PRISMA (Online ISSN: 2614-4611; Print ISSN: 2089-3604) is an academic journal published twice a year (June and December) by Universitas Suryakancana in collaboration with the Indonesian Mathematics Educators Society (I-MES). The journal focuses on mathematics education and scholarly inquiry into the teaching and learning of mathematics. Its scope includes mathematics learning models, instructional media, curriculum in mathematics teaching, assessment and evaluation, ethnomathematics, didactical design, and lesson study in mathematics learning. PRISMA has been accredited at SINTA 3. Submitted manuscripts must be original research articles, written in English, and not under consideration by other journals or conferences. All submissions must follow the author guidelines and will undergo a double-blind peer review process.
More Than AI: Developing Intelligent Chatbot to Empower Algebra Mastery for Grade VII Students
The challenge of learning algebra for junior high students necessitates innovative educational tools. This study aimed to develop and evaluate an intelligent chatbot, powered by a fine-tuned Mistral AI model, to empower algebra mastery for Grade VII students. R&D methodology using the ADDIE model was employed, involving one expert validator, 20 students, and 5 teachers for the evaluation. Data were collected through questionnaires and a post-test. The findings revealed that the chatbot was highly successful, achieving an expert validation score of 91.11% ("Very Valid") and a user practicality score of 84.42% ("Very Practical"). Furthermore, the chatbot was proven effective, as 84% of students achieved the classical mastery threshold on the post-test with a class mean score of 82.0. This research concluded that a specifically customized AI chatbot is a valid, practical, and effective medium for mathematics education.
Copyright (c) 2026 PRISMA https://creativecommons.org/licenses/by-sa/4.0
Algorithmic Reasoning: A Type of Imitative Reasoning in Solving Geometry Problems
This study aims to describe imitative reasoning of the algorithmic reasoning type among junior high school students in solving mathematics problems. Imitative reasoning is a way of thinking that follows procedures that have been taught without fully understanding the underlying concepts of the strategies. Meanwhile, algorithmic reasoning refers to imitative reasoning that relies on recalling strategies learned in previous lessons. This research employed a qualitative descriptive approach and was conducted with grade VIII students at one of the MTsN in Kediri City in the 2024/2025 academic year. Two subjects were selected based on test answer criteria that indicated the use of imitative procedures in problem-solving strategies that were frequently encountered, as well as imitation of strategies derived from information related to the questions. The results showed that the subjects did not fully understand the basic concepts underlying the selection of problem-solving strategies. They focused only on strategies that were familiar or had been learned previously. Interview results revealed that the two subjects had different bases for choosing strategies: S1 selected strategies based solely on those used in familiar problems, while S2 relied on surface information connected to the strategies they remembered. However, both subjects were unable to justify or prove the correctness of the strategies they chose.
Analysis of Students' Mathematical Problem Solving Skills on Opportunity Material
Problem-solving abilities are an important ability in understanding and applying mathematical concepts, including probability material that requires analysis and logical reasoning. This study aims to describe the mathematical problem-solving abilities of vocational high school students on probability material and to identify the difficulties faced by students in solving related problems. This research uses a descriptive qualitative method with a subject group of 27 students from class XI Yankes 3 at Vocational School Bunga Persada Cianjur for the 2024/2025 academic year who have studied probability material. Data collection techniques were carried out through mathematical problem-solving tests, interviews, and documentation. Data analysis was conducted through the stages of data reduction, data presentation, and conclusion drawing. The research results show that students' mathematical problem-solving ability in probability material is still classified as low. Based on the test results, only 3.7% of students are in the high category, 14.8% in the medium category, and 81.5% in the low category. If reviewed based on its stages, the percentage of student achievement is as follows: understanding the problem at 32,2%, planning the solution at 67,1%, executing the solution at 63,9%, and reviewing at 5,6%.The reviewing stage has the lowest achievement. Students' difficulties primarily lie in understanding problems related to probability material, constructing mathematical models to determine formulas for finding event probabilities, and checking the final results of probabilities found in story problems. These findings highlight the importance of reinforcing the understanding of basic concepts and contextual problem-solving exercises in probability learning to enhance the mathematical problem-solving abilities of vocational high school students.
An Analysis of Grade XI Students’ Errors in Solving Statistical Problems Based on Newman Error Analysis (NEA) Theory
This study aims to analyze the mistakes of grade XI students in solving statistical problems based on the Newman Error Analysis (NEA) stages. The research method used is qualitative descriptive with the research subjects of 30 high school students in Praya for the 2025/2026 school year. Data were collected through descriptive tests, interviews, and documentation, then analyzed using the Miles and Huberman model through the stages of reduction, presentation and drawing of conclusions. The results showed that students still made mistakes at almost all stages of Newman, including: reading errors (0.64%), comprehension errors (22.29%), transformation errors (26.75%), process skills errors (23.56%), and encoding errors (26.75%). The most mistakes occur in the transformation and writing stages, while the least mistakes occur in the reading stage. Factors that cause student errors include lack of understanding of concepts, mistakes in choosing formulas, inaccuracy in calculations, and the habit of not writing conclusions. The results of this study are expected to be a guideline for teachers in developing more efficient learning strategies to reduce student errors in statistical materials.
