Mathematical Connection Research Articles

Mathematical connections made by preservice mathematics teachers when solving tasks about systems of linear equations

The study reported had the aimed to identify the mathematical connections made by a group of Mexican preservice mathematics teachers (PMTs) when solving tasks on systems of linear equations. We consider a mathematical connection as a true relationship that a person makes between two or more ideas, concepts, definitions, theorems, procedures, representations, and meanings with each other, with other disciplines or with real life. Four PMTs participated voluntarily in task-based interviews, providing the primary data for analysis. Thematic analysis was employed to analyze the data. The findings revealed that the preservice teachers made mathematical connections of procedural, implication, feature, meaning, and different representations. However, the findings also revealed that some preservice teachers faced challenges when attempting to solve the tasks, leading to difficulties in establishing certain mathematical connections.

Improving the thermal properties of water by adding MWCNTs, cerium oxide, and MgO hybrid nanoparticles at different temperatures and volume fraction of nanoparticles: Experimental investigation

This study aimed to investigate the thermal conductivity (TC) of various nanofluid compositions, including water/MWCNT-MgO-cerium oxide ternary hybrid nanofluids (THNFs) with solid volume fractions (SVFs) ranging from 0.1% to 0.6%. Additionally, the thermal conductivity of water/MWCNT-cerium oxide, water/MWCNT-MgO, and water/MgO-cerium oxide hybrid nanofluids (HNFs), as well as water/MWCNT, water/cerium oxide, and water/MgO mono nanofluids (MNFs), was measured at SVF=0.1% and 0.3%. The experimental temperature was varied between 20, 30, 40, and 50°C for all samples. The MWCNT, MgO, and cerium oxide nanoparticles (NPs) were suspended in the water base fluid (BF) to create the nanofluids (NFs) in a two-step process. MWCNT NPs are 20–30 nm in size, MgO NPs are 20 nm, and cerium oxide NPs are 10–30 nm in size. DLS and zeta potential experiments, which demonstrate the correct stability of NFs, were used to evaluate the stability of NFs. The KD2-Pro instrument was used to test the samples' TC after making sure they were stable. The data obtained demonstrate a rise in TC with rising SVF and rising temperature. The MWCNT/water MNF exhibits the largest rise in TC in SVF=0.3%, with a TC increase of 19.16% at T=40°C. It should be noted that the largest increase in TC is 26.09% compared to the BF for water/MWCNT-MgO-cerium oxide THNF at SVF=0.5% and T=40°C. Finally, a mathematical connection was shown with the comparisons done to estimate the data. The results demonstrate the postulated relationship's high degree of accuracy.

Students' Mathematical Connection Ability in Solving Block and Prism Problems viewed from Cognitive Style

Students' Mathematical Connection Ability in Solving Block and Prism Problems viewed from Cognitive Style

The Impact of Cooperative Learning Activities using the Team-Assisted Individualization (TAI) Technique Combined with Activity-Based Learning on Problem-Solving Abilities and Mathematical Connections Abilities in the Subject of Congruence

The Impact of Cooperative Learning Activities using the Team-Assisted Individualization (TAI) Technique Combined with Activity-Based Learning on Problem-Solving Abilities and Mathematical Connections Abilities in the Subject of Congruence

Mathematical connection skills of junior high school students in solving system of linear equations in two variables problems

Students mathematical connection skills are valuable dimension that teachers must put into consideration so that students can develop and link their mathematical skills with knowledge beyond Mathematics. This research aimed to analyze the mathematical connection skills of Junior High School students when solving the System of Linear Equations in Two Variables (Sistem Persamaan Linear Dua Variabel/SPLDV) problem. Students mathematical connection skills are valuable dimension that teachers must put into consideration so that students can develop and link their mathematical skills with knowledge beyond Mathematics. This research aims to analyze the mathematical connection skills of Junior High School students when solving the SPLDV problem. This research made use of Qualitative approach by which 18 students of grade VIII from SMP Argopuro 1 Panti Jember, East Java, participated. Mathematical connection skill test and interview guideline were conducted for this research. Data triangulation technique was used to process and compile data for the research report. The findings of the research discovered that students with high level of mathematical connection skills were able to relate and implement their knowledge to different kinds of situations, and students with medium level of mathematical connection skills were only able to apply their knowledge to simple situations, meanwhile students with low level of mathematical connection skills were unable to relate and implement their knowledge to a variety of situations.

