The development of technology has brought significant changes in our daily lives, which has led to computational thinking (CT) becoming an essential skill for individuals in the 21st century [1]. This has led to increased attention to the integration of CT in education from the academic literature, which has recognized CT as a key component of digital literacy and considers it a critical skill for success in the modern workforce ^[2][3][2,3]. In response to this, many countries have developed policies and initiatives to promote CT education at all levels with different approaches: as a cross-curricular theme, as part of a separate subject (e.g., informatics) or within other subjects (e.g., Maths) [4].

Mathematics education has traditionally focused on developing students’ ability to perform calculations and solve problems [5]. However, the growing importance of technology in all areas of life has highlighted the need for a new set of skills in mathematics education, including CT skills ^[6][7][8][6,7,8]. CT has been defined as a set of problem-solving skills that primarily include decomposition, pattern recognition, abstraction and algorithmic thinking ^[9][10][11][9,10,11], which are essential for developing and implementing efficient and effective solutions to complex problems via thinking like a computer scientist [12], and whose solutions can be transferable to other contexts [13]. Several studies have acknowledged the potential of CT to enhance students’ mathematical thinking and improve their efficiency in learning mathematics ^[6][14][6,14], a relationship that seems to be reciprocal, as mathematical thinking also helps students solve problems in CT [15].

When it comes to learning CT ideas, the unplugged approach has emerged as an effective teaching strategy for cementing the understanding of CT fundamental principles [16]. This approach, which does not require the use of computing devices, has gained popularity, particularly among younger learners who may have limited experience with coding [11]. However, the potential of CT cannot be fully understood using only unplugged approaches, so they should be complemented with plugged approaches to transfer the CT principles and concepts to real situations and authentic problem solving [16]. This combined approach of unplugged and plugged activities has proven to be particularly effective with younger learners [17] and has been advocated to give students the opportunity to fully understand what computers are capable of as tools and prepare them to succeed in today’s society [16].

Technology plays a crucial role in shaping how students learn and interact with mathematical concepts too [18]. The inclusion of technology and innovative tools and approaches has great potential to enhance students’ math learning experience, including both their learning achievement as well as their motivation and attitudes ^[19][20][21][19,20,21]. Furthermore, the integration of ICT-rich learning environments in mathematics education can take many forms, ranging from the use of digital textbooks and online resources to the use of intelligent tutoring systems and gamified learning environments ^[22][23][22,23]. Therefore, given the rapid advancements in technology, it is imperative for educators to actively explore the potential of these tools and incorporate them into their teaching practices.

Gamification is one of the innovative tools with potential to enhance the learning experience in different educational contexts [24]. Briefly and broadly defined, gamification is “the use of game design elements in non-game contexts” ([25], p. 10), with the purpose of engaging people, motivating action or promoting learning [26]. Although the term should not be limited to digital technology, the overwhelming majority of examples of gamification are digital [25]. Gamification techniques have been proven to have the potential to enhance a range of different educational activities, including learning ^[27][28][29][27,28,29], assessment, feedback and interaction ^[24][27][24,27].

Werbach and Hunter [30] proposed a classification of gamification elements, with components, mechanics and dynamics forming the building blocks of gamified systems. Components, such as achievements, badges, points and leaderboards, form the base of the system and are the tangible elements that users interact with. Mechanics, such as feedback, competition, cooperation and rewards, shape the gameplay experience and drive user engagement. Dynamics, at the top of the pyramid, define the broader context and structure of the game, encompassing aspects such as narrative, constraints and progression. Components, mechanics and dynamics work together to create an immersive and engaging experience for users in gamified systems.

The main reason for efforts to use gamification in education has been its theoretical ability to leverage motivational benefits that can enhance learning [31]. The most common theory associated with gamification’s fundamental purpose, motivation, is self-determination theory (SDT) [32]. This psychological theory developed by Deci and Ryan in the 1980s [33] provides a framework for understanding human motivation and behavior, suggesting that individuals have basic psychological needs for autonomy, competence and relatedness, which need to be satisfied for intrinsic motivation to flourish. Intrinsic motivation refers to the internal drive to engage in an activity simply for the pleasure and satisfaction derived from the activity itself. On the other hand, extrinsic motivation refers to engaging in an activity for external rewards or to avoid punishment.

In the context of gamification, “deep gamification” is designed to promote intrinsic motivation [34] through addressing users’ psychological needs for autonomy, competence and relatedness [35]. It involves incorporating game elements that are meaningful, challenging and enjoyable to the user and that provide a sense of autonomy and control over the experience [36]. Deep gamification aims to create a more memorable and engaging experience for users through leveraging game mechanics that are more immersive and motivating. Examples of deep gamification could include creating a narrative structure, offering purposeful choices or providing opportunities for exploration and discovery [37].

In contrast, “shallow gamification” is typically more extrinsic in nature, relying on incentives and rewards such as points, badges or leaderboards (PBL) to motivate users [34]. PBL, one of the most widely used implementations of gamification [27], can be seen as a “thin layer” of gamification added to the top of the system [38]. Its primary focus is often placed on achieving specific goals or objectives such as earning points or climbing the leaderboard [27]. While these extrinsic rewards can provide initial motivation, they are not as effective in promoting sustained engagement and may even lead to a decrease in intrinsic motivation over time, as users become overly focused on the rewards rather than the task itself [39]. Examples of shallow gamification include social media platforms that reward users with a system of likes or educational apps that offer badges for completing lessons. In essence, a key determinant in differentiating between deep and shallow gamification lies in the alignment of shallow gamification with extrinsic motivation, while deep gamification is associated with fostering intrinsic motivation [34].

The implementation of gamification techniques in CT contexts has been sparsely investigated in the literature, especially in primary education [32]. In [40], a web-based game was designed for learning CT with visual programming. In the game, players were asked to program virtual robots and were rewarded with “stars” depending on the tasks completed.  The findings revealed that the majority of participants (20 undergraduate students studying computer science) expressed satisfaction with the game design and user interface, and that the game promoted CT learning and collaborative learning. Similarly, in another study [41], an online adaptively gamified course called Computational Thinking Quest was presented to 107 first-year undergraduate engineering and information and communication technology students. The results demonstrated that the completion of the gamified course led to improved CT assessment scores. Furthermore, a study by [42] investigated how a game-based teaching sequence based on the fundamentals of computer science could promote engagement in mathematical activities among 28 primary school children aged 10 to 12 years. The teaching sequence was structured into eight levels, with each activity being assigned points based on the execution and the ranking being determined by the team’s performance. The study found that after participating in ludic activities involving CT, the test group demonstrated a significant improvement in mathematical performance.