Mathematical Problem Solving Research Articles

Numerical and Symbolic Analysis for Mathematical Problem-Solving with Maple

This study explores the versatile capabilities of Maple, a widely used mathematical software, in addressing a wide range of numerical and symbolic computations essential for scientific and engineering applications. The researchers investigated Maple's diverse suite of tools, including numerical integration, nonlinear equation solving, polynomial interpolation, symbolic integration, and various numerical methods. Through an in-depth literature review, illustrated case studies, and detailed performance evaluations, the paper demonstrates the effectiveness and accuracy of Maple's computational approaches in dealing with complex problems in various areas of applied mathematics. This study's findings underscored Maple's tremendous value as a reliable and comprehensive software package for researchers, scientists, and professionals involved in advanced mathematical analysis and scientific computing. Furthermore, the paper highlighted Maple's versatility in creating high-quality three-dimensional plots, crucial for visualizing and analyzing complex mathematical and scientific data. Using either sets or lists, the ability to display multiple surfaces in a single three-dimensional plot showcases Maple's power in data visualization and communicating complex ideas. By positioning Maple as a powerful platform for solving versatile mathematical problems, this study highlights the software's indispensable role in advancing scientific discoveries and engineering innovations.

Triangular Fuzzy Cognitive Maps Method for Modelling Interrelation between Causal and Trigger Factors Towards Students' Mathematics Problem-Solving Ability

The purpose of this study is to model the interrelation between causal and trigger factors towards students' mathematics problem-solving ability by using the triangular fuzzy cognitive maps (TrFCM) method. Selection weaknesses and limitations in the method of relational analysis cause the interrelation and influence between variables not to be visualised and do not reveal the characteristics of the actual interaction. As a result, this study demonstrates TrFCM as a more effective way of analysing the relationship between variables based on the complexity that happens in analysing causal factors and triggers for students' problem-solving abilities in mathematics. The results of the influential relations map (IRM) demonstrate that emotion and metacognition are the triggers for problem-solving ability. While executive function is the main cause of success in completing mathematics problems, it is also influenced by additional factors such as motivation, attention, and working memory. These causal and triggering factors also mobilise parts of students' cognitive and behavioural performance to improve the process of solving mathematics problems. Based on the outcomes of this study, computational intelligence methods like fuzzy systems give useful procedures for analysing data from expert surveys. The TrFCM method offers a more accurate relational analysis procedure in modelling interrelation between human factors.

In-depth Analysis of Students' Mathematical Problem-Solving Skills: Influence Factors Motivation and Effective Teaching Strategies

Problem-solving (PS) skills are efforts to find solutions when faced with challenges. This study aims to examine students' mathematical PS skills by focusing on the influence of learning motivation and identifying factors that were previously overlooked. A qualitative approach with a case study design was used, where the researcher acted as the primary instrument. The research also utilized PISA-type test instruments, observation sheets, and interviews. PISA-type questions were designed around content, context, and process components, adhering to the PISA framework. The study was conducted in a school in Surakarta, chosen for its alignment with the minimum competency assessment system similar to PISA. Using snowball sampling, nine students were selected for response analysis. These students were categorized based on their motivation levels: high, moderate, and low. The results show that students with high motivation are proactive in problem-solving, directly addressing the problem, reviewing each step as they proceed, and ensuring accuracy. Moderately motivated students take more time, often using scratch paper, and review their work only at the end. Low-motivation students face greater difficulties, frequently making mistakes, relying heavily on scratch paper, and often skipping the review process due to time pressure. To improve PS skills, future research could explore the integration of interactive digital tools with instant feedback, adaptive learning platforms tailored to student motivation, and collaborative learning exercises. Additionally, incorporating real-world scenarios into problem-based learning could enhance engagement and develop deeper problem-solving abilities across different motivation levels.

ANALYSIS OF STUDENTS' ABILITY TO SOLVE MATHEMATICAL PROBLEMS ON CONTEXTUAL PROBLEMS INVOLVING ALGEBRAIC FORMS

This research is motivated by the fact that problem solving is a basic ability that every student must have. However, observations in the field show that students' mathematical problem-solving skills, especially in the material of algebraic form operations, are still relatively low. This study aims to describe students' mathematical problem-solving skills based on Polya's theory, which consists of four stages: (1) understanding the problem, (2) planning problem solving, (3) implementing the plan, and (4) re-examining the results. This study involved 26 ninth grade students as subjects. The method used was descriptive qualitative with data collection techniques including tests, interviews, and documentation, data analysis conducted based on four levels of problem-solving ability: excellent, good, sufficient, and deficient. The results showed that students' mathematical problem-solving ability on algebraic form operation material obtained as a whole was still relatively low with a scale of 42%. The implications of these findings indicate the need for the alication of more varied and contextualized teaching strategies to improve students' problem-solving skills. This research can be the basis for teachers in providing further assistance to students who are experiencing difficulties, focusing on improving skills in understanding and solving mathematical problems as a whole.

