Mathematical Problem Solving Research Articles

Self-regulated learning while solving mathematical problems among mathematically gifted and talented students’

ABSTRACT Self-regulated learning (SRL) represents a necessary fundamental 21st century skill for children and adolescents and is essential for the development of gifted students. This study explored mathematically gifted (MG) junior high school students’ SRL capabilities while solving mathematical problems compared to typical achievers (TAs). A sample of 71 ninth-grade students from three junior high schools were divided into two study groups (MG and TA). Participants completed Motivated Strategies for Learning Questionnaires (MSLQ) and a Metacognitive Strategy Usage Questionnaire (MSUQ). In addition, students underwent Think-Aloud Interviews while solving mathematical problems (quadratic function) at two levels of difficulty. The results only revealed significant differences between MG and TA students on the organization subscale of the MSLQ. No differences were found between the study groups in the metacognitive strategies used in the questionnaire. MG students outperformed TA students on the Mathematical Problem-Solving Task and generally used more SRL strategies during the qualitative Think-Aloud Interviews. Moreover, the differences in the between-group effect sizes were higher on the high-difficulty level of the problem-solving task than on the low-difficulty level of the task. The findings constitute a significant milestone in the study of SRL capabilities of MG in junior high school.

Effectiveness of The Problem-based Learning Model Assisted with Ruangguru Application on Increasing Students' Mathematical Problem Solving Ability

Effectiveness of The Problem-based Learning Model Assisted with Ruangguru Application on Increasing Students' Mathematical Problem Solving Ability

Pengaruh Model Problem Based Learning Terhadap Kemampuan Pemecahan Masalah Matematis Siswa SMP Negeri 3 Prabumulih

This research aims to determine the effect of the problem-based learning model on the mathematical problem-solving abilities of students at SMP Negeri 3 Prabumulih. This research was conducted at SMP Negeri 3 Prabumulih for the 2023/2024 academic year. The research sample was obtained from two classes consisting of an experimental class (PBL) of 32 students and a control class (conventional) of 32 students. Data collection after treatment was done using tests of students' mathematical problem-solving abilities. From the results of the research and discussion, it can be concluded that there is an influence that the mathematical problem-solving skills of students taught using the problem-based learning model are higher than those of students taught.

Comparison of Problem Based Learning and Guided Discovery Learning in Terms of Students’ Mathematical Problem-Solving Ability

Comparison of Problem Based Learning and Guided Discovery Learning in Terms of Students’ Mathematical Problem-Solving Ability

Enhancing problem-solving abilities through Geogebra-assisted discovery learning model for elementary school students

The students’ low problem-solving ability is due to a less meaningful learning process. This study aims to analyze the effect of applying the discovery learning model assisted by GeoGebra on the mathematical problem-solving abilities of fourth-grade elementary school students. This research employs the quasi-experimental design. The population of this study consisted of fourth-grade students at SDN Dabin III Pecangaan Jepara. The sample was taken using simple random sampling techniques. The data collecting technique used was a test. The data were analyzed using t-tests. The results of the data analysis showed that the average mathematics learning outcome of the experimental class was 81.03, which was higher than the control class (64.65). It can be concluded that using the discovery learning model with the assistance of GeoGebra significantly affects the problem-solving abilities of fourth-grade elementary school students. The implications of this research provide guidelines for curriculum innovation in facing future challenges.

THE EFFECTIVENESS OF MATHEMATICS LEARNING THROUGH A REALISTIC MATHEMATICS EDUCATION APPROACH IN ELEMENTARY SCHOOLS

The research aims to analyze the effectiveness of mathematics learning through the realistic mathematics education approach in learning the concept of counting integers in grade VI elementary school students. The research used a quasi-experiment with one pretest postets design. The research involved 32 grade VI students at SDN 205 Neglasari, Coblong District, Bandung City. The research instrument is in the form of a multiple-choice test that includes addition and subtraction of decimal numbers. Research shows that the RME approach is effective in producing a significant improvement in students' learning completeness in the addition and subtraction of decimal integers, as well as improving mathematical problem-solving, self-efficacy, reasoning, and mathematical literacy. RME encourages students to recognize the practical application of mathematical concepts through real-world contexts and cultural elements, as well as to cultivate creative and imaginative thinking skills so that they can be an important strategy in improving mathematics education in primary schools.

