Problem-solving Steps Research Articles

Prediction of Individual Learning Experience in Terms of “Number Of Steps” as Solution Components of Arithmetic Tasks

The paper is devoted to the study of learning in solving arithmetic problems in the conditions of digital learning. Learning is considered as a functional system, the level of differentiation of which can be related to the number of steps in problem solving. The goal of the paper is to find out the model that could more accurately describe the relationships between the number of steps and task types on Addition data and predict the number of steps on Multiplication data. The hypothesis is that with a given similarity, there is a correlation between the number of steps in solution of addition and multiplication tasks. We have created two experimental courses, “Addition” and “Multiplication” to make participants learn optimal methods of calculation of arithmetic tasks. The courses have the same structure and belong to a common domain (arithmetic tasks). It is a condition for similarity of learning. We have found out significant positive correlation between the number of steps in solution of addition and multiplication tasks on average for the sample. We have used a regression-based classification. Few models have been built for each individual personally and trained on the Addition data, then applied on the Multiplication data. The best of these models correctly predict the number of steps in 33–40% of tasks (SD = 17–22%, max = 88%), in other tasks they give a prediction with a small error of 1–2 units, which indicates its medium predictive ability.

Optimization of Daily Warehouse Storage PT. XYZ with Shared Storage Method

PT XYZ is a company engaged in ship repair and maintenance services and port management services. The problems faced by PT XYZ in carrying out its business lines are related to the effective and efficient operational managerial activities of raw material warehousing. Problem solving steps are carried out by testing data processing and analysis using the shared storage method as a solution step related to the problem of warehousing layout and optimization. Problem solving with the shared storage method is a method of reconditioning the warehousing layout with the principle of First in First out or fast moving where the layout of goods is classified based on the order of the flow of goods movement according to the operational needs of PT XYZ activities. Based on the calculation results, if the company applies the proposed layout, there is an average distance savings of 4 m2. The layout of the placement of raw materials based on the proposed improvements has a more organized condition and facilitates the flow of goods movement as well as inputting the flow of goods in and out which can be more efficient if the goods are organized and inputted administratively, this also affects the quality of goods.

Analysis of Mathematical Critical Thinking Ability based on Students' Ability Level

Analyzing and testing mathematical critical thinking skills based on the ability level of class VIII students of junior high school is the aim of this research. By understanding the level of students' abilities, educators can determine students' mathematical critical thinking abilities and develop appropriate teaching strategies to improve students' abilities. This study uses a qualitative descriptive research method. This research was conducted at one of the junior high schools in Cipatat, West Bandung Regency with heterogeneous abilities of 8 students. This research uses data collection techniques by providing mathematical critical thinking ability questions on SPLDV material which consists of 5 essay test questions based on the following indicators: (1) Checking the completeness of problem solving steps. (2) Look for alternative solutions to problems. (3) Identify spldv equations with certain characteristics. (4) Choose the best way to solve the problem from alternative ways of solving it. (5) Identifying the adequacy of data on a problem. In this study, the results of the analysis have shown that students at a high level of ability can check the completeness of problem solving steps, students with a medium level of ability have little difficulty in identifying spldv equations with certain characteristics, and students with a low level of ability have difficulty finding alternatives problem solution.

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.

The Analysis of Challenges and Opportunities in Integrated Village Government (IVG)

Following the implementation of the Law of Village, the resolution of village government issues proved to be a challenging endeavour. This paper presents a comprehensive systematic analysis to identify themes in village government studies. The primary objective is categorising the problems and possibilities village governments encounter. The research data utilised in this study is obtained from the Scopus Database, covering the period from 2009 to 2023. The data is subsequently analysed using the VOSviewer tool. The findings present five prominent themes and a total of 35 network elements of the governance of rural communities. These themes encompassed many aspects, such as healthcare, economic matters, conflicts, agricultural practices, and government initiatives. The study revealed that despite implementing the Law on Villages, the prevalence of intricate challenges in village government remains prominent. Scholars concur that they advocate for establishing collaborative efforts among stakeholders to delineate the sequential problem-solving steps. However, it is worth noting that rural communities often face challenges in embracing external interactions and adopting the urban commons model to establish an extensive network and facilitate multi-level growth. The findings serve as a foundation for future investigations on village government and a point of reference for more informed decision-making in governance practices. The limits were due to the exclusive use of publications from Scopus for analysis. Hence, conducting research employing a comparative approach and leveraging the Web of Science (WoS) database and other indexes are crucial to promoting the conceptual progress of village government study

