Mathematical Concepts Research Articles

Exploring the relationship between students' attitudes and fraction sense proficiency across lower secondary grades

Understanding fractions is a critical mathematical skill necessary for more advanced mathematical concepts and applications. However, many students struggle with fraction sense, which is the foundational understanding and flexible use of fractions. This study aims to explore the relationship between students' attitudes toward learning fractions and their proficiency in fraction sense in lower secondary grades. Using a descriptive-correlational design, data were collected from 296 students aged 13 to 15 using the Fraction Sense Test (FST) and the Attitudes Towards Learning Fractions Questionnaire (ATLF). The study found that students consistently struggled with fractional concepts, achieving low scores across all grades. Nevertheless, a significant, though diminishing, relationship was observed between positive attitudes towards fractions and fraction sense proficiency from Secondary One to Secondary Three. These findings suggest the need to integrate meaningful fraction learning approaches to maintain students' positive attitudes, thereby improving their overall mathematical competence.

THE EFFECTIVENESS OF MATHEMATICS LEARNING THROUGH A REALISTIC MATHEMATICS EDUCATION APPROACH IN ELEMENTARY SCHOOLS

The research aims to analyze the effectiveness of mathematics learning through the realistic mathematics education approach in learning the concept of counting integers in grade VI elementary school students. The research used a quasi-experiment with one pretest postets design. The research involved 32 grade VI students at SDN 205 Neglasari, Coblong District, Bandung City. The research instrument is in the form of a multiple-choice test that includes addition and subtraction of decimal numbers. Research shows that the RME approach is effective in producing a significant improvement in students' learning completeness in the addition and subtraction of decimal integers, as well as improving mathematical problem-solving, self-efficacy, reasoning, and mathematical literacy. RME encourages students to recognize the practical application of mathematical concepts through real-world contexts and cultural elements, as well as to cultivate creative and imaginative thinking skills so that they can be an important strategy in improving mathematics education in primary schools.

PENGGUNAAN MEDIA SOFTWARE GEOGEBRA UNTUK MENINGKATKAN KEMAMPUAN REPRESENTASI MATEMATIS SISWA SMA

Mathematical representation ability is an important ability in understanding mathematical concepts as an effort to obtain clarity of meaning and understanding in solving problems. Technology-based learning media can simplify the learning process thereby helping students in representing mathematical problems. This research aims to determine the increase in students' mathematical representation abilities using Geogebra software. This research is quantitative research with a quasi-experimental type. The population is students of class XI MIPA at SMA Negeri 1 Lhoong Aceh Besar for the 2023/2024 academic year consisting of 2 classes totaling 60 people. There are 30 people in Class XI MIPA 1 as an experimental class with the Geogebra software learning media, and 30 people in XI MIPA 2 as a control class without the Geogebra program learning media. The data collection technique in this research is using Pretest and Posttest. Meanwhile, the data analysis techniques used in this research are descriptive statistical analysis and inferential statistical analysis. The results of the research showed that there was an increase in students' mathematical representation abilities who were taught using Geogebra software media in class XI MIPA students at SMA Negeri 1 Lhoong. Most students answered the questions according to indicators of mathematical representation ability in the form of visual, symbolic and verbal representations.

The Systematic Review of the Studies Conducted in Turkey on the Topic of Applying 3D Printing in Mathematics Education

3D printing technology is increasingly widely used in all areas of STEM education. Many researchers emphasize that 3D printing in the context of mathematics education unpacks students' mathematical and design thinking, as well as helps them develop spatial skills, and is a key tool for visualizing mathematical concepts, especially in calculus and geometry. However, when the relevant literature is examined, it is seen that there is no existing systematic review that comprehensively describes and synthesizes the findings in the literature on how 3D printers are applied in mathematics education in the context of studies conducted in Turkey. The purpose of this research is to make a systematic review of the studies conducted between 2015-2023 in Turkey on the topic of applying 3D printing in mathematics education. The results of this study show that qualitative research method is more preferred in the analyzed studies. The predominant dependent variable employed in these investigations is mathematics achievement, with the majority of participants being middle school students. The results of this systematic review indicated that applying 3D printing in mathematics instruction usually helps to improve students’ mathematical literacy, and mathematical skills in the context of studies conducted in Turkey.

