Understanding Of Mathematical Concepts Research Articles

Enhancing mathematical function understanding in university students: a comparative study of design thinking vs. traditional teaching methods

Mathematical education requires innovative didactic strategies to enhance the understanding and application of mathematical concepts, as traditional teaching methods often lack relevance. This methodology aims to develop a problem-solving scientific approach called design thinking as a strategy for learning mathematics functions. The study was applied to a sample of 138 students of biochemical, biological, and industrial engineering careers attending the first academic cycle at the Faculty of Natural and Exact Sciences of the Particular Technical University of Loja-Ecuador. The methodology uses a quasi-experimental design with a convenience sampling method. All participants were divided into a control group (C, D, K) and an experimental group (P, Q, R). Knowledge, skills, perceptions, and engagement were measured through pretest, posttest, workshop, rubric, project, and survey instruments. The pretest results indicate that both groups had similar knowledge of mathematical functions (pretest mean experimental group: 1.42/2 and mean control group: 1.55/2). Moreover, after applying design thinking strategy to the experimental group, variables questionnaire, project, and workshop show statistical differences (p < 0.001) between groups related to the traditional learning strategy, increasing the experimental group’s score in the project (posttest mean experimental group: 1.62/2 points, and mean control group: 1.65/2). The survey opinion indicates that 53.5% of the experimental group highlighted the project’s development as positively impacting their academic training. In conclusion, problem-solving design thinking using scientific projects as a mathematical function learning strategy contributes to improving the comprehension of polynomial functions and developing mathematical competencies, abilities, and skills to generate tangible solutions for real problems.

ANALYSIS OF PSEUDO THINKING PROCESS SKILLS IN ELEMENTARY SCHOOL STUDENTS THROUGH ETHNOMATHEMATICS BASED PROBLEM SOLVING

This research aims to analyze process skills in pseudo-thinking through ethnomathematics-based problem solving in elementary school students. The subjects used in this research were 4 students from class IVB of SD Negeri 76 Muaro Jambi involving 4 subjects, namely 2 male and female subjects who thought pseudo-true and 2 male and female subjects who thought pseudo-false. Data collection techniques in this research used tests, interviews and documentation. Data analysis used in this research includes data reduction, data presentation, and drawing conclusions. The research procedures carried out in this research include the pre-field stage, field work stage, and data analysis stage. The results of the study stated that the four subjects showed various characteristics in using pseudo thinking patterns when answering mathematics questions. Each subject has abilities in several aspects of process skills in pseudo-true thinking, such as observing information, however, they still have shortcomings and difficulties in explaining the calculation process, communicating results, and understanding mathematical concepts as a whole. Consequently, further development is required to improve their processing skills in pseudo-thinking.

Increasing High School Students' Understanding of Mathematical Concepts through the Discovery Learning Model Assisted by Powtoon

Mathematics demands a variety of abilities, including understanding mathematical concepts. However, reality shows that students have difficulty understanding mathematical concepts. This research aims to determine the increase in the ability to understand mathematical concepts with the Discovery Learning model assisted by Powtoon compared to ordinary learning models and determine the level of effectiveness. A quantitative approach with a quasi-experimental method and nonequivalent control group design was used in the research, with data collected through a written test of the ability to understand mathematical concepts. The research subjects were class XI students at SMA Pasundan 1 Bandung. The results of research data analysis show that students who studied with the Discovery Learning model assisted by Powtoon experienced a higher increase in understanding of mathematical concepts than students who studied with the regular learning model. The effectiveness of the increase is relatively large with this learning model. In conclusion, the Discovery Learning model assisted by Powtoon is very effective in improving the ability to understand mathematical concepts. Therefore, the Discovery Learning model assisted by Powtoon can be used as an alternative to improve the ability to understand mathematical concepts.

