Mathematical Problem Solving Research Articles

Mathematical modeling and problem solving: from fundamentals to applications

The rapidly advancing fields of machine learning and mathematical modeling, greatly enhanced by the recent growth in artificial intelligence, are the focus of this special issue. This issue compiles extensively revised and improved versions of the top papers from the workshop on Mathematical Modeling and Problem Solving at PDPTA'23, the 29th International Conference on Parallel and Distributed Processing Techniques and Applications. Covering fundamental research in matrix operations and heuristic searches to real-world applications in computer vision and drug discovery, the issue underscores the crucial role of supercomputing and parallel and distributed computing infrastructure in research. Featuring nine key studies, this issue pushes forward computational technologies in mathematical modeling, refines techniques for analyzing images and time-series data, and introduces new methods in pharmaceutical and materials science, making significant contributions to these areas.

The Mathematical Problem-Solving Abilities of Elementary School Students in Solving Story

This research is a thorough effort to understand the ability of elementary school students in solving mathematical problems, particularly in solving word problems by following Polya's steps. Three fourth-grade students from State Elementary School 2 Majene were the subjects of the study, each showing a different pattern in answering the questions: one student answered correctly, one student answered incompletely but correctly, and one student answered incorrectly. Through tests and interviews, their problem-solving abilities were analyzed qualitatively descriptively. The results show that students generally are able to determine relevant information at the stage of understanding the problem, although sometimes they forget to include important information. All students are able to formulate a plan and use appropriate methods to solve problems, although some experience difficulties due to inadequate planning. However, at the stage of rechecking, not all students are able to present conclusions and evidence accurately. This indicates that the ability to draw conclusions and test the correctness of answers still needs improvement, especially for students who previously experienced difficulties in planning solution steps.

Correlation between Relational Understanding and Cognitive Style on Mathematical Problem Solving Ability

Problem-solving ability is needed in mathematics learning. This study aimed to find out about the correlation between relational understanding and cognitive style on the problem-solving ability of students. Relational understanding was taken into account because this understanding is related to a person's ability to use mathematical procedures obtained by correlating various mathematical concepts that are relevant in problem-solving and to understand why such procedures can be used. Cognitive style was also considered because this style is related to how students think and understand, including how they solve problems. The study used multiple correlation analysis with independent variables of relational understanding (X1) and cognitive style (X1), while the dependent variable was problem-solving ability (Y). The samples of this study were 22 High School students in Malang, selected randomly. The multiple correlation analysis resulted in R = 0,965, indicating that there is a significant correlation between relational understanding and cognitive style on problem-solving ability. In addition, the result of F test also showed that the multiple correlation coefficient was significant.

Implementation of Scientific Approach to Increasing Junior High School Students' Mathematical Problem Solving Ability

This research aims to analyze the learning of class VIII students at Nur Al Rahman Middle School in Cimahi City on linear equations of two variables system material using a scientific approach. In learning mathematics using a scientific approach, especially in linear equations of two variables system material, it is hoped that students can play an active, creative, skilled, and noble character, find and solve problems. The research method used was classroom action research with the subjects studied being 15 class VIII students. This research was conducted for 2 cycles with data collection techniques, namely observation, documentation, and tests in the form of essays that match the indicators of mathematical problem-solving ability. The increase in students' mathematical problem-solving abilities can be seen from the achievement of the percentage of test questions on the problem-solving abilities of the 2 cycles carried out. The instrument used in the research results found that the problem-solving ability skills in linear equations of two variables system material were 33% for cycle I, then 80% in cycle II. This means that learning mathematics in linear equations of two variables system material using a scientific approach has a better influence on students' mathematical problem-solving.