Upaya Meningkatkan Pemahaman Konsep Matematika Siswa Melalui Penerapan Model CORE di MA NW Putra Narmada Tahun Pelajaran 2023/2024

This study was conducted as an effort to enhance students' understanding of mathematical concepts through the application of the CORE (Connecting, Organizing, Reflecting, Extending) model at MA NW Putra Narmada, West Lombok Regency. This research is a Classroom Action Research (CAR) carried out in two cycles with stages of planning, implementation, observation, and reflection. The subjects of this research are 34 students from the 10th grade at MA NW Putra Narmada. The research instruments used are observation sheets and test sheets. The data collection techniques employed are testing and observation. The data analysis techniques used are both quantitative and qualitative data analysis. The results of this study indicate an improvement in the understanding of mathematical concepts among the 10th grade students of MA NW Putra Narmada after applying the CORE learning model. Test results show an increase in students' understanding of mathematical concepts in cycle I to 57% with a sufficient category, while in cycle II, it increased to 95.00% with an excellent category. Observation results show 68% in cycle I with a good category and 96.00% in cycle II with an excellent category.

PENINGKATAN PEMAHAMAN PENJUMLAHAN DENGAN TEKNIK MENYIMPAN MENGGUNAKAN ALAT PERAGA DI KELAS II SD NEGERI 218/LIMBUR BARU

ABSTRACT The research problem is the lack of understanding of the material for calculating sequential additions. The aim of this research is to improve understanding of compound addition material by storing techniques through the use of number value racks. Class II students at SD Negeri 218 Limbur who have mild intellectual disabilities will benefit from a better understanding of the concept of multilevel addition operations. This type of research is called Classroom Action Research (PTK). This research was carried out in two cycles, each cycle being carried out in three meetings. Each cycle has four interrelated phases: observation, reflection, action implementation, planning phase, and reflection. The research subjects were four students of SD Negeri 218 Limbur class II. Data was collected through test and observation methods. Quantitative analysis was carried out on the data, and a table was presented showing student learning outcomes. Based on the results of research conducted in cycle I and cycle II, the results of data analysis and reflection show that cycle I research has not met the expected indicators of success, namely better understanding of mathematical concepts because it shows learning outcomes and students' abilities in understanding and carrying out sequential addition operations. using the saving technique, then the average result in cycle II was 62.5%. By using the saving technique, students were able to understand the concept of sequential addition, which not only achieved the desired goal but also improved. This shows that the use of the number value rack display tool can improve students' understanding of the addition material using storing techniques. Keywords : stacked addition, rack of number values.

Alternative ways to initiate students’ intuition, and hence internalization, of why zero factorial is equal to one

Zero factorial, defined to be one, is often counterintuitive to students but nonetheless an interesting concept to convey in a classroom environment. The challenge is to delineate the concept in a simple and effective way through the practice of justification, a familiar concept in mathematics and science education. In this regard two algebraic and one statistical justification using the squeeze theorem are presented. To assess the effectiveness of the justifications, a student survey was conducted at a comprehensive university incorporating the analysis of the pre- and post-presentation statements. They clearly present that the justifications are useful in giving credence to zero factorial equals one. Overall, the result from the online survey supports that the students preferred Justification 1. The justifications provide instructors alternative ways to initiate exploration of students’ intuitive set up of comprehending unobvious facts like zero factorial equals one. For a range of learners with their varied abilities to perform various mental activities most closely associated with learning and problem-solving, the justifications as simple alternative methods offer the potential to raise the current level of cognitive skills to inspire differentiated paths of learning. These are evident from survey results noting the role of statistical thinking and techniques.

Sustaining Retentive Memory of Mathematics Concepts in Adolescents Utilising Game-Based Learning: A Case of Repeated Measures