Analisis Kesulitan Siswa dalam Menyelesaikan Soal Pembagian Materi Bilangan Bulat dengan Menggunakan Metode Porogapit

The background of this research is the importance of mathematics in daily life and the difficulties experienced by students in understanding mathematical concepts, especially division. This study aims to analyze the difficulties of students in solving integer division using the porogapit method in grade IV of SD Negeri Legok II, Indramayu Regency. This study uses a qualitative approach with a descriptive method. The research subjects were 6 people who were selected using the purposive sampling technique. Data was collected through observation, interviews, tests, and documentation. Data analysis uses qualitative data analysis consisting of data reduction, data presentation, and conclusion drawn. The results showed that students experienced difficulties in three main aspects: understanding problems, performing division calculation operations, and solving problems. Most students have difficulty in the division calculation operation even though they already understand the porogapit method. This difficulty has an impact on the understanding and application of mathematical concepts in daily life. This research provides recommendations for improving learning methods that can improve students' understanding and ability in integer division

EFFECT OF BLENDED LEARNING EDUCATIONAL MODEL ON SECONDARY SCHOOL STUDENTS’ MATHEMATICS CONCEPTUAL UNDERSTANDING

The study was conducted to assess the effect of a blended learning educational model on grade ten students' mathematics conceptual understanding in Ethiopia. A non-equivalent pre-test and post-test quasi-experimental design was employed. Two intact classes from different schools were randomly selected and assigned to experimental (n=38) and comparison group (n=45). From the previous semester, students’ record book revealed that both groups have almost an equivalent mathematics performance. A one-way ANOVA and paired sample t-test were used to analyze the data. Moreover, to check the equivalence of the groups, the same pre-test was developed and administered. The result indicates that both groups were equivalent. The test covers tenth-grade topics relations and functions, polynomial functions, exponential functions, and logarithmic functions. The study shows that students instructed through the blended learning approach surpassed those taught via the conventional method in their comprehension of mathematical concepts. The one-way ANOVA statistical result revealed there is a notable disparity between groups with effect size of η2 =.269, which is a large effect size. Moreover, a paired sample t-test shows the experimental group showed a substantial mean difference of 14.327 with a very large effect size (d=1.016) when compared with the comparison group. Thus, the study shows that blended learning was more effective in improving mathematical conceptual understanding when compared with a conventional method of teaching. Based on the findings, the researcher recommends blended learning in mathematics education and suggests stakeholders and policymakers incorporate the model into the curriculum. Keywords: blended learning, conceptual understanding, educational model, lab rotation model, mathematical concept

Best Practice STEM-Based Differentiated Mathematics Learning for Improving Learning Outcomes and Self-efficacy of High School Students

Learning outcomes and self-efficacy are important learning factors. Mathematics learning outcomes can reflect the extent to which students have developed as learners, while self-efficacy reflects students' self-confidence in their own abilities in solving mathematical problems. This study was based on a qualitative approach, best practice. This best practice uses the STAR flow (“Situasi, Tantangan, Aksi, Refleksi”). The situation at SMAN 1 Mande, especially class XI, shows low learning outcomes and lack of self-efficacy. The challenge faced is planning and implementing differentiated learning to improve learning outcomes and student self-efficacy. Through a STEM-based differentiated learning approach, researchers designed and implemented contextual learning on the theme of global warming with integrating science, technology, engineering and mathematics. The results of this best practice indicate an increase in learning outcomes and student self-efficacy. STEM-based differentiated learning can also improve understanding of mathematical concepts at the high school level. Researcher recommend that educators embrace differentiated learning strategies by customizing their approaches to accommodate the diverse needs such as students' level of readiness, interests, and student’s learning profile. The significance of comprehending student characteristics, such as learning styles and thinking abilities is paramount, especially in the implementation of student-centered learning. Additionally, educators are advised to prioritize aligning learning objectives with the curriculum, ensuring relevance and engagement. This various approach aims to create a dynamic learning environment to resonates with students individualized level. Develop interventions to address students' lack of confidence in solving mathematical problems can improve self efficacy.

Analisis Kemampuan Mahasiswa Matematika FMIPA Unimed dalam Menyelesaikan Pertidaksamaan Nilai Mutlak dengan Berbantuan Python

This research aims to analyze the ability of Unimed FMIPA Mathematics students in solving absolute value inequalities with the help of the Python program. The problem faced is that students often have difficulty solving inequality problems manually. The purpose of this research is to see the effectiveness of using Python in helping to solve absolute value inequalities and how it affects understanding of mathematical concepts. The method used was qualitative research with a sample of 20 fifth semester students of the Mathematics Study Program, FMIPA, Medan State University. Students are given absolute value inequality problems to solve manually and with the help of Python. Data was collected through online tests and questionnaires using Google Form. The research results show that the majority of students feel that using Python is very helpful in solving absolute value inequalities. As many as 95% of students consider Python to be effective in making it easier to solve mathematical problems and increasing understanding of the concept of absolute value.