Spatial Ability of Grade VIII Students in Terms of Van Hiele's Level of Thinking
Spatial ability is important in learning geometry, especially related to 3D shapes. This study aims to analyze students' spatial ability based on van Hiele's geometry thinking level. The research was conducted with a qualitative case study approach involving 23 students of grade VIII at one of the public junior high schools in Bandung, West Java. The researchers gave two types of tests to students, namely spatial tests based on spatial perception, visualization, mental rotation, spatial relation, and spatial orientation elements, as well as geometry thinking tests based on van Hiele's five levels of thinking, namely visualization, analysis, informal deduction, deduction, and rigor. The results show that about half of students reached the visualization level with low spatial orientation ability, while the rest of students have not reached the visualization level with very low spatial orientation ability. The spatial ability of students in the spatial perception element is categorized as high, in the visualization and spatial relation elements is categorized as sufficient, and in the mental rotation element is categorized as low. Students' ability to see objects from various directions and to rotate objects still needs to be improved.
Pre-Service Mathematics Teachers Learn the Concept of Conic Sections: A Praxeological Analysis of Textbooks
This study investigates how pre-service mathematics teachers (PSMTs) learn conic sections through the task structures in high school mathematics textbooks by applying the Praxeological-Didactical Analysis (PDA) framework. The analysis focuses on identifying the types of tasks (T), techniques (?), technologies (?), and theories (?) in the textbooks used in the Kapita Selekta Matematika Sekolah Lanjutan course. PDA trace the didactical transposition process from scholarly mathematical knowledge to the taught knowledge represented in textbook materials. Using a qualitative document analysis approach, the findings indicate that textbook tasks emphasize procedural and algebraic techniques, with technological and theoretical explanations. The findings reveal that most tasks in the textbooks are dominated by procedural approaches emphasizing algebraic techniques, while the technological and theoretical justifications are often implicit. The study suggests the need for reconstructing praxeology-based task designs that integrate conceptual reasoning and theoretical grounding to strengthen PSMTs’ understanding and didactical competence in teaching conic sections.
Assessment of Creative Thinking in Cultural Context in Junior High School Students: A Psychometric Validation Study
Creativity is a key component of twenty-first century competencies and an essential element of mathematical problem solving. In Indonesia, the curriculum emphasizes creativity, yet valid and reliable instruments for assessing students’ creative mathematical thinking remain limited. This study aimed to design and validate a culturally contextualized mathematical creativity test that measures fluency, flexibility, and originality through open-ended problem-solving tasks. The instrument consisted of two contextualized items: (1) a task based on Gobak Sodor, a traditional Indonesian game, requiring students to design and analyze geometric field partitions; and (2) a task based on Tempe Sanan, a local food product, requiring innovative cutting designs and area calculations. Responses from 23 junior secondary students were scored on a 1–4 scale for each creativity dimension, resulting in six observed variables. Data were analyzed using Exploratory Factor Analysis (EFA) to identify the latent factor structure, followed by Confirmatory Factor Analysis (CFA) to test model fit. EFA indicated a two-factor solution, with fluency forming one distinct factor and flexibility-originality clustering as another. CFA confirmed the adequacy of this two-factor model, with good fit indices (χ²/df = 1.42, CFI = 0.972, TLI = 0.953, RMSEA = 0.061, SRMR = 0.045). Both factors demonstrated high reliability (α = 0.87 and α = 0.94). The findings provide strong evidence that mathematical creativity in this context is best represented by two dimensions: ideational fluency and structural creativity (flexibility–originality). The study contributes to the development of culturally responsive and psychometrically sound instruments for assessing creativity in mathematics education, aligning with the goals of the Indonesian curriculum.
The Influence of Learning Independence and Self-efficacy on Students' Mathematical Understanding Ability Based on Kinach’s Theory
This study aims to analyze the influence of learning independence and self-efficacy on students’ mathematical understanding ability based on Kinach’s theory. This study employs a quantitative approach with data analysis techniques consisting of simple linear regression and multiple linear regression. The study population includes all 10th-grade students at state Islamic senior high schools (MA Negeri) in Cianjur Regency, with a sample of 34 students from class XA selected through purposive sampling. The instruments used consist of a mathematical understanding ability test based on Kinach’s theoretical indicators in the topic of Arithmetic Sequences and Series, as well as questionnaires on learning independence and self-efficacy. The data were analyzed using simple and multiple linear regression tests, preceded by prerequisite tests including normality, linearity, heteroscedasticity, and multicollinearity. The results show that learning independence has a positive and significant influence on students’ mathematical understanding ability based on Kinach’s theory, with a contribution of 36.3%. Likewise, self-efficacy has a positive and significant influence, contributing 69.4%. Furthermore, learning independence and self-efficacy simultaneously have a significant influence on students’ mathematical understanding ability based on Kinach’s theory, with a combined contribution of 69.7%. These findings indicate that the higher the students’ levels of learning independence and self-efficacy, the better their mathematical understanding ability as conceptualized in Kinach’s theory.
Improving Students' Metacognitive Awareness and Mathematical Communication Ability with Think Pair Share Learning Model
This study aims to analyze and compare the improvement of students’ metacognitive awareness and mathematical communication ability through the implementation of the Think Pair Share learning model and conventional learning. The research method used is quasi-experimental with a nonequivalent comparison group design. The population of this study consists of all students of class XI at SMK Negeri 1 Cipanas in the academic year 2024/2025. The sample includes class XI MPLB 1 (experimental group) and XI TJKT (control group), selected using purposive sampling technique. The instruments used are a mathematical communication ability test and a metacognitive awareness questionnaire with matrix material. Data analysis was conducted using normality test and Mann-Whitney U test. The results showed that there was a difference in the improvement of mathematical communication ability between students who used the Think Pair Share learning model and those who used conventional learning. However, there was no difference in the improvement of metacognitive awareness between students who used the Think Pair Share model and those who used conventional learning.
