at different time points. The hypotheses to be tested is as follows:

H4. 

Students’ global motivation levels improve after the gamification intervention (global motivation post-test > global motivation pre-test).

Additionally, this study performs a correlational analysis to examine the relationship between global motivation scores and academic achievement, holding the following hypothesis:

H5. 

As global motivation increases, academic achievement increases.

3.3. Materials

This study used three data collection instruments within the framework of the gamification intervention.

• Learning Process Motivation Evaluation Questionnaire (EMPA, acronym in its original form). This test consists of 23 items that measure the intrinsic, extrinsic, and global motivation of the student body. The questionnaire aims to determine group and individual motivation and to develop strategies to improve it [25,26]. This material helps operationalise the motivation variable, defined as an intellectual and emotional state that results in a conscious decision to act and increases the effort period to achieve predetermined goals. The EMPA questionnaire is an instrument created and validated in Spain, which consists of 33 items that provide information on motivation, with a Cronbach’s alpha validation index of 0.93, in global motivation. For the Chilean context, the questionnaire was validated with a sample of 248 subjects and included 23 items from the original questionnaire, whose reliability analysis yielded a Cronbach’s alpha of 0.925.
• Lexical Availability Test. The instrument comprises two sections. The first section gathers socio-demographic data of participants including age, gender, year, and school of origin. The second section entails an elicitation test focusing on available words regarding three centres of interest: geometry, trigonometry, and emotions linked to geometry. This material helps operationalise the available lexicon variable, which is defined as vocabulary that is instantly accessible to the speaker when addressing a specific topic [27].
• Geometry test. A mathematical knowledge and skills test on the learning unit specifically implemented in the study. The passing score in this test is 4, with a 60% demand, of a scale ranging from 1 to 7, based on the Chilean assessment regulations. This material helps operationalise the academic achievement variable, demonstrated in a particular subject which is quantitatively measured. It serves as the benchmark for passing rates in specific content areas or predetermined subjects, assuming a qualified social group [28,29,30].

3.4. Design

The research design of this action research study is pre-experimental, utilizing pre- and post-tests without a control group, with a non-probabilistic convenience sample [31,32]. This is a short-term longitudinal study with an exploratory extent, with a correlational approach to establish the level of association between the different variables of the study, motivation, academic achievement, and available lexicon. From an exploratory perspective, this study aims to ascertain the extent to which the implementation of gamification in geometry lessons influences behavioural changes in the studied variables.

Population and Sample

The population corresponds to students at a subsidised secondary school in the Biobío region of Chile, with an enrolment of 89 students in 10th grade. The sample consists of 45 10th grade students, 25 females (55.6%) and 20 males (44.4%), aged between 15 and 17. The students’ participation was voluntary and with the consent of their parents and the school’s academic department.

3.5. Procedure

The intervention started with the EMPA survey to identify motivation levels. This was followed by the generation of an action plan, according to the research cycle of the action research methodology. Secondly, the action plan, in the form of a didactic sequence, was implemented. This intervention included the administration of the geometry content-based test and the lexical availability test before the intervention. The third stage consisted of the administration of both tests and the EMPA survey as post-tests, together with the data processing and analysis of the results.

Didactic Sequence Planning

The didactic sequence was planned to be implemented in a trigonometry learning unit, as part of the geometry curriculum, during 5 weeks of the academic term. The e-TPACK model was used [33], which integrates ICT in the classroom, elements of the e-TPACK model, Bloom’s digital taxonomy, and emotions prompted and elicited by the gamified rewards in each learning step. Based on the above, the didactic sequences included a series of steps described in

Table 1. Implemented e-TPACK Instructional Sequence.