Increasing the Ability to Understand Mathematical Concepts through the Team Games Tournament (TGT) Model Assisted by the PhET Application

This research seeks to assess the enhancement of third-grade elementary students' understanding of mathematical concepts comprehension through the Team Games Tournament (TGT) instructional approach, supported by the PhET application, compared to traditional teaching methods. The study employs a quasi-experimental method using a nonequivalent control group design. A total of 63 third-grade students participated, selected through purposive sampling. Data were collected through multiple techniques, such as tests, observations, discussions, and photo and video records. The assessment tool used was a descriptive test measuring mathematical concept understanding and is stated to have met the requirements for content validity, construct validity, reliability, level of difficulty, and differentiation. The data analysis technique for hypothesis testing uses IBM SPSS Statistics 2.6 software, namely the normalized n-gain hypothesis test. As indicated by the research results, students' ability to understand mathematical concepts at SDN Pancasila Lembang experienced a significant increase after receiving learning using the Team Games Tournament (TGT) instructional approach supported by the PhET application. This is proven by the results of the n-gain data test calculation, which is 0.36 in the medium category. The posttest average score for the experimental group was 67.78 and the posttest average score for the control class was 30.32. This indicates that the improvement in mathematical concept understanding in the experimental group surpasses that of the control group. Consequently, it can be concluded that the Team Games Tournament (TGT) learning model, supported by the PhET application, is a recommended alternative for enhancing elementary students' ability to grasp mathematical concepts.

Students understanding of mathematical concepts: A study based on the integrative learning model

Students understanding of mathematical concepts: A study based on the integrative learning model

A Socio-Constructivist Perspective on Problem-Solving Approaches in Mathematics: Perceptions of Future Primary Education Teachers

This study investigates the perceptions of future primary education teachers regarding the implementation of a problem-solving teaching approach from a socio-constructivist perspective. Although previous research has shown the benefits of problem-solving in mathematics education, few studies have yet focused on preservice teachers in primary education, particularly within a socio-constructivist framework. Therefore, this study addresses this gap by exploring the effectiveness and challenges of the Building Thinking Classrooms approach developed by Peter Liljedahl. The study was conducted through a case study design involving 36 first-year preservice teachers enrolled in a mathematics didactics course at a public university in Chile. Qualitative and quantitative data were collected through surveys, field logs, and classroom observations. The data analysis included descriptive statistics and content analysis to understand the students’ perceptions of problem difficulty, engagement, and the overall approach. The findings reveal that the problem-solving approach was positively perceived by the participants, highlighting its role in fostering critical thinking, collaboration, and a deep understanding of mathematical concepts. However, challenges were identified, particularly regarding group work and the autonomy required in solving problems. Furthermore, the study identified areas in which additional support could enhance the effectiveness of problem-solving approaches. This research underlines the importance of integrating problem-solving approaches into teacher education programmes and highlights the need for future research on the long-term impacts and strategies needed to support autonomy and collaborative learning.

The use of multimedia technologies in the illustrative teaching of the school mathematics course

The article emphasizes the importance of combining traditional teaching methods in the school mathematics course with modern illustrative methods. Traditional methods such as lectures and textbooks play a crucial role in the transfer of basic knowledge and concepts. However, the use of illustrative techniques such as visualization, games, and interactive applications can significantly improve students' understanding and assimilation of mathematical concepts. The combination of these methods allows for a more efficient and modern educational environment, encouraging active student participation and encouraging their creative thinking. In the course of the work, it is proposed to talk about the illustrative method and the traditional method, about the advantages and disadvantages of their application, compare the illustrative method and the traditional method, the results of research and their application. Based on data analysis and pedagogical methods, he proposes strategies for integrating multimedia resources to improve the visual and conceptual understanding of mathematical concepts in the school classroom. Analyzing the results of experiments and teaching methods, the authors discuss the practical use of multimedia resources to increase interest and understanding of mathematical concepts among students. In the course of the work, approaches to learning were considered, the advantages and disadvantages of the illustrative method and the traditional method were identified, analogs were analyzed and recommendations were given.

