Mathematical Problem-solving Skills Research Articles

Enhancing Mathematical Problem-Solving Skills of Indonesian Junior High School Students through Problem-Based Learning: a Systematic Review and Meta-Analysis

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.

Practicality of Learning Design Based on Realistic Mathematics Education of Derivative Topic for Grade XI Senior High School

The derivative is one of the important subjects in mathematics. One of the goals of derivative learning is that students can solve math problems in real life. In this study, derivative learning design was developed based on Realistic Mathematics Education to make the products that consist of teacher books and student books to improve students’ mathematical problem-solving skills. The development models are used Plomp and Gravemeijer & Cobb models. Data collection was the form of questionnaires filled out by teachers and students. Then, the data is analyzed by using descriptive analysis. The results of this study can be concluded that the practical value of teacher response 81.25% and the practicality value of student response is 82.04%, so the design of learning derivative topics based on Realistic Mathematics Education has been categorized as practical. It means the RME-based learning design of derivative topics developed in teacher and student books can be used to develop students’ mathematical problem-solving skills.

A meta-analysis study of the effect of Problem-Based Learning model on students’ mathematical problem solving skills

This study aims at analysing the effectiveness of Problem-Based Learning (PBL) on students’ mathematical problem-solving skills. The Effect Size in some research which applied PBL was examined using the meta-analysis technique. Empirical data were obtained using electronic search engines, including Google Scholar, Portal Garuda, ERIC, SPRINGER, and national journals URL; coding was used as the instrument. Data analysis was conducted using the meta-analysis software, namely Comprehensive V.03. The method included systematic reviews on research findings in Indonesia’s national e-journals, with 16 articles meeting the inclusion criteria selected as the sample. The publication bias test was carried out so that 13 articles were obtained which would be analysed further. The meta-analysis study reveals that the overall effect of implementing PBL on students’ mathematical problem-solving skills had a high category of effect. Moreover, the effect size of the application of the PBL model on solving ability between study groups was not different based on the characteristics of the level of education, class, sample size, and study year. The results of other studies, it was found that there was a significant difference in the effect size between study groups based on the duration of learning.

The Effect of Reading Strategy Education on Problem Solving Skills in Mathematics

Okuduğunu anlama becerisi, ana dili öğretiminde dört temel dil becerisinden biri olmakla birlikte yalnızca ana dilinin gelişmesinde değil diğer derslerin başarısında da oldukça önemlidir. Amacı, okuma stratejisi eğitiminin matematik dersi problem çözme becerisine etkisini belirlemek olan bu araştırmada, ön – son test kontrol gruplu yarı deneysel desen kullanılmıştır. Araştırma, ilgili yerlerden gerekli izinler alınarak 2017-2018 eğitim öğretim yılında, Ankara ilindeki bir devlet ortaokulunun iki 6. sınıf şubesiyle gerçekleştirilmiştir. Sınıf mevcudu, matematik ve Türkçe dersi akademik başarıları birbirine denk olan, Türkçe ve matematik derslerini aynı öğretmenlerin yürüttüğü iki 6. sınıf seçilmiş; yansız atama yoluyla sözü edilen sınıflardan biri kontrol, biri deney grubu olarak belirlenmiştir. Araştırmada, deney grubuna okuma stratejilerine göre hazırlanmış etkinlikler uygulanırken kontrol grubundaki dersler, ders kitabındaki etkinliklerle yürütülmüştür. Uygulama çalışması on haftada tamamlanmıştır. Araştırma sonucunda, okuma stratejisi eğitimi verilen deney grubu öğrencilerinin matematik dersi problem çözme başarı testi puanlarının kontrol grubu öğrencilerinin puanlarından daha yüksek olduğu belirlenmiştir. Deney grubu öğrencilerinin on haftalık uygulama sonrası matematik problem çözme becerilerinin geliştiği sonucuna ulaşılmıştır.

MENINGKATKAN KEMAMPUAN PEMECAHAN MASALAH MATEMATIKA MELALUI MODEL PROBLEM-BASED LEARNING PADA MATERI BILANGAN PECAHAN

This study aims to improve students’ mathematical problem-solving ability through the Problem-Based Learning Model in Fractions learning material at grade VII of Junior High School SMP Negeri 10 Gorontalo. This classroom action research (CAR) involved 25 students as the subject and were conducted collaboratively between the researcher and teachers. This research was carried out in two cycles, and the first and second cycle consisted of three meetings, respectively. The instruments applied were an observation sheet of the teacher’s ability to manage the Problem-Based Learning Model, the observation sheet of students’ activity using the model above, and the ability tests to solve mathematical problems in the Fraction material. Further, the data were collected from observation and written tests. The results show an enhancement of the teacher’s ability in managing the Problem-Based Learning model and students’ activity using this model and the outcomes of mathematical problem-solving skill in the fractions learning material from cycle I to cycle II. Therefore, this finding indicates that the Problem-Based Learning model can be accepted as an alternative in learning Fractions at the research site.