An exact and metaheuristic optimization framework for solving Vehicle Routing Problems with Shipment Consolidation using population-based and Swarm Intelligence

The Vehicle Routing Problem with Shipment Consolidation (VRPSC) is a novel variation of the vehicle routing problem that involves multiple commodities, multiple dimensions, a fleet with different types of vehicles, and the challenge of consolidating shipments during the route. Exact algorithms have been suggested to solve the VRPSC problems. Besides exact algorithms, specific metaheuristic algorithms are employed to deliver solutions of superior quality, albeit not necessarily optimal. The Artificial Immune System (AIS) and Genetic Algorithm (GA) are the metaheuristic optimization techniques applied in this research. Genetic programming is included in evolutionary computing, while AIS is included in swarm intelligence. This research presents a vehicle routing model with product consolidation and different product dimensions. These criteria were selected due to their significant impact on the complexity of mathematical problem-solving in VRPSC. The results from applying these metaheuristic algorithms will be compared with those of exact algorithms to compare and analyse different VRPSC solution approaches.

Evaluating chatGPT-4 and chatGPT-4o: performance insights from NAEP mathematics problem solving

This study assesses the capabilities of OpenAI’s ChatGPT-4 and ChatGPT-4o in solving mathematics problems from the National Assessment of Educational Progress (NAEP) across grades 4, 8, and 12. Results indicate that ChatGPT-4o slightly outperform ChatGPT-4 and both models generally surpass U.S. students’ performance across all grades, content areas, item type, and difficulty level. However, both models perform worse on geometry and measurement than on algebra and face more difficulties with high-difficulty mathematics items. This investigation highlights the strengths and limitations of AI as a supplementary educational tool, pinpointing areas for improvement in spatial intelligence and complex mathematical problem-solving. These findings suggest that while AI has the potential to support instruction in specific mathematical areas like algebra, there remains a need for careful integration and teacher-mediated strategies in areas where AI is less effective.

Self-Regulation Profiles of Pre-Service Mathematics Teachers for Primary Education in Mathematical Problem-Solving Contexts

Self-regulation in mathematical problem solving is of particular importance in the initial training of Primary Education teachers as it can contribute to improving their own competence in mathematics and at the same time enable them to teach effectively and in a personalized way. With this idea in mind, this study identifies self-regulation profiles present in university students in mathematical problem-solving contexts based on data from the application of a validated scale on a sample of 402 pre-service teachers of primary education at University of the Basque Country. The cluster analysis carried out made it possible to identify and characterize three profiles, labelled according to the level of self-regulation represented by each of them (low, medium, high). In view of the results obtained, we perceive a need to design didactic proposals that allow these profiles to evolve from the lowest to the highest levels.

Development of domino media to improve problem solving and mathematical communication for Islamic boarding school students

Mathematical problem solving and communication skills are important factors in learning mathematics. Therefore, it is necessary to develop learning media, especially in Islamic boarding school curricula where the learning load is greater than the regular curriculum. On this basis, the aim of this research is to develop domino card media to improve problem solving and mathematical communication skills of Islamic boarding school students. Development was carried out at Al-Izzah IIBS Batu Middle School, Malang, using the ADDIE model. Data obtained from documents, observations, questionnaires and tests were analyzed using qualitative and quantitative approaches. Based on the results of the validation analysis, the domino card media was declared valid from the aspects of design, material, curriculum, consistency, language, practicality, problem solving development and mathematical communication. Meanwhile, the effectiveness of using domino card media in learning is classified as effective, if seen from the results of the problem solving ability test with an N-Gain score of 76.79%, and the results of the mathematical communication ability test with an N-Gain score of 61.79%. Many factors cause this non-optimality, including a lack of mathematics lesson hours, a busy lesson schedule that is less suited to conditions, many demands on students, and the learning load in the curriculum.

Developing the Ability to Solve Mathematics Problems ‘Polygons’, Through Open Approach Learning Management for Sixth-Grade Students

This action research aims to develop the ability to solve mathematical problems, particularly in polygons, through open-approach learning management for sixth-grade students, with the goal of achieving an average score exceeding 70% of the total possible score. The target group consisted of eight students in the second semester of the academic year 2023. Data collection tools included lesson plans, mathematics problem-solving ability tests, student behavior observation forms, and student journal logs. The data were analyzed using statistical methods, including percentages, means, and standard deviations. The findings showed that an open approach to learning management can effectively enhance mathematical problem-solving skills. Furthermore, it was observed that the students demonstrated various problem-solving approaches, actively engaged in group and inter-group learning exchanges, displayed confidence in problem-solving, and improved their mathematical problem-solving abilities.

