Effective Professional Development and Gamification Enacting Curriculum Changes in Critical Mathematics Education

Abstract

In response to challenges around student engagement and teacher technological proficiency, this paper looks at the impact of gamification on students’ mathematical resilience whilst monitoring their mathematical anxiety plus investigating teachers’ experiences, willingness, and professional development ambitions to utilise gamified instructional tools in the mathematics classroom. Drawing on strategies to motivate students, the aim of this paper is to unbundle gamification in enacting curriculum change and the role of teacher professional development in using the pedagogical approach in mathematics in Ireland. Ireland is currently experiencing second-level curriculum reforms that are placing particular emphasis on digital competence and technological fluency from both teachers and students. With teachers highlighting the gap in educators’ pedagogical skills for the smooth roll out of recent curriculum reform due to the lack of knowledge and competency in technological teaching strategies, this study is both relevant and timely. Games have been used in multiple industries aiming to motivate participants and increase engagement on a particular matter. However, the term “gamification” has been coined by Pelling as the use of games in a non-gaming context. Current students are very technologically savvy due to the exposure of software applications from a young age and the integration of technological appliances in all walks of life. Traditional teaching and learning strategies are potentially seen as monotonous and somewhat boring to today’s students. Utilising game-based design such as leaderboards, points, and badges encourages motivation and enhances engagement of students. With this in mind, and the rate of change in mathematics curricula globally in recent years, there is a significant emphasis on the necessity of professional development initiatives to adapt at the same rate.

1. Introduction

Innovative teaching strategies remain a crucial matter in the field of mathematics pedagogy, due to the rapid development of information and communication technology (ICT). Educators are forced to upskill to become technologically fluent in order to meet the needs of our current student cohort. Subsequently, gamification has gained considerable attention in recent years, highlighting methods of pedagogical engagement and motivation using leaderboards, points, and badges. Motivation, one of the fundamental principles of effective learning, should be further explored and implemented in educational contexts in order to enhance the teaching and learning experience amongst students (Palmer, 2007). With this in mind, gamification acts as a teaching tool that holds a lot of potential to enrich the quality of teaching and learning of mathematics. Whilst previous literature provides valuable insights into the effectiveness of utilising games in a non-gaming context (Deterding et al., 2011), it does not fully address the effectiveness of gaming in the mathematics classroom, nor does it look at the impact it has on students’ Mathematical Resilience (MR). MR is a fundamental aspect of studying mathematics, so students recognise challenges as learning opportunities to foster long-term success in mathematics (Johnston-Wilder & Lee, 2010).

In addition to this, teachers reported their lack of Professional Development (PD) around the application of technological teaching tools. For example, 35% of teachers reported that they had participated in PD on integrating technology into the classroom setting—Ireland reported to have 23.4% of teachers engaged in PD on technology in the mathematics classroom (Mullis et al., 2020). Literature states that the willingness from teachers to implement and explore innovative teaching strategies is evident; however, the lack of knowledge and confidence in the implementation prevents teachers from trying (Bećirović, 2023). As the smooth integration of gamification into the classroom relies heavily on the skill of the teacher, targeted PD is key to ensure that teachers are equipped with the suitable technological and pedagogical expertise.

The purpose of this study is to investigate the impact of employing game-based learning on post-primary first-year students’ MR whilst monitoring their levels of MR and MA. Additionally, the study explores appropriate resources that teachers require to effectively implement gamification in the classroom. An action research methodology was employed with a quasi-experimental design and mixed-methods approach to capture a comprehensive analysis of the effect of using game-based design tools on students’ MR.

2. Literature Review

2.1. Mathematical Curriculum at the Secondary Level

Mathematics curricula worldwide are undergoing periods of change to ensure that students are prepared for life in the 21st century. These curricula posit that it is essential students are equipped with critical thinking skills such as analysing, predicting, and problem-solving while understanding how to collaborate on innovative solutions to real-world issues (ACARA, 2015; NCCA, 2017, 2023; DOE, 2021). Data from the TIMSS in 2019 and PISA in 2022 indicate that students are improving in their mathematics abilities overall, although students’ achievement in reasoning and applying are seeing weak growth (Mullis et al., 2020; OECD, 2022). For example, in Ireland, students at the eighth-grade level scored significantly lower in the reasoning domain on the 2019 TIMSS report than in 2015, with no growth in the other cognitive domains of knowing and applying (Mullis et al., 2020). In response to this data, in recent years, countries have been examining their mathematics curriculum to identify how to prepare students better, resulting in reformed curricula. Although a focus on the mathematics curricula in Ireland permeates this literature review, commonalities among aims, rationale, and pedagogical practices can be seen among the Irish curriculum and countries worldwide.