Updating Calculus Teaching with AI: A Classroom Experience

In the context of mathematics education, the integration of artificial intelligence (AI) in teaching calculus is revolutionizing instructional methodologies and enhancing learning experiences both inside and outside the classroom. This study explores the use of specific AI tools, including ChatGPT, MathGPT, Gemini, and Wolfram Alpha, to deepen students’ understanding of key mathematical concepts such as derivatives and rates of change through continuous interaction with a virtual tutor. By employing well-designed prompts, these tools facilitated problem-solving exercises that were verified and refined by AI, fostering both precision in calculations and conceptual clarity. Observations from the classroom implementation reveal that students not only improved their accuracy in performing derivative calculations but also developed a clear understanding of the distinctions between average and instantaneous rates of change. The AI tools created a dynamic, adaptive learning environment, providing immediate feedback and simulations that significantly boosted student engagement and motivation. These findings underscore the potential of AI to transform mathematics education by making learning more personalized and accessible, ultimately enhancing educational outcomes and preparing students for future academic and professional challenges. Furthermore, this study introduces an innovative approach to refining AI prompts and interactions, highlighting the importance of iterative improvement to enhance the quality of AI feedback. This approach is crucial for developing better problem-solving skills and ensuring a comprehensive understanding of mathematical concepts.

ANALISIS BIBLIOMETRIK: APPROACHING MATHEMATICS FOR SLOW LEARNERS BERBASIS VOS VIEWER

This research presents a bibliometric analysis of mathematical approaches for slow learners using the VOS Viewer analysis tool. Slow learners often encounter difficulties in understanding mathematical concepts, which are key components of the education curriculum. This study aims to explore trends, patterns, and research focus in this domain and to identify key contributors in the field. Bibliometric methods were employed to analyze a dataset consisting of indexed journals relevant to the chosen topic. The bibliometric method involved collecting journal data from 2019 to 2024 via Google Scholar using the Publish or Perish software, yielding 1,000 journals. Variables related to Approaching Mathematics for Slow Learners that have potential and novelty for future research include gamification, e-learning, critical thinking, student perception, student interest, machine learning, mathematical models, STEM, e-modules, digital literacy, science learning, blended learning, contextual teaching, mathematical formulations, artificial intelligence, scoping review, self-efficacy, intervention approaches, mathematics achievement, mathematical concepts, and action research.

Analysis of Mathematical Connection Ability and Self-Confidence on Junior High School Students

This research is motivated by the importance of students’ mathematical connection abilities and self-confidence in learning mathematics. Mathematical connection ability is an important factor in understanding mathematical concepts. The aim of this research is to analyze the level of students’ mathematical connection abilities and junior high school students’ self-confidence. The method used in this research is a descriptive-qualitative method. The research subjects were 37 students in class VIII-C of SMPN 3 Margahayu. The instruments used were four items of mathematical connection test material on the System of Two-Variable Linear Equations and non-tests of students’ confidence in learning mathematics. The results of the analysis show that the average score of all mathematical connection ability test questions in indicator 1 using relationships between mathematical topics is 5%, indicator 2 is understanding equivalent representations of the same concept (36%), indicator 3 uses mathematics in everyday life (52%), and indicator 4 uses mathematics in other subjects (27%). So the average is 30%. So the students’ mathematical connection ability is included in the low category. Most students are unable to solve problems with indicators using relationships between mathematical topics. This is shown by the results of the mathematical connection ability test; students did not connect optimally. But in learning mathematics, students already have good self-confidence.

DESAIN DIDAKTIS UNTUK MENGATASI HAMBATAN BELAJAR SISWA SD PADA PEMAHAMAN KONSEP LUAS BANGUN DATAR

This research focused on students who faced challenges in understanding concepts of two-dimensional area. The primary cause of these learning obstacles was the lack of mastery and comprehension in mathematics. To address this, a didactical design was developed based on the principles of the Realistic Mathematics Education (RME) model, aimed at helping students overcome these difficulties. This design was initially tested with fourth-grade students to observe their responses during the learning process. Despite some unforeseen reactions, the analysis of these initial implementations informed a revised design, which was subsequently tested again. The didactical design was divided into three sessions, each with anticipated student responses in mind. The research employed Didactical Design Research (DDR) using qualitative methods, including learning barrier tests, short fill-in lists, interviews, questionnaires, documentation, and field notes for data collection. The study resulted in a didactical design that could be effectively used to improve students' understanding of two-dimensional area concepts in mathematics.