The Influence of Edugame Wordwall Media on Students’ Ability to Solve Mathematical Problems

The ability of mathematical problem-solving is a crucial element in a mathematical learning process that allows learners to deepen their understanding comprehensively. To overcome the various challenges that arise in this process, effective learning solutions are needed, including the use of tools or media such as Wordwall edugame. This study aims to investigate how Wordwall educational games affect the improvement of students' abilities in solving mathematical problems. The study adopted a quantitative experimental method utilizing a Pretest-Posttest Control and quasi-experimental Design, each class consisted of 40 grade VII students selected through a purposive sampling technique. The research utilizes a test as its measuring tool for mathematical problem-solving ability. The statistical test results revealed that using Wordwall edugame had a profound impact on enhancing mathematical problem-solving ability, with a paired sample t-test value of <0.001. After the treatment was applied, the average scores increased significantly, with the experimental class averaging from 18.85 to 53.2 and the control class from 22.83 to 41.83. The experimental class showed a significant improvement before and after the treatment, while the control class did not show a significant change in this study, indicating that using Wordwall edugame media significantly improved math problem-solving ability.

Exploring the team-assisted individualization cooperative learning to enhance mathematical problem solving, communication and self-proficiency in teaching non-parametric statistics

Exploring the team-assisted individualization cooperative learning to enhance mathematical problem solving, communication and self-proficiency in teaching non-parametric statistics

Effect of Implementing Differentiated Learning Based on Learning Style on Abilities in Mathematical Problem-solving

Effect of Implementing Differentiated Learning Based on Learning Style on Abilities in Mathematical Problem-solving

The Effect of Problem-Based Learing On Students’ Mathematics Problem Solving Ability

The Effect of Problem-Based Learing On Students’ Mathematics Problem Solving Ability

EXPLORING DIFFICULTIES IN TEXTUAL UNDERSTANDING OF MATHEMATICAL WORD PROBLEMS FROM A PSYCHOLINGUISTIC PERSPECTIVE AND USE OF DRAWINGS

Several studies have reported the importance of textual understanding in the solving of verbal mathematical problems. Therefore, the objective of the present study was to analyze the difficulties the secondary-education students presented in the textual understanding of verbal mathematical problems. An instrument was applied with three verbal problems in three different moments: comprehension of the problem, representation of the situation, and the application of a semi-structured interview. An important factor that could be seen in the responses obtained is that the context played an essential role. It was also obtained that the textual understanding and the cultural context show an important relationship when building a representation of the problem. Finally, according to the results obtained in the study, we suggest that it would be important to encourage students to do previous work to familiarize themselves with the context posed in the problem to be able to reach a solution that satisfies the statement.

Integrating self-explanation and operational data for impasse detection in mathematical learning

Self-explanation is increasingly recognized as a key factor in learning. Identifying learning impasses, which are significant educational challenges, is also crucial as they can lead to deeper learning experiences. This paper argues that integrating self-explanation with relevant datasets is essential for detecting learning impasses in online mathematics education. To test this idea, we created an evaluative framework using a rubric-based approach tailored for mathematical problem-solving. Our analysis combines various data types, including handwritten responses and digital self-explanations from 93 middle school students. Using hierarchical logistic regression, we examined feature groups such as Self-Explanation Quality, Handwriting Features, and Overall Level of Action. Models based solely on self-explanation achieved a 74.0% accuracy rate, while adding more features increased the final model’s accuracy to 80.06%. This improvement highlights the effectiveness of an integrated approach. The combined model, which merges generated handwriting features counts with self-explanation features, shows the importance of both qualitative and quantitative measures in identifying learning impasses. Our findings suggest that a comprehensive approach, leveraging detailed operational data and rich self-explanation content, can enhance the detection of learning challenges, providing insights for personalized education in online learning environments.

