As information technology advances and drives global competition, countries need to prepare students with appropriate technical knowledge and communication skills to compete in the 21st century. One way to address this challenge is by incorporating Computational Thinking (CT) into the curriculum ((Bower et al., 2017) ; (Maharani et al., 2019) ). CT is one of the essential skills for successfully overcoming challenges in a complex society shaped by technological advances (Kale et al., 2018).

CT is a fundamental skill for students in education, equivalent to reading and numeracy (Zhong et al., 2015). This is supported by (Maharani et al., 2019), who state that integrating CT into the school curriculum generally enhances students' ability to think abstractly, develop algorithms, and apply logical reasoning. As a result, students are better equipped to tackle complex and open-ended problems. Activity-based learning strategies have been identified as an effective approach to improving adolescent cognition and guiding learning through manipulative activities and verbal interactions (Cho & Lee, 2017). CT is regarded as a key competency because students not only need to master subjects influenced by computing, but also must be able to apply them in everyday situations and in the global economic context.

Mathematics is one of the essential components of the school curriculum. Therefore, the integration of CT into mathematics instruction can enhance students’ conceptual understanding of mathematical content. Mathematics learning activities often require hands-on experience that help students develop their problem-solving skills (Maharani et al., 2021) ; (Sung et al., 2017). CT and mathematics share a mutually reinforcing relationship, where computational methods can enrich learning in mathematics and science. Conversely, mathematical and applied science context can be used to deepen students’ understanding and application of computational concepts (Budyastomo & Yusuf, 2024).

The primary reason for introducing CT in mathematics classrooms stems from the growing understanding that computerization is increasingly being applied across various fields of work. Mathematical ability is considered a key factor in predicting students' learning capacity. (Gadanidis, 2017) and (Rambally, 2017) argue that mathematical thinking plays an important role in the development of CT, as the process of solving mathematical problems is inherently constructive ((Benakli et al., 2017) ; (Junsay, 2016) ; (Maharani et al., 2020) ). This constructive process requires an analytical perspective to solve problems that are both unique and fundamental to students. On the other hand, to teach CT effectively, teachers must have a comprehensive understanding of CT. Mathematics teachers need to consistently integrate CT into their instructional practices. Therefore, it is necessary to examine and understand the CT abilities of prospective mathematics teachers, so that when they enter the teaching profession, they are truly prepared.

However, the implementation of CT in mathematics teacher education in Indonesia still faces various challenges. Research by (Pertiwi et al., 2025) indicates that the integration of CT in mathematics learning across Indonesian educational institutions remains limited and inconsistent. This issue is compounded by teaching approaches that tend to be uniform and do not take into account individual differences in cognitive styles. Cognitive styles, particularly field-dependent (FD) and field-independent (FI), play an important role in how individuals process information and solve problems. (Nicolaou & Xistouri, 2011) found that students with FI cognitive styles demonstrated stronger abilities in structuring and solving mathematical problems compared to their FD counterparts. In the Indonesian context, a study by (Hardiansyah et al., 2024) revealed that FI students are more capable of representing mathematical concepts abstractly, while FD students rely more on concrete representations. Unfortunately, current CT instructional approaches have not yet adapted to these cognitive style differences. As a result, the full potential of individuals in developing CT skills cannot be optimally realized.

Previous research has shown that the integration of CT in mathematics education has been a major focus over the past decade, particularly in the context of K-12 education and teacher training. A systematic review by 2023Ye et al. () highlights that CT-based approaches, such as project-based learning and visual programming (e.g., Scratch), can enhance the understanding of mathematical concepts such as geometry, patterns, and algorithms. However, the study also notes that integration of CT is not always equally successful across all areas of mathematics and that challenge remain in aligning computational thinking with traditional mathematical reasoning.

In addition, a literature review by(Mohmad & Maat, 2023) found that despite growing interest in CT-related activities among mathematics teachers, the number of studies specifically addressing CT practices in mathematics education remains limited. Most existing research has focused on the use of programming and robotics as tools to develop CT skills; however, few have explored how individual cognitive styles influence the application of CT in mathematics instruction. Research conducted by (Reichert et al., 2020) shows that mathematics teachers’ CT skills were still weak prior to receiving training. However, the study did not address aspects of teachers’ cognitive styles, even though their responses and adaptations to CT approaches are likely influenced by the way they process information (e.g., reflective vs. impulsive), their visual or verbal preferences, and their tendency toward global or analytical thinking.