The Implementation of Constructive Approach to Improve Students' Problem Solving Ability and Self Concept Ability

The ability to solve mathematical problems is very important because it is one of the abilities that belong to the ability to think at a high level, therefore it must be trained. One of the factors that can support this is self-concept in doing something and especially in learning mathematics, but this is inversely proportional to the field which stated that self-concept and mathematical problem-solving abilities were still relatively low, the panelists were interested in conducting a research entitled the application of a constructivist approach to improve mathematical problem-solving abilities and self-concept of junior high school students, this study used the experimental method using experimental design and schematized by researchers therefore the researcher chose Krida Utama Middle School Jl. Gedong Lima No. V, Kertamulya, Kec. Padalarang, of course, with class divisions, namely an experimental class and a control class of 30 students. To measure mathematical problem-solving abilities and self-concept towards mathematics, the researcher makes a design or learning that is by the approach and makes measurement tools clear and accurate to see the results of constructivism learning, in the final posttest results from the experimental class obtains a Ngain value of 0.5968 in the learning category the experimental class has a pretty good category, and from the results of distributing the Self Concept questionnaire to learning mathematics using the constructivism approach it gets a percentage score of 77.71%, this indicates that learning using the constructivism approach can have a good effect on students' mathematical problem-solving abilities and concepts students towards learning mathematics.

Literatur Review: The Effect Of Distance Learning on Students' Mathematical Problem Solving Skill

This study was intended to analyze the impact of distance learning on students' ability to solve math problems. Using the literature search method, this research was carried out by analyzing a range of types of information in qualitative and quantitative data from various texts based on previous studies. The literature exploration system uses a variety of references similar to books, exploration journals, and distance literacy operation modules that analyze students’ mathematical problem-solving skills. The results of this study validate that distance learning can affect students’ mathematical problem-solving skills when teachers use innovative methods and interactive learning media. In fact, students can develop their mathematical problem-solving skills through meaningful learning. This means that students can build their own knowledge with learning that requires independent study on the part of students so that they can construct conceptual discoveries from the material being taught. Students' mathematical problem-solving skills can also be affected by the active role played by students in distance learning. For this purpose, it is necessary for educational institutions to apply appropriate methods of learning and media that allow students to have an active role in the educational process. In addition, educational institutions must strive to provide effective and efficient communication, mentoring, and support services to students and parents.

The role of learning anxiety and mathematical reasoning as predictor of promoting learning motivation: The mediating role of mathematical problem solving

Mathematical problem solving stands as a fundamental aspect of 21st-century skills. Extensive educational studies have substantiated the cultivation of this competency, illustrating that exploring specific predictors and related variables can offer valuable insights for its enhancement. The study investigated how solving mathematical problems acts as a mediator between motivation for learning, anxiety about learning, and mathematical reasoning. A total of 345 primary school students participated in this study, responding to online questionnaires. Structural equation modelling was applied for data analysis, revealing satisfactory construct validity and instrument reliability. The findings highlighted a positive relationship between learning anxiety and mathematical reasoning, indicating their predictive role in improving learning motivation. In addition, the research identified mathematical problem solving as a mediator, playing a crucial role in reducing learning anxiety and fostering increased learning motivation. These outcomes have significant implications, underscoring the need to understand the intricate interaction between learning anxiety, mathematical reasoning, and motivation. This understanding could facilitate the development of targeted interventions and support systems, fostering a conducive learning environment that enhances student participation and academic achievement.

Physics difficulty and problem-solving: Exploring the role of mathematics and mathematical symbols

Reports of difficulty in physics has been documented over the years, especially at the senior secondary level. The application of mathematics as a tool for understanding physical phenomena and problem-solving is well-established. The use of symbols and mathematical rigour is essential for effective problem-solving in physics. However, the teaching and learning of physics have encountered barriers, as highlighted in the literature on competencies in this field. This study focuses on exploring the interlink, context, and associated barriers in the teaching and learning of physics by reviewing existing literature on the application of mathematics and mathematical symbols. Through a theory synthesis design, the study examined the current state of literature on mathematical problem-solving in physics, as well as the differences between mathematising and the application of mathematics in physics. The competencies required of teachers and students were also highlighted in order to better equip physical sciences teachers to address the challenges faced by students in learning physics. The literature suggests that a well-sequenced approach to topics by both mathematics and physics teachers can facilitate knowledge transfer among students. Teachers are encouraged to provide step-by-step guidance to address students' mathematical deficiencies, particularly in the physics aspect of the physical sciences curriculum at the further education and training (FET) phase. It is recommended that topics between physics and mathematics be aligned and mathematical concepts be pre-teach to enhance students' contextual knowledge transfer.

