Mathematics education in Indonesia, as in many other countries, plays a pivotal role in developing students’ logical reasoning, problem-solving ability, and critical thinking skills across educational levels ((Ashidiqi & Sugandi, 2023); (Coxbill et al., 2013); (Maulana et al., 2023) ). This is because of the importance of the benefits of mathematics in everyday life. Judging from the importance of mathematics, students must be serious about studying it at school ((Rohimah et al., 2017); Hasanah et.al., 2021). Cornelius identified five essential functions of mathematics: facilitating logical thinking, solving real-world problems, recognizing patterns and generalizations, fostering creativity, and promoting cultural awareness(Abdurrahman, 2012).

One of the primary goals of mathematics instruction is to equip students with the ability to address practical, real-life problems ((Abdurrahman et al., 2021) ; (Blomhøj & Jensen, 2003) ). This is in line with the opinion (Bardu & Beal, 2010) mathematical operations require the ability to solve problems. This objective aligns with the growing emphasis on mathematical literacy—defined as the capacity to formulate, apply, and interpret mathematics in a variety of contexts((Ashidiqi & Sugandi, 2023) ; (Yuberta & Firmanti, 2024) ). In Indonesia, the Ministry of Religious Affairs has initiated the Madrasah Competency Assessment (AKMI), a nationwide program designed to evaluate students’ competencies in literacy, numeracy, and character development. AKMI integrates Higher-Order Thinking Skills (HOTS) to measure how effectively students apply foundational knowledge, particularly through numeracy-based problem-solving. Literacy is defined as the ability to understand, use, evaluate, and reflect on various types of written text to develop the capacity of individuals as Indonesian citizens and contribute productively to society ((Kemendikbud, 2019); (Purwanto, 2021); Handayani, 2022).

Lamada et al. (2019) asserted that the progression of literacy warrants significant attention, as it constitutes a foundational competency essential for individuals to navigate future life challenges. Furthermore, mathematical literacy proficiency facilitates an individual's comprehension of mathematics' role and utility in everyday contexts (Puspitasari et al., 2015). Mathematical literacy is among the most crucial that numeracy is the ability to think mathematically, emphasising the use of mathematical concepts, procedures, facts, and tools to solve everyday problems in various relevant contexts for (Novitasari et al., 2020) ; (Pratama et al., 2019); (Sayekti, 2022) ). Despite these efforts, AKMI results have revealed that many students struggle with literacy and numeracy-based assessments. For instance, (Ratna Sari, 2021) reported that students' performance in geometry questions within the numeracy section was especially low, with only 17.65% achieving correct answers. Such findings point to underlying issues in students' mathematical thinking processes. Understanding the specific nature of these difficulties is essential. Error analysis provides a powerful lens through which teachers and researchers can identify common misconceptions, faulty reasoning patterns, or procedural mistakes. This analysis not only facilitates targeted remediation but also informs pedagogical strategies to support diverse learners ((Chen, 2022) ;(Din, 2020) ).

However, analyzing student errors in computer-based tests like AKMI presents unique challenges, as students’ step-by-step reasoning is not always visible. Therefore, this study aims to investigate the types and patterns of mathematical errors made by students when answering numeracy and literacy-based questions, using a qualitative approach that includes written responses and follow-up interviews. The findings will contribute to improving mathematics instruction, especially in integrating literacy and numeracy skills in primary Islamic education settings.

Furthermore, it is important to acknowledge that identifying student errors in the context of literacy and numeracy-based assessments like AKMI (Madrasah Competency Assessment of Indonesia) presents its own challenges (Arriah & Romba, 2023). The computer-based nature of the test makes it difficult for teachers to directly observe students' thought processes and identify the specific steps where errors occur. Therefore, in-depth research that specifically analyzes student responses to AKMI questions becomes crucial. This analysis should not only focus on final incorrect answers but also on the patterns of errors that emerge in partial answers or the reasons students provide. By understanding these patterns, teachers can gain a more accurate insight into the specific misconceptions or difficulties students face in applying literacy and numeracy skills in the context of integrated questions.

The implication of this need for in-depth error analysis is that teachers need to develop skills in interpreting assessment data, including AKMI data, effectively. This involves more than just looking at students' final scores (Rosyadi et al., 2021). Teachers need to be trained to analyze student responses to each item, identify commonly incorrect answers, and try to understand the reasoning behind these errors. For example, did students misunderstand information in the text of the question, have difficulty translating the problem into a mathematical representation, or make procedural errors in calculations? With good error analysis skills, teachers can design more targeted learning interventions that directly address the specific difficulties experienced by particular groups of students.

In addition, the AKMI results showing a trend of students' numeracy abilities at the C3 level in MIS AS-SUNNAH indicate the need for special attention to the development of this ability. Level C3 generally describes students' ability to apply mathematical knowledge and understanding in familiar contexts. To improve students' abilities to a higher level, learning interventions need to be designed to encourage them to think more critically, solve more complex problems, and apply mathematical concepts in less familiar contexts or those requiring the integration of various concepts. The analysis of student errors in answering literacy and numeracy-based AKMI questions can be an important starting point in designing effective interventions to improve students' abilities holistically.