Improving Students' Mathematical Literacy Skills Through the Application of Genially in the PBL Model
The purpose of this study was to determine the improvement of students' mathematical literacy skills through the application of genially on problem-based learning (PBL) model. This research was conducted at SMA Negeri 6 Garut. The research method used was quasi experimental with pretest-posttest control group design. The experimental class was given treatment by applying genially to the problem-based learning (PBL) model while the control class was given the problem-based learning (PBL) model only. The population in this research were all students of class X, with a sample of two classes namely class X 12 as the experimental class and class X 4 as the control class. sampling based on the random assignment technique. The data collection techniques used were observation, unstructured interview, and mathematical literacy test. The instruments used were student mathematical literacy test. The data analysis technique used the Two Independent Samples Test. Based on the results of data analysis, it can be concluded that there is an increase in students' mathematical literacy skills through the application of Genially in the Problem Based Learning (PBL) model with a significance of 0.03.
Analysis of MTs Students' Critical Thinking Skills in Solving Algebra Problems Based on Facione's Theory
This study aims to analyze the critical thinking skills of Madrasah Tsanawiyah (MTs) students in solving algebraic problems based on Facione’s critical thinking theory. Critical thinking is an essential competence in mathematics learning, particularly in algebra, which requires students to interpret problems, apply appropriate strategies, and draw logical conclusions. This research employed a qualitative descriptive approach to explore students’ cognitive processes in depth. The study was conducted in one eighth-grade class of an MTs in Kediri Regency, involving 25 students. Purposive sampling was used to select research subjects representing high, medium, and low critical thinking ability categories. Data were collected through algebra problem-solving tests and in-depth interviews, which were validated by experts prior to implementation. The analysis followed the Miles and Huberman qualitative analysis model, including data reduction, data display, and conclusion drawing, with method triangulation to ensure data validity. The results showed that only two students (8%) were categorized as having high critical thinking skills, fifteen students (60%) were in the medium category, and eight students (32%) were in the low category. Students with high critical thinking skills fulfilled all Facione indicators, while students in the medium and low categories showed difficulties, particularly in the analysis, evaluation, and inference aspects. These findings indicate that students are not yet accustomed to higher-order thinking skills (HOTS) algebra problems and highlight the need for learning strategies that consistently train critical thinking in mathematics classrooms. Keywords: algebra; critical thinking; Facione’s theory; MTs students; problem solving
Analysis of the Implementation of Quipper Learning in Facilitating the Understanding of Derivatives of Trigonometric Functions in High School
The use of Quipper media in teaching trigonometric function derivatives strengthens learning outcomes compared to conventional methods. The analysis shows that Quipper produces higher posttest scores and N-Gain values, reflecting better conceptual mastery and optimal learning engagement. The findings confirm that Quipper is a digital learning medium that is more effective, especially for abstract and complex mathematical material. Future studies can utilize Quipper for different mathematical concepts or integrate it with technology-based learning models to further improve learning performance and motivation.
Balanced Literacy Learning Model to Enhance Creative Thinking and Problem Solving in Elementary School Mathematics Word Problems
Persistent challenges in students' creative thinking and problem-solving capacities in mathematics — particularly in word problem contexts — call for innovative instructional models that bridge language comprehension and quantitative reasoning. This study aimed to examine the effectiveness of the Balanced Literacy learning model in enhancing creative thinking and problem-solving abilities among Phase C elementary school students in mathematics word problems. This study employed a quasi-experimental method using a non-equivalent control group design with pretest-posttest measurements. A total of 50 Grade V students from MI Assaidiyyah Cipanas, Cianjur Regency, were selected through purposive sampling and divided into an experimental class (n = 25) receiving Balanced Literacy instruction and a control class (n = 25) receiving conventional teaching. Data were collected through validated creative thinking tests, Likert-scale problem-solving questionnaires, and structured observation sheets, then analyzed using descriptive statistics and independent-samples t-tests via IBM SPSS Statistics 25. The results of this study indicate that the Balanced Literacy model significantly enhanced students' creative thinking (posttest mean: experimental 88.0 vs. control 80.8; N-Gain: 0.62 vs. 0.47) and problem-solving abilities (posttest mean: 95.48 vs. 93.04), with statistically significant inter-group differences (sig. < 0.05) for both outcomes. Observation data confirmed 100% implementation fidelity. The Balanced Literacy model, which integrates reading, writing, speaking, and listening within mathematical contexts, is recommended as an effective evidence-based approach for developing higher-order thinking in elementary mathematics. Keywords: Balanced Literacy; creative thinking; elementary school; problem solving; word problems
Copyright (c) 2026 Meli Gusmawati, Deddy Sofyan S, Dadang Jaenudin https://creativecommons.org/licenses/by-sa/4.0
The 4D Model in Developing Nearpod-Based Interactive Media for Reflection Material
Mathematics plays an important role in developing logical, critical, creative, and systematic thinking skills, but it is often considered difficult and boring, requiring innovative learning media. One of the most challenging topics is reflection because of its abstract nature and the need for visualization skills. This study aims to develop interactive media based on Nearpod that is valid, practical, and effective. The method used is Research and Development (R&D) with the 4D model (Define, Design, Develop, Disseminate) and a one-group pretest–posttest design on 35 students in grade XI at Karawang State Senior High School 6, who were selected using purposive sampling. Data were obtained through validation questionnaires, practicality questionnaires, and learning outcome tests. The results showed that Nearpod media was rated as very feasible by media experts, with an overall average score of 3.90. It was also rated as very feasible by subject matter experts, with an overall average score of 3.80, and by students, with an overall average score of 3.85. In terms of practicality, it was categorized as highly feasible based on the results of the teacher questionnaire assessment with an overall average score of 3.60, while based on the student questionnaire assessment, it was categorized as feasible with an overall average score of 3.44. Thus, Nearpod is proven to be valid and practical for use in reflection material.