In Ireland, the Junior Cycle curriculum underwent significant changes between September 2014 and September 2021, including the mathematics curriculum in 2017 (NCCA, 2024). The Junior Cycle in Ireland specifies what students will learn during the first 3 years of post-primary school. The rationale for the 2017 mathematics curriculum is underpinned by the idea that mathematics contains interwoven concepts that appear in everyday life, and therefore, placing students at the centre of the learning is paramount to the curriculum’s success (NCCA, 2017). In addition, five aims were identified that were essential to students’ success in learning and applying mathematics to daily life. These aims include conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition (Findell et al., 2001). The significance of these aims in students learning mathematics was further established in the 2023 Primary Mathematics Curriculum as fundamental to students throughout their entire mathematics education journey. In addition, eight key skills were identified as critical for students to develop throughout the curriculum, including the following: communicating, being literate, managing self, staying well, managing information, and thinking, being numerate, being creative, and working with others. Eight principles provide the foundation for the entirety of the Framework for the Junior Cycle and guide teachers in planning lessons and delivering the curriculum as written. These eight principles—learning to learn, choice and flexibility, quality, creativity and innovation, engagement and participation, continuity and development, inclusive education, and well-being—are essential for teachers to understand and consider when teaching mathematics.

2.2. Mathematical Resilience

MR is one’s ability to persevere during challenging encounters in mathematics whilst understanding that struggle is required to grow (C. Lee & Johnston-Wilder, 2017). MR is not something that is inherited yet must be formed and developed over time with innovative teaching strategies and holistic and supportive teaching and learning approaches. MR students view mistakes as opportunities for growth and learning opportunities (Johnston-Wilder et al., 2015). C. Lee and Johnston-Wilder (2017) identified MR as essential for students to develop, allowing them to avoid negative emotions and corresponding behaviours as they are challenged in learning mathematics. Students who have developed MR may adopt higher levels of self-efficacy. The Junior Cycle mathematics curriculum in Ireland, requires high problem-solving skills that demands persistence in students who solve complex questions (Neururer, 2024).

A focus of developing MR in the classroom is increasingly pivotal as mathematic curriculum reform continues globally as the shift in abstract mathematics to more real-world and cognitive learning dominates the syllabus. Teachers play a key role in fostering students’ MR by creating a holistic learning environment that promotes challenges and struggle as learning opportunities.

2.3. Mathematical Anxiety

Mathematics Anxiety (MA) has received increased attention in recent years as potentially damaging students learning, doing, and applying mathematics within school and in their lives (Hembree, 1990; Luttenberger et al., 2018). Ashcraft (2002) defined MA as “a feeling of tension, apprehension or fear that interferes with math performance”. Wither (1998) built on this definition, describing MA as a very serious problem in many classroom environments. As previously mentioned, the Junior Cycle mathematics curriculum calls for students to learn mathematics through challenging and real-world situations. The curriculum highlights the importance of students developing skills that help them identify complex issues and develop solutions using mathematics that require high cognitive skills. The Junior Cycle mathematics curriculum is a complex field and with this in mind proves demanding on the students’ learning environment and individual’s beliefs, attitudes, and behaviours towards learning mathematics.

Although distinct to MR, MA is often affected by students’ ability to persevere, self-regulate, and their reaction to struggle. Students with low resilience tend to score highly on MA scales when faced with mathematical challenges (Johnston-Wilder & Lee, 2010; Ishak et al., 2020).

For this reason, this study measures students’ MA as the undergo of learning mathematics through online gaming software. Although MR outlines the student’s ability to persevere when undergoing mathematical challenges, MA looks at the student’s potential emotional strain. Given the potential of reducing MA whilst fostering MR, it is important to explore innovative teaching strategies to achieve these objectives. Gamification offers a potentially engaging teaching tool that warrants further research to comprehend its scope to support this and future curriculum reforms.

2.4. Gamification in Mathematics Education

The inquiry into how gamification can be used in educational settings has seen increased attention in recent years; however, definitions and applications of the term are still being developed. Deterding et al. (2011) pointed out that definitions of gamification vary, but based on recent applications, defined it as “the use of game design elements in non-game contexts”. Although gamification has become popular within industries, its application within classrooms is only beginning to increase. As a result, the definitions of gamification in educational contexts, the necessary design components, and the effects on student learning are still emerging (Majuri et al., 2018).

Werbach and Hunter (2015) proposed a gamification toolkit that frames the idea of game-based learning through three main elements: components, mechanics, and dynamics. Components looks at utilising points, badges, leaderboards, and avatars, which enhances the visual progression of learning for the students whilst providing a sense of success and achievement. This relays to the enhancement of motivation and self-efficacy, which directly align with the construct of MR (Johnston-Wilder et al., 2021). Mechanics explores the element of feedback, rewards, and competition that gaming provides. The mechanics component of gamification helps foster habits of perseverance and social support through collaboration. Lastly, the dynamics component of the toolkit provides narrative, progression, and constraints for the user, which in return offers a sense of emotional security that tends to alleviate MA (Hung et al., 2014) and nurtures a learning mindset hence, fostering MR (Johnston-Wilder et al., 2021). Gamification is a multidisciplinary instrument that proves reasoning for implementation (Seaborn & Fels, 2015) and has been implemented in many fields of research. Findings show that the top fields for gamification research are education followed by health and wellness (Seaborn & Fels, 2015). This implies that the employment of gamification in the mathematics classroom has the potential to have a positive effect on students’ MR and academic achievement.

To integrate this new technological tool in the classroom setting, it is crucial that post-primary educators are equipped with meaningful and essential PD for the effective implementation of such instructional tools. In addition to this, prior literature outlines the benefits of employing PD in teacher training courses to enrich the teaching and learning experience and enhance students’ academic achievement (Desimone, 2009). Providing teachers with the required training has the potential to create a more motivating, intriguing, and engaging mathematics curriculum.

