Cross-disciplinary effects of problem-based learning on problem-solving skills in mathematics and beyond: A comprehensive meta-analysis and bibliometric

In general, students’ problem solving skills tend to be in a low category, this is shown by the number of students who have not been able to complete diagnostic tests given in the form of routine and non-routine problems. One of the factors that affect students’ mathematical problem-solving skills is self-efficacy. This study aims to find out students’ mathematical problem-solving and self-efficacy skills in the material of a two-variable linar equation system. The type of research used in this study is qualitative research. The research method used is a descriptive analysis method. The subjects in this study were grade VIII students of the 2020/2021 school year who were in Pakuwon Subdistrict, Garut Subdistrict, Garut Regency which numbered 6 students. The sampling technique in this study is a purposive sampling technique. The data collection techniques used are mathematical problem-solving skills tests, self-efficacy questionnaires, interviews, and field records. The data analysis techniques in this study are data reduction, data presentation, and conclusion drawing. The results showed that students’ problem-solving skills were at 75% with the high category and student self-efficacy was at 68% with the good category.

Many researchers have conducted previous meta-analysis studies regarding problem-based learning (PBL) to enhance problem-solving skills. However, their research does not focus on mathematical problem-solving skills (MPSS). This study aims to summarize, estimate, and evaluate PBL implementation's effect in enhancing the MPSS of Indonesian junior high school (JHS) students and investigate the study characteristics that affect the heterogeneous effect size data. Twenty-nine relevant primary studies published in national and international journals and proceedings during 2011 – 2020 were analyzed using the systematic review and meta-analysis. The analysis tool used the Comprehensive Meta-Analysis (CMA) software by selecting the formula of Hedge to determine its effect size. The result showed that the overall PBL implementation had a medium positive effect (g = 0,743; p less than 0,05), significantly enhancing the MPSS of Indonesian JHS students based on the random effect model. Also, the characteristics of sample size, research area, sampling technique, and publication year did not affect the heterogeneous effect size data. These results suggest that Indonesian JHS mathematics teachers should select PBL as one of the best solutions in implementing mathematics learning in the classroom to enhance students' MPSS.

<p> Mathematical reasoning and problem-solving skills have become a very necessary need at this time. Students who do not have mathematical reasoning and problem-solving skills will have difficulty adapting to current technological advances. The purpose of this study is to design mobile-based mathematics learning to improve students' mathematical reasoning and problem-solving skills. The subjects of this study were junior high school students. The research method developed was ADDIE (Analysis, Design, Development, Implementation, Evaluation). The results of the study showed that improving students' mathematical reasoning skills had a very positive impact on students' mathematical problem-solving skills. These results provide additional contributions and references for mathematics teachers who want to add knowledge related to improving the quality of mathematics learning in the classroom.</p>

The present study analyzes various inconsistent research findings on the effect of problem-based learning (PBL) in enhancing students’ mathematical problem-solving skills (MPSS) in Indonesia. A meta-analysis of 50 primary studies that conform to the inclusion criteria was conducted to summarize, estimate, and evaluate findings of the effect of PBL by analyzing the heterogeneity of the studies. Heterogeneity analysis was conducted by analyzing the effect of moderator variables, namely the characteristics of sample and publication. The analysis tool used the Comprehensive Meta-Analysis (CMA) application by selecting the Hedge’s equation to determine its effect size. The “One study removed” tool in the CMA application was used to analyze the sensitivity of effect size data, and publication bias was assessed by the funnel plot, fill and trim test, and Rosenthal’s fail-safe N test. The findings of the study showed that the overall implementation of PBL had a larger positive effect significantly compared to conventional learning on the students’ MPSS in Indonesia based on a random effect model. The characteristics of the education level and research area significantly affected the heterogeneity of the effect of PBL on students’ MPSS. Thus, these findings suggest that mathematics teachers and lecturers should choose PBL as one of the best solutions in implementing Mathematics learning in the classroom to enhance MPSS. Furthermore, they should pay attention and consider the education level of students and the area where students learn in implementing PBL in enhancing students’ MPSS.

Education aims to foster a variety of potential which exists in human, including the potential to solve any problems, involving solving mathematical problems. This study aimed to describe students’ problem-solving skills during mathematics learning about social arithmetic through Problem-Based Learning (PBL) model. The subjects of this research were 32 Year 7 students in Banda Aceh. This study used a qualitative descriptive approach. Data collection was conducted by problem-solving skills test and interview. The interview data were analysed descriptively, while the data of the test results were analysed based on the assessment guideline of students’ problem-solving skills. It was found that students’ mathematical problem-solving skills through PBL model were already classified as good. High-achieving students of problem-solving skills solved the problem by understanding the problem, planning the solution, doing the solution and rechecking it. Middle-achieving students of problem-solving skills solved the problem by understanding the problem, planning the solution and doing the solution without rechecking it so they get incorrect results. Low-achieving students of problem-solving skills solved the problem by understanding the problem and planning the solution, yet they presented the incorrect solution and did not recheck it. PBL model can be used to improve students’ problem-solving abilities.