Integrating Sundanese Culture and Digital Technology: Designing an Ethnomathematics Based Worksheet Using GeoGebra for Conic Sections
Students struggle to determine simple equations when given the asymptotes and vertices or the equation of a hyperbola and the length of the major axis. This difficulty stems from the limited learning resources educators use when teaching conic sections. This study aims to develop GeoGebra-assisted worksheets that contextualize the concept of conic sections in a way that is valid and practical for high school students. This is a development study based on the ADDIE model, which consists of five stages: analysis, design, development, implementation, and evaluation. The test subjects in this study were 16 students from a private high school in Cianjur during the 2024–2025 academic year. The results of this study indicate that the GeoGebra-assisted worksheets for pupils, featuring contextual problems on the topic of conic sections, are valid and practical. The average expert validation score was 83.3%, meaning the average expert validation score falls within the “Highly valid” category and is suitable for testing. Meanwhile, the percentage of student responses to the GeoGebra-assisted worksheets developed was 75%, falling into the “Practical” category. This indicates that the developed material can be used as a teaching aid for senior secondary school students on the topic of conic sections. Developing mathematics teaching materials in the form of GeoGebra-assisted worksheets on the topic of conic sections for senior secondary school students, which have been tested for validity and practicality. The results of the development show that (1) the assessment of the GeoGebra-supported worksheets regarding the aspect of presentation suitability, using the Guttman scale, yielded an average of 83.3%, meeting the criterion of “highly valid." (2) The results of the practicality test, based on student assessments in the student response questionnaire, yielded an average of 81% for indicator 1, meeting the criterion of “highly practical”; 79% for indicator 2, meeting the criterion of “practical”; and 67% for indicator 3, meeting the criterion of "practical." Thus, it can be concluded that the worksheets teaching materials supported by the GeoGebra application on the topic of Conic Sections for senior high school/vocational school students have been proven to be valid and practical.
Mathematical Numeracy Analysis Based on Learning Style in PBL With Differentiation E-Module
This study aims to examine the effectiveness of Problem-Based Learning assisted by differentiated e‑modules in enhancing junior high school students’ mathematical numeracy and to analyse numeracy development from the perspective of students’ learning styles. A mixed methods approach with a sequential explanatory design was employed. Quantitative data were collected using a quasi‑experimental pretest–posttest control group design, followed by qualitative data obtained through classroom observations and semi‑structured interviews. Participants consisted of Grade VIII students from a public junior high school in Indonesia. The quantitative results show that the experimental group achieved a higher increase in mathematical numeracy scores (from M = 58.75 to M = 78.63) compared to the control group (from M = 59.21 to M = 69.03). An independent sample t‑test revealed a statistically significant difference in posttest scores between the two groups (p = 0.001). In addition, learning mastery in the experimental group (84.37%) exceeded that of the control group (65.62%). Qualitative findings indicate that differentiated e‑modules effectively supported engagement and understanding across visual, auditory, and kinesthetic learning styles. This study demonstrates that the integration of PBL, learning‑style‑based differentiation, and e‑module assistance produces a cumulative effect on students’ mathematical numeracy. The findings contribute empirical evidence for designing inclusive, problem‑oriented, and digitally supported mathematics instruction.
Copyright (c) 2026 Triyono Triyono, Masrukan Masrukan, Bambang Eko Susilo https://creativecommons.org/licenses/by-sa/4.0
Development of Wordwall-Assisted Educational Game Media on Fractions to Improve Mathematical Literacy in Elementary School Students
This study aims to develop Wordwall-assisted educational game media on fraction material to improve the mathematical literacy of elementary school students. The low scores of Indonesian students in international assessments such as PISA 2022, combined with the abstract nature of fraction concepts and the dominance of teacher-centered conventional instruction, highlight the urgent need for innovative, technology-integrated learning media. This research employs a Research and Development (R&D) approach using the ADDIE model (Analysis, Design, Development, Implementation, Evaluation). The subjects included material, media, and language expert validators, 15 teachers for feasibility testing, and 38 fifth-grade students at SDN Batukarut, Sukaraja, Sukabumi, as the experimental group. Data were collected through expert validation sheets, teacher and student response questionnaires, and mathematical literacy tests. Results indicate that the developed Wordwall-based educational game achieved a "very valid" rating from expert validators. Teacher and student responses were both categorized as "very good." The effectiveness test using a one-group pretest-posttest design showed a significant improvement in students' mathematical literacy, with an N-gain value in the medium-high category. This study recommends the integration of Wordwall-assisted educational games as a standard digital learning medium in elementary mathematics classrooms, particularly for abstract topics such as fractions.