Learning Outcome
Demonstrate comprehension of the tangent. Tangent ratios in right-triangles:
- Relating them to the properties of similarity and angles. - Explaining them in a pictorial and symbolic way, using educational software. - Using them to find angles or side measures. - Solving geometric and other related problems or measurements.
	Content
	Trigonometric ratios
Activity	Bloom’s taxonomy	ICT	Emotion
1. Students conduct independent research on “trigonometric ratios and compare them with similarities and angles”. They are given a set amount of time to gather information, images, and other relevant materials and record the significant findings in their notebooks.	- Research - Remember - Understand - Apply	www.google.com	- Interest - Curiosity - Amazement
2. Students create a visual representation of their research findings in a concept map form. They can subsequently orient their classmates with their concepts and compare similarities.	- Create - Analyse - Relate - Understand - Expose - Explain	https://www.mindmeister.com Cmap Tools	- Enthusiasm - Interest - Curiosity - Confidence
3. Students analyse the graph and angles formed within a circle, examine the relationship between angles and the basic trigonometric ratios (sine, cosine, and tangent), and make conjectures about observed characteristics using a technological tool (simulator).	- Analyse - Relate - Conjecture	https://phet.colorado.edu/sims/html/trig-tour/latest/trig-tour_es.html	- Awe - Approval - Curiosity - Interest
4. Students relate the sides of a right-angled triangle to the principles of trigonometry, deducing and proposing the ratios established between these sides to support the concepts presented in the lesson.	- Relate - Recognise - Identify - Conjecture	https://www.cerebriti.com/juegos-de-matematicas/razones-trigonom--tricas-en-tri-ongulo-rect-ongulo-	- Trust - Surprise - Curiosity
5. Students memorise the values of basic trigonometric angles through a TikTok song, which is then applied to solve various problems.	- Learn - Remember - Apply	https://n9.cl/w30e1	- Joy - Enthusiasm - Amazement - Amusement
6. Students use Kahoot! to answer questions and self-assess their preparation for the upcoming formal assessment. The highest scoring participants receive points to contribute towards their assessment score.	- Reply - Analyse - Recognise - Identify	http://www.kahoot.it/	- Curiosity - Joy - Confidence
7. Students complete an evaluation tool on fundamental trigonometric ratios and their usefulness in different problem scenarios.	- Develop - Remember - Understand - Apply - Analyse - Evaluate	Trigonometry test	- Trust - Curiosity - Optimism - Approval

.

With regard to the dynamics and aesthetics employed in the gamification process, the following strategies were utilized: (1) rewards, involving the issuance of distinct emojis as recognition for the performance in each completed activity; (2) interactions, either among players (students) or between players and the adjudicator (teacher); and (3) penalties, which involved deducting emojis collected by each student for any sanctioned action. At the end of the module, every student redeemed their emojis to receive specific benefits (

Table 2. Benefits for emojis collected by students.

Emojis	Benefits
More than 15 emojis	Maximum mark (7.0) extra in the subject.
Between 10 and 14 emojis	5 extra points for any evaluation of the semester.
Between 5 and 9 emojis	Elimination the worst mark in the process tests.
Between 1 and 4 emojis	2 extra points for the unit assessment.

).

The approach of this didactic sequence contrasts with what traditionally follows a geometry lesson. From a general didactic perspective, students typically learn trigonometric functions and their relationships with angles in right-angled triangles. Methods for solving triangles are a fundamental component, involving the application of the laws of sines and cosines. Traditionally, practical exercises concentrate on problems related to angle and distance measurement, often utilizing standard problems to practice the application of learned formulas through individual work and following the guidelines of rote learning. However, this methodology can appear abstract to some students, as it emphasizes mathematical manipulation rather than understanding the practical applications of trigonometry in fields such as physics, engineering, and astronomy [16].

4. Results

The lexical statistical analyses were conducted with Dispogen II (2014 version), a MatLab-based application that focuses on matrix calculations and multivariate statistical analyses, including lexical availability analyses. This program utilizes López and Strassburger’s formula [34], which employs an exponent that asymptotically approaches zero. This method ensures the constant preservation of discriminant capacity. All abbreviations of technical terms will be explained on their first use.

The software calculates several statistics, including the mean number of words, count of distinct words, cohesion index, and a list of words with their corresponding lexical availability indexes (LAI) and personal lexical availability indexes (LAIp). It is possible to perform lexical-statistical analysis to infer individual behaviour and assess the lexical production of a participant in comparison to the entire pool of speakers. According to López and Strassburger [34], a higher LAIp of a participant indicates a bigger contribution to the group’s lexicon, thereby increasing their ability to communicate within the group. For the statistical calculations, IBM SPSS version 23 was used.