Effective mathematics education is pivotal for students’ academic achievements and future career prospects. However, traditional teaching methods are often inadequate for helping students retain mathematical concepts, emphasizing the necessity for innovative approaches such as game-based learning. This research aimed to assess the efficacy of game-based learning in bolstering the retention of trigonometry concepts among senior secondary school students. Employing a mixed between and within measures ANOVA design, the study randomly assigned 60 students (aged 15-16 years, 31 males and 29 females) to either an experimental group (n=28) receiving game-based learning or a control group (n=32) receiving traditional instruction. Data, collected through the study’s tool (Mathematics Achievement Test [MAT]) at the pre-test, post-test, and retention test stages, underwent repeated measures ANOVA analysis. Results indicated significant effects of Group [F(1, 58) = 44.081, p<.001, ?²p=.432], Time [F(1.783, 103.4) = 16.561, p<.001, ?²p=.222], and Group by Time interaction [F(1.783, 103.4) = 18.125, p<.001, ?²p=.238]. The experimental group exhibited notably higher retention scores (Time 3 mean = 74.82) than the control group (Time 3 mean = 44.38). Importantly, gender, age, and location did not significantly moderate the effectiveness of the game-based approach. In conclusion, game-based learning effectively enhances and sustains students’ retention of trigonometry concepts, irrespective of demographic variables. This study furnishes empirical validation for integrating game-based learning into mathematics education, underscoring its potential to fortify conceptual retention, and offering actionable insights for educators and policymakers alike.

Development of Interactive Multimedia Based on ISpring Suite with Corrective Feedback to Improve Student’s Conceptual Understanding Ability

The ability to understand mathematical concepts are one of the abilities that must be achieved. Based on the results of the initial test, the conceptual understanding ability of class IX students at one of schools in Magelang are relatively low. The aim of this research was to produce iSpring Suite-based learning multimedia products with valid, practical and effective corrective feedback in improving students' concept understanding abilities. The research belongs to research and development using the Borg and Gall model. The results of the validity test were 88.44% by material experts in the "very valid" category, and 80.77% by multimedia experts in the "very valid" category. The results of the practicality test were based on the results of the student response questionnaire with an average score percentage of 90% in the "very practical" category, then based on the teacher response questionnaire with a percentage of 88% in the "very practical" category, and based on learning implementation questionnaire, the score was 93.33% with the "very good" category. The results of the test involving 32 students based on the N-Gain were 0.71 in the high improvement category, and the Wilcoxon test obtained Z = -4.941. So, interactive multimedia based on ISpring Suite with Corrective Feedback are valid, practical and effective to improve junior high school students' concept understanding skills in quadratic equation material.

Culturally Contextualized E-Module Based on Papua: Why Teachers and Students Need It for Teaching Linear Programming Material?

The use of e-modules in mathematics learning significantly aids both teachers and students in the teaching and learning process. However, the design of e-modules has not been extensively linked to the cultural context in which students live. Therefore, this study aims to explore and analyze the needs of teachers and students in developing culturally integrated e-modules, particularly those reflecting the culture of Papua, for high school students. The research design employed is phenomenological. Participants included Mathematics teachers for grades X, XI, and XII in Nduga Regency, Papua Highlands, and 64 high school students (42 male and 22 female). Data collected from observations and interviews were qualitatively analyzed using Miles-Huberman Interactive Analysis. Findings revealed that the high schools still use the 2013 curriculum, relying on standard textbooks as teaching materials. These textbooks pose problems for students as they are often uninteresting, use formal language, are difficult to understand due to abstract content, and are not contextualized to students' daily lives. Additionally, the reduction in face-to-face learning hours, due to the school's location in a conflict area, hampers effective teaching and learning processes. Another interesting finding is that high schools in Nduga Regency have not yet utilized technology in learning, despite having internet access. These findings imply the need for teaching materials integrated with technology and local culture to help students understand mathematics concepts and assist teachers in teaching both inside and outside the school.

Caracterización del conocimiento de estudiantes universitarios al relacionar una función con su función derivada desde un enfoque gráfico

This paper aims to show how university students relate a function with its derivative function in a task with a purely graphical approach. This task is part of a diagnostic test used in a broader investigation whose objective is to build the concept of derivative in university students with the help of the APOE theory, which provides mental structures required to understand a mathematical concept: action, process, object, and scheme. Initially the paper shows the details of the test and the analyzed task, then it shows the qualitative and quantitative analysis of the observed responses. In general, the results obtained show deficiencies in students when faced with graphic focus exercises. Likewise, the justifications observed in students show an inclination towards solving exercises from an algebraic aspect, thus leaving aside the graphics of the activity. We assume that future research may use these results as background for their works, and active teachers may encourage their students to resolve this type of conceptual items in the classrooms.