In response to the evolving demands of 21st-century education, particularly the critical need to enhance students' conceptual understanding and problem-solving skills in mathematics, the strategic integration of digital technology has become increasingly vital. This research aims to explore the role of digital technology in improving students' conceptual understanding and problem-solving skills by classifying the types of tools used in previous studies. The method employed is a Systematic Literature Review (SLR). Data were sourced from the Google Scholar database, collected, filtered, and synthesized to form an article. The results of this study indicate that digital technology plays a significant role in students' conceptual understanding and problem-solving abilities in mathematics. The digital tools and products used to enhance students' conceptual understanding in mathematics include Microsoft Teams, Microsoft Form, Nearpod, Kahoot, Construct 2, Geoshape, Miro, Teams Room, Google Docs, Quizizz, Wordwall, FlipPDF, Patt_Art, digital LKPD (Learning Activity Sheets), Digital Games-Based Learning (DGBL), and learning materials based on Internet Technology. Meanwhile, the tools and digital products used to improve students' problem-solving skills in mathematics include Liveworksheet, GeoGebra, Spreadsheet, Schoology, Edmodo, Cloud Technology (Google Docs, Google Slides, Google Drive, Google Meet, Google Classroom, and SlideShare), Desmos, Padlet, digital book media, digital LKPD, and digital games. Future research could explore more effective teaching strategies in utilizing digital technology, ensuring that it not only enhances conceptual understanding and problem-solving skills but also fosters students' independent learning.

This article is derived from the results of research entitled "Improving Students' Mathematical Understanding and Problem Solving Skills and Their Learning Interests in MTs through Contextual Teaching and Learning Learning (CTL)" which aims to see not only the influence of Contextual Teaching and Learning (CTL) in increasing students' mathematical understanding and problems solving skills, but also to see their interests in learning mathematic as well. This research is a quasi-experiment study. The population in this study is all students of MTs Cianjur district. The sample in this research are 36 students of class VII A as experiment class and 36 students of class VII B as control class. The data in this study was analyzed using parametric and non parametric statistics. The results of this study indicate that students' mathematical understanding and problem solving skills, as well as their learning interests when using the approach of Contextual Teaching and Learning Learning (CTL), is better than the students using conventional learning. There is an association between the quality of students' mathematical understanding skill and their mathematical problem solving skill with high enough criteria. There is an association between the quality of students' understanding and their interest in learning mathematic with high criteria. There is an association between students' problem-solving skill and learning interests with fairly high criteria.

This study aimed to investigate differences in the mathematical problem-solving and metacognitive skills of the fifth-grade students in Oman as a function of gender and level of academic achievement. The participants were 90 grade five students randomly selected from one educational governorate in the Sultanate of Oman. They were evenly divided into three groups based on gender and levels of academic achievement. Four instruments were used in the study: a mathematical problemsolving test, a non-verbal metacognitive scale, Raven Coloured Progressive Matrices and a long-term memory test. The results for metacognitive and mathematical problem-solving skills indicate that students with a high level of academic achievement obtained the highest score while students enrolled in a learning disability program obtained the lowest score. In addition, possible interventions were identified that may improve the metacognitive skills of students enrolled in the learning disability program, which could lead to improvement in their mathematical problem-solving skills.
 Keywords: Problem-solving, metacognition, learning disability, academic achievement.

This study aims to develop a mission-based puzzle learning media to enhance elementary school students' problem-solving skills, specifically in understanding the concept of fractions. Mathematics instruction often faces challenges in helping students grasp abstract concepts like fractions, which are considered more difficult than whole numbers. Mission-based puzzles are expected to offer an innovative solution to make learning more engaging and to improve students' critical thinking skills. The development model used in this research is ADDIE (Analysis, Design, Development, Implementation, Evaluation), supplemented by the simplified research and development stages of Borg and Gall as modified by Sukmadinata. The study began with a preliminary investigation, including classroom observations and interviews with teachers to identify the learning needs at SD Negeri Butuh 01. Based on this, a prototype of the mission-based puzzle media was designed with a Problem-Based Learning (PBL) approach. The prototype was validated by subject matter experts, media experts, and instructional design experts, and was tested with fifth-grade students. The results showed that the media effectively enhanced students' problem-solving skills in mathematics, with positive responses to its use. The "Mizzle Math" learning media was validated with excellent results (98%, 96%, and 98% for content, media, and design experts, respectively) and demonstrated a significant improvement in students' pretest and posttest scores, with the average posttest score reaching 80. The evaluation indicated that the mission-based puzzle media effectively teach fractions at SD Negeri Butuh 01 and offer an innovative alternative to enhance student engagement and understanding of mathematics.