Prospective mathematics teachers’ thinking styles and problem-solving skills

The aim of this study is to examine problem-solving skills and thinking styles of prospective mathematics teachers and investigate whether the thinking styles of them are related to their mathematical problem-solving skills and the problem-solving strategies preferred by them differ depending on their thinking styles. The data of the study were collected from 32 prospective middle school mathematics teachers through five non-routine problems and “Thinking Styles Inventory”. Prospective mathematics teachers’ solutions to non-routine problems were analyzed qualitatively. For quantitative data, descriptive statistics, correlation and chi-square were used. The results showed that majority of the prospective teachers have difficulties in using problem-solving strategies appropriately and solving non-routine problems. It was found that prospective teachers mostly preferred legislative, hierarchical and liberal thinking styles respectively whereas they displayed least preferences for oligarchic, conservative and monarchic thinking styles respectively. The results revealed that problem-solving skills were significantly, negatively and moderately related to only monarchic thinking style. High level of problem-solving skills were found to be related to liberal and internal thinking styles significantly, negatively and moderately whereas there was no significant relationship between low level of problem-solving skills and thinking styles. It was also found that there were no significant differences between the thinking styles of prospective mathematics teachers and their problem-solving strategies. This finding was supported by qualitative data. More comprehensive results can be obtained through observing and monitoring prospective teachers for long period.

An Investigation Into Problem Solving Skills of Gifted Students' via Multi-Facet Rasch Analysis

Problem solving, which is an important skill for mathematics, has long been recognized as the focus of the curriculum. This study focuses on both the systematic of problem solving and the use of strategies for different solutions, so aim of this study was to examine gifted middle school students' mathematical problem-solving skills via multi-facet Rasch analysis. For this purpose, data were collected via 12 non-routine mathematical open-ended problems from a total of 276 students who attend Science and Art Centers. The data were scored by two independent researchers according to the criteria in the range of 1-5 points per problem. In the study, it was seen that Grader 1 behaved more tolerant than Grader 2 in terms of evaluation for all problems except 6th problem. In addition, the most difficult and the easiest problems were differed between graders. From the findings of the study, it can be said that even if the evaluation criteria were clearly defined the difference between graders was not resolved. It can be suggested that to take necessary precautions for making vital decisions in all grade levels via teacher made tests and to use more than one grader instead of just one grader for evaluation.

Development of authentic assessment to improve students’ mathematical problem solving ability

This study aims to find out how the implementation of authentic assessment development in producing a valid product by the principles and characteristics of authentic assessment to improve students’ mathematical problem-solving abilities. This research uses research and development methods with the stages of carrying out needs analysis, literature review, pre-test, designing an authentic assessment form, and conducting a post-test to determine students’ mathematical problem solving abilities before and after using authentic assessment. The results of the study concluded that the stages of authentic assessment development had been carried out through a limited validation process and broader validation involving experts to produce a product taking into account the principles and characteristics of authentic assessment. There is a difference in the average results of students’ mathematical problem-solving skills between the results of the post-test compared with the results of the students’ pre-test, so it is said that the development of authentic assessment can improve students’ mathematical problem-solving abilities.

Problem-Based Learning vs Student Teams Achievement Divisions Assessed from Student’s Mathematics Problem Solving Ability

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%.

High School Students’ Mathematical Problem Solving Skills Based on Krulik and Rudnick Steps Reviewed from Thinking Style

This research explains the problem solving skills of students of Grade XII MIPA SMA MTA Surakarta based on Krulik and Rudnick’s steps that are reviewed from the thinking style. This research is a qualitative study that produces descriptive data. The study began by determining the subject of the study by using a thought style questionnaire, given problem solving tasks and interviews. The results showed math problem solving skills; 1) concrete sequential student are systematically worked on and use an inductive mindset and the steps of reviewing and discussing are not implemented; 2) abstract sequential student are easy to present what is known in the question to mathematical symbol forms, collect data in detail, and manage the information obtained regularly and perform all of Krulik and Rudnick’s steps; 3) concrete random student are tend to be consistent in using guessing or experimenting strategies and work without detail and the steps of reviewing and discussing are not implemented: 4) abstract random student are fundamental differences in processing the information received and planning problem solving in a way of their own accord and doing all the steps krulik and rudnick.