Insight into students’ understanding of relational terminology through integrated compare and combine word problems

Previous research examining comparison relations in word problems primarily focused on students’ achievements in word problems with one operation. In this paper, we extend previous research to examine the achievement of students of different ages on word problems that integrate compare and combine word problems, hereafter referred to as ‘compare-combine problems’. The convenience sample in this research consists of 96 second-grade, 103 fourth-grade, and 85 sixth-grade students from Belgrade, Serbia. The results indicate that 2nd, 4th and 6th graders have similar achievement on consistent language problems, but students in higher grades perform better on inconsistent language problems. We identified a type of problem that does not provide insight into students’ understanding – problem in which the order of quantities follows the order of steps in problem solving. We emphasize the importance of using integrated problems of different structures in teaching, as well as in-depth work on understanding relational terminology.

Identifikasi Kemampuan Berpikir Logis Dalam Pemecahan Masalah Matematika Pada Siswa Kelas XI SMAN 6 Madiun

Mathematics is seen as learning material needed to solve problems in life. Learning mathematics can improve students' ability to think logically. Logical thinking means a child's ability to think rationally, by utilizing logical abilities, so that they can think logically. This type of research is descriptive qualitative. This research to describe the ability to think logically in solving mathematical problems in high school students. The subjects of this research were three students, namely students with high, medium and low problem solving abilities from class XI-J of SMAN 6 Madiun for the 2023/2024 academic year. The research instrument consists of test questions and interview guidelines. The results of research show that in solving mathematical problems: high ability subjects show the characteristics of logical thinking ability, able to think coherently, can provide arguments in each step of problem solving, able to provide appropriate conclusions; moderately capable subjects show characteristics of logical thinking ability, able to think coherently, able to provide arguments in each step of problem solving, able to provide conclusions but are not precise; Low ability subjects show characteristics of logical thinking ability, able to think coherently, unable to provide arguments in each step of problem solving, unable to provide conclusions.

Representation Process of Prospective Teachers in Solving Mathematical Problems Based on Cognitive Style

This study investigates the correlation between cognitive styles and the thinking process utilized when solving mathematical problems, emphasizing the significance of aligning problem-solving strategies with problem representations. Employing a qualitative approach, the research examines two cognitive styles—Field Independent (FI) and Field Dependent (FD)—chosen based on participants' mathematical abilities. Conducted at Cenderawasih University's Mathematics Education Study Program, the study reveals that students' mathematical problem-solving proficiency remains relatively low, warranting further exploration of their thinking processes. While FI subjects demonstrate competence in aligning thinking processes with mathematical representations, particularly in structuring problem-solving steps, FD subjects exhibit limitations in articulating meaning and verbal representations. These findings underscore the importance of instructing educators not only in teaching mathematical concepts but also in guiding students to articulate problem-solving steps using verbal representations. This study highlights the need for a holistic approach to mathematical education, integrating conceptual understanding with effective problem-solving strategies tailored to individual cognitive styles.

AN ANALYSIS of MATHEMATICAL PROBLEM SOLVING PROCESS BASED on LEARNING STYLE

This research aimed to describe the process of solving mathematical problems based on the learning style of class VII students at SMP Negeri 1 Dobo. The subjects in this study consistend of three students, consisting of one students, consisting of one student with an auditory dominant learning style (SA), one student with a kinesthetic dominant learning style (SK), and one student with a visual dominant learning style (SV). Determining research subjects was carried out by distributing learning style questionnaires to 32 class VII students and then analysing them. The results of the research show that the process of solving mathematical problems is as follows: 1) SA was able to understand the given problem very well and find the correlation between recognized information and prior concept. Thus, SA could solve the problem correctly with considerably systematic solving steps; 2) SK was able to understand the given information very well and designa structured problem-solving step. However, during the implementation of the step, SK directly entered numbers without writing down the complete equation in advance; 3) SV lacked understanding the given problem and hence often asked other students how to solve the problem. Nevertheless, after several times recalling the previously learned concepts, SV started to solve the problem correctly by using a comparison and difference table. After getting the answer, SV rechecked the mathematical problem-solving process several times in order to ensure the final answer.

