Understanding Of Mathematical Concepts Research Articles

Teaching mathematical concepts based on the principle of "Consistency in Explanation"

This paper explores the importance and methods of achieving "self-consistency" in the teaching of mathematical concepts. It first emphasizes the central role of mathematical concepts in learning mathematics and, through the example of teaching the eccentricity of an ellipse, points out the complexity of understanding mathematical concepts. Then, by exploring the history of "eccentricity," the paper demonstrates the human conventions and historical development behind mathematical concepts, highlighting the need for teachers to delve into the origins and meanings of concepts in their teaching. The paper proposes four strategies to achieve "self-consistency": sorting out the history of mathematical development, finding applications of mathematics in daily life, rebuilding connections between mathematical knowledge, and utilizing perspectives from other disciplines. Finally, the paper argues that "self-consistency" is not only a teaching method but also a teaching philosophy, aimed at helping students gain a deep understanding of mathematical concepts.

The Effect of Interactive Learning Media on Students' Understanding of Basic Mathematical Concepts in SDN 1 Tebaban

This study aims to determine the effect of the use of interactive learning media (wordwall) on the understanding of basic mathematical concepts of grade IV students at SDN 1 Tebaban. This type of research is a quantitative research of experimental methods with a quasi-experimental design of pretest-posttest control group design. The population of this study is class IV A and IV B which totals 35 students. The sample of this study uses a saturated sampling technique. The data collection technique in this study uses observation sheets, questionnaire sheets and pretest and posttest test sheets. The data analysis techniques in this study include observation and questionnaire data analysis, descriptive analysis, normality test, variance homogeneity test and independent samples test. The results of the observation sheet showed that the students' understanding of basic mathematical concepts in the experimental class reached 75% ('Very Good'), higher than the control class which only reached 62.99% ('Good'). Based on the results of the questionnaire, the use of wordwall interactive media was proven to be more effective in improving students' understanding than mind mapping learning media and teaching aids in the control class, with 91% of students in the experimental class supporting the use of wordwalls, compared to 80% in the control class. The t-test showed a value of Sig. (2-tailed) 0.02, so that the alternative hypothesis was accepted, indicating a significant influence of interactive learning media on the understanding of mathematical concepts of grade IV students at SDN 1 Tebaban.

TEACHING ANGLES AND POLYGONS USING GEOGEBRA SOFTWARE

The objective of this paper is to describe a didactic-pedagogical sequence developed to teach angles and polygons to an 8th grade class of a public state school in Palmeira dos Índios, Alagoas, Brazil. The sequence is part of the Extension Project "Mathematics and Active Methods" and addresses some common difficulties in teaching geometry, such as the abstraction of formal concepts and the students' lack of understanding of the connection of these concepts to real situations. Studies indicate that the use of digital technologies facilitates the visualization and interaction with mathematical concepts, promoting more dynamic and meaningful learning. In view of this, the sequence, applied in four classes, involved activities contextualized to sports, using the GeoGebra software. The results show that, although some students still face difficulties, the interactive and contextualized approach improved engagement and understanding of formal mathematical concepts, especially geometric ones.

A Review of Implementations of Math Competency Oriented Teaching-Learning Systems

Mathematical skills are fundamental to students' cognitive and practical development and are essential to their academic and professional success. The implementation of effective teaching-learning systems is crucial to facilitate the acquisition of these competencies, providing students with tools and methodologies that promote a deep and lasting understanding of mathematical concepts, these systems must be interactive, adaptive and designed to address the individual needs of students, ensuring that each student can reach his or her maximum potential. This paper seeks to identify the methods used in the implementation of these systems, the technology and the relevant factors for their construction. The results show that gamification and game-based learning are popular and effective methods, while block-based programming is considered to be efficient. Factors include curriculum design, interactivity and content. Among the most used technologies, scratch and virtual reality (VR) are mentioned.

Choose your own T-cell fate: creation of a narrative-based, decision-making activity to engage students in immunology.