NEUROPSYCHOPEDAGOGICAL PERSPECTIVE: RELATIONSHIPS BETWEEN WORKING MEMORY AND MOTOR, INHIBITORY CONTROL, AND LINGUISTIC DEVELOPMENT IN ELEMENTARY SCHOOL

Working memory plays a pivotal role in cognitive functioning, serving as a dynamic interface for processing and integrating information across various domains. It is crucial for executing complex tasks such as reading comprehension, mathematical problem-solving, and logical reasoning. This study investigates the relationship between working memory and motor skills, inhibitory control, and language abilities in elementary school students, highlighting the role of specific assessment instruments in this analysis. The research involved 1107 students, aged 7 to 10 years, from public schools in Joinville, Brazil. Working memory was evaluated using the Neuropsychopedagogical Screening Scale for Working Memory (NSSWM), which comprises 23 items that assess the temporary storage and processing of information needed for tasks such as language comprehension, arithmetic, and problem-solving. Motor skills were assessed using the Neuropsychopedagogical Screening for Children's Motor Development, a 7-item scale focusing on motor coordination, fine motor control, and organizational skills during school activities. Inhibitory control was measured with the Child Inhibitory Control Screening Scale (CICS), which includes 18 scenarios that evaluate inhibitory responses, planning, and impulsivity. Phonological skills were assessed using the Screening Scale for Phonological Skills (SSPS), which measures the ability to recognize formal language characteristics through 17 items. Lastly, reading and writing skills were evaluated using the Children's Reading and Writing Screening Scale (CRWSS), a 16-item scale designed to identify potential difficulties in acquiring these skills in a school setting. The results revealed significant correlations between working memory and other cognitive domains, with motor skills exhibiting the strongest association (r=0.916, p=0.012). Additionally, inhibitory control (r=0.732, p=0.028) and phonological awareness (r=0.815, p=0.034) showed strong correlations with working memory, indicating that students with better-developed skills in these areas tend to perform better in working memory tasks, which, in turn, positively impacts their academic performance. The study underscores the importance of early neuropsychopedagogical interventions that address both cognitive and motor development. By employing specific, targeted assessment instruments, educators and mental health professionals can better identify students at risk of academic difficulties and implement effective strategies to enhance their cognitive and behavioral development, ultimately fostering a more supportive and inclusive learning environment.<p> </p><p><strong> Article visualizations:</strong></p><p><img src="/-counters-/soc/0525/a.php" alt="Hit counter" /></p>

PENGARUH MODEL PEMBELAJARAN SEARCH, SOLVE, CREATE, AND SHARE (SSCS) TERHADAP KEMAMPUAN PEMECAHAN MASALAH MATEMATIS PESERTA DIDIK

This study aims to determine whether there is an effect of the Search, Solve, Create, and Share (SSCS) learning model on students' mathematical problemsolving ability and to see how much influence the SSCS learning model has on students' mathematical problemsolving skills. This research uses a quantitative approach with a quasi-experiment method with a pretest-posttest control group design. The population of this study were all VIII grade students in one of the junior high schools in Bogor Regency. The samples used were class VIII-2 as the control class using conventional learning model and class VIII-4 as the experimental class using SSCS learning model. Data was collected through a mathematical problemsolving ability test in the form of five description questions on Social Arithmetic material. The data obtained were analyzed using T test and Effect Size test. The results of data analysis showed that there was an effect of SSCS learning model on students' mathematical problemsolving ability. The effect size of SSCS learning model on students' mathematical problemsolving ability is 0.39 with moderate category.

The Development of Contextual Approach E-Modules to Improve Students’ Mathematical Problem Solving Ability on Junior High School

This study aims to develop an E-Module that can be used by teachers to support the learning process so that students more easily understand material in interactive mathematics at SMPN 4 Cipeundeuy. In order to do so, this research using research and development (Reaserch and Development) with the 4D development model (Define, Design, Develop, and Disseminate). Research conducted using this model is limited to step 3 (Define, Design, Develop) due to time and cost constraints during the research. The subjects of this study were class IX students for limited trials and class VIII students for wide trials. The data that has been collected is then analyzed using Microsoft Excel. The results of the study on the feasibility of teaching materials were seen from the results of the assessment of lesson plans, worksheets, and media with a percentage of 93.80% and the results of assessments by two mathematics teachers with a percentage of 89%. Teaching materials were tested for practicality using a student response questionnaire with a percentage of 90%. Thus this teaching material can be implemented and can be used. The results of this study can be categorized as valid, practical, and very feasible because they have received a good due diligence.