Developing a Framework for the Integration of Artificial Intelligence in Technology Education

This study aimed to create a foundation for the integration of AI in technology education. The framework of this study was based on the important problem-solving learning process in technology education. The developed framework structures the problem-solving steps of such types of problems into problem solving, design, development, and evaluation. Each technological problem and problem-solving step area can be implemented using Intelligent Tutoring System (ITS), Dialogue-Based Tutoring System (DBTS), and Exploratory Learning Environment (ELE) of AI convergence education. Technology education supports learners develop Technological knowledge and develop critical and creative thinking when attempting to resolve real-life technological glitches. Since the process of solving technological problems is complex in itself, it was necessary to categorize technological problems in real life and organize the procedure for resolving technical issues into a series for formal education in schools. In this process of technological problem solving learning, explicit knowledge may be necessary, and interpretive or procedural knowledge may be necessary. Methods of utilizing AI convergence education vary depending on the target knowledge. Therefore, structuring and presenting a plan to apply various AI convergence educations to the process of solving highly complex technological problems is meaningful in that it suggests the basis for educational direction. Based on the framework developed in this study, expected that AI convergence education methods appropriate for each problem-solving process of various technological problems will be systematically researched and implemented in the future.

EVOLUTION OF PRE-SERVICE MATHEMATICS TEACHERS’ SPATIAL VISUALISATION SKILLS DURING A COGNITIVE LOAD THEORY-BASED EDUCATION

This study explores how pre-service mathematics teachers’ spatial visualisation skills evolved during a Cognitive Load Theory (CLT) based education. The study used the qualitative theory-testing case study method, which guided the identification of participants, the design of technology-supported education, and the data collection and analysis process. The four participants meeting specific criteria were selected as the study sample. A CLT-based education equipped with technology was provided to help participants overcome difficulties in spatial visualisation problems, improve their existing schemas, and build higher-order schemas. Various teaching approaches (e.g., worked examples) were applied to optimise participants’ learning in CLT-based education. The study data (e.g., transcripts of interviews) were analysed using the pattern-matching technique, in which the observed patterns were compared with the derived hypotheses from the theoretic models regarding the problem-solving process and novice-expert schemas. The study achieved remarkable results: In CLT-based education, where teaching approaches have an important role, the improvement in their spatial visualisation skills happened as the participants overcame their challenges in problem-solving steps throughout their cyclic problem-solving processes and gained more knowledge and skills. The participants’ acquisition of expertise in spatial visualisation skills went through various developmental stages. They strengthened their initial spatial problem-solving schemas by completing the deficiencies in their prior knowledge. They gained practicality in same-category tasks and constructed higher-order problem-solving schemas when dealing with high-category tasks by activating their assimilation and adaptation processes. Keywords: Cognitive Load Theory, the development of spatial visualisation skills, theory-testing method, acquiring an expert spatial problem-solving schema

Students' ‘Looking Back’ in Solving Algebraic Word Problems

Solving mathematics problems is a complex cognitive process that involves a series of steps. These steps typically include understanding the problem, devising a plan, carrying out the plan, and looking back (checking the solution). While each of these steps is crucial, the ‘looking back’ step has not received much attention in mathematics education research. This study investigated Grade 10 mathematics students’ looking back in solving algebraic word problems in Namibia. The study followed a qualitative approach. The sample of the study was 351 Grade 10 students from ten secondary schools in the Ohangwena Region in Namibia. Data was collected using the Algebra Word problem-solving Achievement Test and Interview. The results show that, in general, the students did not look back on their solutions to the algebraic word problem. While some students indicated that looking back necessitates the consolidation of their work, others said looking back on their solutions could be time-wasting and confusing. These findings point to the need for mathematics teachers in Namibia to incorporate and model the looking-back step of mathematical problem-solving in their mathematics teaching.

