Publication Search

This study aims to analyze students’ mathematical reasoning abilities in quadratic function material through the use of Desmos. The research employed a qualitative descriptive approach using a case study and usability testing method. Data were collected through post-tests and interviews involving students’ responses in solving quadratic function problems. The analysis focused on several indicators of mathematical reasoning, including procedural skills, conceptual understanding, and analytical ability. The results show that students generally demonstrate adequate procedural reasoning, particularly in substitution and computation tasks. They are also able to relate algebraic representations to geometric interpretations, such as determining intercept points and analyzing the direction of parabolas. However, limitations were found in conceptual understanding, especially in identifying graph characteristics without relying on procedural steps. The use of Desmos significantly supports the development of students’ mathematical reasoning by providing real-time visualization, facilitating exploration of function parameters, and enabling verification of results. Overall, Desmos contributes to enhancing procedural, conceptual, and analytical dimensions of mathematical reasoning, although its effectiveness depends on proper instructional design.

Learning mathematics not only focuses on mastering concepts and calculation skills, but also requires creating a conducive learning environment so that students can think critically, logically, and creatively. A conducive learning environment plays a crucial role in fostering student motivation and active engagement, making the success of the learning process highly dependent on the strategies implemented by the teacher. This research aims to describe mathematics teachers' strategies in creating a conducive learning environment thru the application of active and contextual learning strategies. The method used is library research, which involves collecting and reviewing various scientific sources such as books, journals, and academic articles relevant to the research topic. The research results indicate that active learning strategies are able to increase student participation, strengthen reasoning abilities, and foster learning motivation. Teachers play an important role as facilitators, motivators, mediators, and evaluators, directly influencing the learning climate in the classroom. Contextual learning strategies like REACT (Relating, Experiencing, Applying, Cooperating, Transferring) have proven effective in connecting mathematical concepts with students' real-life experiences and creating a fun and meaningful learning environment. In addition, humanistic classroom management, the use of technology, and adapting learning to students' different abilities are supporting factors in achieving a conducive learning environment. The implications of this research indicate that the success of mathematics learning is not solely determined by the methods used, but also by the teacher's ability to build positive relationships with students and create an interactive, adaptive learning environment that optimally fosters students' potential development.

Mathematics learning plays an essential role in developing students’ logical, systematic, and analytical thinking skills. One of the higher-order thinking abilities that serves as a main focus in mathematics education is mathematical reasoning. This ability is closely related to the process of mathematical proof, which functions to justify the truth of a statement logically. This study aims to examine the relationship between the understanding of proof concepts and the development of mathematical reasoning among junior high school students through a library research approach. Data were obtained from various sources such as textbooks, journal articles, research findings, and relevant educational documents. The analysis was conducted using the content analysis method to review both conceptual and empirical findings from the literature. The results indicate that understanding the concept of proof not only helps students comprehend the logical structure of mathematics but also contributes to the development of deductive and reflective reasoning skills. Engaging in proof activities enables students to shift from merely imitative reasoning toward independent logical construction (creative reasoning). However, teaching proof at the junior high school level still faces several challenges, such as students’ limited understanding of basic logic, time constraints, and the lack of teacher training in teaching proof effectively. Therefore, learning strategies that emphasize students’ thought processes, provide opportunities for exploration, and integrate proof activities into meaningful learning contexts are needed.

This study investigates the algebraic reasoning processes of university students when expanding mathematical expressions in the context of nonroutine problem-solving. The research adopts a qualitative approach to explore how students interpret algebraic structures, apply symbolic transformations, and construct logical explanations while working through unfamiliar tasks. Data were collected through written tests, task-based interviews, and detailed analysis of students’ solution strategies. The findings reveal significant variation in students’ ability to generalize patterns, recognize structural relationships, and justify algebraic procedures. Students with strong conceptual understanding demonstrated flexible reasoning, coherent explanations, and appropriate use of algebraic properties. In contrast, students who relied heavily on procedural rules often struggled with symbolic manipulation, produced fragmented reasoning, and exhibited misconceptions related to variables and distributive operations. These results highlight the importance of fostering conceptual understanding, metacognitive awareness, and reasoning-oriented instruction in university mathematics. The study provides insights for educators seeking to design learning environments that promote deeper algebraic thinking and enhance students’ ability to solve complex, nonroutine problems.

