Mathematical Understanding Research Articles

Self-concept, Self-efficacy, and Academic Achievement of Prospective Mathematics and Biology Teachers

This study investigates the intricate interplay between self-concept, self-confidence, and academic achievement among aspiring mathematics and biology teachers. Through a quantitative research approach and survey design, we explore the relationships among these psychological factors and their potential influence on the educational paths of future educators in these distinct disciplines. Seventy-six prospective biology education teachers and 115 prospective mathematics education teachers voluntarily participated as respondents in filling out the provided survey. Utilizing standardized self-concept and self-efficacy assessments in conjunction with academic performance records, we gather comprehensive data to analyze these dynamics by inferential statistics, independent t-tests, and Pearson's correlation. Our findings show that there is a significant difference in the self-concept of prospective biology education teachers and mathematics education teachers when studying mathematics or statistics material, highlighting significant correlations between self-concept, self-efficacy, and academic achievement. However, the nature of these relationships varies between mathematics and biology domains, suggesting the need for tailored strategies in each field. While a positive self-concept and self-efficacy foster academic success, their impact differs based on the subject matter. The findings from these analyses can shed light on how self-concept and self-efficacy in mathematical understanding and problem-solving contribute to the academic achievement of prospective teachers in mathematics and biology. This information has implications for teacher training programs and educational strategies aimed at enhancing both self-perception and teaching efficacy in mathematics-related subjects.

Analisis Kemampuan Penalaran dan Pemecahan Masalah Matematika pada Siswa Bimbel SIBABA

The purpose of this study was to analyze the ability to think mathematically and solve problems of students who are members of the SIBABA Bimbel. The research methodology used in this research is descriptive qualitative. Participants in this study were fifth grade elementary school students who were members of SIBABA Bimbel. Data is collected through observation, documentation and relevant references. Students are given tests that assess their reasoning abilities, problem-solving skills, and understanding of mathematics. Data analysis used is descriptive analysis. The results showed that students had difficulty in reasoning because they did not fully understand the concept of reasoning itself. This causes difficulties for students in solving problems, finding solutions, and answering questions. However, students were able to solve problems well and achieve all the maximum indicators, demonstrating their understanding of the form and meaning of problems and how to solve them. Therefore, further guidance in the aspect of reasoning is very important for student progress.

Exploring the Influence of Adaptive E-Learning Technology on Learners’ Perceptions of Mathematical Modeling and Simulation in South African Schools

This study investigates the influence of adaptive e-learning technology on learners’ understanding of mathematical modeling and simulation. Through a comprehensive literature review, theoretical framework development, and empirical analysis, the study examines the relationship between learners’ qualifications, geolocation, and their perceptions of e-learning technology. It utilized a quantitative research approach with a sample size of 66 learners and administered structured questionnaires to urban and rural school learners and analyzed data at p < .05 using the factorial multivariate analysis of variance (FMANOVA). The findings reveal variations in opinions among learners at different qualification levels regarding the use of e-learning technology in mathematical concepts. Moreover, urban and rural learners show disparities in their association of e-learning technology with mathematical understanding. The study emphasizes the need for practical approaches to e-learning, addressing challenges related to access, reliability, and ease of use. Recommendations include integrating adaptive e-learning technology into school curricula and providing adequate training and support for teachers. Furthermore, suggestions for future research encompass exploring long-term impacts, individual differences, teacher roles, assessment and feedback, equity and accessibility, professional development, and comparative studies. Overall, this study contributes to understanding the role of adaptive e-learning technology in mathematics education, providing valuable insights for practitioners and policymakers to enhance teaching and learning experiences.

Understanding mathematical concepts of comparison materials based on webquiz

Background: Comparison is a complex mathematical concept that often leads to misconceptions among students. This study is focused on evaluating the understanding of comparative material among PGSD students at Sanata Dharma University, Yogyakarta.Aim: The main objective of this study is to assess the level of understanding of comparative material concepts, including mathematical comparison, comparative mathematical understanding, the ratio of turning around, and mathematical understanding of scale, among the students.Method: A survey method was employed for this research. The study involved 46 PGSD students at Sanata Dharma University who participated through Quizizz and Google Drive. The instrument consisted of 10 conceptual questions and 5 discussion questions, followed by reinforcement material to enhance understanding. Participants were instructed to complete questions via https://join.quizizz.com, and the completed steps were submitted through Google Drive.Result: The analysis revealed that 1) the mathematical understanding of the concept of comparison was at 83%; 2) comparative mathematical understanding stood at 68.67%; 3) the mathematical understanding of the ratio of turning around was 73.2%; and 4) the mathematical understanding of scale was at 83%.Conclusion: The study indicates that the understanding of mathematical concepts related to comparative material among PGSD students at Sanata Dharma University is in the high category. These findings could serve as a foundation for further instructional design aimed at bolstering comparative concept understanding.