Previous studies have highlighted the importance of integrating Computational Thinking (CT) into mathematics education and the need for approaches tailored to the individual characteristics of teachers.

However, there remains a lack of understanding regarding how the cognitive styles of prospective mathematics teachers influence the development and integration of CT. Therefore, by exploring the relationship between cognitive style and CT ability, this study aims to provide valuable new insights for designing more effective and personalized teacher training programs, while also enriching the existing literature on the integration of CT in mathematics education.

This research offers novelty by integrating two important domains that are still rarely explored explicitly in the literature: Computational Thinking (CT) and cognitive style, particularly in the context of prospective mathematics teachers. To date, most CT-related research in mathematics education has focused on evaluating the effectiveness of CT-based instructional approaches or developing CT-oriented educational tools. Meanwhile, studies that examine how variations in cognitive style influence CT abilities—especially among future mathematics teachers—remain scarce. Using an exploratory approach, this study aims to investigate how field-independent and field-dependent cognitive styles affect individuals’ tendencies to develop CT components such as decomposition, abstraction, and algorithms. These findings are expected to serve as a foundation for designing teacher training programs that are more adaptive and responsive to individual differences, and to contribute to the advancement of differentiated CT learning models in mathematics education. The CT indicators used in this study are presented in Table 1.

The research question is what is the level of CT ability in prospective mathematics teachers? What are the cognitive styles that prospective mathematics teachers have? What is the relationship between cognitive style and the CT ability of prospective mathematics teachers? What are the challenges and potentials in the development of CT based on different cognitive styles?

This section describes the approaches, strategies, and procedures employed in the research to achieve the objectives and address the research questions. The study aims to explore the computational thinking (CT) abilities of prospective mathematics teachers based on their cognitive styles.

The results showed differences in CT between FI (Subjects S1 and S2) and FD (Subjects S3 and S4). All subjects met the CT criteria, but Subjects S1 and S2 showed different tendencies compared to Subjects S3 and S4. FI subjects tended to be analytical and reflective, while FD subjects were more practical and focused on numerical strategies.

The results show that all four subjects (S1–S4) demonstrated good decomposition skills, albeit with different approaches. The field-independent (FI) subjects, S1 and S2, tended to break down the problem in a more systematic and structured manner. S1 employed algebraic symbolism to represent the problem abstractly, while S2 adopted a more numerical strategy, yet still organized the sub-problems based on the types of boxes. These findings are in line with (Suryanti & Masduki, 2024), who state that students with a field-independent (FI) cognitive style are able to divide problems into logical components based on the internal structure of the problem, and tend to use analytical and individualistic approaches in mathematical problem solving. On the other hand, field-dependent (FD) subjects (S3 and S4) were also able to perform decomposition, but with a more practical and contextual strategy. S3 began from box capacities (bottom-up), while S4 started from the total distribution of donuts (top-down). This corroborates the findings (Kozhevnikov et al., 2014) which explains that FD individuals are more dependent on the global context and less exploratory of the internal structure of the problem.

The FI subjects demonstrated excellent symbolic abstraction, as evidenced by their use of the general equation m = q × n + r. S1, in particular, emphasized generalizable forms of the model, indicating a strong capacity for abstract reasoning. This suggests that FI students possess a high ability to model concrete information into symbolic representations, a skill that is crucial for the development of CT. Research by (Fauzan et al., 2024) shows that FI students excel in abstraction and reversible thinking strategies, enabling them to formulate mathematical solutions with symbolic flexibility. In contrast, FD subjects (S3 and S4) demonstrated a preference for numerical abstraction—focusing on extracting relevant information and simplifying the problem context—but without utilizing algebraic symbolism. Their approach reflects a practical orientation toward problem solving rather than a symbolic or theoretical one. This is consistent with the findings of 2005Zhang and Sternberg () who stated that students with the FD style tend to choose concrete experience-based strategies over theoretical modeling.