As gamification used within education aims to increase students’ positive experiences in learning, understanding its applicability within post-primary mathematics is essential. As previously discussed, students’ MA and MR can impact their success in learning mathematics at high levels. Although the research is still in its infancy, the application of gamification in learning mathematics has positive outcomes on students’ engagement and motivation (J. Y. Lee et al., 2023) including problem-solving and mathematics skills development (Yığ & Sezgin, 2021). While these initial findings indicate positive outcomes of gamification in mathematics, a large portion of the research stems from primary and post-secondary education and pinpoints engagement and motivation as primary areas of interest. As a result, it is essential for more research to be conducted at a post-primary level and to understand the effects that gamification may have on students’ MA and MR.

2.5. Continuous Professional Development and Curriculum Reform

As curricula are reformed and educational research evolves, it is essential for teachers to learn and effectively implement the necessary pedagogical skills for teaching mathematics. Eighth-grade teachers who participated in the 2019 TIMSS reported that they desire more Continued Professional Development (CPD) in the area of mathematics (Mullis et al., 2020). Teachers in Ireland identified the greatest need in the areas of integrating technology into mathematics instruction and improving students’ critical thinking skills (Mullis et al., 2020). Furthermore, the Technological Pedagogical Content Knowledge (TPACK) framework offers an important toolkit used by educators for implementing digitalised teaching strategies in the classroom as opposed to employing technology in isolation from pedagogical objectives (Mishra & Koehler, 2006).

As more is learned about the role that gamification may play in students’ learning of mathematics, it is also crucial to understand how teachers can learn how to best interject it into mathematics lessons. CPD will undoubtedly play a crucial role in helping teachers who want to use gamification in teaching mathematics. Understanding how gamification can impact students’ achievement in mathematics is a key first step, closely followed by ensuring that teachers have the pedagogical knowledge and skills to effectively implement it into mathematics lessons. Research in both these areas is still in its infancy, calling for additional exploration into the role that gamification may play in students’ academic success.

With this in mind, the following research questions were identified with the intention of seeking answers to:

RQ1. 

What is the impact of utilising gamification on first year post primary students’ mathematical resilience and mathematical anxiety in Ireland?

RQ2. 

What are post-primary educators’ perceptions of the advantages and challenges of integrating the educational gaming software Blooket (Season 6) into the classroom and, furthermore, is there a demand for teacher PD in gamification?

3. Materials and Methods

3.1. Research Design

This study followed an action research methodology with a mixed-methods approach that employed a quasi-experiment with control and experimental groups in which student participants engaged with two instruments that measured their MR and MA. This study was ethically approved by the University of Galway in June 2023 with data collection commencing in September 2023. The qualitative data provided an insight into the participants’ personal classroom experience with the gaming tools through semi-structured interviews that were conducted with students of high and low MR. A focus group was conducted with teachers to gather insights into their experience of teaching with game-based learning and their interest in PD in this area.

3.2. Gamification Intervention

Blooket is an educational gaming software that is used all over the world to enhance motivation and bring an element of fun to the learning environment. Educators can design games on the software, inputting their own questions to align with the curriculum they are teaching. The game creator inputs a question that users will then answer using an array of answering tools, for example, true/false, multiple-choice answers, or short-answer questions. On the other hand, educators can access readily available games that were created by other users. On deciding the game to use, the educator can choose from a multitude of gameplay modes such as Monster Brawl, Tower Defense, Café, Racing, Classic, etc. The variety of game modes feature various key components to the gamification toolkit (Werbach & Hunter, 2015) such as points, badges, leaderboards, and avatars (components); competition, immediate feedback, and social interaction (mechanics); and narrative, strategy, and progression (dynamics). On completion of a game, the educator has access to the performance analytics of the users that provides a comprehensive report on students’ progress and performance.

For the purpose of this study, the principal investigator created the games to directly align with the Junior Cycle curriculum and, furthermore, scheme of work of the year group. The games included a multitude of answering formats such as, multiple choice questions, true/false, and short-answer questions. The games were played intentionally using Blooket’s various game modes that mirrored Werbach and Hunter’s (2015) gamified framework:

Components: These included points, badges, leaderboards, and avatars. These features of Blooket provided an interactive and engaging method of learning mathematics. Earning points encouraged participation and accuracy in answers, while the leaderboards provided real-time ranking of student performance that fostered competition. Badges and avatars unlocked a visual aspect of the game, enhancing a personalised experience for the user.

Mechanics: On answering a question, students are met with instant feedback, which reduces the uncertainty and encourages persistent learning. Throughout the intervention, the gaming mode varied and included an element of teamwork where students collaborated with others, which increases focus, participation, and motivation. In addition to this, the games incorporate a timing element, which is a realistic element to the state examinations in Ireland.

Dynamics: The dynamic element of the framework was illustrated through the different game modes that created a playful storyline experienced by the students, which fosters emotional security building on MR and MA.

The Blooket games were designed to directly align with the gamification framework of Werbach and Hunter (2015) to incorporate points, collaboration, leaderboards, instant feedback, to nurture self-efficacy, and in return foster MR with the intention of mitigating MA by creating a holistic narrative and opportunity for progression.