Logic is an important foundation in mathematics learning because it shapes critical and systematic thinking skills. Introducing the concept of proof early on plays a strategic role in developing reasoning skills, identifying patterns, and providing simple arguments. This article aims to examine the role of logic in mathematics learning by emphasizing the importance of introducing the concept of proof from the outset. The methods used are a literature review of various relevant studies and descriptive analysis based on learning practices in early childhood education. The results of the study show that play, exploration, and concrete experience-based learning activities can improve children's ability to understand cause-and-effect relationships, make predictions, and convey logical reasons. In addition, social interaction and dialogue in the learning process have been proven to strengthen simple reasoning skills. In conclusion, the integration of logic and reasoning from an early age not only supports the development of mathematical abilities, but also builds the foundation for critical and analytical thinking needed for further education.

This study aims to develop a junior high school mathematics e-module based on local culture at the Van der Wijck Fortress complex to enhance students’ mathematical reasoning skills and learning interest. Specifically, the objectives are: (1) to describe the characteristics of the local culture-based e-module that can improve reasoning ability and learning motivation, and (2) to produce a high-quality e-module that meets the criteria of validity, practicality, and effectiveness. The research employed the ADDIE development model (Analysis, Design, Development, Implementation, and Evaluation). The participants consisted of one teacher, 31 students in the experimental class, and 32 students in the control class at a public junior high school in Kebumen Regency. The instruments used included validation sheets for media and material, competency tests, mathematical reasoning tests, learning interest questionnaires, and practicality assessment forms for teachers and students. The results showed that the e-module possesses characteristics of being self-instructional, self-contained, stand-alone, adaptive, and user-friendly. Product validity was confirmed through expert validation with average scores of 4.26 for media and 4.35 for material (very valid). The validation of instruments obtained average scores ranging from 4.5 to 4.92, categorized as very valid. Practicality was demonstrated through teacher assessments of 92%, student assessments of 85%, and learning implementation of 94% (all very practical). Effectiveness testing using the Multivariate Hotelling’s T² test indicated significant differences between experimental and control classes in competency test scores, mathematical reasoning, and learning interest. Therefore, the local culture-based mathematics e-module is proven valid, practical, and effective in enhancing students’ mathematical reasoning and learning motivation.

This study aims to compare the effectiveness of the Deep Learning and Differentiated Instruction models in improving junior high school students’ mathematical problem-solving and reasoning abilities. The background of this research stems from the low level of mathematical literacy among Indonesian students, which demands innovative and reflective learning approaches. A quasi-experimental method was used with a Nonequivalent Control Group Design. The sample consisted of two eighth-grade classes at SMP Negeri Satu Atap 01 Ciseeng, each receiving different instructional treatments: one class was taught using the Deep Learning approach, and the other using the Differentiated Instruction approach. The instruments employed included mathematical problem-solving tests, observation sheets, and student perception questionnaires. The data analysis results indicated that the class taught with the Deep Learning model experienced a more significant improvement in mathematical reasoning ability compared to the class using Differentiated Instruction. These findings suggest that Deep Learning-based instruction is more effective in promoting students’ higher-order thinking skills. It encourages deeper engagement with mathematical concepts, fosters critical and analytical thinking, and allows students to construct knowledge through meaningful learning experiences. However, Differentiated Instruction remains relevant in providing learning comfort and addressing diverse student needs, making it beneficial in inclusive classroom settings. The theoretical and practical implications of this research highlight the importance of integrating both depth of thinking (Deep Learning) and flexibility in learning (Differentiation) within mathematics instruction. Such integration could offer a balanced learning environment that supports both cognitive development and emotional engagement, leading to more effective and equitable mathematics education. In conclusion, this study recommends educators and curriculum developers to consider incorporating Deep Learning strategies to enhance students’ mathematical reasoning while maintaining the adaptive and student-centered principles of Differentiated Instruction. Future research could explore hybrid learning models that combine the strengths of both approaches to maximize student outcomes in mathematics learning.