Standardized Assessment of TKA Equivalent for Junior High School Students
This research aims to develop a mathematical assessment instrument equivalent to the Academic Ability Test (TKA) for junior high school students who have good measurement quality. This research uses a Research and Development (R&D) approach by adapting the ADDIE model which includes the stages of analysis, design, development, implementation, and evaluation. The instrument developed consists of three question items that are arranged based on the TKA preparation grid with emphasis on mathematical reasoning skills, problem solving, and critical thinking. The research subjects consisted of expert validators including experts in mathematics and educational evaluation experts, as well as 80 junior high school students as respondents to the instrument trial. The data collection technique is carried out through expert validation sheets and tests of student work. Data analysis was carried out descriptively to assess the feasibility of the instrument's contents, while empirical validity was analyzed using corrected item-total correlation and reliability was analyzed using Cronbach's Alpha coefficient with the help of IBM SPSS Statistics software. The results showed that all question items had a corrected item-total correlation value that was greater than the r-value of the table (0.220) so that it was declared valid. In addition, the results of the reliability test showed a Cronbach's Alpha value of 0.953 which was in the very high category. These findings show that the assessment instruments developed have a very good level of validity and reliability so that they are suitable for use as an alternative assessment to measure the academic ability of junior high school students that are in line with TKA standards.
The Use of Problem-Based Learning Model Assisted by Quizizz to Improve The Mathematical Problem-Solving Ability of Junior High School Students
This study aims to determine whether the mathematical problem-solving ability of students who receive the Problem-based Learning model assisted by Quizizz is better than students who receive the conventional learning model. This study uses a quantitative approach with a quasi-experimental design. The subjects of this study consisted of two classes, namely class VIII D as the experimental class that received the Problem-based Learning model assisted by Quizizz, and class VIII C as the control class that received the conventional model in one of the state junior high schools in West Bandung district. The instrument used in this study was a test of mathematical problem-solving ability. The data analysis technique for the mathematical problem-solving ability test used a two-sample test (t-test), which was processed using the IBM SPSS Statistics 23 for Windows software. The study's results showed that the mathematical problem-solving ability of students who received the Problem-based Learning model, assisted by Quizizz, was better than that of students who received the conventional learning model.
‘Matcha-Act’ Website as Learning Media for Linear Equation in Junior High School
One of mathematic topic that often considered difficult is linear equation. This research aims to develop “Matcha-Act” website as learning media for linear equation that is both valid and practical for mathematic learning. Adopting a Research and Development (R&D) framework, the study employed ADDIE model (Analysis, Design, Development, Implementation, Evaluation). The subjects of this research were 8th grade junior high school students. The data gathered via media validation instruments and response questionnaires. The result indicated that the “Matcha-Act” website were valid and achieving a score of 3.2 or 80%. Furthermore, practicality test yielded a score of 3.1 or 77.5%. It means that “Matcha-Act” website-media were practical to use. The advantages of “Matcha-Act” website media include its accessibility and convenience, an engaging and interactive interface, and its ability to assist students in discovering concepts independently under teacher guidance. Consequently, the Matcha-Act” website is verified as a valid and practical learning media, making it suitable for mathematics learning, particularly on the topic of linear equations.
Students' Mathematical Connections in Solving Word Problems Based on Polya's Stages
The purpose of this study was to describe the mathematical connection ability of grade XI students in solving story problems of linear equations of three variables in terms of problem solving steps according to Polya. The method used in this research is qualitative research. Student connection data was collected using tests and interviews. Then the students' connection data were analyzed based on three types of connections, namely modeling connections, connections between concepts and procedure connections. The results showed that the modeling connection process occurred in the understand the problem and carry out the plan steps. The connection process between concepts occurs at the device a plane and carry out the plan steps. While the procedural connection in the carry out the plan and look back steps. Students' mathematical connection skills are shown in translating problems into mathematical models, connecting between mathematical concepts and procedures. The connection component that has not been mastered by students is not understanding the concept of simplifying equations by grouping similar terms. Students tend to use the operation of moving segments in simplifying the equation.
The Relationship Between Mathematical Resilience and Critical Thinking Ability of Student
Critical thinking ability is one of the important abilities in mathematics learning, while mathematical resilience acts as an affective factor that encourages students to persevere in the face of difficulties. This study aims to analyze the relationship between mathematical resilience and students' critical thinking skills in the context of mathematics learning. The research method used a correlational quantitative approach involving 20 Al-Hikmah Junior High School students as samples. Data were collected through mathematical resilience questionnaire and mathematical problem-based critical thinking ability test, then analyzed using correlation test (Pearson/Spearman) and crosstab test. The results showed that there was no significant relationship (r = 0.266 < 0.05) between mathematical resilience and critical thinking ability. This finding indicates that other factors, such as learning motivation, teaching model, or learning environment, may have more influence on students' critical thinking ability. Nonetheless, this study contributes to the understanding of students' cognitive and affective abilities in the context of mathematics learning.
Comparative Study of Elementary School Students’ Understanding of Geometry Concepts through Ethnomathematics and Conventional Approaches
This study aims to investigate and compare differences in elementary school students’ understanding of geometric concepts between those who experienced ethnomathematics-based learning and those who received conventional instruction. This study employed an ex post facto comparative design involving 54 fifth-grade students divided into two groups. Data were collected using a geometry concept understanding test that met validity (0.92) and reliability (Cronbach’s Alpha = 0.86) criteria. The data were analyzed using descriptive and inferential statistics. The results showed that the mean score of the ethnomathematics group (M = 83.96; SD = 4.74) was higher than that of the conventional group (M = 71.15; SD = 2.58). Welch’s t-test indicated a statistically significant difference between the two groups (t = 12.33; df = 40.17; p < 0.001). These findings indicate that ethnomathematics-based learning is associated with higher levels of students’ understanding of geometric concepts compared to conventional instruction. However, due to the ex post facto design, the findings should be interpreted as associative rather than causal.