4.1. Academic Achievement

To examine possible significant variations in academic achievement, the mean scores achieved pre- and post-gamification intervention were scrutinised using a paired-samples t-test. This aimed to compare the differences regarding two numerical variables (be-fore/after) within the same cohort. Before applying Student’s t-test, the Shapiro–Wilk normality test was conducted. The pre-test resulted in p = 0.062, while the post-test resulted in p = 0.189. Furthermore, the results of Student’s t-test indicated a value of p = 0.000, which rejected the null hypothesis of any major differences in academic performance after the gamified intervention in the geometry class (

Table 3. Student’s t-test for academic achievement.

Paired Differences
	M	SD	MSE	95% CID		t	df	Sig. (Bilateral)
				LB	UB				Cohen’s d
Pre Post	−11.644	6.630	0.988	−13.636	−9.652	−11.781	44	0.000	1.139

Note. Results obtained through SPSS 23 in Spanish.

).

With this p-value, we reject the null hypothesis in favour of H1: $\overline{x}$ post > $\overline{x}$ pre. Consequently, it can be concluded that there is a significant difference in the average academic achievement of students before and after the geometry intervention, and that the embedded gamification has a significant effect. Specifically, the students’ marks improved from an average grade point of 4.1 in the pre-test to an average of 5.3 in the post-test, on a 1-to-7 scoring scale. This is supported by a large effect size (d = 1.139), indicating a substantial difference between pre and post measurements. In summary, the t-value and the associated Cohen’s d suggest a significant and substantial increase in the measured variable from pre- to post-test.

4.2. Lexical Analysis

The lexical analysis was conducted using the lexical availability methodology statistics. Initially, the number of words produced by the students during both research phases was examined. To compare the average numbers of words mentioned by the students regarding our three areas of interest, namely “emotions, geometry, and trigonometry”, the following analysis was performed. Subsequently, statistical analyses were conducted for the LAI and the LAIp (Dispogen, 2014 version).

4.2.1. Word Mean on Emotions, Geometry and Trigonometry

Students were given a lexical availability test to elicit words linked with the centre of interest ‘emotions’. The prompt question was: “What emotions do you associate with geometry?” In relation to the centres of interest ‘geometry’ and ‘trigonometry’, learners were requested to compile a list of terms related to each one (

Table 4. Words produced in each centre of interest.

Centres of Interest
	Emotions		Geometry		Trigonometry
	Number	Average	Number	Average	Number	Average
Pre-test	244	5.42	557	12.37	255	5.79
Post-test	211	4.68	524	11.64	492	10.93

). Statistical tests were conducted, considering the normality of the distribution using Student’s t-test for normal distributions and Wilcoxon for non-normal distributions. The only significant difference (p = 0.000) was observed for the ‘trigonometry’ centre of interest.

Based on these results, it can be concluded that the increase in acquired lexis in the domain of ‘trigonometry’ partially supports the second research hypothesis. In this area of study, the total word count mean in the post-test was higher than that of the pre-test. An analysis of the vocabulary used in the sample suggests that the lack of significant differences in word averages between “emotions” and “geometry” may be explained by the fact that some emotion words mentioned in the pre-test may have been replaced by new ones in the post-test. The same applied to the terminology related to geometry. It is possible that this was influenced by the group’s motivation level during the study.

4.2.2. Lexical Availability Index on Emotions, Geometry, and Trigonometry

The lexical availability index (LAI) allows us to understand how a community approaches a particular concept and reveals gaps, weaknesses, or the relationship between words and that concept. In this study, this technique was used to provide access to the lexical richness of the student sample and to serve as a diagnostic tool to comprehend the addressed variables.