This research focuses on exploring the mathematical reasoning abilities of Madrasah Aliyah students in solving problems that integrate mathematical concepts with the Islamic science of faraidh (inheritance law), specifically within the topic of fractions. The study employs a qualitative approach with a case study design and was conducted among 11th-grade students enrolled in the Religious Program at MA Raudlatul Ulum Putri. Data collection techniques included written tests, semi-structured interviews, and classroom observations, focusing on three selected students who represented high, moderate, and low levels of mathematical ability. The analysis centers on several key indicators of mathematical reasoning: identifying problems, formulating hypotheses, presenting logical arguments, and drawing conclusions. The results show that most students fall into the moderate reasoning category, while a smaller number are categorized as high or low. Students in the high category demonstrate a strong capacity to approach problems systematically and accurately, combining mathematical logic with a proper understanding of Sharia-based inheritance rules. In contrast, students in the low category struggle with interpreting problem contexts and executing fraction calculations correctly, which indicates gaps in both conceptual understanding and application skills. These findings underscore the importance of contextual and integrative learning, particularly the combination of mathematics with Islamic values, to enhance deeper comprehension. By embedding religious relevance into mathematical instruction—especially through real-life contexts such as inheritance laws—educators can support the development of more meaningful reasoning abilities. The study suggests that integrating mathematics and Islamic teachings can significantly benefit student learning outcomes and foster stronger conceptual foundations.

The purpose of this study is to examine how deep learning influences students’ mathematical critical thinking skills. In mastering mathematics—which requires reasoning, analysis, and systematic review—critical thinking is essential to address the challenges of the 21st century. This research employs a quasi-experimental design using a pretest-posttest control group model. The subjects of the study were eighth-grade junior high school students, divided into an experimental group and a control group. The main instruments used were a mathematical critical thinking skills test and a learning activity observation sheet. The findings indicate that students who participated in instruction based on a deep learning approach showed a significant improvement in critical thinking skills compared to those who received conventional instruction. Unlike students who underwent standard learning methods, those exposed to deep learning strategies experienced a notable enhancement in their critical thinking abilities. Based on these findings, the implementation of deep learning is recommended more broadly in mathematics classroom instruction.

Mathematical reasoning skills are an important aspect of mathematics learning that supports students in understanding concepts deeply and logically. With the development of technology, the use of interactive learning media such as Geogebra has become a promising alternative to improve the quality of learning. This study aims to analyze the effect of Geogebra-assisted learning on students' mathematical reasoning skills through a meta-analysis approach. The method used is a Systematic Literature Review (SLR) guided by the PRISMA guidelines, covering publications from 2015 to 2025 that meet specific inclusion criteria. The analysis of seven research articles revealed that six of them showed a large to very large effect on improving mathematical reasoning skills, while one article showed a small effect. These findings reinforce the conclusion that Geogebra is generally effective in supporting the development of students' mathematical reasoning skills and is worthy of being part of mathematics learning strategies in the digital age.

Mathematics plays a crucial role in everyday life, as it enhances students' abilities to absorb lessons more effectively and develop rational, critical, logical, analytical, and systematic thinking. This study employs the literature review method, which involves gathering relevant information from various sources to support the research topic. The author collects references from articles and journals using Google Scholar, an open-access database that simplifies the process of locating topic-specific materials. Difficulties faced by students in learning mathematics are not always due to a lack of mathematical knowledge. They may stem from other issues such as memory problems, difficulty in recalling mathematical problems, weak calculation skills, confusion with operational signs, or reversing numbers. Students with learning disabilities may particularly struggle with both mathematical reasoning and basic computation. Furthermore, mathematical learning difficulties are also associated with cognitive challenges, such as solving complex word problems and understanding numerical concepts. These learning difficulties often result from internal and external factors that hinder the brain’s ability to process, analyze, and retain mathematical information effectively.