In terms of pattern recognition, all subjects demonstrated good ability. FI subjects recognized patterns both procedurally and symbolically—for example, S1 applied a similar formula to all box types, while S2 identified patterns between box capacity and the remaining donuts. These findings support the research of (Alvinaria et al., 2022), who found that FI students operate at a multistructural to relational level in pattern recognition and are capable of forming generalizations from numerical or symbolic representations. Meanwhile, FD subjects recognized patterns through numerical and practical approaches. S3 demonstrated a deeper understanding through factorization, while S4 intuitively recognized patterns between box sizes and leftover donuts. This suggests that while FD students are able to recognize patterns, they tend to do so more effectively in visual or concrete contexts.

FI subjects (S1 and S2) demonstrated high algorithmic ability. S1 composed systematic steps using symbolic representations, while S2 arranged numerical steps explicitly and logically. This supports the findings of (Saraswati & Putranto, 2021) who stated that FI students tend to think algorithmically with a high level of planning and reflection and are capable of formulating solution strategies systematically. Meanwhile, FD subjects (S3 and S4) were also able to construct algorithms, but with a more practical approach based on real-world sequences. S3 exhibited strong process control and verification at each step, while S4 provided a more concise yet still logical sequence. These findings are consistent with(Kholid et al., 2020); (Nouri et al., 2020) who noted that FD students can form clear procedures when the problem context is concrete and tangible.

The S1 subject demonstrates strong potential as a prospective mathematics teacher with the ability to think computationally in a systematic manner. He could serve as a model in developing contextual problem-solving strategies based on computational thinking (CT) in the classroom. The subject exhibits a high level of CT ability, particularly in symbolic modeling and algorithmic structuring. This aligns with findings that effective CT training can enhance prospective teachers’ understanding of CT concepts, problem-solving, and algorithmic thinking skills (Avcı & Deniz, 2022) ; (Kite & Park, 2023) ; (Ye et al., 2023) ).

S2 is a subject with very high computational thinking (CT) ability and can serve as a model in developing CT modules that integrate algebraic and heuristic strategies. S2 represents a group of prospective teachers with strong symbolic modeling skills and can serve as a point of comparison to subjects who demonstrate more numerical or concrete thinking styles. S2’s CT strength is particularly evident in the integration of algebra and heuristic reasoning. This highlights the importance of integrating CT into teacher education, emphasizing the development of training modules that address both theoretical and practical aspects ((Kong, 2016) ; (Sengupta et al., 2013) ; (Yang & Lin, 2024), ; (Yang, 2012) ).

S3 demonstrates compatibility with a CT approach grounded in concrete numerical activities, such as the use of manipulatives or visualization-based heuristic strategies. To strengthen symbolic abstraction skills, S3 could be trained through tasks involving mathematical modeling or introductory programming (e.g., pseudocode). This subject tends to rely on concrete numerical reasoning in CT, making them well-suited for activity-based learning strategies that emphasize hands-on and visual learning. Research indicates that programming- and engineering design-based activities can enhance CT understanding among prospective teachers ((Saad & Zainudin, 2024) ; (Xu et al., 2022), ; (Yun & Crippen, 2025) ).

S4 can be viewed as a representative of the field-dependent cognitive style with strong computational thinking (CT) abilities. Appropriate CT learning strategies for this type of student include contextual, exploratory, and numerically concrete-based activities. S4 demonstrates that a practical, experience-based thinking style can lead to effective CT performance, even in the absence of symbolic abstraction. This subject reflects the characteristics of field-dependent learners who approach CT in an exploratory and context-driven manner. Learning strategies grounded in real-world problems and numerical reasoning have been shown to be effective in fostering CT among prospective teachers ((Agbo et al., 2021); (Angeli & Giannakos, 2020) ; (Umutlu, 2022) ).

Prospective mathematics teachers generally exhibit two main types of cognitive styles: field-independent (FI) and field-dependent (FD). The FI cognitive style is characterized by an analytical thinking tendency, the ability to separate information from its context, and a high level of independence in formulating problem-solving strategies. In contrast, the FD style relies more on external contexts, adopts a global thinking approach, and tends to depend on concrete examples and external assistance to comprehend information ((Herlina et al., 2023) ; (Nicolaou & Xistouri, 2011) ). In the context of mathematics learning, FI individuals are better able to identify essential information from problems and construct mathematical models independently, whereas FD individuals tend to perceive problems holistically without filtering for critical details.

