Computational thinking (CT) is an essential skill in the era of the 21st century ((Park & Kwon, 2022); (Selby, 2015)). Facilitating learning that enables students to cultivate critical thinking is a crucial aspect of mathematics education ((Fadel et al., 2015); (Vourletsis & Politis, 2020); (Yadav et al., 2017)). Various global organizations, including the European Commission, the United Nations Educational, Scientific and Cultural Organization (UNESCO), and the Organization for Economic Co-operation and Development (OECD), regard CT as a crucial competency linked to the growing demand for students' digital literacy skills, necessitating its prioritization in education and curriculum development ((Bocconi et al., 2022); (Lee et al., 2023); (O.E.C.D., 2018); (U.N.E.S.C.O., 2021)). International assesment, such PISA and TIMSS, have incorporated technological advancements by offering exam content and forms that necessitate CT abilities for accessing assessments and solving problems (Jameson et al., 2019).

The PISA 2022 findings indicate that Indonesian students' mathematics scores fall below the international average score (O.E.C.D., 2023) PISA evaluates students' competencies in problem-solving and reasoning ((Apriandi et al., 2023); (Rosana et al., 2020)). Consequently, PISA findings serve as a benchmark for evaluating students' competencies in addressing intricate problems and advanced reasoning. The capability of CT is evident in an individual's approach to solve mathematical problems (Supiarmo et al., 2022). The PISA results indicate that the CT abilities of Indonesian students are classified as low.

Previous studies revealed the students' shortcomings in CT abilities for addressing mathematical problems. A multitude of students struggles to dissect complex problems into manageable elements, faces difficulties in recognizing patterns, and finds it challenging to identify relevant information ((Hartawan et al., 2024); (Nurwita et al., 2022)). Further research reveals that students find it challenging to distinguish between familiar and unfamiliar material, translate problems into mathematical equations, perform procedures systematically and accurately, and commence evaluating the validity of the obtained solutions ((Vidad & Quimbo, 2021)). Moreover, students face difficulties in transforming data into variables, incorporating irrelevant knowledge to tackle challenges, and articulating real-world problems into mathematical terminology or models (Dwita & Retnawati, 2022). These results present a challenge in assisting students in the development of CT abilities. Proficiency in CT abilities will enable students to tackle more intricate and demanding mathematical problems.

A hallmark of 21st-century learning is STEAM-based education. STEAM is crucial for cultivating the competences required to navigate the 21^st century era. STEAM is a contextual learning approach that amalgamates various disciplines to guide students in cultivating problem-solving abilities, CT, and creativity ((Conradty et al., 2020); (Herro et al., 2022); (Karampelas, 2023)). Furthermore, the incorporation of STEAM in education can enhance student engagement, motivation, and academic performance ((Cabello et al., 2021); (Hong et al., 2020); (Juškevičiene, 2020)). Consequently, the inclusion of STEAM in education is anticipated to enhance students' CT abilities.

The implementation of STEAM-based learning is aligned with the Indonesia’s Curriculum which emphasizes on students’ 21^st century skills, including critical thinking, creativity, collaboration and communication (Kemdikbudristek, 2021-10-22). Previous research has examined the implementation of STEAM-based learning in Indonesia. In physics education, the implementation of STEAM-based learning enhances creative and critical thinking skills, facilitating students' comprehension of subjects (Amiruddin et al., 2022). The integration of STEAM-based learning in secondary school science has also enhanced conceptual mastery and creativity (Wandari et al., 2018). Furthermore, the implementation of STEAM-based learning can cultivate students' interest in STEAM courses and promote the integration of technology within the educational environment (Huda et al., 2024). Even though STEAM-based learning offers significant advantages in enhancing students' 21st-century competencies, its implementation in Indonesia faces several constraints. The majority of teachers are insufficiently informed on the principles and methodologies for executing STEAM-based learning (Roshayanti et al., 2022). The absence of specialized training, resources, insufficient learning materials, and support systems hinders the efficient implementation of STEAM approaches in educational settings (Amiruddin et al., 2022). Consequently, it is imperative to facilitate teachers in the integration of STEAM-based learning within their classrooms, for instance a module as part of learning material.