Undergraduate courses in immunology are content-heavy and combined with a new, complex vocabulary, can be an overwhelming subject for students. In-class active learning approaches have been found to improve understanding of difficult concepts in science, technology, engineering and mathematics (STEM) disciplines; however, many undergraduate courses maintain a high dependence on lecture-style teaching because of time constraints, content demands and student resistance. We designed an online, out-of-class activity, the "Life and Death of a Tcell", to complement a lecture on a complex immunological concept, T-cell development. Inspired by the "Choose Your Own Adventure" children's books, a fictional narrative was created in which students assume the role of a cell with a dream of becoming a helper Tcell. Decision-making scenarios then prompt students to draw on their knowledge from the lecture to successfully navigate the steps of T-cell development. The activity was built on two platforms, Google Forms and H5P (HTML 5 Package), both of which are readily accessible and allow the inclusion of branching logic and the creation of a decision tree-based activity. An anonymous survey revealed that students found this interactive approach enjoyable, and their perceived understanding of the content significantly increased. Students appreciated the inclusion of a novel learning resource, with requests for similar activities to be developed for other immunological concepts. In conclusion, we developed a narrative-based, decision-making activity to complement a lecture on T-cell development. As an out-of-class activity, this style of learning approach can potentially capitalize on the benefits of active learning, while also overcoming barriers of student resistance.

Pedagogical responsiveness of mathematics instruction at inclusive secondary schools: A particularistic case study

This qualitative particularistic case study explores the perspectives and experiences of learners with visual and hearing impairments regarding the teaching of mathematics. Extreme-case sampling was employed to select four learners (three hearing impaired and one visually impaired) from the only two inclusive secondary schools in the northern part of Namibia. The study qualitative study utilised open-ended questionnaires and interviews. Verbatim quotes from the research participants were used as inferences to identify descriptors within the first-generation Cultural Historical Activity Theory, which served as a theoretical and analytical tool. The findings revealed that the activity system of learners with visual and hearing impairments exhibited tensions that negatively affected their performance in mathematics. Learners experienced marginal responsive pedagogy in mathematics classrooms due to teachers' lack of knowledge and pedagogical skills for delivering meaningful mathematical instruction. While learners without disabilities struggled with comprehension and effective communication skills, learners with visual and hearing impairments faced a lack of equipment to support the conceptualisation and visualisation of mathematical subject content. The authors emphasise the critical importance of addressing communication barriers and adapting teaching practices to support the learning and inclusion of visually and hearing-impaired learners in mathematics, with an emphasis on mathematical language that promotes a better understanding of mathematical concepts. Teacher training should also incorporate responsive pedagogy to enhance outcomes and foster a more inclusive learning environment that promotes academic success and positive social experiences for all learners. Recommendations at a policy level, including advocating for a decolonised curriculum were made.

Integration of Calculator.oi Application in Improving Mathematics Learning Outcomes of Students in Elementary Schools

This study aims to evaluate the effectiveness of the Calculator.oi application integration in improving students' mathematics learning outcomes in Elementary Schools. This study focused on fourth-grade students at SDN 22 Ketapang and used a quantitative approach with an experimental method. In this study, the experimental method was applied to compare the differences in students' learning outcomes before and after using the Calculator.oi application. Learning outcome data were collected and analyzed using the Wilcoxon test, after the normality test showed that the data were not normally distributed. The results showed a significant increase in students' mathematics learning outcomes after using the Calculator.oi application. Analysis of the differences between pre-test and post-test scores revealed that all students experienced significant progress in their understanding and achievement in mathematics. The significance value obtained from the statistical test was below 0.05, indicating that this application had a significant positive impact and was effective in improving students' learning outcomes. Based on these findings, it is recommended that the Calculator.oi application be integrated more widely into the mathematics learning process in Elementary Schools. The use of this application is considered an innovative and effective learning medium in supporting the understanding of mathematical concepts. Further research is recommended to involve a larger sample size and different class variations in order to obtain more comprehensive and representative results. In addition, exploration of students' perceptions regarding the use of this application as a learning tool is also important. This will provide a deeper understanding of how the Calculator.oi application can be accepted and utilized in a broader learning context.