Interference Thinking Students’ to Solve Proportion Problems Based on Cognitive Style
Thinking interference is defined as a disruption in information processing caused by overlap between old and new knowledge, which can hinder students' problem solving. The purpose of this study is to describe the forms of interference junior high school students thinking in solving ratio problems, as viewed from the cognitive styles of Field Independent (FI) and Field Dependent (FD). This study employs a descriptive qualitative approach, with the research subjects being three seventh-grade junior high school students who are suspected of thinking interference. Research data were collected through the Group Embedded Figures Test (GEFT), a ratio quiz, and interviews. The data analysis techniques used in this study were data reduction, data display, and conclusion. The results showed that FI students experienced retroactive interference characterized by students using the reverse proportion procedure to solve equivalent proportion problems. FD students experienced retroactive interference characterized by students solving problems using the reverse proportion procedure in equivalent proportion problems, and FD students experienced proactive interference characterized by students solving problems using the equivalent proportion procedure in reverse proportion problems. This occurs due to the similarity in solution procedures between equivalent proportion and reverse proportion. This study shows that both cognitive styles contribute to the emergence of thinking errors in solving comparison problems when students do not re-evaluate the appropriateness of the procedure to the problem context.
Comparative Study: Differences in Students' Geometric Reasoning Viewed from Van Hiele's Levels of Geometric Thinking
This study aims to determine the differences in students' geometric reasoning in terms of Van Hiele's thinking levels in spatial geometry. This study used an ex post facto method with a quantitative approach. The population of this study was ninth-grade female students at SMP Negeri 2 Majalaya, with a sample of 86 students selected using simple random sampling. Data were obtained through diagnostic tests, geometric reasoning tests, and unstructured interviews with several samples. This study uses several inferential statistical tests such as normality tests, homogeneity tests, and ANOVA. The results of this study indicate that there are significant differences between the geometric reasoning abilities of students at level 0 and level 1, as well as between level 0 and level 2. The number of students classified as level 0 (visualization) is 69.77%; level 1 (analysis) is 24.42%; and level 2 (informal deduction) is 5.81%. No students were classified as level 3 or 4.
An Analysis of Students' Pseudo-Thinking Processes in Solving Algebra Problems from The Perspective of Self-Confidence
This study aims to describe the pseudo-thinking processes of eighth-grade junior high school students in solving algebra problems, as viewed from the perspectives of high, moderate, and low levels of self-confidence. This study was conducted in the eighth grade at SMP Negeri 7 Palu during the 2025/2026 school year. A total of 3 students were selected from a group of 29 students. This research method uses a qualitative approach of a descriptive nature.The researcher employed a self-confidence questionnaire, an algebraic problem-solving test, and interviews. The results indicate that students have high self-confidence in their ability to solve problems correctly and follow problem-solving steps; however, they still struggle to explain their reasoning conceptually, suggesting that their thinking is pseudo-correct. Students with moderate self-confidence are able to solve problems fairly well, but they still make mistakes in their approach and conceptual understanding, so they tend to engage in pseudo-correct thinking, although not to the same extent as students with high self-confidence. Students with low self-confidence tend to have difficulty understanding and solving problems, leading them to give incorrect answers; however, they are able to correct their mistakes after reflecting on them, thus demonstrating pseudo-errors.
Students’ Mathematical Abstraction in Constructing Quadrilateral Concepts: A Learning Style Perspective
Mathematical abstraction is an important aspect in mathematics learning, especially in helping students form and understand geometric concepts such as quadrilaterals. However, in practice, students' mathematical abstraction process does not always occur uniformly. This is due to differences in individual characteristics, one of which is learning style. Therefore, this study aims to describe the profile of students' mathematical abstraction in forming the concept of quadrilaterals in terms of learning style. This study uses a qualitative approach with a descriptive type. The research subjects consisted of three seventh-grade junior high school students with visual, auditory, and kinesthetic learning styles. Data were collected through a learning style questionnaire, mathematical abstraction tasks on quadrilaterals, and interviews. Data analysis used data condensation, data display, and conclusion drawing and verification. The results of the study showed that students' mathematical abstraction processes differed in each learning style. Visual students were able to go through all aspects of mathematical abstraction (recognizing, building-with, constructing, and consolidation) gradually by utilizing visual representations. Auditory students also achieved all aspects by relying on verbal understanding, although the constructing and consolidation aspects were not systematically arranged. Meanwhile, kinesthetic students rely more on concrete experiences and physical activity in recognizing and consolidating. Therefore, it can be concluded that learning styles determine how students carry out the mathematical abstraction process in forming the concept of quadrilaterals, so this needs to be taken into consideration when designing mathematics learning. Keywords: Mathematical Abstraction; Quadrilaterals; Learning Styles
Hypothetical Learning Trajectory (HLT)-Based Learning Design Analysis
Mathematics learning trajectory is one of the key concepts in student-centered mathematics learning design. This article aims to analyze and describe the development of Hypothetical Learning Trajectory (HLT) as a framework for designing effective mathematics learning at the Junior High School level. The method used is design research with a qualitative approach through three phases: preparation phase, experimentation phase, and retrospective analysis phase. Research subjects consisted of 32 seventh-grade students at SMP Negeri 37 Medan. Research instruments included observation sheets, concept understanding tests, and semi-structured interviews. The results showed that HLT-based learning significantly improved students' conceptual understanding of integer material, with average scores increasing from 58.4 to 81.7. In addition, student learning motivation increased as demonstrated through the level of active participation in learning activities. The conclusions of this study confirm that systematic and reflective HLT development has great potential as an innovative strategy in meaningful and student-centered mathematics learning.