Analysis of Elementary School Students' Problem-Solving Abilities in Solving HOTS Questions

This study aims to describe the problem-solving skills of fifth-grade elementary school students in solving HOTS-type mathematics problems. This study applies Polya's problem-solving steps. Type of this research is descriptive quantitative. The subjects of this study were 26 students in the odd semester of 2022/2023 the academic year 2022/2023 academic year at SDN 61 Bengkulu City. Instruments and data collection techniques used in this study were test sheets and interviews. Data analysis was carried out in descriptive analytical way. The results showed that 75% of fifth-grade students at SDN 61 Bengkulu city had the ability to understand problems, 63% had the ability to plan a settlement, 45% had the ability to solve problems according to plans that had been made, and 45% had the ability to look back at the answers. Only 45% of students have problem-solving skills. Keywords: geogebra, group investigation, learning outcomes, quasi experiment

Penalaran Proporsional Siswa dalam Strategi Worked Example

Elementary school students need proportional reasoning inside or outside the classroom. However, students still have difficulties in using proportional reasoning. The worked example strategy has been empirically proven to facilitate students' proportional reasoning. The study aimed to analyze the effect of the implementation of the worked example strategy on students' proportional reasoning. The research method used mixed methods with a sequential explanatory design. The research was conducted in one of the elementary schools in Krembung, East Java, Indonesia. The sample technique used was random and purposive sampling. The instruments used include proportional reasoning tests and interview guidelines. Data analysis used paired-sample t-test and thematic analysis. The results showed that there was a significant influence on proportional reasoning in the implementation of the worked example strategy. The success of proportional reasoning can be seen in the aspects of changes in two quantities and proportions. The results of this study have implications for mathematics learning. Teachers can apply the worked example strategy so that students are accustomed to imitating problem-solving steps, which can then be developed into more complex solutions to solve other problems.

Using Remap-STAD Learning Assisted by The GitMind Application to Improve Students' Problem-Solving Skills in Biology Education

Several studies have highlighted the essential nature of students' problem-solving skills. However, these studies have also revealed that students' problem-solving skills in Indonesia are currently lacking. Consequently, there is a need to empower and improve these skills. This research aims to investigate the impact of implementing the Remap-STAD learning model, with the assistance of the GitMind application, in order to enhance students' problem-solving abilities in the field of biology. The research design employed in this study is a pretest-posttest non-equivalent control group design. The research sample comprises 70 students from class X MIPA at SMAN 9 Malang, East Java. The experimental group was taught using the Remap-STAD learning model, supplemented with the GitMind application, while the control group was taught using the STAD learning model alone. Problem-solving skills were assessed through a description test comprising eight questions. Greenstein's (2012) scoring rubric, which encompasses eight indicators including problem identification, application of problem-solving steps, identification and evaluation of solutions, defense of solutions, real-world applications, inductive reasoning, and deductive reasoning, was employed for scoring. ANCOVA was utilized to analyze the data on problem-solving skills, with a significance level set at 5%. The Kolmogorov-Smirnov test was conducted to assess the normality of the data, while Levene's Test of Equality of Variances was used to evaluate homogeneity. The data analysis findings indicate significant treatment effects for the learning model (p < 0.05), thereby accepting the research hypothesis. The results demonstrate that the Remap-STAD learning model, combined with the GitMind application, can notably enhance students' problem-solving skills in the context of biology education. Consequently, the implementation of Remap-STAD, with assistance from the GitMind application, necessitates the development of instructional tools tailored to the chosen learning model and the specific skills being measured. This approach will promote and enhance learning activities, particularly in improving students' problem-solving capabilities.

KEMAMPUAN REPRESENTASI DALAM MEMECAHKAN MASALAH MATEMATIKA BERDASARKAN GAYA BELAJAR

Solving problems requires the ability to recall the information needed and represented both visually and verbally. This information is obtained, managed and recalled through a system called learning style. This research was conducted at Asy-Syifa Al-Inayah Middle School, Jambi City, with the aim of obtaining a description of student representation in solving mathematical problems. Subjects in this study were selected using purposive sampling based on visual, auditory and kinesthetic learning styles. It is hoped that this research will provide benefits in improving mathematics learning. The results of the research show that the representation of auditory students and visual students in solving mathematical problems each fulfills three indicators, while kinesthetic students only fulfill two indicators of mathematical representation. In presenting information, visual and auditory subjects each tend to present it in the form of images (geometry or number patterns) and create situations based on the problem given. Meanwhile, kinesthetic subjects tend to only create images to clarify problems and facilitate their resolution. In solving problems, both visual and auditory subjects are able to solve problems by making patterns based on the problem given and making conclusions from a pattern. It's just that auditory subjects can shorten problem solving steps by using mathematical expressions. Meanwhile, kinesthetic subjects experience problems in solving combinatorics problems, where they are unable to present images or patterns that can help solve the problem.