The intervention was carried out over an 8-week period where Blooket was integrated into the experimental groups daily classes offering an interactive engaging learning experience that emphasised on feedback, reinforcement of content, and collaboration. The content covered in the experimental group mirrored that of the control group and was delivered by the same teacher in order to ensure consistency. What differed between the control and experimental group was the delivery method—the control group experienced traditional teaching methods using textbooks, written homework, and no opportunity of class collaboration. Whereas the experimental group engaged in the same lesson but received instructional delivery and practice questions/tasks through online games. The content of the practice questions that both of the groups engaged in were identical; however, the means in which they were answered differed (i.e., the control group wrote their answers, whereas, the experimental group practiced questions using Blooket).

3.3. Participants

The participants of this study consisted of 100 first-year, second-level students in four classes within a secondary school in rural Ireland. First-year students are typically 12–13 years of age in their first year in secondary school in Ireland, more commonly known as post-primary school. Typically, though not always, students are placed in a mainstream class when entering post-primary school, with streaming based on ability occurring in the second year of education, carried out at the school’s discretion. The experimental and control group were established quasi-experimentally. The class groups had been carefully selected by the school’s senior management team to ensure balance in gender, academic performance, and class size. The four classes that took part in the study were randomly assigned to the control teaching methods and experimental intervention. Students chosen for the study had access to advanced technological resources such as Chromebooks and student computers to effectively implement Blooket into the mathematics classroom.

First-year students were selected for this study based on an array of reasons, the key one being that first-years are placed in classes of mixed ability upon entering post-primary school. This structure allowed for the assessment of the impact of Blooket on students of all abilities along with increasing the generalisability of the findings. In addition to this, the first year was deemed most appropriate due to the time flexibility that the curriculum allows. While other year groups are quite time-sensitive due to the enormous course content that is involved, first-year students are given the opportunity to engage in teaching and learning without the immense time pressure that other year groups encounter. With this in mind, two cycles of research took place. In the first cycle, 25 students acted as the experimental group and were exposed to teaching and learning through the use of Blooket. The second class of 25 students acted as the control group and were subjected to more traditional teaching methods, which focused on teacher-directed classes with little resources other than the traditional textbook and freedom of collaboration. Both the experimental and control group were taught by the same teacher.

As part of the qualitative component of this study, a focus group was held with 21 teacher participants in order to explore the personal experiences from teachers using game-based design learning in the classroom. The focus group had the objective of providing teachers with the opportunity of sharing their professional opinions on the employment of educational games in the classroom. Participants volunteered to take part in the study and the opportunity to volunteer was given to all teaching staff in the school of study. The focus group lasted for 30 min and was hosted by the principal investigator. The focus group consisted of open-ended questions that provided opportunities for fluency in conversation amongst participants. The focus group was audio recorded and transcribed ahead of thematic analysis of the script.

The focus group and broader study is underpinned by the Technological Pedagogical Content Knowledge (TPACK) framework (Mishra & Koehler, 2006), which outlines the effective integration of technology in teaching (Taopan et al., 2020). TPACK directly aligns with the focus of this study through its three-element framework: technological knowledge, pedagogical knowledge, and content knowledge. The integration of online game-based learning in the classroom requires time and the correct teacher knowledge for the smooth and effective implementation into the classroom (Hsu, 2015). Furthermore, TPACK’s three-pillar framework directly aligns with this study.

Technological Knowledge: Blooket—gamification framework: component, mechanic, dynamic (Werbach & Hunter, 2015), and teacher focus groups on the implementation of digital gaming in the classroom.

Pedagogical Knowledge: Teachers given the opportunity to voice their opinion on their interest of PD opportunities regarding gamification.

Content Knowledge: The curriculum content being taught and integrated in the Blooket games reflects the content knowledge aspect of the study.

As previously mentioned, the focus group took a semi-structured format that was directed using open-ended questions that included the following:

• Are you aware of educational gaming software such as Kahoot, Blooket, or Quizizz?
• How often, if ever, do you use such tools in the classroom and what has your experience been?
• What is your opinion on the use of educational gaming tools to meet learning objectives of the curriculum, and do you think it supports or hinders achieving learning outcomes?
• How confident are you with utilising technological gaming tools in the classroom on a regular basis?
• What PD on gamification have you engaged in, or would you be willing to engage in, and in what medium is most appropriate for delivery?

The above questions provided flexibility in conversations whilst simultaneously encouraging discussions amongst the group. On completion of the focus group, the discussion was transcribed and coded by thematic analysis using the software NVivo 15.

3.4. Intervention

The study involved an experimental group that was exposed to the Mathematical Resilience Enrichment Course and a control group that was subject to traditional teaching methods in a lecture-style class utilising resources such as textbooks and written assignments. In the experimental group, students received instruction on how to use the software Blooket (Season 6) to ensure that all participants’ understanding of the platform was universal. The Blooket games, designed by the principal researcher, which directly aligned with the school’s scheme of work and national curriculum, were played during class time. The participants engaged in playing multiple games that incorporated various answering formats such as true/false, multiple choice, and short-answer questions.

Simultaneously, the control group received a traditional teaching approach, which typically involved teacher-led instructional lessons utilising textbook activities and written assignments. The lessons also incorporated direct instruction and passive learning experiences with little opportunity for collaboration or interactive participation from the students in their teaching and learning of the curriculum.