MATHEMATICAL BELIEFS, ENGAGEMENT, AND PROBLEM-SOLVING SKILLS OF GRADE 9 STUDENTS

The purpose of this quantitative study, which used descriptive and correlational designs, was to investigate the mediating effect of student engagement on the relationship between mathematical beliefs and problem-solving skills in Mathematics among students. One hundred thirty-eight Grade 9 students from four public secondary schools in Davao del Norte Division, School Year 2023-2024, were selected as respondents using stratified random sampling. This study used two adapted survey questionnaires to determine students' mathematical beliefs and engagement and a validated researcher-made test to assess their problem-solving skills in mathematics. Mean and Pearson-r were used to calculate numerical data. The results of this study revealed that the level of mathematical beliefs and engagement of the students is high. Additionally, the level of student’s problem-solving skills in terms of test scores is average. Moreover, there is a significant relationship between mathematical beliefs and student engagement. However, results showed no significant relationship between mathematical beliefs and students' problem-solving skills. Further, mediation analysis was initially intended to be conducted as a part of the study; however, it was not executed since the conditions were not met. Additionally, future researchers may utilize the findings to analyze the study's variables and look into other variables or characteristics that mediate the relationship between mathematical beliefs and problem-solving abilities. KEYWORDS: problem-solving skills, mathematical beliefs, student engagement, grade 9 students, descriptive-correlational approach, Pearson-r, Kapalong, Davao del Norte, Philippines

What does it take to be original? An exploration of mathematical problem solving

This study focused on original mathematical problem solving among elementary students. The purpose of this study was to investigate originality in the solving of mathematical problems in K-6 students. Guided by this purpose, we investigated to what extent scores on accuracy, fluency, and application of concepts predict originality in producing solutions to mathematical problems. The participants included 520 K-6 students who attended a public elementary school which was located in a multicultural metropolitan area of New South Wales, Australia. The DISCOVER Mathematics Assessment was used to assess the students’ problem solving skills. To answer our research question, we conducted binary logistic regression analysis to predict the relationship between the independent variables (accuracy, fluency, and application of concepts) and the predicted binary variable (originality in solutions to mathematical problems). The logistic regression model was statistically significant and explained 11.6% of the variance in producing original solutions and classified 91.3 % of cases correctly. The results of the binary logistic regression analysis showed that increases in accuracy and application of concept scores were associated with an increase in the odds of being able to produce original solutions in mathematical problem solving. Unlike accuracy and application of concepts, a change in fluency scores was not significantly associated with a change in the odds of being able to produce original solutions in mathematical problem solving. The findings of this domain specific research on originality provided insights for the notion of creativity in mathematical problem solving among K-6 students. We discussed the implications of our findings as well as our recommendations for research, practice and policy to develop students’ creative potential.

Analisis Kemampuan Pemecahan Masalah Matematika ditinjau dari Kepercayaan Diri Siswa pada Materi Himpunan di Kelas VIII SMP Torsina II Singkawang

This study aims to describe the ability to solve mathematical problems from the perspective of students' confidence in the set material in grade VIII of SMP Torsina II Singkawang. This research method is a descriptive method with a qualitative research type. The subjects in this study are 32 grade VIII students. The object of this study is the ability to solve mathematical problems and students' confidence in the set material. The data collection instrument is in the form of a written test in the form of a description in accordance with indicators of mathematical problem-solving ability, confidence questionnaires and interviews that have been tested with the validity of the content, validity of the construct, reliability, level of difficulty and discriminating power. The overall results of the study showed that the level of confidence and mathematical problem-solving ability of grade VIII students at SMP Torsina II Singkawang in the set material had a medium category. While specifically showing that: 1) there is a significant relationship between confidence and mathematical problem-solving ability, which means that if confidence increases, students' mathematical problem-solving ability also increases and vice versa; 2) the form of mistakes made by students in solving problems with mathematical problem-solving skills in the set material in the form of errors in understanding problems, errors in using formulas or principles, errors in process or operation skills, and errors in drawing conclusions or checking the correctness of the results obtained.

The Structure of Students’ Mathematical Errors in Solving Calculus Problems Based on Cognitive Style

The understanding mathematical concept is an error that often occurs in classroom learning among students when solving mathematical problems. The most difficult part for students is solving problems, because it requires numeracy skills, high concept mastery, as well as the ability to use good language, and so on so that students don’t make any more mistakes when working on math problems. Student errors in solving mathematics problems are (1) errors in connecting concepts, (2) errors in operations and (3) errors in constructing concepts. The problem is what is the structure of students’ mathematical misconceptions in solving mathematical problems based on cognitive style. The method in this research, namely an exploratory descriptive approach, aims to determine the structure of students’ errors based on cognitive style in solving mathematical problems. Analysis of research data, namely: (1) Data reduction, (2) Data exposure, (3) data triangulation and (4) drawing conclusions. The cognitive styles referred to are field dependent and independent. The conclusions are (1) the structure of conceptual errors with an applied field dependent cognitive style begins with disequilibrating, then solving by linking applicable concepts, and (2) the structure of conceptual errors with a field independent cognitive style begins with disequilibrating, then solving using analyse.