The relationship between cognitive style and CT ability is highly significant. Research by (Suryanti & Masduki, 2024) shows that prospective teachers with a field-independent (FI) style tend to excel in the abstraction and algorithmic aspects of CT, as they are able to simplify problems into symbolic forms and think systematically. In contrast, prospective teachers with a field-dependent (FD) style demonstrate stronger abilities in solving concrete, numerical, and practical problems but often face challenges with abstraction and generalization. In other words, cognitive style plays a crucial role in shaping how individuals represent problems and develop solutions using a CT approach.

The development of cognitive style-based computational thinking (CT) also faces several challenges. One of these is the continued use of uniform learning approaches that fail to accommodate individual thinking preferences, which hinders the optimal development of CT skills, particularly in field-dependent (FD) individuals (Papadopoulos, 2020). Additionally, limitations in abstract thinking and a reliance on external guidance pose further obstacles for FD students in developing independent and flexible CT ((Fauzan et al., 2024) ; (Zhang & Sternberg, 2005) ). Nevertheless, there remains significant potential for CT development. By designing adaptive, cognitive style-based learning modules for both field-independent (FI) and FD learners, CT development can be personalized. Prospective teachers with an FI style may benefit from symbolic activities and programming, while those with an FD style can be supported through contextual, visual, and manipulative approaches ((Gadanidis, 2017) ; (Nouri et al., 2020) ). Integrating CT into mathematics teacher education curricula that take cognitive style into account is a strategic step in preparing future teachers who not only master content, but also think computationally and reflectively.

The results of this study confirm that cognitive styles influence students' CT, particularly in problem-solving approaches, symbolic modeling, and pattern recognition strategies. Field-independent (FI) students tend to be abstract, reflective, and analytical, whereas field-dependent (FD) students are more concrete, contextual, and numerically oriented. Prospective mathematics teachers with an FI cognitive style tend to excel in conceptual abstraction and algorithmic thinking, making them well-suited for programming-based CT development or symbolic modeling. In contrast, aspiring mathematics teachers with an FD cognitive style demonstrate strengths in practical decomposition and numerical pattern recognition, making them more compatible with visualization- and context-based CT approaches. These differences in cognitive characteristics indicate that although all four subjects successfully completed the CT tasks, the approaches they used reflected distinct thinking styles. This is important to consider when designing learning that adapts to students’ cognitive styles.

Among prospective mathematics teachers with a Field-Independent (FI) cognitive style, two primary tendencies in computational thinking (CT) were identified. The first is Symbolic-Structural CT, characterized by the ability to formulate solutions symbolically, structurally, and in a generalizable manner, as well as by logical thinking using formal models. The second is Reflective-Tactical CT, which involves breaking down and formulating solutions systematically, reflectively, and numerically based on symbolic logic. Meanwhile, among prospective teachers with a Field-Dependent (FD) cognitive style, two different CT tendencies also emerged. The first is Concrete-Procedural CT, a thinking style that relies on concrete numerical calculations and a sequence of practical procedural steps to solve problems. The second is Exploratory-Conceptual CT, which involves the use of numerically based exploratory strategies to produce intuitive and easily understandable solutions.

The practical implication of this study is the importance of differentiating CT-based learning according to students’ cognitive styles to enhance the effectiveness of teaching strategies. For example, FI students may benefit from algorithm-based challenges and mathematical modeling, while FD students are better suited to visual, concrete-numerical, or real-world context-based approaches.

Based on the findings of this study, it is recommended that future research develop learning instruments or Computational Thinking (CT) training modules tailored to the cognitive styles of prospective teachers. In-depth research using a mixed-method approach could be conducted to test the effectiveness of differentially designed CT-based learning strategies for individuals with both field-independent and field-dependent styles. Additionally, further studies could explore the relationship between CT and other variables such as metacognitive abilities, technology-based problem-solving, or digital teaching competencies. Large-scale classroom trials are also necessary to ensure the generalizability of findings and the sustainability of CT implementation in mathematics teacher education

We would like to express our sincere gratitude to all parties who have supported this research from beginning to end. The support, guidance, and contributions, both direct and indirect, have been invaluable to the smooth progress and successful completion of this study. We hope that all acts of kindness will be rewarded appropriately.