3.5. Tools and Resources

A multipart questionnaire was issued to participants in the experimental and control group, both pre- and post-intervention. The questionnaire consisted of two scales for the student participants; to address the research questions, it was essential to utilise questionnaires that were specifically tailored to MR and MA. With this in mind, the Mathematical Resilience Scale (MRS) (Kooken et al., 2016) and the Mathematical Anxiety Scale (MAS) (Betz, 1978), along with some contextual questions such as name, class, etc., were used to measure the changes encountered from the intervention. The teacher participants engaged in one focus group to express their thoughts on PD in utilising game-based design elements in the classroom. In addition to this, semi-structured interviews were conducted in groups for the student participants. The data collected were analysed and compared using the statistical software SPSS (Version 29.0.2.0 (20)) and NVivo 15.

3.6. Mathematical Resilience Scale

The Mathematical Resilience Scale (MRS) is a 24-item scale developed from the MR construct (Johnston-Wilder & Lee, 2008, 2010) by Kooken et al. (2016). The MRS is divided into three categories: value, struggle, and growth. The participants responded to the 24-item survey using a 7-point Likert scale, with 7 being strongly agree, 5 I do not know, and 1 being completely agree. Regarding the scoring, 18 questions are scored 1–7, whilst 6 statements have reversed scoring (i.e., 7–1). There are 8 value-categorised items on the scale, meaning value scores range from 8 to 56 (V1–V8); this domain measures the participants’ views of the importance and significance of mathematics. There are 9 struggle questions scoring from 9 to 63 (V1–V9); this category measures the participants’ understanding of the aspect of challenge involved in problem-solving and mathematics. Finally, the growth section contains 6 statements scoring from 7 to 49 (G1–G7), which calculates the level of growth mindset one has in performing mathematical tasks. Items G2–G7 were reversed scores in correspondence with Kooken et al. (2016), resulting in the overall score range of 24–168. The higher the score obtained by a participant, the stronger mathematically resilient that individual is.

3.7. Mathematical Anxiety Scale

The Mathematical Anxiety Scale (MAS) (Betz, 1978) is a 10-item scale with 5 positively worded and 5 negatively worded statements based on feelings and emotions that one may encounter while studying mathematics. The scale contains statements that refer to carrying out mathematics both in class and in test situations. The participants respond to each statement using a 5-point Likert scale, with 5 being strongly disagree, 3 undecided, and 1 strongly agree. Likewise, with the MRS, the MAS score is calculated using a reverse scoring system where the negatively worded statement responses are reversed in score (i.e., 5–1) and then summed together. The higher the score, the higher the MA, although Mahmood and Khatoon (2011) suggested that the scale illustrates different levels of MA—scores exceeding 32 are seen as a high level of mathematically anxious students that can be clearly observed by others while scores exceeding 27 also shows mathematically anxious students; however, they may not be as easily observed by others yet still present and causing issues.

3.8. Research Procedure

As previously mentioned, the study consists of two groups—the experimental group and the control group—with each group containing 25 students. Each cycle entails one control and one experimental group, meaning 50 participants engage in one cycle of the intervention. Each cycle runs for 8 weeks, where participants engage in three 1-h classes per week, totalling 24 h of intervention.

Experimental Group Treatment: The experimental group was introduced to Blooket prior to the intervention to ensure the participants’ baseline understanding levels for consistency and fairness when playing. The principal investigators designed games on Blooket, which directly aligned with the course curriculum. The participants engaged with playing games on Blooket using school-provided Chromebooks or, alternatively, desktop computers located in computer rooms in the school. The games incorporated various answering formats such as multiple choice, short answer, and true or false to enhance students’ thought processes and engagement in the activity. Instant feedback provided by the software was known to help motivation and with the participants’ level of engagement. The teacher used the platform’s features to measure the students’ progress and academic achievement.

Control Group Treatment: The control group received traditional teaching methods that typically involved teacher-led lecture environments employing resources such as textbooks along with written classwork and homework. The teacher presented the curriculum through verbal explanations and notes that were recorded in the students’ copy books. Regarding classwork and homework, the students were instructed to complete written assignments independently based on exercises illustrated in the textbook. The overall teaching of the control group incorporated direct instruction with reduced collaborative and interactive activities.

3.9. Quantitative Data Analysis

A quasi-experimental approach was integrated into this action research study to investigate a cause-and-effect relationship between using Blooket in the mathematics classroom and its impact on students’ MR. This paper reports of two cycles of intervention containing 50 participants in each cycle: 25 in the experimental group and 25 in the control group.

To ensure equivalence between the experimental and control groups in each cycle, independent sample t-tests were conducted on the quantitative findings on the MRS and MAS pre-intervention. The results of these tests are presented in

Table 1. Illustrates the equivalence between the experimental and control group pre-intervention MRS score.