Assemblr Edu Based Augmented Reality Flipbook Media to Enhance Critical Thinking Skills of Vocational High School Students
Mathematical critical thinking ability is an essential competency that remains a challenge in Vocational High Schools (SMK). This study aimed to (1) develop a valid and practical Augmented Reality (AR) flipbook media based on Assemblr Edu, and (2) examine its effectiveness integrated with the Problem Based Learning (PBL) model on students' mathematical critical thinking ability. The study employed a Research and Development (R&D) approach using the ADDIE model for media development, and a one-group pretest-posttest quasi-experimental design for effectiveness testing. The sample consisted of 35 Grade XI Electrical Power Installation Engineering (TITL) students selected through simple random sampling. The instrument was a descriptive mathematical critical thinking test declared valid and reliable. Validation by three expert validators in language, content, and media indicated that the media was categorized as highly valid. The practicality test confirmed the media was categorized as highly practical. The effectiveness test demonstrated a significant improvement in students' mathematical critical thinking ability from pretest to posttest, classified in the high category. These findings prove that the Assemblr Edu-based AR flipbook media integrated with the PBL model is significantly effective in improving the mathematical critical thinking ability of SMK students. Keywords: augmented reality Assemblr Edu; mathematical critical thinking; digital flipbook; Problem Based Learning; Vocational High School
Students’ Creative Thinking in Solving Open-Ended Problems in Geometry Transformation Material
This study aims to describe students’ creative thinking abilities in solving open-ended problems in geometry transformation material. The problem used in this study was designed as a multiple solution task (MST) because it provides students with opportunities to generate more than one strategy or solution. This study employed a descriptive qualitative approach involving 27 students of Class XII-B at a Catholic senior high school in Surabaya. Data were collected through a written test and interviews and were then analyzed based on the indicators of fluency, flexibility, and novelty. The findings show that students were classified into three creativity groups. S1 represented the high-creativity group and demonstrated novelty through a non-routine strategy and by rechecking the solution. S2 represented the moderate-creativity group and demonstrated fluency and flexibility by producing more than one form of solution and using several methods, although the variation remained limited. S3 represented the low-creativity group and did not yet demonstrate fluency or flexibility because the student used only one method and produced a single answer. These findings indicate that open-ended problems in the form of MST can reveal differences in students’ creative thinking abilities in geometry transformation material. Keywords: creative thinking; open-ended; transformation geometry
Exploring Students’ Mathematical Reasoning Through Discovery Learning with Gamification Media on the Pythagorean Theorem
Reasoning is an important foundation in solving mathematical problems. Reasoning is a thinking process that allows students to understand concepts, connect ideas, and draw logical conclusions. This study aimed to explore students’ mathematical reasoning in Discovery Learning supported by gamification media on the Pythagorean Theorem. The study used a qualitative case study approach involving two eighth-grade students at a junior high school in Malang. Data were obtained through observation, interviews, and mathematical reasoning tests, then analyzed using the Miles and Huberman model. The findings revealed that Discovery Learning, supported by gamification media, created an interactive learning experience that enabled students to gradually explore concepts in context. High-ability students demonstrated strong reasoning skills, including analyzing problems, constructing arguments, applying inductive and deductive reasoning, making generalizations, and drawing conclusions. Low-ability students also showed improvement in several reasoning indicators, particularly in analyzing problems, applying deductive reasoning, and developing mathematical arguments during the learning process. Keywords: Reasoning, Discovery Learning, Gamification, Pythagorean Theorem
Google Sites Based E-book to Improve Mathematical Connectivity Skills in Probability
This study aims to develop a Google Sites-based e-book to improve high school students’ mathematical reasoning skills in probability. This study employs the Research and Development (R&D) method using the ADDIE model, which consists of the analysis, design, development, implementation, and evaluation stages. The research subjects included 40 11th-grade science students to measure the effectiveness of the media, 17 students to assess the practicality of the media, and 3 expert validators consisting of a media expert, a language expert, and a subject matter expert. Data collection techniques were conducted through validation sheets, student response questionnaires, and pretest and posttest assessments. The research results showed that the media received a validation percentage of 86.15% from the media expert, 89.23% from the language expert, and 93.33% from the content expert, all falling into the “highly suitable” category. The effectiveness test results showed that the average pretest score of 59.18 increased to 88.51 on the posttest, with an N-Gain value of 0.72 in the “high” category. Additionally, the classical mastery rate reached 93.33%, and the questionnaire results indicated that the medium falls into the practical category. Thus, the Google Sites-based e-book is deemed suiTabel, practical, and effective for enhancing students’ mathematical connection skills in probability material.