The difficulties students experience when solving problems that require calculation indicate a need to improve their arithmetic skills. This research aims to describe students' numeracy skills in solving number problems while also identifying the obstacles they encounter in developing these skills. Specifically, this study explores the mathematical numeracy literacy abilities of fourth-grade elementary school students in facing the Minimum Competency Assessment (AKM) questions on number material at one elementary school in Indonesia. This research uses a descriptive qualitative approach with data collection techniques including AKM numeracy tests, observation, interviews, and documentation. The research findings show that students' mathematical numeracy literacy ability is in the moderate category, with an average achievement of 65.8%. The main difficulties experienced by students include: (1) recognizing mathematical information from contextual problems, (2) performing numerical calculations, (3) interpreting calculation results in the context of real-world problems, and (4) communicating mathematical reasoning in writing. Based on these results, this research recommends strengthening numeracy learning that connects material with everyday life contexts, as well as improving students' mathematical reasoning abilities through problem-based learning approaches, to optimize the mathematical numeracy literacy of elementary school students.

Mathematics is often referred to as a field of knowledge developed through logical reasoning and is considered essential in everyday life, particularly in problem-solving. One effective way to apply problem-solving skills in mathematics education is through the use of word problems. This study aims to explore and analyze the various obstacles students encounter when solving mathematical word problems. The research employs a descriptive qualitative approach, with data collection methods including tests, interviews, and a project involving the construction of a staircase using standard units of length. The subjects of the study were four third-grade elementary school students in Batusangkar who had previously studied standard units of length. The findings reveal that students faced a range of difficulties, such as challenges in understanding the problems, failure to organize solution steps systematically, and limited comprehension of the concept of standard measurement units. Additionally, a lack of interest in learning was found to negatively impact students’ ability to solve word problems. Therefore, conceptual understanding and increased motivation to learn are crucial factors in enhancing students’ mathematical problem-solving abilities.

Mathematics is often referred to as a field of knowledge developed through logical reasoning and is considered essential in everyday life, particularly in problem-solving. One effective way to apply problem-solving skills in mathematics education is through the use of word problems. This study aims to explore and analyze the various obstacles students encounter when solving mathematical word problems. The research employs a descriptive qualitative approach, with data collection methods including tests, interviews, and a project involving the construction of a staircase using standard units of length. The subjects of the study were four third-grade elementary school students in Batusangkar who had previously studied standard units of length. The findings reveal that students faced a range of difficulties, such as challenges in understanding the problems, failure to organize solution steps systematically, and limited comprehension of the concept of standard measurement units. Additionally, a lack of interest in learning was found to negatively impact students’ ability to solve word problems. Therefore, conceptual understanding and increased motivation to learn are crucial factors in enhancing students’ mathematical problem-solving abilities.

This research examines how conceptual comprehension, mathematical reasoning, and problem solving affect computational thinking. 122 students from class XI SMA Negeri 1 Pematang Siantar were given essay assessments on conceptual comprehension, mathematical reasoning, problem solving, and computational thinking. AMOS version 21 was used to analyze the test using Structural Equation Modeling (SEM). This study found that conceptual understanding, mathematical reasoning, and problem solving have a positive and significant effect on computational thinking ability with a contribution of 0.528. This means that 52.8% and 47.2% of computational thinking abilities are built by these three abilities, depending on other variables.

Mathematical representative ability is a person's ability to express mathematical ideas, objects, and relationships in various forms of representation, both visually, symbolically, verbally, and contextually. This study aims to analyze the mathematical representative ability of students through counting operations in grade III elementary school in the form of story problems. The method used was descriptive qualitative research with written test instruments to assess cognitive abilities and observation to assess psychomotor skills. The research subjects consisted of five grade III elementary school students, by giving test questions on mathematical reasoning skills, observing students directly in solving and understanding story problems, conducting documentation to obtain accurate data when in the field by classifying students' mathematical representative abilities based on math scores. The results showed that most learners had a very good level of cognitive ability in completing arithmetic operations, but there were some learners who were still lacking in understanding story problems. This finding confirms that the importance of appropriate learning strategies so that learners are not only able to solve problems in the form of operations but also able to understand problems in the form of story problems that are applied in real life.