Tool	Group	N	Mean	S.D	t-Test	p
MRS Cycle 1	Experimental	25	112.88	11.293	0.849	0.404
	Control	25	111	8.737	0.849	0.404
MAS Cycle 1	Experimental	25	31	7.450	0.205	0.839
	Control	25	31.36	5.423	0.205	0.839
MRS Cycle 2	Experimental	25	91.36	14.989	0.785	0.218
	Control	25	94.64	14.546	0.785	0.218
MAS Cycle 2	Experimental	25	34.16	4.041	−0.113	0.455
	Control	25	34	5.8	−0.113	0.455

. There were no statistically significant differences between the paired groups on the pre-intervention scores on the MRS and MAS as outlined by the p-value that is less than the chosen level of significance (0.05). This suggests that the students in both groups had the same resilience and anxiety towards mathematics prior to the intervention. Thus, subsequent differences achieved post-intervention can be confidently attributed to the utilisation of Blooket in the mathematics classroom. Knowing this pre-existing equivalence between groups strengthens the credibility of any differences in data post-intervention, attributing them to the work of the intervention and the impact of Blooket on the students’ MR.

Group statistics for the MRS and the Mathematics Anxiety Scale (MAS) across two cycles are illustrated in Table 1. There was no statistical difference between the experimental and control groups pre-intervention as outlined in Table 1, thereby establishing baseline equivalence. Although the independent t-tests illustrated no significant difference between the experimental and the control groups, the principal investigator performed an ANCOVA test to allow for minor baseline differences between the two groups. Importantly, MA is seen as the barrier in this study with MR acting as the construct being nurtured within the students through the intervention, as building MR can have the potential to proactively lessen MA within mathematical students (Johnston-Wilder & Lee, 2010).

3.10. Qualitative Data Analysis

Qualitative data were collected to contextualise the study and provide a more in-depth analysis (Creswell & Creswell, 2019) of the impact of gamification on students’ MR and MA whilst exploring educators’ interest in PD of gamification in the classroom. Qualitative data were collected through semi-structured interviews from the student participants throughout the 8-week intervention. Teacher participants engaged in one focus group, which gave an insight of the teachers’ perspective on using game-based design elements in the classroom and on teachers’ interest in potential PD opportunities. The interviews took place during school hours in a quiet classroom to ensure the confidentiality of the participants. The questions were open-ended designed to encourage conversation amongst the participants.

Both the student interviews and teacher focus group were thematically analysed using Braun and Clarke’s (2006) 6-phase thematic analysis approach. The first stage included familiarity with the transcript and initial note taking of any emerging patterns. The initial codes were then identified following the initial themes. Finally, reviewing, defining, and naming the themes took place before the write-up stage took place. All qualitative data analysis took place on the qualitative data analysis software—NVivo.

3.11. Students’ Experience with Game-Based Learning

All students in the experimental group engaged in semi-structured interviews over the course of the intervention that provided an insight into the students’ perceptions of the interventions. The interviews followed a structured, yet free-flowing format where participants answered open-ended questions that encouraged participation in sharing their experiences of gaming in the mathematics classroom.

The interviews were transcribed and read numerous times by the PI to familiarise any emerging patterns and themes. Initial codes were then manually identified followed by identifying themes looking at the entire dataset. Finally, the PI produced a narrative through the qualitative data transcript, themes, and codes that were identified, such as increased motivation to engagement in the teaching and learning taking place. Furthermore, willingness to collaborate was another key theme that was evident throughout the transcripts. Subsequently, participants said that the use of gamification in the mathematics classroom has transformed traditional teaching methods into a more accessible and enjoyable learning experience. One student claimed that she “loved seeing the leaderboard. Even if I wasn’t on the top I still wanted to try again”. This statement from the student backs the idea of competitiveness and motivation to persist in the face of challenges. Various students $(n=12)$ expressed a desire for collaboration during mathematics gamified classes with one student claiming “I preferred playing [Blooket] when we were put in teams because I wanted to do well for the rest of the group and I seen how I wasn’t the only one getting questions wrong”. Similarly, a different student explained how they “liked playing against other teams and it was good to see how other people were doing the questions”. This idea of connection through collaboration that was created through game-based designs and directly aligns with the tenets of MR (Johnston-Wilder et al., 2015) assisted in nurturing MR whilst also proved a shift in mathematical attitudes amongst the students and recognising mistakes as learning opportunities.

3.12. Teachers’ Experience with Utilising Game-Based Learning

To understand teachers’ perspectives on utilising gamification in the classroom, a focus group was conducted. During the focus group, teachers shared prior experiences with gamification in their classrooms, what instructional game-based tools are available, and the level of student engagement with game-based learning. Subsequently, teachers expressed interest in potential PD opportunities and expressed concern about a lack of confidence and knowledge on using technological teaching strategies. Teacher focus groups were thematically analysed using the same method that was used for the student semi-structured interview (Braun & Clarke, 2006).

4. Results

Various statistical methods of data analysis were utilised to address the research questions. To assess the effectiveness of implementing Blooket in the mathematics classroom to foster mathematical resilience amongst second-level, first-year students (the first research question), the mean and standard deviation of the MRS and MAS were computed.

Mathematical Resilience Scale (MRS)

The participants’ MR was measured using the MRS (Kooken et al., 2016). A total mark was analysed followed by a more in-depth analysis based on the three subheadings of the scale: value, struggle, and growth defined by Kooken et al. (2016). With this in mind, the overall score ranges from 24 to 168; although the study (Kooken et al., 2016) did not determine any scores that categorise users as mathematically resilient, further studies claim that users scoring less than 67 have low resilience, 67–117 moderate resilience, and 118 or above are seen to be highly mathematically resilience. The higher the score obtained by a participant, the stronger the individual’s MR.