Assessment Strategies for Enhancing Students’ Mathematical Problem-solving Skills: A Review of Literature

Students’ ability to apply mathematical knowledge to various situations has been one of the major concerns in mathematics education research. However, little is known about the assessment strategies that have a substantial contribution to the development of mathematical problem-solving skills in kindergarten children through to upper secondary school students. In this review of existing literature, we discuss the contribution of assessment strategies in the last three decades in strengthening learners’ acquisition of mathematical problem-solving skills. Twenty peer-reviewed conference papers and journal articles published from 1997 to 2020, downloaded from Google Scholar, Academia, and ERIC databases have been analyzed and discussed. Based on this review, it has been noted that the application of assessment strategies such as Structure of the Observed Learning Outcomes taxonomy, Higher-Order Thinking Skills model, performance assessments, authentic assessments, dynamic assessments, and video games-based assessments alongside the learner-centered/active learning methods like problem-based and cooperative learning is bound to strengthen students’ mathematical problem-solving skills.

Teaching to Self-Regulate in Mathematics: A Quasi-Experimental Study with Low-Achieving Elementary School Students

Teaching students to self-regulate enhances their mathematics performance, yet few studies have investigated the long-term differential impact of particular self-regulation strategies specifically for low-achieving students. This quasi-experimental study evaluates the effect of teaching different self-regulation strategies on mathematical problem solving in low-achieving students. The participants were 69 sixth-grade elementary school students randomly assigned to one of three experimental groups (and taught predominantly cognitive, metacognitive or volitional strategies, while verifying intervention fidelity) or a control group for 16 sessions. Mathematical problem-solving skills were evaluated prior to the intervention, upon completion, and two months later. While all three intervention groups obtained significantly better results compared to the control group immediately after the intervention, volitional and metacognitive strategies showed the strongest and most lasting positive effects. We conclude that low-achieving students could benefit from learning self-regulation strategies, particularly when these strategies take into account the affective and motivational dynamics of learning.

Teaching to Self-Regulate in Mathematics: A Quasi-Experimental Study with Low-Achieving Elementary School Students

Teaching students to self-regulate enhances their mathematics performance, yet few studies have investigated the long-term differential impact of particular self-regulation strategies specifically for low-achieving students. This quasi-experimental study evaluates the effect of teaching different self-regulation strategies on mathematical problem solving in low-achieving students. The participants were 69 sixth-grade elementary school students randomly assigned to one of three experimental groups (and taught predominantly cognitive, metacognitive or volitional strategies, while verifying intervention fidelity) or a control group for 16 sessions. Mathematical problem-solving skills were evaluated prior to the intervention, upon completion, and two months later. While all three intervention groups obtained significantly better results compared to the control group immediately after the intervention, volitional and metacognitive strategies showed the strongest and most lasting positive effects. We conclude that low-achieving students could benefit from learning self-regulation strategies, particularly when these strategies take into account the affective and motivational dynamics of learning.

An Analysis of Students’ Mathematical Problem Solving Skill in Completing Multiplication and Division of Fractions

The mathematical ability and mathematical problem solving skill can be separated in learning mathematics. In the fourth industrial revolution, one of learning objectives of learning mathematics is the student has a skill in solving mathematical problem. Meanwhile, mathematical problem solving skill can be obtained if the students’ mathematical concept understanding is high including multiplication and division of fractions. They stated that understanding fraction concept was very difficult. This study aimed to analyze the student mathematical problem solving skill of the tenth grade of Junior High School in completing multiplication and division of fractions. This research had 8 informants. Data was collected using interview and test and applied qualitative and quantitative analysis. The initial data was obtained from elementary school with three categories of mathematical ability level, namely (1) one student had high skill, two students had moderate skill and one student had low skill. The indicator of mathematical problem solving was based on George Polya (1983) consisting of four steps, they are (1) understanding problem, (2) planning a problem, (3) completing the problem, and (4) rechecking the result. The research result indicated that the student mathematical problem student was low, especially the problem solving of fraction division and multiplication. The student was difficult to make a solving plan. This situation effected on problem solving caused by the indistinctness of problem solving plan or mathematical model and/or mathematical formula about verbal sentence of mathematical problem solving. The result of interview described that the teacher did not explain the ways of completing mathematical problem solving based on G.Polya’s steps. In addition, the students were less practice in completing the problem solving questions. Besides, the teacher did not integrate the objectives of basic competence 3 and 4 in each meeting.

Mathematical problem-solving skills on relation and function through Model-Eliciting Activities (MEAs)

Mathematics relation and function is one of important topics in junior high school. This study aims to see differences in the problem-solving a bilities of junior high school students who use the Model-Eliciting Activities (MEAs) and conventional models in learning mathematics relation and function. This research is a quantitative study using a quasi-experimental approach with a non-equivalent control group design. The population in this study was all of the seventh-grade students at a State Junior High School in Sungai Penuh, Jambi, Indonesia, and the sample was two groups experimental group and control group. The data collection technique used is a test of mathematical problem-solving skills. The data were analyzed by using he independent t-test to find comparisons or differences. The research result showed that there were differences in the mathematical problem-solving skills of junior high school students who used MEAs and other students who did not use MEAs. This difference occurs as a result of different treatment received by students, by MEAs students are required to be more active in understanding and formulating problems.