Mathematical Representation Ability-Based Mathematical Contextual Problems of Sequences and Progression Material

This research objective is to analyze and explain the student’s capacity for mathematical representation based on mathematical contextual problems of arithmetic and geometric sequences and progression material. Students enrolled in SMA 1 Sukoharjo X.E10 were the subject of this research. The data collection process used interviews, tests, and documentation. This research used a descriptive research approach with a qualitative research type. Based on the findings of this research, students who have visual representation skills in mathematics are more likely to complete challenges that involve visuals, such as diagrams. Typically, mathematically symbolic representation-capable pupils utilize mathematical formulas and symbols to solve problems. Furthermore, students who have the ability to verbally represent mathematics have a tendency to encrypt problem-solving steps into words.

과학, 비과학 주제에 대한 문제해결 전략 및 평가에서 나타난 중학생의 인식

This study analyzed the characteristics of problem-solving strategy formulation as perceived by students and the development of evaluation criteria for such strategies. For this purpose, we analyzed the outputs of six classes of 52 middle school students participating in a university-affiliated gifted education center. The main findings were as follows: First, students presented their problem-solving strategies in three to six steps, with responses of five, four, three, and six. Second, the problem-solving steps proposed by the students could be categorized into the first half of “recognizing the problem, preparing for the investigation, making predictions, setting hypotheses, making plans, and collecting data” and the second half of “organizing results, testing hypotheses, concluding, and writing reports” based on the execution. Third, there was a difference between scientific and non-scientific problem-solving topics that students perceived in their daily lives. In terms of topics, tools were the most common among both scientific and non-scientific problem-solving. Fourth, students identified a variety of similarities and differences between scientific and non-scientific problem-solving strategies, and “process” was characterized by both similarities and differences. Fifth, students mostly gave three to five criteria for evaluating their peers’ problem-solving strategies, with a total of 20 different criteria. Among them, feasibility, solvability, and efficiency were selected by the majority of students. In addition, we discuss the implications for science education based on the results of this study.

Developing MoAR-Integrated Printed Learning Modules to Improve Mathematical Problem-Solving Abilities in Geometry Learning

This research develops an interactive printed learning module with Augmented Reality (AR), adopting the design research methodology and ADDIE model. The primary focus is to improve students’ mathematical problem-solving abilities by integrating AR technology to contextualize abstract concepts in real-life scenarios in a printed module on geometry learning. This study presents a MoAR-integrated printed learning module that combine meticulously planned educational materials, engaging activities, evaluation, 9E learning cycle syntax, problem-solving steps, and QR-code markers. The module seamlessly integrates with the MoAR apps, further the learning experience. The module’s validity is confirmed by a panel of seven experts, yielding a high V-coefficient of 0.92. The implementation was done at Public Junior High School SMPN 2 Mantup, involving 68 students in experimental and control classes. Practicality and effectiveness analysis measured through questionnaires and N-gain score comparison indicate that the developed learning module is practical and led to a higher increase in problem-solving abilities in the experimental class compared to the control class. This study represents an innovation in mathematics learning by integrating AR technology into a comprehensive printed learning module designed for independent use. It is recommended for further researchers to include the development of more specific AR content for particular mathematical topics and analyzing the long-term impact of AR use on improving mathematical abilities.

Mathematical Problem-Solving Ability of Junior High School Students Based on Polya

Mathematical problem-solving ability is the ability to identify known information, ask questions, adequacy of the information needed, skill in creating or compiling mathematical models, being able to find the right solution strategy, and being able to explain and check the correctness of the solution obtained. This research aims to analyze students' mathematical problem-solving abilities in the topic on mixed integer arithmetic operations based on Polya's problem-solving steps. This research uses a qualitative approach with a narrative research type. The research subjects consisted of 32 junior high school students. Data collection was carried out using mathematical problem-solving ability test instruments and interviews with several selected participants. Data was analyzed based on Polya's problem solving steps. Based on the results of data analysis, students' problem-solving abilities obtained based on these four steps are in the form of students who can determine important information in the problem and can plan solutions resulting in them being able to solve problems more regularly, namely by executing the plans they have planned. After that, students who understand the problem well can also check the correctness of the answers they have obtained. Therefore, it is hoped that this research can help teachers to implement a learning process that can develop problem solving abilities.