Meta-Analisis Model Project Based Learning terhadap Kemampuan Pemecahan Masalah dalam Pembelajaran Matematika

This research aims to analyze the effect size of using the Project-Based Learning (PjBL) model on problem-solving abilities in mathematics learning and investigate the effect size based on educational levels. The research method employed is quantitative with meta-analysis, aiming to summarize, evaluate, and integrate the results of several published studies. Data collection techniques involve documentary studies by searching national and international journals published between 2015 and 2023. A total of 24 studies met the predetermined inclusion and exclusion criteria, and the effect sizes of each study were calculated. Subsequently, the overall average effect size and effect sizes based on educational levels were calculated. Data analysis was conducted using JASP software version 0.18.1.0. The results of this research indicate that the effect size of the Project-Based Learning model on problem-solving abilities in mathematics learning is significantly large, with an effect size of 0.973. Furthermore, statistically significant differences were reported in the effect sizes of the PjBL model on problem-solving abilities in mathematics learning across educational levels. The implementation of the PjBL model has a very large effect size on problem-solving abilities in mathematics learning for elementary, and college-level students. Meanwhile, at junior high school and the senior high school level, the PjBL model on problem-solving abilities in mathematics learning has a large and amoderate effect size.

Exploring students' proportional reasoning in mathematical literacy problem solving: recognition of multiplicative relationship strategies

Introduction. A multiplicative relationship represents the association between two or more variables in the form of multiplication. For example, when one variable increases, the other variable also escalates proportionally. Accordingly, it is important for students to have the ability to identify the pattern of multiplicative relationships, describe them in the form of equations or comparisons, and apply them in different situations. This study describes the strategies used by students in recognizing multiplicative relationships, particularly in solving mathematical literacy problems containing proportional situations. Study participants and methods. The research was conducted in three junior high schools located in Malang, Indonesia, involving 191 ninth-grade students. They were asked to work on a mathematical literacy question, and then their answer sheets were corrected and grouped based on the developmental stage of proportional reasoning, particularly in recognizing multiplicative relationships. Furthermore, the subjects were interviewed in-depth concerning their experience in solving literacy problems in proportional situations. This study used a qualitative approach with a phenomenological research type. the subject's experience was investigated holistically, along with the appearing phenomenon. The garnered data were interpreted through continuous reflection and analysis for a deeper understanding. The results were then summarized. Results. In this study, two variations of strategies have been identified being used by students at the stage of recognizing multiplicative relationships in solving mathematical literacy problems, namely the multiple strategies and the pattern strategy. This finding serves as a valuable contribution to understanding students' strategies and behaviors in recognizing multiplicative relationships, which has not been revealed in previous studies. The main difference between these two strategy variations lies in the approach used in solving the problem. The multiples strategy emphasizes the conceptual linking of quantity values between objects, relying on the conceptual shifts that transpire as students navigate through their additive reasoning steps within the framework of multiplication. In this case, students need to comprehend various number concepts and number relationships, with frequent focus on multiplication as a form of repeated addition. On the other hand, pattern strategies rely on students' ability to match patterns, use the arrangement of numbers constituting the pattern, and relate them to other patterns in solving problems. Practical significance. The results of this study serve as a crucial reference for more effective and efficient mathematics learning formulation for improving students' proportional reasoning.