Mathematical and neuro-mathematical connections activated by a teacher and his student in the geometric problems-solving: A view of networking of theories

The research goal is twofold: to articulate neuro-mathematics with the extended theory of mathematical connections that uses onto-semiotic approach tools and to explore the connections established by a teacher and his student when solving a problem about the volume of two boxes, one of toothpaste and the other of tomato. This research was developed in two stages: the theories were articulated assuming concordances and complementarities, highlighting the notion of connection, and a context of reflection was considered carried out in three phases where the participants were selected, participant observation was carried out in the classroom during solving a problem and then analyzing the data with the new tool to explore mathematical and neuro-mathematical connections. The findings present the mathematical connections established by the teacher and the student of meaning, feature, procedural, different representations (alternate, equivalent, and from a horizontal mathematization view), and part-whole, as well as neuro-mathematical connections of: recognition of terms and symbols; visual perception, spatial skills and motor coordination; association of mathematical concepts and formulas; intermediate calculations and unit conversion; solve operations step by step and understand the process; verification and conclusion, activated in the brain areas linked to each mathematical practice sequentially.

Thermodynamical Proofs of the AM-GM Inequality

Summary Though most proofs of the AM-GM inequality utilize mathematical axioms or connections from other fields of mathematics, we show that it can also be proven via the laws of thermodynamics. We provide a brief primer on thermodynamics before continuing into two thermodynamical proofs of this inequality, including a novel one due to the author.

The Effectiveness of Missouri Mathematics Project Learning Models for Improving Students’ Mathematical Connection Ability on Junior High School

Mathematical connection ability is one of the high level abilities but is still classified as low because students' understanding of the conceptual material given by the teacher, there are still students going through steps in working on the problems given, such as describing a symbol, in completing mathematical concepts, therefore This research aims to examine the effectiveness of using the Missouri Mathematics Project Learning Model carried out at MTs Ibnu Sina Jl. Tegal Overtime No. 105, Pamekaran, District. Soreang, Bandung Regency, West Java 4091, by taking a sample of 60 students consisting of control and experimental classes. The research method used in this action was the experimental method. Based on the results of descriptive analysis of students' mathematical ability data before being given treatment, it showed the highest score was 70, the lowest score was 55 and the average score was 61. Meanwhile, the results of descriptive analysis of students' mathematical ability data after being given The treatment showed the highest score of 70, the lowest score of 55 and the average score of 61. Those given the treatment showed the highest score of 87, the lowest score of 69, and the average score of 77.83. So the average mathematical connection ability of students after being given treatment is higher than the students' mathematical ability before being given treatment.

An investigation of students’ mathematical connection and metacognitive skills in the mathematical modelling process

The purpose of the study is to investigate the changing mathematical connection and metacognitive skills of students in the process of applying mathematical modelling. The data used for the study were collected from modelling activities, students’ written responses to modelling activities, audio recordings, semi-structured interviews, and observation notes. The data obtained were analysed using content analysis. As a result of the data analysis, it was found that metacognitive skills were used in each activity in the mathematical modelling process and were developed in interaction with each other. Although inter-concept and real-world connection skills are most commonly used in mathematical connection skills, modelling activities were found to enhance connection skills by allowing students to use connection skills with different disciplines and between different representations of the concept. It was found that metacognitive skills and mathematical connection skills develop interdependently, and it was found that mathematical modelling activities can be used as a tool for developing both of these skills.

Vacuum entanglement probes for ultra-cold atom systems

Abstract This study explores the transfer of nonclassical correlations from an ultra-cold atom system to a pair of pulsed laser beams. Through nondestructive local probe measurements, we introduce an alternative to destructive techniques for mapping Bose–Einstein Condensate (BEC) entanglement. Operating at ultra-low temperatures, BEC density fluctuations emulate a relativistic vacuum field. We show that lasers can serve as Unruh–DeWitt detectors for vacuum BEC phonons. A quantum vacuum holds intrinsic entanglement, transferable to distant probes briefly interacting with it—a phenomenon termed ‘entanglement harvesting’. Our study accomplishes two primary objectives: first, establishing a mathematical connection between a pair of pulsed laser probes interacting with an effective relativistic field and the entanglement harvesting protocol; and second, to closely examine the potential and persisting obstacles for realising this protocol in an ultra-cold atom experiment.