This study aims to evaluate the impact of the Think Talk Write (TTW) learning model supported by LKPD based on Polya's theory on fifth-grade students' problem-solving skills in mathematics at SD Negeri 2 Batubulan. The study employs a quasi-experimental design with a pre-post non-equivalent control group design, involving two groups of fifth-grade students: the experimental group and the control group. Participants were selected using random sampling, and data were collected through tests designed to measure problem-solving abilities in mathematics. Data analysis was conducted using descriptive statistics to examine score distributions and inferential statistics to test hypotheses. The results indicate that the experimental group achieved an average n-gain of 0.71 (high category), while the control group had an average n-gain of 0.57 (medium category). The t-test showed a t-value of 10.461 compared to a t-table value of 1.991 for df = 76, with a significance value of 0.000 (< 0.05). These findings suggest that the TTW model, supported by LKPD based on Polya's theory, has a significant impact on improving students' problem-solving skills in mathematics.

This article describes mathematical problem solving and critical thinking skills and examines the relationship between junior high school students’ problem solving skills and critical thinking skills in learning mathematics. The research samples consisted of thirty-six students at the age of 13 to 14 having mathematical abilities on above average who were selected through purposive random sampling technique from one public junior high school of Yogyakarta. Data were obtained from tests of problem solving skills and critical thinking skills. Both instruments are essay questions. Quantitative analysis is used to determine level of problem solving skills, level of critical thinking skills, and relationship between them. The results revealed that the average of students’ problem solving skills and mathematical critical thinking skills was in the medium criteria where critical thinking skills were slightly higher than problem solving skills. Besides, the relationship between them belonged to medium category.

This study aims to determine the effectiveness of using Realistic Mathematics Education (RME)-based Students’ Worksheets (LKPD) to improve students' mathematical problem-solving skills. This type of research is experimental research with pretest posttest control group design. The samples in this study were class X-E2 as the experimental class with 36 students and class X-E3 as the control class with 36 students. Data collection techniques using interviews, observations, and pretest and posttest assessments of students' problem-solving skills on statistics material. The hypothesis of this study is that the use of RME-based LKPD is more effective in improving students' problem-solving skills than learning without using RME-based LKPD. The results obtained from this study are the use of RME-based LKPD which contains indicators of problem-solving skills proven effective to improve students' problem-solving skills. This conclusion is obtained based on the results of statistical tests, namely the Wilcoxon Signed Rank Test where the test results from the experimental class and control class have sig. 2 tailed < 0.05, Mann-Whitney U Test which has sig. 2 tailed <0.05, and the mean difference test which shows an increase in the experimental class of 28.05 and in the control class of 11.39 which shows that learning using RME-based LKPD is more effective in improving students' problem-solving skills than learning without using RME-based LKPD.

Purpose of the study: This study aims to systematically examine the role of Information and Communication Technology (ICT) in supporting students’ mathematical problem-solving processes at the secondary school level. It addresses the current gap in the literature by providing a focused synthesis of how ICT is utilized in mathematics education to enhance students’ problem-solving abilities. Methodology: A Systematic Literature Review was conducted following the PRISMA protocol. Articles were sourced from reputable databases, such as Scopus, Taylor & Francis Online (Tandfonline), and Education Resources Information Center (ERIC). Through a rigorous selection process based on relevance and quality criteria, 25 peer-reviewed articles published within the past ten years were analyzed and synthesized. Main Findings: The review reveals that ICT is widely employed to improve the quality of instruction and students’ problem-solving skills in mathematics. ICT supports learning across various topics such as geometry, calculus, and algebra, mainly through visualization tools and interactive simulations. Furthermore, ICT serves multiple roles: as a medium for ICT-assisted instruction, a complement to instructional materials, a platform for online learning, an assessment tool and a resource for student-directed learning, and as an adaptive and diagnostic learning systems. Novelty/Originality of this study: This study contributes a focused and systematic analysis of how ICT specifically enhances mathematical problem-solving at the secondary level, a perspective that has been underrepresented in existing reviews. By identifying the specific functions and impacts of ICT in this context, the study lays the groundwork for future research and development of ICT-based pedagogical strategies in mathematics education.

This research aims: (1) to find out the effect of the PBL (2) to find out the effect of the STAD (3) and to find out the effectiveness between the PBL and STAD Models to mathematical problem-solving skills of third-grade students at SD N Mejing 2. This type of research is a Quasi Experiment with a research design Pretest-Posttest Only Control Design. The instruments used in this research are problem-solving skills test and observation of learning activities. Data analysis in this research used t-test with a significant level of 5%. The final results of this research show that: (1) There is an influence between students’ problem-solving skills before and after the PBL model applied. The results of the analysis are t count = -10,081 < t table = -1,703; (2) There is an influence between students’ problem-solving skills before and after the STAD learning model applied. The results of the analysis are t count = -5,403 < t table = -1,703; (3) Learning with PBL more effective than STAD against students’ mathematical problem-solving skills, analyzed by t-test of two samples. The results of the analysis are t count = 2.970 > t table = 1.674, the significance level of 5%.

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