When analysing the LAI in relation to the centre of interest “emotions that come to mind when you think of geometry”, it is observed that in the pre-test, certain words like ‘fear’ stand out with high coincidence and a LAI of 44.2%, while ‘sadness’ and ‘laziness’ had a coincidence rate of 42% in the sample. On the contrary, the post-test indicates a shift towards positive emotional language in the lexicon of the sample. ‘Happiness’ received 49% of agreement, ‘joy’ received 40% of agreement, and ‘thrill’ received 28% of agreement (

Table 5. Top five available words.

Emotions				Geometry				Trigonometry
Pre		Post		Pre		Post		Pre		Post
Word	LAI	Word	LAI	Word	LAI	Word	LAI	Word	LAI	Word	LAI
Fear	0.327	happiness	0.411	Square	0.456	Angle	0.468	Triangle	0.605	Triangle	0.495
Sadness	0.302	Joy	0.306	Triangle	0.413	Triangle	0.458	Geometry	0.264	Cosine	0.482
Laziness	0.262	Thrill	0.214	Area	0.396	Square	0.415	Number	0.249	Sine	0.467
Tiredness	0.208	Stress	0.156	Shape	0.355	Shape	0.396	Measure	0.222	Tangent	0.389
Boredom	0.193	Curiosity	0.174	Rectangle	0.332	Rectangle	0.302	Three	0.21	Angle	0.371

).

It should be noted that several emotions mentioned by the students during the pre-test may have resulted from low motivation towards geometry, as they were predominantly negative emotions or expressions of discomfort. In contrast, during the second phase of the research, positive emotions were the main theme, indicating a rise in students’ motivation towards geometry. Nevertheless, it is pertinent to mention that negative emotions were also observed; however, with a significantly lower frequency.

When examining the LAI for ‘geometry’ before and after, some similarities have been observed in the language used. It is worth noting that, in the pre-test, certain terms were more commonly used: ‘square’ had a 57.7% occurrence, followed by ‘triangle’ with 57.7% and ‘area’, which had a coincidence rate of 68.8%. In contrast, the post-test exhibited the highest levels of similarity with ‘angle’ at 64.4%, ‘triangle’ at 55.5%, and ‘square’ at 53.3%.

It is noteworthy that the pre-test revealed a basic understanding of the subject among the participants, as evidenced by their use of terms associated with core geometric shapes and mathematical calculations. Although the terms were related to fundamental geometric shapes, their order of importance varied among participants. An interesting finding is that the post-test showed a higher degree of overlap in the students’ LAI, suggesting effective communication within the group and a shared understanding of the language.

In relation to the focus of interest ‘trigonometry’, there was a considerable increase in both the total number of words mentioned (237 words) and the average number of words per subject (5.137), with an increase of 8 in the number of words. It is worth noting that in the pre-test, ‘triangle’ accounted for 65.9% of the mentions; ‘geometry’ 34.09%; and ‘number’ had an agreement of 31.8%. Similarly, in the post-test, significant overlaps were observed: ‘triangle’ with 64.6% of mentions, ‘cosine’ with 66.6%, and ‘sine’ with 62.2%. This reflects the incorporation of new concepts acquired during the intervention.

4.2.3. Overall Group Motivation Results

From the EMPA questionnaire, the scores for intrinsic and extrinsic motivation were calculated. Afterwards, these scores were transformed into percentiles using the reference tables of the questionnaire. The corresponding percentiles were then identified based on students’ gender and age. Generally, as the outcomes showed a non-normal distribution, the Wilcoxon test was used. The test produced a p-value of 0.000, lower than an alpha of 0.05. Thus, there was a significant difference in overall motivation between the pre-test and the post-test. Particularly, the results showed that while 4 students had higher global motivation in the pre-test, 36 students had higher global motivation in the post-test. Only five students had a consistent motivation value at both points in time.

4.2.4. Correlation between Academic Achievement and Global Motivation

Academic achievement was evaluated through written knowledge assessments before the geometry unit, and the other after the completion of the unit which integrated a gamification approach in the lessons. Both tests were scored using a scale of 1 to 7 and were evaluated against the school’s assessment criteria that demanded 60% proficiency for the minimum passing mark of 4.