Rapid technology breakthroughs, such as augmented reality (AR), exert a substantial influence across all domains, including education. AR is a technology that facilitates the visualization of objects in the physical environment, enhancing the interactivity of the learning experience ((Lai & Cheong, 2022); (Sousa & Rocha, 2019)). The incorporation of augmented reality in education can assist students in comprehending complex and challenging problems (Sungkur et al., 2016). Furthermore, the integration of augmented reality can enhance communication abilities, mathematical reasoning, mathematical literacy, and CT abilities which essential for addressing complex problems ((Pujiastuti & Haryadi, 2023); (Schutera et al., 2021); (Suwayid Alqarni & Rezqallah Alzahrani, 2022)). Unfortunately, the integration of technology in education in Indonesia faces several significant challenges that hinder its effectiveness and accessibility. Students face internal challenges like self-regulation and digital literacy. Besides, teachers also struggle with skills and experience in IT-based learning (Rasimin et al., 2024). Moreover, limited access to technological resources, especially in remote areas, lack of training program, technical support, and lack of time poses a significant barrier to effective technology integration (Habibi et al., 2020)(Habibi et al., 2023). Therefore, it is imperative for all stakeholders to facilitate teachers to integrate technology into education. This research merged AR technology with STEAM-based modules to provide teachers with learning materials aimed at enhancing students' CT abilities.

Various strategies have been employed to foster students' CT abilities, including the use of virtual reality (VR)-based gaming media ((Agbo et al., 2023); (Sukirman et al., 2022)(Sukirman et al., 2024)), augmented reality (AR) ((Abdul Hanid et al., 2022); (Hanid et al., 2022); (Lin et al., 2021)), and integration with the STEAM approach ((Bati et al., 2018); (Sun et al., 2023); (Tan et al., 2021)). Previous studies revealed that integrating STEAM education with AR offers several key benefits. The integration AR in STEAM education has been shown to motivate students and enhance their understanding of key concepts ((Delgado-Rodríguez et al., 2023); (Demitriadou et al., 2020); (Wang et al., 2024)). AR also promotes students the use of CT by facilitating the decomposition of problems and the construction of logical answers. These competencies are essential throughout STEAM disciplines, equipping students for difficulties in both engineering and creative domains (Demitriadou et al., 2020). Nonetheless, the incorporation of AR in STEAM education is primarily focused on science education. There are few studies that concentrate on mathematical education. In this context, the integration of AR and STEAM in mathematics education is essential to cultivate students' 21st-century skills, particularly CT.

Learning modules that incorporate specific pedagogical strategies, i.e. discovery and project-based learning, can foster students' mathematical reasoning, critical thinking, communication skills, CT, and creativity, which are essential for addressing complex mathematical problems ((Khotimah et al., 2023); (Siregar et al., 2020);(Wardani et al., 2021)). Nevertheless, there is still room for further investigation into the development of mathematics learning modules that integrate STEAM-AR. Consequently, it is essential to develop a mathematics learning module that integrates STEAM-AR to enhance students' CT abilities.

However, the decision to integrate the innovative teaching methods in the classroom significantly influenced by the teachers’ perceptions ((Akram et al., 2022); (Boonmoh et al., 2021); (Celeste & Osias, 2024)). Positive perceptions can encourage the teachers to adopt the new instructional methods in the classroom, while negative views may hinder them ((Abel et al., 2022); (Al-Takhayneh et al., 2022)). In addition, the quality of students' learning can be influenced by teachers' perceptions and attitudes toward teaching and learning processes ((Edson et al., 2021)).

Thus, the current study investigates teachers’ perceptions about the need for STEAM-AR learning module to enhance the student's computational thinking. In addition, the influence of gender differences and teaching experience on teacher perceptions was also examined. To achieve this aim, six research questions were formulated, as follows:

The findings revealed that teachers recognize students' deficiencies in CT for solving mathematical problems. This view aligns with findings from prior research. Numerous students are unable to decompose intricate problems into manageable components, encounter challenges in seeing patterns, and find it difficult to ascertain which information is pertinent (Hartawan et al., 2024) (Nurwita et al., 2022). Additional research indicates that students struggle to differentiate between known and unknown information, convert problems into mathematical equations, execute procedures systematically and accurately, and initiate the assessment of the correctness of the derived solutions (Vidad & Quimbo, 2021). Furthermore, students encounter challenges in converting data into variables, including extraneous information to address difficulties, and translating real-world issues into mathematical language or models (Dwita & Retnawati, 2022). The teacher's insights and prior studies indicate a pressing necessity for the enhancement of students' CT abilities which is essential in the 21st century ((Park & Kwon, 2022); (Selby, 2015)).