Application of STAD Model Cooperative Learning To Improve Mathematics Learning Activities of Grade VI Students of SDN XI No. 40 Blimbing, Malang Regency

The implementation of education in schools makes various kinds of lessons to students that must be taken in realizing their ideals. The subjects received and taught to students must be developed and improved in accordance with changes in the school curriculum. The purpose of learning mathematics is expected that students are able to provide knowledge to learn and understand mathematical concepts and be able to apply scientific methods that provide process skills to solve problems in everyday life. Based on research conducted by researchers for two weeks in the field from the 03rd to the 15th, researchers managed to collect some data that the number of samples studied was 26 students in a column and read the pressure in the table of the average value r product moments with a signification level of 5% we will find the number 0.388. This number shows the signification limit number, while the average calculated value of 0.8915 means that the relationship between the learning outcomes of cooperative students and non-cooperative groups through the STAD model cooperative learning is quite good. Because the calculated value obtained by r = 0.8915 means that jau is above the signification limit of 0.388. According to the results of the data analysis obtained, the relationship between the learning outcomes of cooperative students with non-cooperative groups with the cooperative learning strategy of the STAD model is very significant between the learning outcomes of cooperative students of group X with the learning outcomes of non-cooperative students of group Y.

Monitoring resilience in bursts

The possibility to anticipate critical transitions through detecting loss of resilience has attracted attention in many fields. Resilience indicators rely on the mathematical concept of critical slowing down, which means that a system recovers more slowly from external perturbations when it gets closer to tipping point. This decrease in recovery rate can be reflected in rising autocorrelation and variance in data. To test whether resilience is changing, resilience indicators are often calculated using a moving window in long, continuous time series of the system. However, for some systems, it may be more feasible to collect several high-resolution time series in short periods of time, i.e., in bursts. Resilience indicators can then be calculated to detect a change of resilience between such bursts. Here, we compare the performance of both methods using simulated data and showcase the possible use of bursts in a case study using mood data to anticipate depression in a patient. With the same number of data points, the burst approach outperformed the moving window method, suggesting that it is possible to downsample the continuous time series and still signal an upcoming transition. We suggest guidelines to design an optimal sampling strategy. Our results imply that using bursts of data instead of continuous time series may improve the capacity to detect changes in resilience. This method is promising for a variety of fields, such as human health, epidemiology, or ecology, where continuous monitoring can be costly or unfeasible.

There’s a Thin Line Between Numerators and Denominators: Addressing Academic and Behavioral Needs of Students With EBD Using SRSD Fractions

Fractions are an imperative skill for students to master to achieve success in future mathematics concepts and classes. Yet many students, especially those experiencing math difficulties and/or characteristics of emotional and behavioral disorders, continue to exit elementary school without a concrete foundation of fractions skills required to successfully transition into higher level math courses. In this article, we present an overview of SRSD Fractions, a strategy instructional framework to teach adding and subtracting fractions with unlike denominators. We highlight the benefits of using the framework to promote student engagement and skill mastery and identify free-access resources for educators to successfully implement the math intervention in their own classrooms.

Affectivity in mathematics teaching: using playfulness to combat resistance to new practices in the context of basic education

This article investigates the effectiveness of playful approaches and affectivity in teaching mathematics in basic education. The goal is to analyze how these methodologies can overcome resistance to new pedagogical practices and improve engagement and understanding of mathematical concepts. A literature review and practical experience report demonstrate that playful activities, such as games and challenges, increase student interest, facilitate the understanding of abstract concepts, and develop socio-emotional skills. Affectivity, by creating an emotionally safe environment, reduces math anxiety and promotes a positive attitude. It is concluded that combining playful elements with an affective approach transforms the teaching-learning experience, making mathematics more accessible. Therefore, it is essential to invest in continuous training, school infrastructure, and educational policies that encourage pedagogical innovation.