Regarding the students’ collective motivation, the Learning Process Motivational Evaluation Questionnaire (EMPA) was used. Scores for the various categories of motivation were initially computed. This was accomplished by summing the values assigned to each response for the constituent items of each category. The analysis of the outcomes differentiated gender and age. The resultant direct scores for global, extrinsic, and intrinsic motivation were subsequently converted into percentile scores to aid comprehension. These scores range from 0 to 100, with 50 representing the average motivation level of the students. Values below 50 represent low motivation, whereas values exceeding 50 indicate high motivation. To determine the percentile score, the direct value is consulted against the appropriate scales for the person’s age, gender, and type of motivation, whether intrinsic or extrinsic.

Pre-Test Correlation between Motivation and Academic Achievement

The Shapiro–Wilk normality test was employed to examine the correlation between two variables resulting from a reduced sample size (n ≤ 50). The findings indicated that the variable of academic achievement has a normal distribution with a significance level of 0.062 (>0.05). Conversely, the variable ‘motivation’ displayed a non-normal distribution, with a significance level of 0.005 (<0.05). Descriptive statistics provided evidence for this observation in regard to both quantitative variables. As the distribution of one variable is not normal, Spearman’s non-parametric test was used to investigate its correlation.

Since the p-value obtained in the results is 0.108, the null hypothesis is accepted. Therefore, there is insufficient statistical evidence to support an association between global motivation and student achievement. In addition, Spearman’s correlation coefficient of 0.243 indicates a low positive correlation between the variables. This implies that an increase in student performance is accompanied by a slight increase in global motivation (

Table 6. Academic achievement and motivation correlation in the pre-test.

			Academic Achievement	Motivation
Spearman’s rank	Academic achievement	Correlation coefficient	1.000	0.243
		Sig. (bilateral)		0.108
		n	45	45
	Motivation	Correlation coefficient	0.243	1.000
		Sig. (bilateral)	0.108
		n	45	45

).

Post-Test Correlation between Motivation and Academic Achievement

Since one of the compared variables does not follow a normal distribution, Spearman’s non-parametric test was used to evaluate the correlation between the two variables. The results indicate a p-value of less than 0.05, hence the null hypothesis is rejected. Consequently, there is adequate statistical evidence to confirm a connection between student academic achievement and global motivation.

In addition, Spearman’s correlation coefficient of 0.661 shows a significant positive association between better academic achievement and higher global motivation (

Table 7. Academic achievement and motivation correlation in the post-test.

			Academic Achievement	Motivation
Spearman’s rank	Academic achievement	Correlation coefficient	1.000	0.661 **
		Sig. (bilateral)		0.000
		n	45	45
	Motivation	Correlation coefficient	0.661 **	1.000
		Sig. (bilateral)	0.000
		n	45	45

**. Correlation significance at level 0.01 (2 tails).

). To summarize the analysis, prior to the intervention, there was no identified relationship between global motivation and performance, but after implementing gamification in geometry lessons, a strong correlation between the two variables was highlighted. As global motivation rises within the sample, academic achievement also increases. Thus, the fifth research hypothesis can be supported, heightened global motivation is related to enhanced student accomplishments in the sample.

5. Discussion

5.1. What Impact Does the Implementation of Gamification Have on Students’ Motivation in the Geometry Class?

Several studies have corroborated that learning is not solely reliant on students’ cognitive abilities, but also on their motivation to learn [35,36,37,38,39,40]. To strengthen motivation, gamification, which makes use of game mechanics and techniques in non-game environments, has grown in popularity because it entertains and offers a different approach to traditional methods of learning [41,42,43]. Gamification strengthens the learners’ intrinsic motivation and assists in developing decision-making, problem-solving, and autonomy skills [44]. Antipolo [43] emphasises that educators need to discover gamified content aligned with the curriculum that enables students to engage in thorough exploration and tackle complex problem-solving. He also concludes that it is essential for teachers to use gamification that contribute to the cultivation of robust mathematical skills and practices as they foster motivation.