THE RELATIONSHIP BETWEEN LEARNING STYLES AND UNDERSTANDING MATHEMATICAL CONCEPTS IN QUADRATIC FUNCTIONS

The research teka-teki is that students are experiencing difficulties in understanding the concept of quadratic functions. The aim of the study is to determine the relationship between learning styles and mathematical concept understanding in solving quadratic function problems among 9th grade students at SMP Negeri 3 Ulunoyo. This research adopts indah ambang quantitative approach with indah ambang correlational study type. The population in this study consists of 20 9th grade students from SMP Negeri 3 Ulunoyo, and the sampling technique used is besaran sampling. The instruments used are questionnaires and tests of mathematical concept understanding. Based on the research results, indah ambang correlation coefficient of 0.64 was obtained, indicating indah ambang positive and strong correlation. The coefficient of determination is 40.96%, showing that the contribution of learning styles to concept understanding is 40.96%, with the remaining contribution attributed to other factors. The calculated t-value is 3.50324, and to determine the critical t-value at indah ambang 0.05% significance taraf, the t-table value is 2.100922. Since the calculated t-value (3.50324) is greater than the t-table value (2.100922), it can be concluded that there is indah ambang relationship between learning styles and mathematical concept understanding among 9th grade students at SMP Negeri 3 Ulunoyo, with the correlation taraf falling into the moderate category. Therefore, the researcher suggests (1) students should recognize their own learning styles and optimize them to facilitate better learning and achieve optimal performance, and (2) teachers are encouraged to adapt their teaching styles to meet the needs of all students, not just those with specific learning styles.

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.

MATHEMATICS LEARNING STRATEGIES THAT SUPPORT PANCASILA MORAL EDUCATION: PRACTICAL APPROACHES FOR TEACHERS

This study aims to identify and develop mathematics learning strategies that support moral education based on the values of Pancasila. Using a qualitative approach, the research involves mathematics teachers from several elementary and secondary schools to explore effective methods for integrating Pancasila values into mathematics instruction. The findings indicate that learning strategies, including contextual learning, collaborative projects, and reflective discussions, can enhance students' understanding of mathematical concepts while also strengthening their character. Additionally, the study identifies challenges in implementing these strategies, including time constraints and a lack of training for teachers. It is hoped that these findings can serve as a reference for developing more effective educational practices in integrating moral values into mathematics learning.

MATHEMATICS EDUCATION BASED ON LOCAL WISDOM: LEARNING STRATEGIES THROUGH HOMBO BATU

This study aims to explore the application of local wisdom-based mathematics education through learning strategies using the traditional game Hombo Batu. Local wisdom is considered a valuable resource for enriching the learning process and enhancing students' understanding of mathematical concepts. Through this approach, students not only learn theoretically but also connect the material to their daily experiences, which increases their motivation and engagement. The results of the literature review indicate that Hombo Batu can serve as an interactive learning medium, supporting the development of social skills and strengthening students' cultural identity. Although there are challenges in its implementation, such as a lack of training for teachers and limited resources, recommendations for integrating local wisdom into the mathematics education curriculum can help create more meaningful learning experiences. This study is expected to provide insights for the development of more relevant and effective teaching methods in the educational context.

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.

Modelling School Zone Border as Rich Modelling Problem for Secondary School Students

This article explores the potential of using the school zoning problem in Indonesia as a vehicle for teaching mathematical modeling to secondary school students. This problem is highly suitable for students as a modeling challenge because it is (i) contextual, (ii) rich, (iii) challenging, and (iv) within students' Zone of Proximal Development (ZPD). School zoning involves a concept called Voronoi, essentially a partitioning problem. For simpler or special-case problems, these partitions can be created using concepts already taught in secondary schools, such as perpendicular bisectors and radical axes. However, for more complex problems with multiple sites, an algorithm is required, which involves advanced mathematical concepts beyond the typical secondary curriculum. Yet, with the rise of visual programming languages like Scratch, Snap!, StarLogo, and TurboWarp, it becomes possible to tackle these partitioning challenges using coding and only basic mathematical principles. This approach not only enhances students' understanding of foundational mathematical concepts but also fosters the integration of computational thinking and coding within mathematics. In summary, the school zoning problem serves as an ideal topic for mathematical modeling for secondary school students, promoting the integration of mathematical concepts, computational thinking, and coding skills. Doi: 10.28991/ESJ-2024-08-05-019 Full Text: PDF

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