Mathematical Problem Research Articles

Students’ metacognitive activities in contextual mathematical problem solving

Students’ metacognitive activities in contextual mathematical problem solving

Exact bifurcation analysis of the static response of a Fermi–Pasta–Ulam softening chain with short and long-range interactions

This paper is devoted to the static bifurcation of a nonlinear elastic chain with softening and both direct and indirect interactions. This system is also known as a generalized softening FPU system (Fermi–Pasta–lam nonlinear lattice) with p=2 nonlinear interactions (nonlinear direct and second-neighbouring interactions). The static response of this n-degree-of-freedom nonlinear system under pure tension loading is theoretically and numerically investigated. The mathematical problem is equivalent to a nonlinear fourth-order difference eigenvalue problem. The bifurcation parameters are calculated from the exact resolution of the fourth-order linearized difference eigenvalue problem. It is shown that the bifurcation diagram of the generalized softening FPU system depends on the stiffness ratio of both the linear and the nonlinear parts of the nonlinear lattice, which accounts for both short range and long range interactions. This system possesses both a saddle node bifurcation (limit point) and some unstable bifurcation branches for the parameters of interest. We show that for some range of structural parameters, the bifurcations in (n−1) unstable bifurcation branches prevail before the limit point. In the complementary domain of the structural parameters, the bifurcations in (n−1) unstable bifurcation branches prevail after the limit point, which means that the system becomes unstable first, at the limit point. At the border between both domains in the space of structural parameters, the bifurcation in (n−1) unstable bifurcation branches coincide with the limit point, with an addition unstable fundamental branch. This case is the hill-top bifurcation, already analysed by Challamel et al. (Int J Non-Linear Mech 156(104509): 1-11, 2023) in the case p=1 interaction. We also numerically highlight the possibility for such a generalized FPU system to possess possible imperfection sensitivity. Numerical results support the fact that the structural boundary of the hill-top bifurcation coincides with the transition between imperfection sensitive to imperfection insensitive systems.

Path selection algorithms for connecting wireless base stations to power centers in a mine

Relevance. Necessary condition for the systems of safety and process control functioning in a mine is to provide power supply to the relevant facilities. The paper deals with one of the tasks of designing a power supply network in a mine within the framework of a hierarchical approach to organizing the network structure. Within this approach, power controllers are connected to mine lighting breaker. To supply base stations to power controllers, a multi-core cable is used. The number of such cores, as well as the number of such cables emanating from a power controller, are the parameters of the problem. Aim. To consider the problem of choosing routes for connecting base stations of wireless communication in a mine to power centers. It is assumed that base stations and mine lighting breakers are already located in a mine, having the ability to connect a given number of power controllers to them. The connection scheme must be optimal in terms of cost, which is determined by the cost of the cable used. Methods. The authors have proposed several algorithms for solving the mathematical problem, including a greedy algorithm, based on the “go to the nearest point” strategy, and a simulated annealing method. Results. To solve the problem, several approximate methods were proposed and tested. The number of cores is parameter of the problem. The best of the considered algorithms is the annealing simulation algorithm. However, if power centers need to be placed as well, brute force enumeration in the algorithm also gives good results with an appropriate combination of the number of power controllers and the number of possible locations for their placement. Practical relevance. The mathematical problem stated and the mathematical methods make it possible to find minimum cost routes for connecting wireless base stations by multi-core cables to power sources.

Swarm Intelligence in Multiplexed Robots Problems Identified

Although kindling with the very consciousness of the human mind may have been banned, this did not stop scientists from tinkering and innovating with all the technology they were surrounded by. Stumbled by mathematical problems, mathematicians developed certain tactics we call algorithms. Algorithms are the layman's logic language for any device to function according to the desired task.Well, Mother Nature has already built us an unimaginable and incomprehensible algorithm propelled by personal choices, emotions, feelings, and sometimes rationality. For people who still didn't get it, we call it brain in day-to-day language. Our mind subconsciously designs such algorithms for us to efficiently function in our every day to day lives. Our project is an effort to reconstruct such rationality of thinking by artificial means through the use of reinforcement learning and robots to conclude the following 1) Is it possible to recreate human understanding? 2) If yes, then how do we channel it into something practical and physical? 3) How do we utilize this so-formed machine as a result of the conclusion of the second question? Asking this to ourselves we pursued to make our project P3 Hexa which is an endeavor to tinker with swarm intelligence and physically experience the functioning of a self-designed algorithm