PENGARUH PEMBELAJARAN MATEMATIKA BERBASIS PROYEK TERHADAP KEMAMPUAN PEMECAHAN MASALAH SISWA KELAS X SMAN 1 PEGAJAHAN

This study aims to examine the impact of Project-Based Learning (PjBL) on the problem-solving abilities of tenth-grade students at SMA Negeri 1 Pegajahan within the context of the Merdeka Curriculum. The research employs a quantitative method with a quasi-experimental approach, utilizing a Pretest-Posttest Only One Group Design. The population includes all tenth-grade students, with samples selected using Cluster Random Sampling techniques. Data were collected through pretests and posttests and analyzed using descriptive and inferential statistical tests, including normality tests, homogeneity tests, and the Paired Sample t-Test. The results indicate a significant improvement in students' problem-solving abilities following the implementation of PjBL. The t-test results demonstrate a positive effect of PjBL on students' problem-solving skills. Based on these findings, it is concluded that PjBL is an effective teaching method for enhancing students' mathematical problem-solving abilities. This study provides valuable contributions to the development of more innovative and relevant teaching methods, particularly in supporting the implementation of the Merdeka Curriculum in Indonesia.

A Hierarchical Linear Models Approach to Explaining Reflective Thinking Skill Through Problem Solving

The purpose of this study is to identify the student and teacher level factors that explain the reflective thinking skills through problem solving of elementary school pupils. The research was conducted in public elementary schools in three Van districts: Pekyolu, Tuşba, and Edremit. The study's sample consists of 52 mathematics teachers and 1126 elementary school pupils. "Participant Information Form," "Reflective Thinking Ability Through Problem Solving Scale," and "Mathematics Problem Solving Attitude Scale" are data gathering tools for pupils. Teachers' data was gathered using the "Participant Information Form," the "Reflective Thinking Tendency Scale for Teachers and Preservice Teachers," and the "Scale for Learner Autonomy Support." According to the results, it is found that the 90 % of variance in dependent variable can be explained by student level variables. Teacher level variables could explain 10% of outcome variance. The gender of students, receiving private tuition, book reading frequency, time devoted to studying mathematics, and attitude through problem solving are significant factors that can predict the dependent variable. Moreover, students' reflective thinking ability can be significantly influenced by teacher-level factors, such as teachers' knowledge of problem-solving steps and their tendency for reflective thinking. The authors recommend education or seminars that develop teachers’ reflective thinking tendency and problem-solving courses be provided in mathematics teaching undergraduate programs. Students should be supported in gaining reading habit and activities that have positive impact on the students’ problem-solving attitude.

Meningkatkan kemampuan pemecahan masalah matematis siswa: Pengembangan modul pembelajaran berbasis studi etnomatematika pada budidaya tanaman hidroponik

This study aims to develop an ethnomathematical study-based learning module on hydroponic plant cultivation to improve the mathematical problem-solving ability of class VII junior high school students on social arithmetic material that meets the criteria of validity and effectiveness. This research method is research and development with the ADDIE model (analysis, design, development, implementation, evaluation). Data collection instruments include interviews, validation sheets, questionnaires, and pre-test and post-test questions. The data were analyzed using qualitative and quantitative data analysis techniques. The results showed that ethnomathematics research-based learning modules were considered effective and feasible, with a percentage of 90% results verified by material and ethnomathematics experts, 96% by media experts, 90% teacher assessments, and a pass rate of group examination assessments of 87.3%, and a pass rate of on-site examination evaluations of 88.61%. The modules developed are also claimed to be effective in improving students' mathematical solving skills, with the experimental class having an average N-gain score of 0.78 in the "very high" category, better than the control class with an average N-gain score of 0.32 in the "medium" category. Both data were tested using a two-sample t-test and obtained 0.00 results less than 0.05 then H0 was rejected and H1 was accepted.

Analysis of Open-Ended Problem-Solving Ability in Mathematics in Terms of Cognitive Style

Problem-solving ability is a fundamental skill. Problem-solving is an effort to find a way out of a difficulty to achieve a goal to be achieved. There are 4 stages in solving problems as follows: understanding the problem, planning a solution, implementing the plan, and checking back. This research method uses a qualitative approach. The goal is to explain the ability of open-ended problem-solving mathematics students in terms of cognitive style type Field Independent and Field Dependent. Selection of the subject of this study using cognitive style test instrument Group Embedded Figure Test (GEFT). The results of this study showed that the FI subject was able to answer correctly without any doubt and was able to answer the question independently while the FD subject was able to answer the question there was doubt but answered correctly and when answering the question asked the researcher.