Development of Mobile Learning Teaching Materials on Opportunities to Improve Students' Mathematical Communication Skills in Vocational High Schools

Another fact that was discovered was the low average daily mathematics test scores in one of the State Vocational Schools. This fact influences mathematics learning and the greatest difficulty is carrying out mathematical communication and problem solving on the questions given. The following is the average value of daily tests on Opportunity material for the last three years at SMKN. To respond to the problem of students' low mathematical communication skills, the enormous demand for progress in science and technology, it is very necessary to make changes to the learning process, especially the selection of appropriate mathematics teaching materials. One example is developing an Android-based teaching material or mobile learning. The use of smartphones in learning allows students to carry out learning activities by accessing learning materials, directions and information anywhere and at any time without limited space and time. Mobile Learning also overcomes time constraints and is able to train students to learn independently from various sources. Students whose learning received procedural scaffolding with the help of smartphones were better than students who received conventional learning. This mobile learning teaching material is said to be effective based on student response questionnaire data and mathematical communication test results data obtained. The results of the student response questionnaire obtained a percentage of 95% with the criteria of being very effective for use in learning. Meanwhile, the percentage of learning completion results was 98% with a very high learning completion interval. The use of mobile learning teaching materials has an influence on students' mathematical communication skills. The average score of the experimental class students' mathematical communication ability test results in each school was higher than the control class. The average score for the experimental class at SMKN 1 Rejotangan was 85.00 while the average score for the control class was 76.15. The average score for the experimental class at SMKN 1 Boyolangu was 85.64, while the average score for the control class was 78.62. The average score for the experimental class at SMKN 2 Tulungagung was 82.79 while the average score for the control class was 75.99. After comparison and analysis, it was concluded that there was a difference in the test results of students' mathematical communication skills between the classes given the action and the control class.

Mathematics for a Better World: Promoting Social Values in Mathematics Education

Social values are integral part of the norms that are emphasized into the educational systems, and their integration in the school curricula is essential for nurturing responsible citizens. The current paper discusses the outcomes of learning social values within mathematical content and problem solving. The research was conducted in an academic course that social values was one of its topics. The participants were 18 pre-service mathematics teachers who study in an Arab college in Israel. They underwent a training process in studying social values within mathematical content and subsequently applied it in schools. Employing qualitative methods, the research examined how to integrate social values in mathematics class, and how the pre-service mathematics teachers evaluate the importance of the subject. The findings indicated a notable improvement in the pre-service teachers' interest in the subject even it was a challenging experience. They realized that integrating social values into mathematical content is possible and applicable to various mathematics subjects. The findings may contribute to highlight the importance of integrating social values into mathematical content both at schools and at the academic education institutions.

How do Math Anxiety and Self-Confidence Affect Mathematical Problem Solving?

Problem-solving performance requires both cognitive and affective aspects related to math anxiety and self-confidence. This study aims to determine the effect of math anxiety and self-confidence on geometry problem-solving skills and then explore students' geometry problem-solving based on their level of math anxiety and self-confidence. This study utilized a mixed-methods approach with a sequential explanatory design and involved 106 students. The quantitative portion of the study employed a multiple linear regression test to examine the influence of math anxiety and self-confidence on problem solving. Furthermore, qualitative research was done to thoroughly examine the effect through in-depth interviews. The results demonstrate that math anxiety and self-confidence influenced geometry problem-solving (R = 0.476; p = 0.000) and contributed 22.6% based on the value of R-square. Furthermore, the present study also found differences in the performance of a subject with low math anxiety and high self-confidence and a subject with high math anxiety and low self-confidence.

EEG alpha and theta time-frequency structure during a written mathematical task.