Enhancing constrained MOEA/D with direct mating using hybrid mating strategies and diverse crossover methods

Abstract The direct mating strategy, which is a constraint-handling method in multi-objective evolutionary algorithms, selects a second parent on the basis of the optimal direction in the objective space, disregarding feasibility. This approach, although effective in early generations, encounters difficulties as solutions better than the current Pareto solutions become scarce, reducing diversity and hindering exploration. Herein, we introduce a hybrid approach that combines direct mating with newly proposed local mating strategies, aiming to generate offspring around the Pareto optimal solutions to improve the solution search performance via a direct mating strategy. Our method addresses the limitations of conventional direct mating, thereby improving its applicability to real-world design problems. Our hybrid strategy employs local mating to select an additional parent close to the initially chosen parent, preserving solution diversity and effectively exploring the solution space. This enhances the effectiveness of direct mating across all generations. In addition, we introduce two types of crossover methods, i.e., simulated binary crossover and differential evolution, for parents selected by direct and local mating, respectively. The synergy among these techniques facilitates a robust search process that can efficiently yield superior solutions. We evaluated the proposed approach using three mathematical problems with distinct Pareto fronts and two practical applications, including an aerospace design problem. The performances of these methods were assessed on the basis of the averages and standard deviations of the hypervolume and inverted generational distance metrics across multiple solution attempts to determine the average performances and the dependencies on initial population variance. The obtained results demonstrate that the hybrid method significantly outperforms the existing methods in the case of constrained multi-objective optimization. Specifically, the hybrid method yielded higher average hypervolumes and lower dependency on initial population variance than the existing methods. The hybrid method also yielded a lower average and less dependency on initial population variance in the inverted generational distance compared to existing methods. This result suggests that the proposed method can obtain high-quality non-dominated solutions, regardless of the initial population.

Neural Associations between Inhibitory Control and Counterintuitive Reasoning in Science and Maths in Primary School Children.

Emerging evidence suggests that inhibitory control (IC) plays a pivotal role in science and maths counterintuitive reasoning by suppressing incorrect intuitive concepts, allowing correct counterintuitive concepts to come to mind. Neuroimaging studies have shown greater activation in the ventrolateral and dorsolateral pFCs when adults and adolescents reason about counterintuitive concepts, which has been interpreted as reflecting IC recruitment. However, the extent to which neural systems underlying IC support science and maths reasoning remains unexplored in children. This developmental stage is of particular importance, as many crucial counterintuitive concepts are learned in formal education in middle childhood. To address this gap, fMRI data were collected while fifty-six 7- to 10-year-olds completed counterintuitive science and math problems, plus IC tasks of interference control (Animal Size Stroop) and response inhibition (go/no-go). Univariate analysis showed large regional overlap in activation between counterintuitive reasoning and interference control, with more limited activation observed in the response inhibition task. Multivariate similarity analysis, which explores fine-scale patterns of activation across voxels, revealed neural activation similarities between (i) science and maths counterintuitive reasoning and interference control tasks in frontal, parietal, and temporal regions, and (ii) maths reasoning and response inhibition tasks in the precuneus/superior parietal lobule. Extending previous research in adults and adolescents, this evidence is consistent with the proposal that IC, specifically interference control, supports children's science and maths counterintuitive reasoning, although further research will be needed to demonstrate the similarities observed do not reflect more general multidemand processes.

Approaches to Supporting and Measuring Mathematical Problem Posing: A Systematic Review of Interventions in Mathematics Education

Approaches to Supporting and Measuring Mathematical Problem Posing: A Systematic Review of Interventions in Mathematics Education

Tactical flight optimizer: a novel optimization technique tested on mathematical, mechanical, and structural optimization problems