Other findings revealed that students encountering challenges in solving mathematical problems that necessitate reasoning and critical thinking. Prior studies indicates that students facing obstacles in solving real-world mathematics problems ((Ali, 2021); (Baidoo & Ali, 2023)). Additionally, students continue to exhibit deficiencies in their ability to connect mathematical concepts to real-world contexts ((Pascual & San Pedro, 2018); (Tangkawsakul et al., 2024)) and in their problem-solving abilities ((Pavković & Marangunić, 2024); (Yeni et al., 2020)). In addition, prior research has also demonstrated that students encounter challenges when confronted with mathematical problems that necessitate critical and creative thinking abilities ((Dhungana & Thapa, 2023); (Polat & Aydın, 2020);(Silberman et al., 2021)). The study's findings align with teachers' perceptions of students' inadequate skills in problem-solving, critical thinking, creativity, and the application of mathematical principles to real-world scenarios. Consequently, the integration of STEAM-based learning is essential for cultivating the skills required to confront intricate future challenges

The incorporating technology in education is currently indispensable for enhancing the quality of the learning experience. Moreover, proficiency in technology is important alongside the progression of technological advancements. Teachers' high perception of student’s attitude toward the use of technology in the classroom aligns with earlier research showing students' positive responses to the use of technology in math classes ((Gallegos-García et al., 2022);(Gqoli, 2024); (Canilao et al., 2023)). Furthermore, the incorporation of technology in education also enhances students’ motivation(Canilao et al., 2023) and improves students' mathematical visualization skills (Aini Jaafar et al., 2022).

The finding also revealed that teachers typically possess a strong awareness of the importance of STEAM-AR oriented mathematics instruction modules. Numerous researchers have examined the necessity of modules to enhance the quality of learning. Primary school teachers necessitated STEM project-based learning modules to cultivate essential 21st-century abilities, including scientific literacy and critical thinking (Septiadevana & Abdullah, 2024). A survey of 124 prospective mathematics teachers revealed that 95% of respondents believe that the use of STEM-based mathematics modules can enhance the quality of mathematics instruction (Khotimah et al., 2021). Additionally, a survey of 146 high school students revealed a strong interest in mathematics learning combined with the STEAM approach (Muzakkir et al., 2024). They consider that the STEAM-based module is one of the best learning media for learning mathematics. The findings of prior studies align with the outcomes of the need’s analysis concerning the development of STEAM-AR modules (Table 7), which are at a high level. Consequently, STEAM-AR learning modules are essential for teachers to enhance the quality of education, specifically to cultivate students' CT abilities.

This study has yielded results indicating the necessity for STEAM-AR-based mathematics instruction modules to foster students' CT abilities. In sections B and C, the mean score instruments indicate a high level, suggesting that teachers perceive students as lacking proficiency in CT and STEAM-based learning activities. Then, in section D, the mean score instrument is at a high level, suggesting that the learning process will be of higher quality if integrated with technology. Additionally, learning modules that integrate the STEAM and technology approaches are much required as presented in section E. The research findings also indicate that there is no disparity in teacher perceptions concerning gender and teaching experience. This study's findings indicate that teachers must incorporate STEAM and technology in classroom instruction to foster students' CT abilities. Finally, students might gain confidence in addressing complex problems, particularly in the future workplace.

The researchers wish to express the gratitude to the Directorate of Research, Technology and Community Service (DRTPM), Directorate General of Higher Education, Research and Technology, Ministry of Education, Culture, Research, and Technology for funding this research activity under the Basic Research Scheme (Penelitian Dasar) in 2024, with the specified contract number: 007/LL6/PB/AL.04/2024, 196.34/A.3-III/LRI/VI/2024. We also express our appreciation to the teachers who wish to take part as responden.