Similarly, Ince [35], reports a direct correlation on motivation and academic achievement in secondary school science class students. Likewise, in a meta-analysis study carried out by Van Iddekinge et al. [39], they found that state-like assessments of motivation (instrumental motivation) proved to be more effective predictors of performance compared to trait-like motivation assessments (intrinsic). This is particularly important for education as it implies pedagogical motivational challenges that can be supported by the use of innovative techniques like gamification and technology. In this regard, a study conducted by Wajeeh [40] in seventh graders learning mathematics with and without technology, discovered that the students greatly favoured the technology-based class. These differences were evident across three key aspects: interest, mastery, and self-efficacy. More specifically, on gamification for learning, Papp’s study [41], reports an agreement within the participating groups (primary school and college students) suggesting that they perceived the gamified approach as captivating, inspiring, and a favoured method for learning. She also concluded that gamification can be implemented without the need for extensive technology or costly software investments. The belief, the author asserted, is that it can be customized to suit individuals of all age groups.

In terms of mathematics, numerous students face difficulties in comprehending the subject as they perceive it as challenging and solely focused on rote learning [1,41,42]. Nonetheless, mathematics, and more particularly geometry, does in fact, assist in developing reasoning skills [38,39,40]. Roos [42] explains that mathematics is an essential subject in education, geometry included, and that educators must comprehend the challenges students face in comprehending the topic. Thus, the emotional aspect plays a pivotal role in learning its contents and developing its skills, as students need to understand what is being taught to them to maintain motivation. She concludes by addressing the connection found between students’ access to mathematics and their level of participation. Consequently, the organization of the mathematics classroom, as well as lesson planning and execution, with an emphasis on facilitating students’ access and involvement, holds significance for the learning outcomes of all students. The issue of participation raised here is consistent with the didactic sequence planned and implemented in the present study, which sought to involve students and provide instances of active participation by means of a rewards/incentives approach to the completion of the learning tasks included in the gamification intervention.

The higher motivation levels found in the present study are also evidenced by the results of the lexical availability test. While the five most available words in pre-test were mostly negative words like ‘fear’, ‘sadness’, ‘laziness, ‘tiredness’, and ‘boredom’, the five most available words in the post-test were mostly positive ones like ‘happiness’, ‘joy’, ‘thrill’, ‘stress’, and ‘curiosity’. Words like ‘happiness’ and ‘joy’, with an agreement of 49 and 40%, respectively, show how their attitudes changed over the course of the intervention. This fact contrasts greatly with the latent words produced in the pre-test when asked about emotions related the mathematics and, more particularly, geometry. This shift contravenes the notion most students have about mathematics of being tedious and boring [1,41,42], or at least contributes to this needed change in this perspective.

5.2. What Impact Does the Implementation of Gamification Have on Students’ Academic Achievement in the Geometry Class?

In education, gamification is a dynamic and innovative approach that permits interaction between students and teachers, facilitating learning experiences and improving academic achievement [45]. This approach is particularly useful for developing skills that can be applied in work settings, while also increasing student motivation. It is important to keep in mind that gamification is different from educational games. Gamification entails including game elements to achieve specific targets or goals, while educational gamification incorporates gameplay into learning objectives. Along these lines, Uz Bilgin and Gul [46], in their quasi-experimental research study, examined two groups, a gamified group consisting of 44 students, and a traditional group consisting of 48 students. While no notable distinction was found between the gamified and traditional groups regarding students’ attitudes toward group learning environments, the gamified group demonstrated superior performance in terms of both group cohesion scores and evaluations of team members compared to the traditional group. This study also explored the impact of gamification on academic achievement whose results matched prior findings, as the group exposed to gamification showed superior learning performance compared to the traditional (control) group.

The significant positive association between better academic achievement and higher global motivation found in the present study, influenced by the gamification intervention, is consistent with the findings of Uz Bilgin and Gul, and those of later studies which have consistently shown positive results regarding student academic performance with gamification [47,48]. More current evidence also supports the use of gamification to improve academic achievement. For example, Zhan et al. [49] confirmed the beneficial influence of gamification in programming education, with the greater effect of gamification on students’ motivation, followed closely behind by academic achievement. Also, Alam et al. [50] explored student experiences and academic achievements using a gamified dashboard in a large, introductory STEM course. Their main findings indicate that with low costs and little time invested, gamified dashboards could have a significant impact on student performance.