Abstract The current study presents a novel gradient-free metaheuristic search algorithm named Tactical Flight Optimizer (TFO), tailored to meet the growing need for high-performance optimization techniques in solving complex engineering and mathematical problems. The main contribution of this study is the development of a method that simulates tactical air combat formations, offering a sophisticated alternative to conventional search algorithms. In the proposed method, the location of each agent is updated based on a resultant vector derived from three updating vectors. The updating vectors incorporate total information stored by the agents in each iteration. Consequently, the navigation process is guided by a more logical mechanism rather than a simple random process. The search performance of the TFO is initially benchmarked by solving a set of constrained mathematical functions. Subsequently, it is evaluated by addressing a suite of constrained mechanical and structural problems, containing both discrete and continuous decision variables. The obtained results are compared with five other well-stablished metaheuristic techniques. Acquired numerical results indicate that the TFO algorithm can provide promising results in solving both mathematical and engineering problems in terms of computational cost, accuracy, and stability.

Profile of Students' Critical Thinking Skills in Solving Mathematical Problems Reviewed from the Learning Style of Grade IV Students of SD Inpres Teamate, Pattallassang District, Gowa Regency

This study aims to describe the critical thinking skills of grade IV students from auditory, visual, and kinesthetic learning styles in mathematics problem solving at SD Inpres Teamate. This study adopts a qualitative approach with a descriptive type of research. The population of this study is grade IV students consisting of 30 people who will be grouped based on their teaching style, each learning style is represented by 1 student, so that the research subject is 3 students. The data collection techniques used are questionnaires, tests, interviews, and documentation which start from giving learning style questionnaires to 30 students then selecting 1 person each representing audio, visual, and kinesthetic learning styles to be given a critical thinking test. The data analysis techniques used are condensation, data presentation, and verification. Based on the data analysis, it was concluded: 1) the critical thinking ability of students with auditory learning styles is able to meet the indicators of interpretation, analysis, evaluation, inference and explanation well; 2) the critical thinking ability of students with visual learning styles is able to meet the indicators of interpretation, analysis, evaluation, inference and explanatory very well; 3) the critical thinking ability of students with a kinesthetic learning style is less able to meet the indicators of interpretation, evaluation and explanatory but less able to meet the indicators of analysis and inference.

Korpelevich Method for Solving Bilevel Variational Inequalities on Riemannian Manifolds

The bilevel variational inequality on Riemannian manifolds refers to a mathematical problem involving the interaction between two levels of optimization, where one level is constrained by the other level. In this context, we present a variant of Korpelevich’s method specifically designed for solving bilevel variational inequalities on Riemannian manifolds with nonnegative sectional curvature and pseudomonotone vector fields. This variant aims to find a solution that satisfies certain conditions. Through our proposed algorithm, we are able to generate iteration sequences that converge to a solution, given mild conditions. Finally, we provide an example to demonstrate the effectiveness of our algorithm.

Kemampuan Literasi Matematika Siswa SMP Dalam Menyelesaikan Soal Matematika Realistik

Questions that can be used to measure mathematical literacy skills are realistic mathematics questions. Thus, research was conducted to identify students' mathematical literacy abilities in solving realistic mathematics problems. The research method used is a quantitative descriptive method by providing 6 questions describing material on a two-variable linear equation system that can measure mathematical literacy abilities. The results showed that 51.9% were in the low category, 18.5% were in the medium category and 29.6% were in the high category. Based on the results of students' answers, students are still less capable in interpretation and calculations using existing methods in a two-variable linear equation system, students tend to use calculations outside of these methods so that students cannot write down how the calculation process works. Based on the results of research that has been carried out, it show that the mathematical literacy abilities of junior high school students are in the low category.

Pengembangan Media Pipa Puzzle untuk Meningkatkan Kreativitas Belajar Siswa pada Mata Pelajaran Matematika Materi Bangun Ruang Kelas VI SD PAB 23 Medan

This research aims to develop Puzzle media to increase students' learning creativity in mathematics in spatial building material in Class VI of SD PAB 23 Medan. Observation results showed that 67.8% of students had low creativity and 57.1% of students felt bored in the learning process. The contributing factors are the lack of learning media and teachers who still focus on guidebooks. Therefore, researchers are interested in developing puzzle media with the Pipe Puzzle type to increase student creativity. Media development uses the ADDIE model (Analysis, Design, Development, Implementation and Evaluation). This media is validated by media experts, material experts and teachers. The validation results show that this media is suitable for use with a percentage of 80% from media and material experts, and 94% from teachers and students. This research is expected to provide benefits for teachers, students, schools and researchers in improving the quality of education, enriching knowledge about innovative learning media, and increasing students' abilities in solving mathematical problems. Apart from that, this research can also help increase learning motivation, awareness of the importance of creativity, and develop students' critical thinking abilities. It is hoped that the research results can contribute to the development of innovative and effective mathematics learning media.