From cycle 1 of the 25 participants to complete the MRS in the experimental group, 15 (60%) students’ overall scores increased, 10 (40%) students’ scores decreased, and no students’ scores remained unchanged. All 25 participants scored in the upper half of the scale in the first cycle (i.e., scoring 72 or above). In the control group, 21 (84%) students’ scores slightly decreased over the 8-week period and 4 (16%) students’ scores remained the same. Paired t-tests were used to determine the statistical significance of differences in mean scores between pre- and post-intervention.

From cycle 2 of the 25 students to complete the MRS, 23 (92%) students’ overall scores increased, although various scores had a very slight increase, 2 (8%) students’ scores decreased, and no students’ scores remained the same. Unlike cycle 1, 2 (8%) students’ initial scores that were recorded pre-intervention lay in the lower half of the scale. The control group findings reported like that of cycle 1’s control group; 17 (68%) students’ scores experienced a very slight decrease over the 8-week period whereas, 8 (32%) students’ scores remained unchanged.

The null hypothesis stated that there was no significant difference between the means, and was tested under a 95% significance level; hence, a p-value below 0.05 would be rejected. Results of the paired t-tests on the experimental group in cycle 1 and 2 are outlined in

Table 2. MRS Paired t-test results.

Cycle	Pre-Intervention		Post Intervention		p-Value	Null Hypothesis
	Mean	SD	Mean	SD
1	112.88	11.293	119	17.557	0.093	Fail to reject null
2	91.36	14.989	120.36	13.829	0.001	Reject null

.

The result of the paired t-test from cycle 1 rejected the null hypothesis. The mean score increased marginally over the course of the intervention.

While prior research, although limited, has measured the three categories of the MRS a single paradigm during analysis, the validation study by Kooken et al. (2016) examined each category individually, particularly regarding the research participants and their prominence to MR. With this in mind, the principal investigators also examined the findings from each individual category from the MRS with the intention of gaining an insight on the participants’ responses to each of the three domains: value, struggle and growth. The division in the scale allows for comparison of particular areas of growth from pre- and post-intervention results. Paired t-tests were once again utilised to establish the statistical significance of differences in mean scores between the various cycles of intervention.

All three paired t-tests calculated for the domains value, struggle, and growth in cycle 1 found two statistically significant change in the participants’ scores as illustrated in

Table 3. MRS value, struggle, and growth comparison of pre and post-test.

Category	Cycle	Pre-Intervention		Post-Intervention		p-Value	Null Hypothesis
		Mean	SD	Mean	SD
Value	1	39.28	5.62376	43.68	8.59127	0.058	Fail to reject null
	2	37.36	9.214	43.64	6.707	0.009	Reject null
Struggle	1	44.56	8.1825	49.64	8.33107	0.021	Reject null
	2	29.16	6.944	52.04	6.74833	0.001	Reject null
Growth	1	29.04	6.00333	25.68	7.28995	0.067	Fail to reject null
	2	28.04	8.339	24.68	7.459	0.194	Fail to reject null

. Students’ initial mean scores on the MRS show evidence of a strong prior MR. In cycle 2, however, there was only one statistically significant difference in pre- and post-intervention scores and that was in the struggle domain of the questionnaire. Students in the experimental group also engaged in semi-structured interviews to voice their opinions and perceptions experienced over the course of the intervention. Groups of students from the experimental group engaged in these semi-structured interviews with the PI. The interviews were thematically analysed under Braun and Clarke’s (2006) framework where the dominant themes that arose were “increased motivation” and “desire for collaboration”. One student claimed, “I didn’t feel as stupid as a normal when I got a question wrong, I just wanted to be sure I got it right the next time … it is way better [practicing maths] this way than in our copies as you actually want to try again”. This student showed both motivation for engagement and persistence when faced with challenges in the content. In addition to this, he shows a shift in attitude in his emotions towards the subject, comparing his feelings when carrying out mathematical activities in a traditional instruction as opposed to a gamified teaching strategy.

The results from both cycle 1 and 2 as referenced in

Table 4. MAS Paired t-test results.

Cycle	Pre-Intervention		Post Intervention		p-Value	Null Hypothesis
	Mean	SD	Mean	SD
1	31	7.45	27.2	6.627	0.003	Reject null
2	34.16	5.8	23.64	5.438	0.001	Reject null

prove a statistically significant reduction in MA on completion of the intervention. In cycle 1, the mean dropped from 31 (SD = 7.45) to 27.2 (SD = 6.627) after the intervention, with a p-value of 0.003 preceding to rejecting the hypothesis. Similarly, in cycle 2, the mean decreased from 34.16 (SD = 5.8) to 23.64 (SD = 5.438), with a p-value of 0.001 also indicating rejecting the null hypothesis. These findings suggest that the use of gamification in the classroom alleviates students’ MA.