This study investigates the impact of contextual problem-solving on students' mathematical reasoning abilities, comparing it to traditional problem-solving exercises. The study employs a quasi-experimental design with two groups: an experimental group exposed to contextual problem-solving activities and a control group using conventional methods. The experimental group demonstrated a 24% improvement in their mathematical reasoning abilities compared to the control group. Contextual problem-solving, which integrates real-world problems into the learning process, was found to be more engaging and effective in promoting deeper understanding and application of mathematical concepts. The study highlights the benefits of contextual learning in making abstract mathematical concepts more tangible and relatable to students. The findings suggest that by connecting mathematical knowledge to real-world scenarios, students develop stronger reasoning skills and improve their problem-solving capabilities. Moreover, the study recommends incorporating more contextual problem-solving exercises into curricula and providing teachers with training on how to implement these strategies effectively. It also suggests that future research explore the long-term effects of contextual problem-solving on other learning areas, such as critical thinking and creative problem-solving. This approach not only enhances students' mathematical reasoning but also fosters a more engaging and meaningful learning environment, thus preparing students to apply their mathematical knowledge in real-life situations.

This research was aimed at analyzing the enhancement of students' mathematical reasoning abilities through problem-based learning. The experimental design was pre-post control group design. The research population was all junior high school student of SMP Al-Muhajirin Purwakarta. The research sample was taken randomly, was the class VIII C students as the experimental group who participated in instruction with problem-based learning and the other class VIII D as control group who participated in instruction with conventional learning. Data was collected through test and questionnaires. The statistical analysis used is the Gain test for the results of students' mathematical reasoning ability tests. The analysis of gain score showed that the enhancement of students’ abilities who participated in instruction with problem-based learning was better than those who participated in instruction with conventional learning. Problem-based learning in mathematics lessons shows a positive response which shows that students like the method used.

This research aims to comprehensively examine students’ mathematical proof abilities, including the factors that influence them and the efforts that can be made to improve these abilities. The method used in this study is a systematic literature review by analyzing various related research articles published in reputable scientific journals such as Springer Link and Semanthic Scholar. The results of the study show that students’ mathematical proof abilities are still relatively low, influenced by various factors such as conceptual understanding, reasoning ability, and experience in constructing proof. Several ways that can be done to improve students’ mathematical proof skills include developing teaching materials, implementing learning models that encourage proof activities, and providing systematic training and feedback. This study provides important implications for the development of mathematics learning in higher education, especially in efforts to improve students’ mathematical proof skills.

This research aims: (1) students' mathematical reasoning ability using the Discovery Learning learning model is higher than students' mathematical reasoning ability using conventional learning models in class VII MTs Yaspi Labuhan Deli, (2) the process of solving answers made by students in solving problems in the Discovery Learning learning model and Conventional learning model. This type of research is quantitative research with Quasi-Experimental methods. This research was conducted at MTs Yaspi Labuhan Deli. The sampling technique in this study uses Purposive Sampling techniques, namely class VII-A as a class taught with a Discovery Learning learning model and class VII-B as a class taught with a conventional learning model. The data collection instrument used was in the form of observation sheets and student mathematical reasoning ability test sheets in the form of 3 essay questions. Data analysis in this study used t-Test with Independent Sample t-Test technique with the help of SPSS 20 program. The results of this study showed that the average score of classes taught using the discovery learning model was 78,01 and classes taught using conventional learning models were 72,22. For hypothesis testing carried out using a t-test, from the calculation results obtained a value of  (2.664) >  (1.66757) with a Sig.2-tailed level of 0.010 < 0.05, which means that  rejected and  was accepted, so that it is concluded that there is a significant difference in the average mathematical reasoning ability of students using the Discovery Learning learning model and the Conventional learning model. Based on the analysis of the process of completing students' answers to the mathematical reasoning ability test that get Discovery Learning learning is better than students who get conventional learning.