Analysis of Mathematics Problem Solving Ability Viewed from Self-Regulated Learning

Analysis of Mathematics Problem Solving Ability Viewed from Self-Regulated Learning

Analisis Kemampuan Pemecahan Masalah Ditinjau dari Self-Efficacy Matematis

Problem solving skill is an essential component of mathematics learning. However, in reality, students's problem-solving skills are still low. Internal factors are among the causes that affect students in learning mathematics. One of these internal factors is mathematical self-efficacy. This study aims to examine mathematical problem solving skill in relation to the mathematical self-efficacy of eight-grade students at SMP Negeri 16 Sungai Raya on the topic of linear equations in two-variable. The method used in this research is qualitative descriptive, with data collection techniques including questionnaires, written tests, and interviews. The subjects of study consisted of 6 students representing each category of mathematical self-efficacy. The results indicate that students with high mathematical self-efficacy have very good problem-solving skills. Students with moderate mathematical self-efficacy demonstrate good problem-solving skills, although they have not maximally met all problem-solving indicators. Meanwhile, students with low mathematical self-efficacy exhibit less satisfactory problem-solving skills.

Promoting mathematical competence development through programming activities

Abstract The reasons for teaching programming in school are indeed manifold. Programming can for example be utilized as a vehicle for understanding and learning particular mathematical subject matter, or as a tool for solving mathematical problems. In this paper, however, we propose to utilize programming as a vehicle for developing mathematical competencies such as problem-solving, exploration, modeling, reasoning, representation, generalization, and abstraction. We perform a design study utilizing a systematic, iterative development process for designing teaching sessions, focusing on one mathematical competence at a time. We apply the proposed methodology on a set of teaching sessions that are developed, implemented, and tested in a range of classroom settings. Based on this development process, we conclude that programming can be used to develop mathematical competencies. Furthermore, we identify a set of teacher practices that can be used to facilitate mathematical competence development in programming activities.

Analyzing resource saving and environmental safety in oil and gas waste processing system to provide sustainable development

The problems of environmental safety and resource conservation in the processing of industrial waste at Russian oil and gas enterprises are becoming more and more significant, especially in the context of current trends focused on decarbonization and sustainable development. The growth of industrial waste is not compensated by the corresponding growth in the volume and quality of processing, since only 10% of oily waste is processed, and the rest is buried or incinerated, which has an additional harmful impact on the environment. The article proposes a new approach to multifactor analysis of resource conservation and environmental safety in the integrated processing of industrial waste from oil and gas enterprises to achieve sustainable development goals. The algorithm developed by the authors, the theoretical basis of which is the method of data envelopment analysis (DEA), determines the sequence of solving interrelated problems of multifactor comparison of objects of the waste processing system by heterogeneous quality criteria: resource value, resource potential, resource saving and environmental safety. These problems are formulated on the basis of the super-efficiency model of the DEA method as a mathematical programming problem. The presented and tested approach to multifactor analysis of resource conservation and environmental safety of the waste treatment system allows: (1) to obtain and analyze relative comparative assessments of waste storage facilities and technologies regarding heterogeneous quality criteria, and (2) forming local and general decision-making strategies that provide sustainable development goals. The proposed approach appears promising for multiple prospective applications in the oil-bearing regions of the Russian Federation, where the growth in the formation of industrial waste has severe and irreversible environmental consequences.