Systematic Literature Review: Kemampuan Komunikasi Matematis Siswa Ditinjau dari Gaya Berpikir

Mathematical communication skills encompass the oral and written abilities of students regarding the mathematical concepts they possess. The aim of basic mathematics education involves cognitive and social activities so that in communicative situations, students can enhance their learning interactions with others to obtain mathematical ideas. They should be capable of conveying their mathematical thoughts to others, developing mathematical concepts and strategies, and reflecting on their understanding of mathematics. Thinking styles are cognitive patterns that differentiate how students receive and process information and then use that information to solve problems, particularly in mathematical problem-solving. The objectives of this research are (1) to identify the types of research used in mathematical communication skills concerning thinking styles published in the last 5 years, (2) to identify research trends on mathematical communication skills and thinking styles in the last 5 years, and (3) to reveal the influence of students' thinking styles on mathematical communication skills, including the interpretation of mathematical problems, the selection of solution strategies, and mathematical problems solving abilities. The research method employed in this study is the Systematic Literature Review (SLR). Data collection involves reviewing articles related to students' mathematical communication skills concerning thinking styles published between 2018 and 2023. The findings indicate that (1) qualitative research is the most commonly used type of research, (2) research is predominantly conducted at the junior high school level, and (3) thinking styles significantly influence students' mathematical communication skills.

Solving exact solution of time independent Schrodinger wave equation and visualizing eigenfunctions using XCOS

Time independent Schrodinger wave equation (SWE) for a quantum system can be solved computationally which involves application of numerical method. Different computational tools used to solve SWE involving different potentials were reviewed. XCOS, an inbuilt tool of Scilab for modelling and simulating hybrid dynamic system and is an open-source is used to solve the Schrodinger wave equation for different quantum systems. Only basic understanding of mathematics up to high school level is required to solve Schrodinger wave equation using XCOS. Different quantum systems considered are free particle in a well bounded by infinite potential at the boundaries, radial part of SWE for Hydrogen atom under coulombic potential, screened coulombic potential. Radial part of Schrodinger wave equation for a particle under harmonic and anharmonic potential were also solved using XCOS computational tool. Eigenvalues and eigenvectors were obtained by solving radial part of Schrodinger wave equation for molecules under Morse potential. Advantages and limitation of XCOS computational tools were also discussed. We argue in favour of the academic use of computational tool XCOS to solve Schrodinger wave equation in introductory quantum mechanics courses.

Fast synthesis of high-entropy oxides for lithium-ion storage

High-entropy oxides (HEOs) have been considered conspicuous battery materials due to their tunable properties and stable crystal structure. In this work, several kinds of high entropy oxides (HEOs) are prepared by an ultra-fast Joule heating method in several seconds. This simple and effective method enhances the efficiency of near four orders of magnitude than that of the common sintering methods. As anode materials of lithium-ion batteries (LIBs), they have considerable rate capacity and cycling stability. For example, quinary (MgCoNiCuZn)O HEO delivers a high capacity of ∼150 mAh g−1 even at ultrahigh current density of 10 A g−1 and cycle stability up to 2,600 cycles. By in-situ transmission electron microscopy, the full lithiation/de-lithiation process is tracked down to the atomic scale in real time, observing the distinct reaction dynamics and structural evolutions in rock-salt-type (MgCoNiCuZn)O during cycling. Conversion/alloying reaction kinetics are identified by the disappearance of the original rock-salt phase and the formation of polyphase with the intercalation of lithium-ions. While upon de-lithiation, the post-lithiation polyphase state can be recovered to the original rock-salt-structured (MgCoNiCuZn)O. Our work provides valuable guidelines to high-efficient synthesis and mathematical understanding of lithium storage mechanisms of HEOs for next-generation long-life energy storage.