Problem Based Learning Using Open Ended Questions Improves Students’ Mathematical Critical Thinking Ability in Elementary Schools

Primary school students' critical thinking abilities in mathematics are still very low. This is caused by teachers who only provide learning with rote concepts without any problem solving activities. Based on this problem, a learning model is needed that can help students learn the concept of problem solving in mathematics. So research was conducted which aimed to prove the effect of the Problem Based Learning model using Open-Ended Questions on critical thinking skills in class III students' mathematics learning. This research uses a non-equivalent control group research design. The population of this research was 324 students. The research sample was 31 students as the experimental group and 29 students as the control group. Data collection methods and instruments were obtained by giving essay tests. Data analysis uses descriptive statistical techniques and inferential statistical analysis with polled variance t-test. The results of the hypothesis test show that the Problem Based Learning learning model using Open-Ended Questions has an effect on critical thinking skills in mathematics learning for third grade elementary school students. The results of the research carried out provide a good contribution to mathematics learning in elementary schools. It is hoped that the results of this research can be used to develop future research ideas.

Effectiveness of Schema-Based Instruction Strategy in Improving Mathematical Word Problem Solving and Working Memory of Students with Learning Disabilities in The Sultanate of Oman

This study aimed to examine the effectiveness of a schema-based instruction strategy in improving mathematics word problem solving and working memory performance of third grade students with learning disabilities in schools in Oman. Students received a diagnosis of specific learning disability (SLD) based on the aptitude discrepancy model in which an achievement test and an aptitude test (Raven’s Coloured Successive Matrices) were used to determine the existence of a discrepancy. Students were then divided into two matched groups, a control group and an experimental group; each group included (20) students. Study instruments included a mathematics word problem solving test, a working memory test, and the schema-based intervention program. Results of the study showed that participants in the experimental group differed from controls in word problem solving and working memory performance following exposure to the intervention program. More specifically, performance of experimental group participants in the word problem solving varied across the pre, during the implementation, and post intervention phases in favor of the post intervention phases and in favor of the type of Assembly problems. Implications of using schema-based instruction strategy with students with SLD are discussed in the light of the study findings.

Analisis Kesalahan Siswa dalam Menyelesaikan Soal Pemecahan Masalah Matematika Berdasarkan Newman’s Error Analysis di Kelas V Sekolah Dasar

The error analysis in this research is to determine the errors made by students in solving mathematics problem solving questions based on Newman's Error Analysis, which is a method for analyzing errors in problem solving problems. This research involved 19 students in class VB at SDN 14/I Sungai Baung. The interview subjects were 6 out of 19 VB class students, each consisting of 2 students from the upper, middle and lower groups. The selection of interview subjects was carried out using purposive sampling. Data collection techniques include tests and interviews. Validity of data using technical and time triangulation. The research results showed that of the five stages of error according to Newman's procedure, the subject made four errors in working on the data presentation material. The four errors are errors in understanding the problem, there are 42 errors with a percentage of 21.87%, transformation errors there are 27 errors with a percentage of 14.06%, process skills errors there are 58 errors with a percentage of 30.20%, errors in writing answers there are 65 errors with a percentage 33.85% and students did not make mistakes reading the problem. The reasons why students do this are not being used to writing down what they know/are asking about, not understanding/interpreting the problem in the question, not being skilled enough in carrying out the calculation process, not being careful/careless, and making mistakes at the previous stage.

Interactive Learning Media Oriented Problem-Based Learning to Improve Students Mathematical Problem Solving Skills

The importance of using learning media in mathematics learning so that learning is more interesting has not been optimized, learning is still conventional which affects the low ability to solve students' mathematical problems. This research develops interactive learning media oriented to Problem-Based Learning designed to improve students' mathematical problem-solving skills. The research procedure used is the procedure from Plomp which consists of 3 phases, namely, the Preliminary Research Phase, the Prototyping Phase, and the Assessment Phase. The subjects of the study were two validators, as well as 26 students in the limited trial, 35 students in field trial I, and as many as 43 students in field test II. The result of the product is an interactive learning media oriented to problem-based learning that is of valid, practical, and effective quality. Product quality obtained an average score of 3.60 with a very valid category, practical quality in terms of student response, teacher response, and media implementation in classroom learning, and effective quality in improving students' mathematical problem-solving skills as evidenced by gain-score with a fairly effective category.