ANALISIS ATURAN ASOSIASI KESALAHAN STATISTIKA SISWA KELAS X-11 SMA NEGERI 10 SAMARINDA BERDASARKAN KRITERIA WATSON

Mathematics plays an important role in forming systematic thinking patterns, logic, and financial management skills. However, many students have difficulty in understanding mathematical concepts due to various factors, which affect the success of learning. This study aims to identify and classify common errors of class X-11 students of SMA Negeri 10 Samarinda in solving statistics problems using mixed quantitative and qualitative methods. solving statistics problems using mixed methods, namely quantitative and qualitative. Using the apriori algorithm with a minimum support of 20% and 80% confidence, four types of errors were found that were often made by students, namely incorrect data errors, procedural errors, missing conclusions, and skill hierarchy problems. Data analysis and interviews showed a strong correlation between these errors, where errors in data collection often lead to data manipulation and incorrect conclusions. To overcome this problem, the school has implemented more effective learning strategies, such as additional guidance, material adjustments, and contextual approaches. These strategies are expected to improve students' conceptual understanding, reduce errors, and improve academic achievement in statistics.

Gamified recreational exercise focused on Markov Chains

The gamified recreational exercise focused on Markov Chains is an innovative methodology that combines learning with play to facilitate the understanding of statistical and mathematical concepts. Markov Chains are models that describe systems that transition between different states, where the probability of moving to a future state depends only on the current state and not on previous ones. By integrating game elements, such as challenges, rewards and competition, we seek to motivate students to actively engage in the learning process. This approach makes learning more engaging and gives participants a hands-on experience of how Markov Chains work in real situations. Exercises may include simulations, board games, or digital applications that represent scenarios where students must make decisions based on probabilities. Through gamification, teamwork and problem solving are encouraged, essential skills in today's world. The gamified recreational exercise is a favorable tool for teaching Markov Chains, it makes learning more dynamic and effective.

Enhancing Measurement and Calculation Education in High School through 3D Printing Technology

Mathematics education often grapples with the challenge of teaching abstract mathematical concepts, particularly those existing in 3D space. Visualizing, manipulating, and comprehending these abstract objects can be a formidable task for learners. While 3D printing technology has found applications in various fields, its utilization in mathematics education remains limited. This research explores the potential and effectiveness of 3D printing technology in enhancing the teaching of measurement and calculation topics in high school mathematics. We designed 3D printed models with a specific focus on shapes, polyhedra, pyramids, and cylinders. These models were created to facilitate hands-on learning experiences for students, enabling them to directly measure, calculate, and experiment with these tangible mathematical objects. The experimental results reveal that students not only learned how to employ measuring tools to gauge the dimensions of tangible mathematical objects but also conducted mathematical experiments related to the 3D printed models. This practical engagement allowed students to gain valuable experiences and foster a deeper understanding of abstract mathematical concepts.

Penerapan model pembelajaran problem-based learning dalam meningkatkan kemampuan pemahaman konsep matematika siswa

This study investigated the effectiveness of problem-based learning (PBL) model in improving seventh-grade students’ conceptual understanding of mathematics at SMP Negeri 13, Ternate City, Indonesia. This study used a quantitative approach using a pre-experimental design, specifically a one-group pretest-posttest design. The sample consisted of 34 seventh-grade students at one of the public junior high schools in Ternate City. Data were collected using a written test, and analysis was conducted using inferential statistics, specifically the Paired Sample T-Test. The findings showed that the implementation of the PBL model significantly improved students’ ability to understand mathematical concepts, with the results showing a medium effect size. In addition, the effect size test classified the impact of PBL on students’ mathematical understanding in the high category.

Analysis of Comprehension Difficulties in Chemistry and Their Impact on Student Interest in Learning

Chemistry is often considered a difficult subject for learners due to its abstract concepts and complex terminology. This can lead to difficulties in understanding the material and a decrease in students' interest in studying chemistry. The aim of this research is to describe and explain the factors of difficulty understanding in solving chemistry material experienced by students. The research method used is descriptive qualitative. The results show that 62.3% of students experience slight difficulty and 37.7% experience moderate difficulty in understanding chemistry material. The interest in learning chemistry of class XII MIA students is categorized as sufficient with a percentage of 46.68%. Factors causing difficulties in understanding chemistry material include a lack of understanding of mathematical concepts, the predominance of lecture methods, limited learning media, and the suboptimal use of chemistry laboratories. The conclusion of this research provides an overview that the factors causing difficulties in understanding chemistry material affect students' interest in learning. Therefore, these findings can be used as evaluation material to improve the quality of chemistry education in schools.