INOVASI APLIKASI ENVIRONMENTAL MATHEMATICS PADA SMARTPHONE SEBAGAI MEDIA INTERAKTIF PEMBELAJARAN MATEMATIKA BERBASIS LINGKUNGAN

This research is development research (R&amp;D) which refers to the ADDIE model. Development procedures include Analysis, Design, Development, Implementation, and Evaluation. The results of this research product are in the form of an android application based on environmental mathematics to improve understanding of learning mathematics based on the environment. The application is accompanied by attractive images, sounds, animations, and text narration. The results of the study show that the android application for learning environmental mathematics is feasible and effective in learning data collection, as seen from the average pretest and posttest scores carried out by fifth-grade students at SDN 1 Talang Padang. The average value obtained during the pretest was 41.57 while the average value obtained during the posttest was 82.10. Based on the Mann-Whitney test with a sample of two different schools, the resulting data shows a significant difference between the learning outcomes of schools that use the Android application media and those that are not treated, as seen from the posttest average score of SDN 1 Talang Padang of 82.10. While the average posttest score of SDN 1 Banding Agung is 66.31.

Beyond computation: Assessing in-service mathematics teachers’ conceptual understanding of fraction division through problem posing

Problem posing has long been recognized as a critically important teaching method and goal in the area of mathematics education. However, few studies have used problem posing to assess in-service teachers’ mathematical understanding. The present study investigated in-service teachers’ mathematical understanding of fraction division, which is often considered challenging content in elementary school, from three angles: computation, drawing, and problem posing. Two studies involving 66 and 193 primary and middle school teachers were conducted to reveal the in-service teachers’ mathematical understanding and whether drawing and problem posing affected each other. Although the in-service teachers rarely had the opportunity to pose mathematical problems in their daily teaching, they were able to pose mathematical problems in this study. In addition, problem-posing tasks were more useful in diagnosing the in-service teachers’ conceptual understanding than were computation or drawing. Thus, problem posing seems to have contributed to their conceptual understanding of fraction division on the drawing task.

A review of flipped learning in innovative math education

&lt;span lang="EN-US"&gt;Many systematic reviews have examined flipped learning models in various fields. However, there is little research on the use of the flipped learning model in mathematics education, which could help researchers and practitioners use and develop a model to implement mathematics learning processes. To fill this gap, this study aimed to analyze and synthesize current knowledge and practices in the implementation of flipped learning in mathematics education. Systematic literature review was adopted as the research method following an article selection and screening process using the preferred reporting items for systematic review and meta-analysis (PRISMA) protocol. Articles published from 2012 to 2021 in some reputable databases (Web of Science, Scopus, and ERIC) were reviewed, and 17 of 137 articles were included for detailed analysis and synthesis. The findings of this study showed that research in the implementation of the flipped learning model in mathematics education focused on documenting the affectivity of the implementation of the flipped learning model, developing learning processes, and sharing preliminary findings and student feedback. Future research is highly recommended to examine different aspects of flipped learning implementation, promote longitudinal data based on multi-year research for implementing flipped learning, and review various learning media to strengthen students’ understanding of mathematics.&lt;/span&gt;

Applying APOS Theory to Enhance Algebraic Logic Skills: Comparing Traditional Teaching and Computer-Assisted Instruction

This study aims to assess how effectively applied science students use equations to express connectivity in algebraic logic and understand their cognitive framework. This research measures students' understanding of mathematical logic connectors in line with the polytechnic curriculum and uses APOS theory as a basis. It compares the effectiveness of traditional teaching methods with the computer-assisted instruction (CAI) approach. The results show that students learning with CAI perform better in applying connectivity equations. These findings underscore the importance of students' cognitive schemes in understanding the relationship between algebra and logic. Students with a more mature conceptual understanding tend to overcome conceptual application difficulties better. For future research, it is suggested to explore the application of CAI methods in various learning contexts and other disciplines, as well as to assess its long-term impact on students' cognitive skills and mathematical understanding. Additionally, it is essential to compare the effectiveness of CAI with other innovative learning methods to determine the best approach to developing students' logic and algebra skills.

ANALYSIS OF PRIMARY SCHOOL STUDENTS' MATHEMATICAL CONCEPTUAL UNDERSTANDING BASED ON LEARNING INTEREST

This research utilized a qualitative approach to providing a descriptive and in-depth exploration of elementary school students' mathematical and conceptual understanding of their learning interests. The study includes 20 participants, selected based on the categories of their learning interests, with three representatives chosen from each category. Participants are also selected based on their age, according to Piaget's theory, and communication abilities. Data collection techniques involve data reduction, data categorization, and data verification. Based on the research findings and discussions, it can be concluded that students with high learning interests demonstrate a strong understanding of mathematical concepts. Similarly, students with moderate learning interest exhibit a commendable grasp of mathematical concepts, while students with low learning interest tend to have lower conceptual understanding. For future research, it is recommended to explore the use of instructional media to assess children's learning interests.