GIRILOYO WRITTEN BATIK MOTIFS VIEWED FROM AN ETHNOMATHEMATICS PERSPECTIVE

School mathematics which is often studied is generally formal, rigid and strict. Students still experience difficulties in applying mathematical concepts in everyday life. The results of PISA of Indonesia 2023 show that the mathematical literacy skills of Indonesian students are currently still relatively low. The independent curriculum provides flexibility for teachers to develop mathematical literacy skills with innovative mathematics learning models based on real life contexts, one of which is culture. Ethnomathematics as a research study that links culture and mathematics. The aim of this research is to find out the results of an ethnomathematics study on giriloyo batik motifs, especially on sidomukti, sidoluhur and sidoasih motifs. This type of research is qualitative research with an ethnographic approach. The methods used for data collection are interviews, observation and documentation. The results of this research showed that the giriloyo batik motif contains the concept of geometric transformation in the form of reflection. Keywords: Ethnomathematics, Written Batik, Geometric Transformation

Development of Blog-Based Learning Media With Sarong Context on Lines and Angles Material

This study aims to produce learning media based on blogs with the context of covers on lines and angles material using the PMRI approach which was valid, practical and has a potential effect on the ability to understand mathematical concepts in class VII students of SMP LTI IGM Palembang. The research method used was the development research method using the Tessmer flow (1993) which consists of the preliminary stage (preparation and design stages) and the formative evaluation stage, namely self-evaluation, expert review, one-to-one, small group and field tests). Data collection was carried out using validation sheets, questionnaires, interviews and tests. From the results of the study it was concluded that the blog-based mathematics learning media developed was qualitatively valid in terms of comments and suggestions from the validator, besides that quantitatively the percentage of validity was 4.129 and practically both qualitatively and quantitatively by looking at the comments and suggestions it was stated that blog-based learning media was practically used and the result of the analysis of the practical average of the questionnaire calculation is 76.263. Then the results of a high potential effect on students' conceptual understanding abilities with an average of 82.033.

Improving the Prospective Math Teacher's Literacy Skills by Using Digital Images in STEM-Based Instruction

The demands of high school education are not only increasingly complex and difficult subject content, students are also required to be able to think critically and reason in solving everyday problems. This mathematical ability is known as mathematical literacy proficiency. This is where the teacher's role as a facilitator who provides stimulus in the form of learning strategies, guidance and assistance when students experience learning difficulties is a key factor. For this reason, students as prospective mathematics teachers need to have good mathematical literacy skills and knowledge and skills to guide students to achieve 21st century abilities and skills. This research was conducted to apply a STEM approach in learning so that students can improve the mathematical literacy skills of students majoring in Mathematics Education as prospective teachers and introduce and equip them with knowledge about STEM. The research was carried out using problems related to the relationship between mathematics and digital images in STEM. Data is collected through tests and assessments of student activities that integrate STEM in solving problems. The research results show that digital images have the potential to help students understand mathematical concepts in various fields, especially computer graphics. Students' literacy skills also increased significantly at the significance level α = 0.05. Students' mathematical literacy proficiency level increased from 90% at maximum level 1 to 90% at minimum level 5

Exploring the linguistic factors influencing concept identification

ABSTRACT This study investigates how the semantic differences, if any, in the Arabic and Hebrew terms for “tangent line” and “rectangle” affect students’ understanding and application of these concepts, as evidenced by their definitions, identification of examples, and explanations given during performance test tasks. We conduct our research with Arabic and Hebrew-speaking high school students enrolled in mathematics classes in Israel. Our goal is to explore how language influences how students define and recognize concepts and examples of geometric shapes. Specifically, we examine how the specific meaning associated with concept names in Arabic and Hebrew impacts the process of defining and identifying these mathematical concepts examples, including the reasoning students use for examples identification.

The triviality of dihedral cohomology for operator algebras

This article delves into algebraic topology, specifically (co)homology theory, which is essential in various mathematical fields. It explores different types of (co)homology groups such as Hochschild, cyclic, reflexive, and dihedral, focusing on dihedral cohomology generated by the dihedral group operating on simplicial complexes. The text discusses when dihedral and reflexive cohomology vanishes and provides examples, along with proving a homomorphism between dihedral cohomology groups. Mathematical concepts like Banach spaces, C*-algebras, and tensor products are elucidated to understand the algebraic structures involved. Theorems and proofs establish the relationships and properties of these cohomology groups, culminating in a canonical isomorphism theorem for the product of two algebras. Overall, the article aims to provide a comprehensive exploration of dihedral cohomology and its interplay with other algebraic structures, offering insights into its applications and theoretical foundations. Additionally, it studies the (co)homology theory of C*-algebras, focusing on the triviality of cohomology groups of operator algebras and discovering the canonical isomorphism between any two unital K -algebras A and A′: HDn(A×A′)≅HDn(A)⊕HDn(A′).