In summary, to guarantee successful and engaging mathematics education, effective teaching and learning methodologies are critical. Teachers must take into account students’ motivation, make use of suitable teaching techniques, and incorporate technology and gamification, as much as possible. By adopting a comprehensive approach to education and acknowledging students’ motivations, educators can enable learners to acquire the essential competencies and knowledge required to face the demands of an ever-evolving world.

6. Conclusions

The primary aim of the study was to introduce a didactic module employing gamification in secondary school geometry lessons to enhance student motivation. This study also aimed to assess the correlation between motivation and academic achievement in the selected group, alongside other variables. The unit on geometry focused on the fundamentals of trigonometric ratios. To facilitate the learning process, gamified activities were introduced, which encompassed mechanics, dynamics, and aesthetics, and incorporated rewards, punishments, and interactions. All these components were symbolized by distinct emojis that the learners were acquiring throughout the module. This enabled the students to maintain their motivation and focus during the sessions. Exercises were also incorporated in platforms like Phet, Kahoot, and TikTok, attracting the learners and keeping them captivated throughout the module. They were also willing to propose new problem-solving methods.

As a result of the intervention, the students exhibited increased motivation, participation, responsibility, and confidence in their knowledge. After assessing motivation and knowledge levels throughout the intervention, several conclusions could be drawn. The motivation was measured with the Learning Process Motivation Evaluation Questionnaire (EMPA). The EMPA demonstrated an increase in global motivation for the entire sample. The post-test results confirmed the fourth hypothesis of the research, as the average global motivation of the post-test was higher than that of the pre-test. Similarly, the application of the parametric t-test confirmed the hypothesis that the students’ average performance in the post-test was higher compared to the pre-test. The pre-test results showed an average performance of 40.9, whereas the post-test results showed an average of 52.6, indicating a significant difference in the two stages of the study.

The study also analysed the lexical availability index (LAI) of the group to understand the relevance of words in the participants’ minds and the proximity of an individual’s lexicon to that of the group. This information enabled us to speculate on the effectiveness of communication within the group and its learning potential, especially when it comes to relate emotion words to motivation and how engaged they felt with the learning tasks. Under the parameters of Spearman’s non-parametric test, we confirmed the presence of correlation between overall motivation and student performance. This test helped us confirm the fifth and final hypothesis of the research stating that an increase in global motivation results in an increase in student performance. In conclusion, it can be argued that gamification is a pertinent tool to enhance mathematics learning in secondary school students. It serves as a significant motivator for students, and it mitigates the stress that arises from challenging classes, boredom, and other related factors. In terms of implementing gamification in mathematics, a positive impact of this approach has been observed in the advancement of calculation skills and mathematical logic in students. Through the use of various software tools, students were able to develop effective strategies to progress to higher levels and achieve defined goals. Consequently, this motivation led them to strive for better understanding of each topic covered, and ultimately achieve better marks.

Limitations and Further Research

Despite the favourable outcomes of the intervention regarding the impact of gamification on motivation and academic performance, there are certain limitations to the study. Firstly, although the sample’s effect on the 10th-grade population displayed significant consistency, a larger sample size could offer more reliable results for generalization. It is noteworthy that the sample was exclusively composed of students from one educational institution, limiting the generalizability of the findings to other populations. Regarding future projections, it should be considered that students from different institutes or cultural backgrounds may respond differently to gamification treatment. Additionally, a control group would have provided a better understanding of the actual impact of gamification.

Furthermore, the duration of the intervention may not have been sufficiently long to fully capture the long-term impact of gamification on students’ motivation and academic performance. Lastly, the study solely focused on gamification as a predictor of motivation and academic achievement. However, other factors may influence these outcomes, such as the student’s personality, teacher quality, and family support, among others. It is crucial to consider these factors in future studies to gain a more comprehensive understanding of the other intervening aspects influencing motivation and academic achievement.