FRACTALS IN QUANTUM MECHANICS: FROM THEORY TO PRACTICAL APPLICATIONS

This article examines the use of fractals to estimate the probability of classical events controlled by quantum processes. A hypothesis explaining the opposite charges of the positron and electron is discussed, as well as the relationship with the main modern theories of quantum mechanics, such as quantum electrodynamics (QED), string theory, etc. The relationship with the tunnel effect and the pulsed tunnel effect is considered. Examples of practical application of fractals are given, for example, in photocatalysts. The concepts of the effective mass of a photon and the quantum nature of elementary particles, the idea of their internal structure and the formation of matter from the point of view of quantum mechanics are touched upon. Particular attention is paid to the fractal structure of the quantum field as a probability associated with the formation of a positron or electron, and the mathematical connection with the Dirac equation, QED and the Schrödinger equation.

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.

Learners’ algebraic and geometric connections when solving Euclidean geometry riders

In this article, we explored Grade 11 learners’ algebraic and geometric connections when solving Euclidean geometry riders. A qualitative interpretive case study design was followed. Thirty Grade 11 learners from a non-fee-paying secondary school in the Capricorn North district of South Africa were conveniently sampled to participate in this study. Data were collected through learners’ responses to classwork, homework exercises, and task-based interviews. Data were analysed thematically. The findings revealed that to solve Euclidean geometry riders successfully, learners need to establish the feature connections embedded in the given figure or diagram. The ability to make feature connections provides a point of departure in the solution process of a geometric problem.Contribution: Once the feature connection is established, other connections will subsequently emerge. In addition, the reversibility connections become a form of feature connection when solving Euclidean geometry riders. Therefore, we recommend that mathematics teachers emphasise and use mathematical connections in their daily teaching of mathematics.

Investigation of the Mathematical Connection Self-Efficacies of Pre-Service Teachers: A Quantitative Study From Turkey

Investigation of the Mathematical Connection Self-Efficacies of Pre-Service Teachers: A Quantitative Study From Turkey

Mathematical Understanding Based on the Mathematical Connections Made by Mexican High School Students Regarding Linear Equations and Functions

Mathematical Understanding Based on the Mathematical Connections Made by Mexican High School Students Regarding Linear Equations and Functions

DEVELOPMENT OF FLAT-BUILT DIGITAL COMIC MEDIA BASED ON ETHNOPEDAGOGY TO IMPROVE THE MATHEMATICAL CONNECTIONS OF LOWER CLASS PRIMARY SCHOOL STUDENTS

Meaningful and enjoyable learning is a strategy developed by teachers to optimize learning objectives. This strategy encompasses various aspects, including the approach used, material delivery, engaging instructional media, and creating a pleasant learning environment (Tisza & Markopoulos, 2021). The research was conducted using the Research and Development (R&D) approach, commonly known as development research that results in a product. The purpose of this study was to develop a digital comic-based flat geometry learning media grounded in ethno-pedagogy to enhance elementary school students’ mathematical connections in lower grades. The ADDIE model, developed by Dick and Carey in 1996, was employed as the framework for designing the instructional system (Mulyanitiningsih, 2016).The research outcomes, based on expert validation and field testing, indicate that the digital comic-based flat geometry learning media grounded in ethno-pedagogy aligns well with usability, appropriateness, accuracy, and suitability. The expert validation resulted in an 86% score, with an average material expert score of 96%, categorized as ‘Highly Suitable.’ Additionally, the language experts provided an average score of 82.5%, categorized as ‘Suitable.’ Overall, the combined scores from the experts yielded an 88.16% rating of ‘Highly Suitable’ for use with elementary school students. Based on the effectiveness test, the digital comic-based flat geometry learning media grounded in ethno-pedagogy demonstrated a positive impact on mathematical connections. The N-Gain calculation resulted in an average N-Gain score of 0.7061, categorized as "High.”