DEVELOPMENT OF PROBLEM-BASED LEARNING DEVICES TO FACILITATE MATHEMATICAL UNDERSTANDING ABILITY IN NUMBER PATTERN MATERIALS IN CLASS VIII SMP/MTs

The background of this research is the students' low mathematical understanding ability (KPM) and the teacher's difficulties in preparing learning tools. To facilitate the Mathematical Understanding Ability, the teacher must improve the learning process using a learning model. One of the appropriate learning models is the Problem Based Learning model. Applying the Problem Based Learning model can be implemented if this model is packaged in the form of learning tools. Thus, packaging the Problem Based Learning model in learning tools is the initial development that must be carried out. The development design used in this study is 4-D with the stages: (1) define; (2) planning (design); (3) development (develop); (4) spread (disseminate). The research instruments used were interview guides, validation sheets, observation sheets and student response questionnaires. The results showed that the syllabus, lesson plans and worksheets obtained a validity value of 3.82; 3.53; and 3.48 with a very valid category. The practicality of the LKPD in the small group trial obtained a score of 3.67 in the very practical category.

The Formal Layer of {Brain and Mind} and Emerging Consciousness in Physical Systems

AbstractWe consider consciousness attributed to systems in space-time which can be purely physical without biological background and focus on the mathematical understanding of the phenomenon. It is shown that the set theory based on sets in the foundations of mathematics, when switched to set theory based on ZFC models, is a very promising mathematical tool in explaining the brain/mind complex and the emergence of consciousness in natural and artificial systems. We formalise consciousness-supporting systems in physical space-time, but this is localised in open domains of spatial regions and the result of this process is a family of different ZFC models. Random forcing, as in set theory, corresponds precisely to the random influence on the system of external stimuli, and the principles of reflection of set theory explain the conscious internal reaction of the system. We also develop the conscious Turing machines which have their external ZFC environment and the dynamics is encoded in the random forcing changing models of ZFC in which Turing machines with oracles are formulated. The construction is applied to cooperating families of conscious agents which, due to the reflection principle, can be reduced to the implementation of certain concurrent games with different levels of self-reflection.

Representasi Konsep Transformasi Geometri Melalui Pembelajaran Etnomatematika Menggunakan Sumber Objek Budaya Klenteng Sam Poo Kong

The low mathematical understanding and reasoning skills of students along with abstract mathematical concepts make it difficult for students to understand mathematical concepts. So, new development innovations are needed in presenting mathematics learning to improve students' basic math skills. This research aims to explore the buildings in the Sam Poo Kong temple in finding mathematical concepts. This research is exploratory, the research method used is descriptive-qualitative, and the approach is ethnography because it studies cultural phenomena in society. The results of this study show that in the Sam Poo Kong temple there are ethnomathematics concepts related to geometric transformation material including 1) translation on the roof, pillars, and statues; 2) reflection on the overall structure of the temple building, ornaments, and the entrance gate of Sam Poo Kong; 3) rotation on lanterns and walls of hope; and 4) dilation on the structure of the roof and lanterns. From the research, it can be concluded that Sam Poo Kong temple presents the concept of geometry transformation, namely translation, reflection, rotation, and dilation.

Boundary Behavior of Conformal Maps on Domains with Corners

This paper investigates the behavior of conformal maps near corner points and other non-differentiable boundary points of planar domains. Conformal maps that preserve angles locally will exhibit singular behavior when approaching corners or other less smooth parts of the boundary. We classify types of isolated corner singularities and characterize the magnitude, derivatives, and integral properties of analytic functions near such points. Explicit mappings are constructed between model domains with cusps, wedges, slits, and logarithmic-type corner points. The behavior of the mapping functions is analyzed as the boundary coordinates approach the singular points. We establish several theorems describing the boundary limits, convergence, boundary correspondences, and boundary integrals of these conformal maps on domains with corners. The mapping properties provide insight into the effect of geometric singularities on analytic functions in application areas such as physics, fluid flow, and engineering problems involving complex mappings. The boundary behavior classifications developed here expand the mathematical understanding of conformal maps on domains with sharp corners or discontinuities.