During the focus group with teachers, the participants spoke positively about their prior experiences with gamification in their teaching practice; however, they expressed deep concern about the long-term effects of teaching through game-based designs. Although implementing technological games in the classroom serves as a great tool for motivation alongside enhancing student motivation, the long-term effects of achieving learning objectives, and preparing students for state examinations, remain a concern of educators. Upon a thematic data analysis (Braun & Clarke, 2006) of this focus group using the software NVivo, various recurring themes appeared and were coded including lack of digital fluency (19 of 21 participants—90%), increased student participation in classroom activities (15 of 21 participants—71%), and fear of technological-based design teaching methodologies (14 of 21 participants—66%), which reflect the gap that the TPACK recognise as crucial for the effective integration of technology in teaching and learning (Mishra & Koehler, 2006). The teachers that participated in the focus group established the potential of gamification in the classroom from prior experiences, with one teacher saying, “I find that weaker students’ who tend to find maths challenging, boring and uninterested to come into the classroom let alone participate in the classroom activities suddenly seem excited and motivated to take part in the class when I use Kahoot during class”. Subsequently, teachers claimed that the utilisation of Kahoot in the classroom provides immediate feedback on questions. Alongside this, the same teacher claimed that students tend to be more motivated in redoing the questions in order to rectify errors made.

Although the teachers that participated in the focus group valued the positive impact that gaming had on students’ quality of learning, they also highlighted the negative associations with the instructional tool, particularly around the timing constraints involved with making the game alongside the timing pressure for course curriculum completion. One teacher voiced their concern that “whilst playing Kahoot or Blooket is very engaging and fun for the students in the class it takes me a massive amount of time to make a game that matches the course content that I intend on covering that day. Not only this, but the time pressure to get the course finished before the end of the year, it seems crazy for me to play games frequently during class as opposed to delivering content”. Subsequently, a different teacher claimed that she “loved the idea of incorporating a fun and engaging activity with her classes, particularly the weaker ordinary level students; however, it can be challenging to integrate this into the classroom effectively due to the lack of either computer rooms or working and charged chrome books the school offers”. Finally, numerous teachers explained their lack of expertise in basic computer applications let alone designing computer games.

Subsequently, the consensus from the group was the willingness to engage in PD in this area in order to upskill their technological competencies. Of the focus group, 80% (16 participants) favoured in-person PD as opposed to online training, with one teacher saying that “I feel more at ease asking questions during in person sessions than putting up your hand in a zoom call”. Others expressed that their engagement level during in person training was a lot higher than when online. Subsequently, one teacher claimed that she preferred in-person training; however, she is a lot more willing to sign up to training when it is available online and suggested that hybrid training may be the ideal scenario giving teachers the opportunity of engaging with both online and in-person PD and the freedom of convenience and opportunities for interactive learning experiences.

Overall, the focus group provided valuable insights into the teacher’s perspective of utilising gamification in mathematics pedagogy. The findings underpinned by the TPACK framework sanctioned the need for PD of gamification in second-level teachers.

5. Discussion

Throughout the intervention, students expressed a new excitement for engaging in the mathematics curriculum, claiming that gamification enhanced their motivation and participation levels as expected from Deterding et al. (2011) and J. Y. Lee et al. (2023). In return, the use of game-based design elements in the mathematics classroom resulted in a significant increase in individual MR; however, gamification can only impact students’ MR and achievement if implemented using effective pedagogical methods that is underpinned by the TPACK framework (Mishra & Koehler, 2006).

With regards to the RQ1, “What is the impact of utilising gamification on first year post primary students’ MR and mathematical anxiety in Ireland?”, the analysis of the MRS showed an overall increase in MR in the experimental group, particularly in cycle 2, showing a statistical significance $(p=0.001)$, suggesting that the implementation of Blooket in the mathematics classroom helps nurture MR of first-year students. Subdomain analysis offered additional insight to the study, the most prominent statistic being the struggle domain $\left(\mathrm{c}\mathrm{y}\mathrm{c}\mathrm{l}\mathrm{e} 1:p=0.021, \mathrm{c}\mathrm{y}\mathrm{c}\mathrm{l}\mathrm{e} 2:p=0.001\right),$ indicating that students are more comfortable with mathematical challenges. This aligns with the qualitative findings where students claimed they were willing to try again when getting questions incorrect, which shows a shift in mathematical attitudes conspicuously, aligning with a decline in MA. Similarly, the MAS findings were statistically significant $(\mathrm{c}\mathrm{y}\mathrm{c}\mathrm{l}\mathrm{e} 1:p=0.003, \mathrm{c}\mathrm{y}\mathrm{c}\mathrm{l}\mathrm{e} 2:p=0.001)$. These findings not only highlight the potential that game-based learning has on students in the classroom but also reinforces the importance of educators having the correct knowledge and skill to implement technologically innovative teaching strategies such as gamification in order to foster MR and mitigate MA of students.

Regarding RQ2, “What are post-primary educators’ perceptions of the advantages and challenges of integrating the educational gaming software Blooket into the classroom and, furthermore, is there a demand for teacher PD in gamification?”, the analysis of the focus group outlines the demand for PD in post-primary school educators. Teachers acknowledged that motivation and engagement levels significantly spike when technology and more specifically gamification is used during class time. Although teachers showed great enthusiasm to using gamification, the common trend amongst the group was the lack of confidence in utilising gamification in the classroom; thus, demonstrating the demand for continuous PD with the majority expressing their preference being in-person PD, although some advocated for a hybrid to accommodate different schedules.

As a result, offering PD sessions to teachers on gamification is a likely avenue for increasing teachers’ pedagogical knowledge that will help them to implement reformed curricula, which aim to develop students into mathematicians who have a productive disposition towards mathematics and can solve challenging real-world tasks that require resilience and a growth mindset.