The influence of the Knisley mathematics learning model on the mathematical connection ability and self-confidence of high school students

This research aims to conduct a study that focuses on the effect of applying the Knisley mathematics learning model on students' mathematical connection abilities and self-confidence.This research is research using a quasi-experimental method with a research design in the form of a pretest-posttest control group design. The sampling technique used was cluster random sampling. The population in this study were all class XI students at SMAN 1 Tirtayasa, with a sample of 2 classes to be used as experimental classes, namely class The instruments used in this research were mathematical connection ability tests, self-confidence questionnaires, observation sheets and interviews. Based on data analysis, it was concluded that (1) Learning using the Knisley mathematics learning model had a positive effect on students' mathematical connection abilities, (2)Learning using the Knisley mathematics learning model has a positive effect on students' self-confidence.

Spurious negative eigenvalues of numerical variance-covariance matrices in many-body systems correlate with the existence of frozen degrees of freedom

The principal component analysis (PCA) is widely used to reduce the dimensionality of a dataset to its essential components. To perform PCA, the covariance matrix is constructed and its eigenvalues and eigenvectors are computed. In practical numerical applications, the tail of the sorted eigenvalues is sometimes found to contain negative eigenvalues, which are prohibited mathematically and are a pure consequence of finite-accuracy numerics. The present study suggests that in the case of a many-body dynamical system, the spurious negative eigenvalues of the covariance matrix may in fact be related to the frozen degrees of freedom in the system. Here, we outline the mathematical connection between the eigenvalues of the covariance matrix and the frozen degrees of freedom and validate the connection through two case studies: a model system of coupled harmonic oscillators and a molecular dynamics simulation of a small protein in solution.

Development of Mathematics Learning Tools Based on Education for Sustainable Development (ESD) Using the Outdoor Learning Mathematics Method to Enhance Mathematical Connections in Junior High School

This research aims to develop mathematics learning tools based on Education for Sustainable Development (ESD) using the Outdoor Learning Mathematics method with the goal of enhancing mathematical connections of junior high school students in statistics. The research method employed is a mixed-methods approach combining qualitative and quantitative methods, both conducted through developmental research comprising planning, development, and evaluation stages. The sample for this research was two classes at SMPN 1 Tempeh with homogeneous mathematical abilities, where one class will be used as the experimental group and one class as the control group. Determining the research area using a purposive area sampling technique with the consideration that learning using the outdoor learning mathematics method with educational sustainable development (ESD) based learning tools has never been implemented at SMPN 1 Tempeh. The selection of eighth-grade classes is based on the consideration that statistics material is currently being taught in eighth grade, and eighth-grade students have not been subjects of research for similar studies before. The learning tools developed are designed in accordance with ESD principles and utilize outdoor mathematics learning approaches to enhance students’ understanding and skills in statistics. The results from Hypothesis Testing for Pretest indicate that a p-value of 0.648 is obtained, where this value > 0.05 means H0 is accepted and H1 is rejected. Therefore, it can be concluded that there is no difference in the mean between the control and experimental groups in the pretest. Whereas the result of Posttest Hypothesis Test indicate that a p-value of 0.028 is obtained, where this value < 0.05 means H0 is rejected and H1 is accepted. So the use of ESD-based mathematics learning tools with the Outdoor Learning Mathematics method is effective in improving students’ mathematical connections in statistics. The implication of this research underscores the importance of integrating mathematics education with sustainable development principles to reinforce students’ understanding and skills in mathematics while also fostering awareness of environmental and social issues.

INCORPORATING ETHNOMATHEMATICS AND REALISTIC MATHEMATICS EDUCATION ON DEVELOPING MATHEMATICS CONNECTION USING THE MENARA KUDUS

This research was motivated by students' low mathematical connections and lack of knowledge about the local culture around where they live. This research aims to develop a student digital worksheet using the concepts of ethnomathematics and Realistic Mathematics Education following the ADDIE procedure. A number of 30 students of year five in a primary school in Kudus District, Province of Central Java, Indonesia, involved in the study. The learning material used the local cultural object namely Menara Kudus. This bulding is part of muslim gathering venue and known its adaptation to the Hinduism as it was built during the era. A digital worksheet is defined as a set learning activity that can be accessed using electronic gadgets, like computer or smartphone. Validation of the development resutls included experts and students to collect data on the feasibility assessment of the digital worksheet which consists of assessments by material experts and media experts. In addition, the use of web based interactive worksheets at Menara Kudus based on Ethno–RME shows a significant increase in students' mathematical connections. This means that the Ethno–RME based Digital worksheet at the Menara Kudus was declared feasible and can be used in mathematics learning.