Since the first electroencephalogram (EEG) was obtained, there have been many possibilities to use it as a tool to access brain cognitive dynamics. Mathematical (Math) problem solving is one of the most important cortical processes, but it is still far from being well understood. EEG is an inexpensive and simple indirect measure of brain operation, but only recently has low-cost equipment (mobile EEG) allowed sophisticated analyses in non-clinical settings. The main purpose of this work is to study EEG activation during a Math task in a realistic environment, using mobile EEG. A matching pursuit (MP)-based signal analysis technique was employed, since MP properties render it a priori suitable to study induced EEG activity over long time sequences, when it is not tightly locked to a given stimulus. The study sample comprised sixty healthy volunteers. Unlike the majority of previous studies, subjects were studied in a sitting position with their eyes open. They completed a written Math task outside the EEG lab, wearing a mobile EEG device (EPOC+). Theta [4 Hz-7.5 Hz], alpha (7.5 Hz-13 Hz] and 0.5 Hz micro-bands in the [0.5 Hz-20 Hz] range were studied with a low-density stochastic MP dictionary. Over 1-min windows, ongoing EEG alpha and theta activity was decomposed into numerous MP atoms with median duration around 3s, similar to the duration of induced, time-locked activity obtained with event-related (des)synchronization (ERS/ERD) studies. Relative to Rest, there was lower right-side and posterior MP alpha atom/min during Math, whereas MP theta atom/min was significantly higher on anteriorly located electrodes, especially on the left side. MP alpha findings were particularly significant on a narrow range around 10 Hz-10.5 Hz, consistent with FFT alpha peak findings from ERS/ERD studies. With a streamlined protocol, these results replicate previous findings of EEG alpha and theta activation obtained during Math tasks with different signal analysis techniques and in different time frames. The efficient application to real-world, noisy EEG data with a low-resolution stochastic MP dictionary shows that this technique is very encouraging. These results provide support for studies of mathematical cognition with mobile EEG and matching pursuit.

Defragmenting students’ reflective thinking levels for mathematical problem solving: does it work?

ABSTRACT Study on fragmentation and defragmentation of reflective thinking structures has never been conducted. Therefore, the purpose of this study was threefold: (1) to identify the types and forms of fragmentation of students’ reflective thinking structures in solving mathematical problems, (2) to describe attempts to defragment students’ reflective thinking structures in each type and form of fragmentation, and (3) to find out if such defragmentation attempts can work for reflective thinkers who experience fragmentation. This research was qualitative, exploratory, and descriptive. The subjects included in this study were students who thought reflectively and experienced fragmentation at each level of reflective thinking when solving mathematical problems. Data collection was conducted using tests, interviews, think-aloud protocols, and observation. Data analysis was conducted using constant comparative method. Data validity was established using method and source triangulation. The results showed: (1) Scanning Defragmentation work for Less-Strict Fragmentation, (2) Schema Emergence Defragmentation work for Pseudo-True Fragmentation, (3) Schema Activation work for Pseudo-False Fragmentation, (4) Connection Emergence Defragmentation work for Nonexistent-Connection Fragmentation, (5) Compare-Reflect Defragmentation work for Confidence-False Fragmentation. The results of this study can be reference for mathematics researchers and educators to develop learning models that can prevent the occurrence of fragmentation of reflective thinking structures.

Computational and Problem-Solving Skills in Mathematics of AIMS Students

Life is an arena of problems. A human child has to meet and solve problems as he grows; problems on his physical surroundings, his intellectual associations, and in his social contacts. These dilemmas grow in number and complexity as we age. His success in life is, in large measure, determined by the capacity and competence to solve them. Mathematics is a subject of problems and studying Mathematics is different from studying other subjects because it is learned by doing and solving boundless problems. For this reason, the efficiency and ability in solving problems are guarantees for success in learning this kind of subject. The researchers, being Mathematics instructors, observed that the students find difficulty in solving Mathematics problems. The researchers generally identified the salient reasons for this kind of conflict namely: poor background in algebra, poor verbal and contextual understanding, and poor logical ability. Conclusively, a direct relationship can be inferred between the problem-solving skills of students and the salient factors affecting the specified ability. From this observation, the researchers want to conduct an immediate action in order to quench this growing phenomenon. Seventy-five (75) or 63.0% of the respondents are graduates of private schools while 44 or 37.0% are graduates of public schools. On computational skills, the respondents can perform the four basic operations in real numbers, apply the properties of equalities of real numbers as well and derive formulas from a given equation. On problem solving skills, the result indicates that respondents are not good in problem solving which involves plane and solid figure. Recommendations were arrived at to enhance the computational and problem-solving skills of the students.