Analysis of Mathematical Problem-Solving Ability on The Pythagoras’ Theorem

Since mastery of problem-solving techniques is one of the main objectives of studying mathematics, such techniques are very important in the field of mathematical education. With the help of the Pythagorean theorem, the problem-solving skills of eighth-grade students will be assessed. SM Muhammadiyah 01 Field, Class VIII-1 Integrated Facilities, is the location of this research. This research uses qualitative research methodology. The instruments used in this study are four and ten-question model questionnaires labeled Highly Agree (SS), Agreed (S), and Disagreement (TS). This research resulted in high categories whose presentation scores reached 57 to 60 were obtained by 2 students, a medium category where its presentation ratings reached 35 to 46 was achieved by 21 students, and a low category where the presentation value reached 2 compared to 31 was achieved by 5 students.

THE STUDY OF MATHAYOMSUKSA 2 STUDENT' APTITUDE FOR MATHEMATICAL PROBLEM-SOLVING WHEN IT COMES TO APPLYING RATIOS AND PERCENTAGES USING TEAM-GAMES-TOURNAMENT TECHNIQUES COMBINED WITH THE BAR MODEL

In this research, the study focused on the use of collaborative learning with TGT technique combined with the Bar model to enhance the mathematical problem-solving. The collaborative learning with TGT technique combined with the Bar model approach stimulates students to interest in learning, find it enjoyable in learning, and an enthusiastic about studying. The research sample consists of 25 Mathayomsuksa 2 students at Khambokwittayakan School, Khamcha-e District, Mukdahan Province. Participants were randomly selected through Cluster random sampling method. The data were analyzed using the mean, percentage, standard deviation, and t-test. The research tools include lesson plan and mathematical problem-solving ability test. The research findings indicated that: 1) The mathematical problem-solving abilities of Mathayomsuksa 2 students after participating in collaborative learning with TGT technique combined with the Bar model have average score at 16.08 points and surpassed the 75 percentiles with statistical significance at the .05 level. 2) The mathematical problem-solving abilities of Mathayomsuksa 2 students after using collaborative learning with TGT technique combined with the Bar model were higher than those before using collaborative learning with TGT technique combined with the Bar model. The learning difference was statistically significant at the .05 level.

Project-Based Learning in Fostering Creative Thinking and Mathematical Problem-Solving Skills: Evidence from Primary Education in Indonesia

The interdependence between the Project-Based Learning (PjBL) Model and the growth and enhancement of Creative Thinking and Mathematical Problem Solving Skills in Elementary Schools is unquestionable nowadays. Prior studies have yet to discover concrete evidence regarding the interdependence being discussed. This study highlighted cognitive abilities related to creative thinking and mathematics problem-solving by implementing the Project-Based Learning Model. This research was a quasi-experiment with a pretest-posttest control group design involving 43 students in the sixth grade of two elementary schools; data was collected through test and classroom observation, and then the data was analyzed using Multivariate Analysis of Variance (MANOVA). Conversely, students exposed to project-based learning models exhibit higher skill levels in creative thinking and problem-solving than those instructed using conventional learning models. The project-based learning model significantly impacted elementary school children’s creative thinking and mathematics problem-solving skills. These findings suggest that the Project-Based Learning Model is acceptable for instructors seeking to foster creativity in teaching mathematics at the primary school level in Indonesia or other countries with comparable settings.

TÍCH HỢP WEB SKETCHPAD VÀO KHÓA HỌC TRỰC TUYẾN TRONG DẠY HỌC CHUYÊN ĐỀ PHÉP QUAY

Web Sketchpad is a new technology based on The Geometer’s Sketchpad software, featuring a highly simplified user interface and customizable tools, allowing learners to focus on mathematical exploration experiences to construct their own knowledge. This study integrated two dynamic mathematical representations designed on Web Sketchpad into an online course to support students in exploring the topic of Rotations in the plane. The results show that Web Sketchpad on the Moodle platform supports students well in conducting mathematical explorations related to rotations. It can serve as a cognitive tool and support different stages of mathematical problem-solving. The students in the experiment demonstrated problem-solving and creative competency, independently constructing new mathematical objects, searching for and discovering mathematical relationships. Additionally, they had the opportunity to practice self-directed learning and self-study through heuristic exploratory activities with dynamic mathematical representations. Keywords: Web Sketchpad; rotation; online-learning; moodle platform