Interaction of Mathematics Learning in Inclusive School

Interaction becomes a very important thing in mathematics learning activities because it can help students gain good conceptual understanding, including in inclusive schools that involve regular students and students with special needs in the same scope. This study aims to describe the interaction in mathematics learning in grade VII at one of the inclusive middle schools in Bandar Lampung, Lampung Province. The subjects in this study were 23 regular students, 2 slow learners, and 1 autistic student. This study used a qualitative approach with a case study method on teacher-student interaction in mathematics learning. The research instruments used were observation sheets, Flanders Interaction Analysis Category System (FIACS) matrix, and unstructured interviews. Furthermore, data analysis was carried out through three stages, namely data reduction, data presentation, and conclusion drawing. The results showed that the dominance of teacher talk proportion was in the aspect of encouraging with an average of 34.31% and the aspect of closed response in student talk to the teacher amounted to 70.65% which appeared during the core learning activities in understanding mathematical concepts and problems, while discussions conducted by students with special needs dominated the aspect of discussion during learning activities involving peer tutors, which was 21.88%. This means that mathematics learning in this study forms student activities in following procedural instructions from the teacher, students and teachers communicating mathematics, and jointly constructing mathematical truths. The interaction that occurs in mathematics learning forms a multi-directional pattern involving reciprocal interactions between teachers, regular students, and students with special needs.

Analysis of TPS Learning (Think, Pair, Share) Based on Differentiation Process on Students' Numeration Abilities

Numeracy is a skiil in applying number concepts, artihmetic operations skiils and solving mathematical problems in various contexts related to real life. So cooperative learning type TPS (Think, Pair, Share) based on process differentiation is learning that is able to adapt to the needs and level of understanding of each student and has the potential to improve students’ numeracy abilities. This research aims to find out if there is a difference in increasing the numeracy skills of the low group, the middle group and the high group before and after treatment and aims to evaluate students’ numeracy abilities in cooperative learning type TPS (Think, Pair, Share) based on process differentiation. The research method used is One Group Pretest-posttest. The subjects in this research were students in class VIII-B of SMP Plus Arroudhoh with a total of 32 students. The data collection techique uses a pretest-posttest of data content and uncertainty in the event material, involving a total of 6 descriptive questions. Based on the research results, there were differences in the increase in numeracy skills of the low group, middle group, and high group before and after treathment. This is based on the results of the One-Way Anova test analysis of the N-Gain Score of the pretest-posttest data for the three group showing that the Sig. equal to 0.004< 0.05 then H0 s rejected. As well as the average posttest score for each group, it can be seen that the indicator most mastered by students is the 1st indicator and the indicator less mastered by students is the 3rd indicator.

Study on the Influence of Multiple Derivation Method of General Term Formula of Series on Students' Logical Ability

This paper discusses the influence of multiple derivation method on students' logical reasoning ability. By comparing traditional derivation method with multivariate derivation method, this paper analyzes how the latter can improve students' flexibility and accuracy in solving problems through various strategies such as graphic method, induction method and recurrence method. The research shows that adopting multiple derivation method can strengthen students' logical reasoning ability, enhance the depth and creativity of students' mathematical thinking, and promote students' multi-angle thinking divergence when solving mathematical problems. This method helps students better understand the knowledge of number series, and exercises their rigorous logical thinking and the ability to solve practical problems. It opens up a new teaching idea and operation direction for mathematics teaching.

Peningkatan Motivasi dan Hasil Belajar Matematika Siswa Kelas X SMA Negeri 2 Medan melalui Model Problem-Based Learning berbantuan teknologi Quiziz

This research aims to increase the motivation and mathematics learning outcomes of class X students at SMA Negeri 2 Medan through the application of the model Problem-Based Learning (PBL) combined with the use of Quizizz technology. This research uses the Classroom Action Research (PTK) method with the Kemmis and McTaggart model, which consists of four stages: planning, implementation, observation and reflection. The research subjects were 36 class X students, with instruments in the form of observation sheets, questionnaires and tests. The research results show that the implementation of PBL assisted by Quizizz is effective in increasing student motivation and learning outcomes. In the first cycle, 77.78% of students showed high learning motivation, and this figure increased to 100% in the second cycle. Improvements in student learning outcomes were also seen in cognitive, affective and psychomotor aspects, which experienced significant increases from the first cycle to the second cycle. The PBL model allows students to be more active in learning by presenting contextual mathematical problems, so that abstract material becomes easier to understand. In addition, the use of Quizizz creates an interactive and fun learning atmosphere through game elements. This research concludes that the application of PBL assisted by Quizizz is not only able to improve student learning outcomes holistically, but also motivates them to actively participate in learning. This approach is relevant for improving the quality of mathematics learning, especially in the digital era