Scratch Assisted Educational Game Development on Data Presentation Material
This study aims to develop a Scratch-based educational game for data presentation materials and to determine its feasibility and student responses. The research method used is Research and Development (R&D) with the ADDIE model (Analysis, Design, Development, Implementation, and Evaluation). This study was conducted at SMAN Jatinunggal and involved two Mathematics Education lecturers from Siliwangi University as validators and 10th grade students as research subjects. Data were collected through validation sheets and student response questionnaires analyzed using a Likert scale. The results of the material expert validation showed that all aspects, including suitability, language accuracy, and presentation systematics, were in the very feasible category. Media expert validation on the interface display, navigation, supporting information, and learning design aspects also obtained a very feasible category. In the implementation phase, small group trials obtained a percentage of 90.42% and field trials increased to 93.66%, both of which were categorized as very practical. These findings indicate that the developed Scratch-based educational game is feasible and practical to be used as a mathematics learning medium for data presentation materials, and is able to increase students' interest and motivation in learning mathematics.
An Analysis of Students’ Mathematical Representations in Solving Algebraic Problem of Seventh Grade Based on Gender
This study aims to describe the mathematical representations of male and female students in solving algebraic problem. This study employed a qualitative descriptive approach. The subjects consisted of two seventh -grade students from SMP Negeri 9 Palu selected through written tests and interviews. The research results show that during the understanding the problem stage, male subjects used verbal, symbolic, and visual representations, whereas female subjects used only verbal and symbolic representations. During the making a plan and carrying out the plan stages, both subjects used symbolic representations by writing down formulas, forming equations, and performing algebraic operations to arrive at the solution. In the looking back stage, the female subject used verbal and symbolic representations more comprehensively by rechecking the solution and providing a coherent explanation, whereas the male subject only wrote down the final conclusion without performing a thorough recheck.
Ethnomathematics-Based Flipbook E-Module
Mathematical literacy skills are an essential competency of the 21st century that demands innovation in digital teaching materials. Based on the needs analysis in the field, the use of interactive, self-contained web-based learning media still requires variations and has not explicitly integrated local cultural elements in the Data Centrality Measurement material. This study aims to produce a digital learning media prototype in the form of a flipbook e-module based on Deli Malay ethnomathematics assisted by the Heyzine platform integrated with the Discovery Learning flow, and to test the theoretical feasibility of the product. This type of research is a research and development (R&D) using the 4D model. In accordance with the limitations of the initial feasibility objectives, the development procedure is limited to the Develop stage in the theoretical validity testing phase by experts. Data collection techniques are carried out through documentation studies, structured interviews with teachers, and distribution of Likert scale assessment questionnaire instruments to experts. The assessment data are then analyzed quantitatively using the Aiken's V agreement index formula. The results of the development stage research indicate that the accumulated average content validity index of all learning device instruments is 0.92 with the criteria of Very Valid. In detail, the validity values were obtained from the Teaching Module instrument (0.88), LKPD (0.90), material aspects (0.91), flipbook media (0.94), cultural context (0.92), and the mathematical literacy ability test instrument which achieved the highest coefficient of 0.96. The conclusion of the study confirms that this ethnomathematics-based flipbook e-module product is declared valid, theoretically feasible, and recommended as a variation of independent teaching materials to support the achievement of 21st-century competency mathematics learning.
The Influence of Resilience and Mathematical Literacy on Students' Mathematical Problem Solving Abilities
Mathematics learning in schools is often viewed as a mechanical process that emphasizes memorizing formulas, resulting in students being less able to relate concepts to real-world situations and experiencing difficulties in solving non-routine problems. This condition demands strong resilience and mathematical literacy skills so that students can survive, adapt, and think flexibly when facing problems. This study was conducted to analyze the influence of resilience and mathematical literacy on the ability of junior high school students to solve mathematical problems. The method used is a quantitative correlational study with a population of all seventh grade students of SMPN 27 Kota Tangerang in the 2025/2026 academic year and a sample of 36 students selected through cluster random sampling. Data in this study were obtained through resilience and mathematical literacy questionnaires and mathematical problem solving ability tests. All instruments have undergone validity and reliability tests before use. Data analysis using multiple linear regression with the help of SPSS version 29. The results showed that resilience significantly influenced students' mathematical problem solving abilities, while mathematical literacy did not. Simultaneously, resilience and mathematical literacy have not shown a significant influence on students' mathematical problem solving abilities. The coefficient of determination of 15.5% indicates that mathematical problem solving ability is influenced by resilience and mathematical literacy, while the remaining is influenced by other factors outside the research. Thus, resilience is a crucial factor that needs to be developed in mathematics learning to support students' mathematical problem solving abilities.
Analysis of Students’ Mathematical Problem-Solving Abilities in Single Variable Linear Equations and Pythagorean Theorem Material
This study aims to analyze students' mathematical problem-solving abilities in Single Variable Linear Equations and the Pythagorean Theorem based on Polya's problem-solving stages. The study uses a descriptive qualitative approach involving 40 eighth-grade students VIII junior high school students through descriptive tests and interviews. The results of the analysis show that students' mathematical problem-solving abilities are in the moderate category for both subjects, with an average score of 74.85 for Single Variable Linear Equations and 74.67 for the Pythagorean Theorem. Students in the high category are able to go through all stages of problem solving systematically. Students in the moderate category were able to understand the problem and plan a solution strategy, but often made computational errors. Conversely, students in the low category had difficulty understanding information, constructing mathematical models, and implementing solution procedures. Overall, the results of this study confirm the need to strengthen problem-solving-based learning that emphasizes understanding concepts and solution strategies to optimally improve students' mathematical problem-solving abilities.