Differences in Increasing Students' Communication Skills and Mathematical Problem Solving through Project-Based Learning with Virtual Manipulative and Physical Manipulative Media at SMP Plus Jabal Rahmah Mulia Medan

This study aims to analyze the differences in the improvement of mathematical communication skills and mathematical problem solving of students who are taught using manipulative virtual learning media and physical manipulative learning through project-based learning models (PjBL), as well as analyzing the performance of class VII students of SMP Plus Jabal Rahmah Mulia Medan in solving problems. questions that measure communication skills and mathematical problem solving. Data obtained through subjective tests or essay tests, each of which measures the students' mathematical problem solving and communication skills. Data were analyzed using ANACOVA test. The population in this study were all students of class VIII of the private high school Jabal Rahmam Mulia for the 2020/2021 academic year. While the sample in this study is class VIII1 which is the first experimental class which is taught using manipulative virtual learning media and class VIII2 is the second experimental class which is taught using physical manipulative learning media. Based on the results of the ANACOVA calculation, the analysis results obtained F_hitung = 3,450 ˃ Ftable = 3.38 and with sig = 000, because the significant level is smaller than 0.05 so that H_0 is rejected and H_a is accepted. Thus, there are differences in problem-solving abilities between students who are given a realistic mathematics approach assisted by macromedia flash and students who are given a contextual approach assisted by macromedia flash. Based on the results of the analysis F_count = 20.889 ˃ F table = 3.38 and with sig = 000, because the significant level is smaller than 0.05 so that H_0 is rejected and H_a is accepted. Thus, there are differences in mathematical communication skills between students who are given virtual manipulative assisted project-based learning (PjBL VM) and students who are given physical manipulative assisted project-based learning (PjBL PM).

The Effectiveness of Mobile Blended Problem Based Learning on Mathematical Problem Solving

&lt;p&gt;This study aimed to examine the effectiveness of mobile blended compared to conventional problem-based learning on mathematical problem-solving skills and look for students' responses about the use of online learning. The study was conducted using a pretest-posttest quasi-experimental research design supported with descriptive qualitative responses involving 188 students taken by applying cluster random sampling as subjects of research distributed from vocational high schools in &lt;em&gt;Bojonegoro&lt;/em&gt; City, East Java, Indonesia. Research findings revealed that mathematical problem-solving skills for students treated with mobile blended problem-based learning were higher than those who have been treated with purely problem-based learning. In addition, students have responded positively to the usage of mobile blended problem-based learning that was applicable and acceptable for effectively improving mathematical problem-solving skills.&lt;/p&gt;

Developing Interactive Mobile Mathematics Inquiry to Enhance Students' Problem-solving Skill

The research aimed to develop interactive multimedia based on scientific inquiry to improve student mathematics problem-solving as a provision for the era of Society 5.0. The research method used is the Agile Method, which is a software development method. This study involved 120 students from the first, second, to third years who were programming mathematics-related subjects at the Madrasah Ibtidaiyah Teacher Education department, Universitas Muhammadiyah Sidoarjo. The results of the development of Interactive Mobile Mathematics Inquiry (IMMI) were valid and proven to improve student problem-solving abilities. In particular, this increase is significant in planning and implementing student plans for a problem. The significance is due to the training in the inquiry aspects during the use of IMMI. The implication of this research in the field of educational technology is that IMMI can be a preliminary study and a pioneer for lecturers, experts, and practitioners to use and further develop IMMI to improve students' mathematical problem-solving skills at the tertiary level more broadly as preparation for media availability following the values of technological advances in the future Society 5.0 era.

Review of problem-based learning trends in 2010-2020: A meta-analysis study of the effect of problem-based learning in enhancing mathematical problem-solving skills of Indonesian students

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.

Problem based learning and mathematical problems solving skills of junior high school students: a preliminary research

This study is research and development (R & D). A preliminary research of this R & D aims to get information about students' Mathematical Problem Solving Skills (MPSS) and learning device (known as RPP and LKPD) that the teacher used in learning. Initial observations at SMPN 1 Pariaman and SMPN 2 Pariaman show that: (1) students' MPSS is still low, (2) only a small portion of students are actively involved in the learning process and only some of the students take the learning seriously, (3) The LKPD that the teacher used in learning can’t help students in learning mathematics. Based on this, follow-up is needed in the form of R & D to develop mathematics learning devices based on problem-based learning for junior high school students.