This study employed a qualitative descriptive approach to analyze students’ mathematical errors in solving numeracy and literacy-based problems. The design was selected to allow in-depth exploration of students’ cognitive processes and error patterns through their written responses and verbal explanations. The participants comprised 15 fifth-grade students from a private religion elementary school at Kediri, East Java, Indonesia, during the 2023/2024 academic year. Purposive sampling was used to ensure a varied representation of ability levels. Students were grouped into three categories—low, medium, and high mathematical ability—based on the results of a diagnostic test. Grouping was guided by the standard deviation method as suggested by Arikunto (2006), with the average score and standard deviation used to determine the thresholds. The test sheet consists of two types of questions, namely, mathematical ability test questions and AKMI numeracy literacy test questions. hree instruments were used in this study: First, Mathematical Ability Test. This diagnostic test included: three questions on numerical operations (complex multiple choice), one item on basic statistics (true/false format), and a short-answer question on sequences and series. This test served to categorize students into ability groups and provided a baseline for their general mathematical proficiency. Second, AKMI-Type Numeracy Literacy Test. This consisted of three contextualized mathematical problems aligned with the AKMI framework, focusing on geometry and algebra. These items were designed to assess students’ ability to apply mathematical knowledge in real-life contexts. Responses to these items formed the core data for error analysis. Third, Structured Interview Guide. Follow-up interviews were conducted with selected students to clarify their reasoning and explore the thought processes behind their answers. This instrument allowed triangulation of data and provided insights into misconceptions that were not evident in written responses.

Based on the study by (Hidayat & Pujiastuti, 2019) and (Mulyati, 2016), student errors in answering story-based research questions are defined as deviations made by students in completing the given story-based questions, following Polya's problem-solving steps. The types of errors in the questions include: error in understanding the question, error in formulating a plan, error in carrying out the plan and error in inspecting the solution. A more detailed explanation of the indicators for each error type is presented in Table 1.

Based on the results of the general mathematical ability test, students were classified into three ability levels using the standard deviation method (Arikunto, 2006). The average score was 62.22, and the standard deviation was 18.72. The cut-off scores for classification were: high ability: > 80.94, medium ability: 43.5 – 80.94, low ability: < 43. From the total sample of 15 students: 3 students were classified as high-ability, 9 students as medium-ability, and 3 students as low-ability.

Information :

A: Error Understanding the Question

B: Error In Formulating Plan​

C: Error In Carrying Out The Plan

D: Error In Inspecting The Solution

E: Not Found Error

F: Question Not Answered

Based on the students' answers to the story-based questions, an analysis was conducted to identify the types of errors made by students and the percentage of each error type. The analysis revealed four types of errors: an Error in understanding the question, an Error in formulating a plan, an Error in carrying out the plan, and an Error in checking the solution.

Table 2 presents the findings on the four types of errors made by students in answering literacy and numeracy AKMI questions, based on the instrument administered by the researchers. The percentage of each type of mistake made by low-ability students is presented in Table 3 below. From Table 3, we can conclude that low-ability students most frequently made errors in formulating a plan, carrying out the plan, and checking the solution, with a percentage of 29.4%. In the Figure 1, we can see these students often wrote solutions without a clear order or made errors in determining the steps and calculations, leading to incorrect conclusions. Errors in checking the solution were also common, resulting in students not being able to arrive at the correct final answer. Students who made errors in understanding the question accounted for 5.88% of the total. The remaining 5.88% did not exhibit any significant errors in their work.

The percentage of each type of mistake made by high-ability students is presented in Table 5. From Table 5, it can be concluded that, in general, high-ability students did not experience significant difficulties in their work. This is evidenced by the fact that 62.5% of the answers were error-free. We can see in Figure 3 that across all ability groups, errors in geometry-related problems were the most prevalent.

One high-ability student (ST01), for example, made errors in planning, execution, and evaluation for a geometry-based task, suggesting that visual-spatial reasoning remains a challenge even for advanced learners. High ability student (ST01 and ST02) were able to formulate definitions and write arguments, as well as read and comprehend a problem and articulate it into an idea, despite making multiplication errors(execution). Consequently, their derived conclusions were incorrect. Therefore, interviews were conducted with ST01 and ST02 as follows:

Based on the results of the mathematical errors, students with low ability have erorr in understanding question 5.88% but medium ability and high ability there is no problem with this case. All students have problems in formulating plan, carrying out the plan, and erorr in inspevcting the solution with the percentages showing 29.40% for low ability, 25% for medium ability and 12.50% for high ability. We can see all the problems in the graphic below.

This study analyzed students' mathematical errors in solving literacy- and numeracy-based problems from the Indonesian Madrasah Competency Assessment (AKMI). Using Polya’s four-stage problem-solving framework, the findings reveal a consistent trend across ability levels: the most frequent errors occurred in the stages of devising a plan, carrying out the plan, and checking the solution, rather than in understanding the problem. This suggests that students can comprehend problem statements but face challenges in strategy formulation, procedural execution, and solution validation.

This study examined the types of mathematical errors made by fifth-grade students at a private religion elementery school in solving literacy- and numeracy-based questions from the Indonesian Madrasah Competency Assessment (AKMI). By analyzing student responses using Polya’s four-stage framework, several key findings emerged: low-ability students most frequently made errors in devising a plan, carrying out the plan, and checking the solution, with each error type comprising 29.4% of their total errors. Errors in problem comprehension were minimal (5.88%), indicating basic reading ability but difficulty in applying mathematical strategies. medium-ability students also showed consistent issues in the stages of planning, execution, and checking, each accounting for 25% of their total errors. These students demonstrated adequate comprehension of problem statements but struggled with mathematical reasoning and accuracy. high-ability students generally performed well, with 62.5% of their responses error-free. However, errors still occurred in complex items, particularly in geometry-based problems, indicating areas for targeted reinforcement. Overall, geometry emerged as a significant challenge for students across all ability levels. The results underscore the importance of implementing instructional strategies that strengthen students’ conceptual understanding, procedural fluency, and reflective thinking.

The authors would like to thank Universitas Muhammadiyah Malang, Mathematics Education Study Programme, mathematics education experts, teachers, and students who have been involved in the development and validation of mathematical abstraction test instruments.