Danish Students’ Understanding of Fractions: A Replication Study

Abstract In this paper, we report on a conceptual replication of a fractions test originally administered in the 1970s in England as part of the ‘Concepts in Secondary Mathematics and Science’ (CSMS) research programme documenting lower secondary students’ understanding of mathematics. We present data from a recent study conducted in Denmark with 336 students aged between 12 and 14 years, presenting descriptive results as in the original research. In addition, we use Rasch modelling — a technique that was not widely used in the 1970s — to further analyse the students’ understanding of fractions and to validate the test. Our findings indicate that Danish students’ fractional understanding in word or diagrammatic contexts is slightly stronger in comparison to that of the English students in the original study, whereas the case for computations involving fractions is the reverse. We discuss the possible reasons for these differences. Our study provides evidence that fractional knowledge involves a number of components and suggest ways in which the test might be improved. The Impact Sheet to this article can be accessed at 10.6084/m9.figshare.24219673

Phase-resolved wave prediction with linear wave theory and physics-informed neural networks

Deterministic wave elevation prediction is crucial for improving the power generation efficiency of offshore energy structures (OESs). Although phase-resolved wave models may predict deterministic wave information, a comprehensive understanding of wave theory and mathematics is necessary to guarantee their accuracy. Inspired by the capability of physics-informed neural networks (PINNs) in solving physical equations, we propose an irregular long-crested wave prediction model named LWT-PINN that combines the linear wave theory (LWT) with PINNs. To the best of our knowledge, this is the first time that PINNs are used to predict waves. Five sets of wave elevation time series with steepness ranging from 0.0174 to 0.0349 are generated in a wave basin to optimize and evaluate the LWT-PINN. The computing time for LWT-PINN is 0.13 s, close to real-time. When predicting downstream wave elevation, the LWT-PINN significantly outperforms the linear wave prediction (LWP) model in terms of accuracy and prediction length. Specifically, the LWT-PINN achieves satisfactory accuracy with only 100 s upstream wave elevation, whereas the LWP requires 175 s; LWT-PINN’s high-precision prediction duration is 13.7 s, which is 2.5 times longer than that of LWP (5.5 s). Moreover, LWT-PINN can provide wave autoregressive predictions of around 5 s without the aid of statistical methods, which offers a new direction for developing wave autoregressive prediction methods. The excellent performance of the proposed model can substantially assist the stable operation of OESs.

Uncovering Ethnomathematics and Indigenous Epistemology: A Study of Chundara Culture

The primary aim of this paper is to delve into the realm of ethnomathematical concepts and indigenous epistemology of Chundaras culture. To accomplish this, I employed a methodology that included in-depth interviews and participant observations conducted at various stages of the process, focusing on professionals selected for the study. My analysis encompassed a comprehensive exploration of the Chundaras' daily routines, their workplaces, their actions, methods, and the outcomes they produced, with particular attention to uncovering the hidden mathematical knowledge woven into various aspects of their lives. The study revealed that the Chundaras' approach to teaching and learning was marked by participatory and cooperative methods, where they acquired knowledge with the guidance of their parents. This aligns with Vygotsky's perspective, which views learning as a social activity through which shared mathematical understandings are collectively constructed. However, it became evident that the conventional pedagogy followed in schools stood in stark contrast to the indigenous knowledge of the Chundaras, appearing distant and disconnected from their unique ways of knowing and learning.

Pengaruh Pendekatan Permainan dalam Kartu Pinmat Math Hero terhadap Pemahaman Matematika di Tingkat Sekolah Dasar

This qualitative research investigates the use of the Math Hero Flashcards in elementary school children's mathematics education. Math Hero Flashcards are specially designed learning tools aimed at enhancing mathematical understanding, accuracy, and mastery of arithmetic operations for numbers 1-10 through interactive games. The study involves direct observation, interviews, and interactive play with children with the aim of understanding the effects of Math Hero Flashcards on children's mathematical understanding, learning motivation, and interest. The results of the research indicate that the use of Math Hero Flashcards enhances elementary school children's mathematical understanding, fosters motivation for learning, and creates a more enjoyable learning experience. However, some interview participants mentioned that they had found alternatives in the form of math game apps on their phones. Therefore, this research underscores the need for integration between physical learning tools like Math Hero Flashcards and learning technology to achieve holistic and engaging mathematics education for children.