Parental support for mathematical problem solving: Proximal and distal influences within the religious practice of tithing

This study examined the relation of mathematical learning and problem-solving to influences close to the child (proximal) and social structures more removed (distal). A socio-ecological lens enables examination of multi-level influences within the religious practice of tithing (giving 10% of one’s earnings to the church). Distal influences (e.g., tax law) and proximal influences (e.g., norms for payment, parental practices) are investigated to explain the emergence of mathematical problems during the practice of tithing. Exploration of children’s success and strategy use as a function of problem context found differential success and strategy use when children solved problems of tithing, as compared to a mathematically similar school context. This research demonstrates how proximal and distal factors can illuminate the contours of everyday mathematical performance.

Students’ Creative Thinking Ability in Solving Mathematical Problems

This research aims to determine the description of students' creative thinking abilities in solving mathematical problems in learning Trigonometry. The research design is descriptive qualitative. The research subjects were Class X high school students. Data collection instruments included Creative Thinking Ability TESTs and interviews. The data analysis technique used is time triangulation. This research explores students' creative thinking abilities in solving mathematical problems. The results show that the ability to think creatively Students' mathematics is described based on a review of the answers to the mathematical creative thinking ability test which consists of 4 aspects, namely fluency, flexibility, novelty and detail. Based on the average results of students' answers in solving questions regarding mathematical creative thinking abilities, there were 5 questions, which had different averages, although none of their creative thinking abilities reached the very high category. This shows that students are less able to solve problems with mathematical creative thinking skills. The ability to think creatively at the high strata is at high criteria with an average of 28.6. The highest score achieved by students was 32 and the lowest score was 23.

Pemanfaatan Media YouTube dan Blog Pembelajaran Materi Statistika dan Hubungannya dengan Kemampuan Pemecahan Masalah Matematis dan Prestasi Belajar

This research aims to examine the use of learning media that is good, effective and appropriate to the needs and characteristics of students through YouTube media and Learning Blogs and its relationship with mathematical problemsolving abilities and learning achievement. The method used was quantitative quasi-experiment with correlation tests on mathematical problem solving abilities and learning achievement for classes VIII C and VIII D at SMP Tarakanita 2 Jakarta with 58 respondents. The Cronbach's Alpha test on the YouTube media test instruments (0.83), Blog (0.82), Problem Solving (Pretest 0.92 and Posttest 0.86), and Achievement (0.90) shows high validity and reliability. Based on non-parametric hypothesis testing using the Spearman Test method, it is known that there is a correlation between the use of YouTube media and Problem Solving (R-count 0.37), YouTube and Achievement (R-count 0.41), Blogs and Problem Solving (R-count 0. .42), and Blog with Achievement (R-count .39). The non-parametric Mann Whitney test in the control class and experimental class regarding achievement was stated to be identical with the same mean and variance so that there was no difference in the increase in NGain in the two classes.

How can procedural flowcharts support the development of mathematics problem-solving skills?

AbstractSupporting students’ problem-solving skills, solution planning and sequencing of different stages that are involved in successfully developing a meaningful solution to a problem has been a challenge for teachers. This case study was informed by reflective investigation methodology which explored how procedural flowcharts can support student mathematics problem solving in a senior Mathematical Methods subject in Queensland. The paper used thematic analysis to analyse and report on teachers’ perceptions of the utility of procedural flowcharts during problem solving as well as content analysis on how student-developed flowcharts can support their problem-solving skills. Results show that development of procedural flowcharts can support problem solving as it helps with integration of problem-solving stages.