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Mathematics lessons are lessons that are able to provide students with insight into gaining knowledge systematically or how to solve a mathematical problem. One of the goals of learning mathematics is to develop problem solving abilities. This indicates that problem solving is a very important ability to hone in learning mathematics. The method used is literature study or literature review. The study sources are in the form of reference books, published scientific journals, and references on websites accessed via the internet. Theoretical references obtained through literature study research will be used as the basic foundation and main tool for further practice which will be followed up with field research. Polya's theory is a systematic approach to solving mathematical problems which consists of four main steps, namely understanding the problem, planning a solution, implementing the plan, and checking again. This theory has been applied in various mathematics learning contexts, such as in analyzing the difficulty of solving mathematical problems on various materials and levels of difficulty.

Problem-solving is so important that it makes mathematics teaching a common goal. It is estimated that students who are capable of solving these problems can contribute to the economic growth of their country. Therefore, researchers are interested in analyzing students' ability to solve mathematical problems. Data is taken using the essay test instrument and analyzed using a descriptive quantitative approach. The subject of this study is a student of class XI SMAN 3 Sungai Penuh of 29 people. This research found that students' abilities in composition functions material were well assessed. However, in the problem-solving capabilities measured based on problem-solving indicators, there is still an obstacle to the first indicator, which is to display what is known and what is asked. But for the other three indicators, there are only a few obstacles even no obstacles at all. It is hoped that the obstacles experienced by students in this research can also be the background for further research.

The aim of this research is to identify whether there are differences in students' mathematical problem-solving abilities before and after the implementation of the Student Teams Achievement Divisions (STAD) Learning Model. The study was conducted on 14 fifth-grade students at SD 1 Karangmalang. Data were collected using a multiple-choice test to measure students' mathematical understanding. The research method used was a quasi-experimental design. Data analysis was performed using a paired sample t-test. The results of the study showed that the average score in the posttest was higher compared to the average score in the pretest, indicating an improvement in students' mathematical problem-solving abilities after the implementation of the STAD learning model. Furthermore, the research results also showed that the obtained significance value was 0.000, which is smaller than 0.05. Therefore, the null hypothesis (Ho) is rejected. This indicates that there is a significant difference between the mathematical problem-solving abilities before and after the use of the STAD learning model

Problem solving skills are important for students to overcome various problems related to learning and community life. This involves students actively exploring, observing, trying, and investigating using the knowledge and abilities they have. Problem solving is the main focus of developing students' higher order thinking skills in mathematics. This research was conducted by means of observation, interviews, and post-test methods on the 4th grade students of SD Negeri 7 Gondosari. In the results of the discussion, there are 10 data from 31 students which can describe a good level of problem solving. Some students experienced difficulties in implementing the problem and re-examining the results of the solution. Therefore, it is important for students to continue to hone their problem solving abilities using the Polya procedure and to re-check the correctness of the solutions that have been done.

This research aims to describe and analyze the mathematical problem solving abilities of class VIII students at SMP Negeri 5 Pematangsiantar on two-variable linear equation systems material, with treatment in the form of a Contextual Teaching And Learning (CTL) learning model. The approach taken in this research is a quantitative approach. Sampling was carried out using a simple random sampling technique. The research subjects were class VIII-6, totaling 30 people. The data collection technique in this research is in the form of a test to determine students' mathematical problem solving abilities in the research process carried out. Data analysis techniques were carried out using normality tests and hypothesis tests. From the results of data analysis, the results of students' mathematical problem solving abilities showed that the average pre-test score was 54336 and the average post-test score = 79,400. A significant value (2-tailed) 0.000 < 0.05 indicates that there is a significant difference between the initial and final variables. Thus, the independent variable has a significant effect on the dependent variable. So it can be concluded that by applying the Contextual Teaching And Learning CTL learning model) it can improve the mathematical problem solving abilities of class VIII students at SMP Negeri 5 Pematangsiantar on the material of two-variable linear equation systems.

The aim of this research is to determine the effect of the Thinking Aloud Pair Problem Solving (TAPPS) method on the mathematical communication skills of class VIII students at SMP Negeri 9 Pematangsiantar after applying the Thinking Aloud Pair Problem Solving (TAPPS) method. The type of research used is experimental research. In this research the author used a quantitative approach. The design used in this research is One Group Pretest-Posttest Design. This research involved an experimental class that was treated with the Thinking Aloud Pair Problem Solving (TAPPS) learning method and then given pre-test and post-test treatment to draw conclusions. For more details, see table 3.1 below. The research results obtained showed that the Thinking Aloud Pair Problem Solving (TAPPS) method had an influence on students' mathematical communication skills, reaching an average pre-test score in the Experiment class of 48.63, while the average score was 48.63. Post-test average in the Experiment class was 78.63. This proves that the Experimental class has further improved abilities after being given treatment using the TAPPS Method.

Abstract. This study aims to determine whether there is an influence of the problem based learning model integrated with video animation on the mathematical problem solving abilities of class VIII students. This research was conducted at SMP Negeri 6 Percut Sei Tuan, TA 2022/2023. The research method used is a quasi-experimental design method. The sample in this study consisted of two classes namelyclass VIII-3 as the experimental class and class VIII-4 as the control class. The experimental class uses a problem-based learning model integrated with video animation and a control class with conventional learning. Obtaining the average score of the final test (posttest) of the experimental class students is equal to 89.22, whereas in the control class the average result of the student's final test score was 72.55, in the hypothesis test, the results obtained from the average difference test (t-test) with statistical values t_hitung>t_tabel(10.56 > 1,671 ) which means there is an influence from the usea problem-based learning model integrated with video animation that is applied to the experimental class. This indicates that the mathematical problem solving abilities of the experimental class students are better than the control class.

This research aims to see how the mathematical thinking abilities of students who have a field independent cognitive style are based on Shafer and Foster's theory. This research uses a descriptive approach. The sample for this research is 3 class VII students of SMP Negeri 6 Purworejo. The technique for selecting subjects in this research was purposive sampling technique. The data collection techniques used were mathematical thinking test methods, interview methods and documentation. The data analysis technique used is reduction, presentation and drawing conclusions. The results of research regarding the level of mathematical thinking ability based on Shafer and Foster's theory in solving algebra material problems showed that students at SMP Negeri 6 Purworejo who had a field independent cognitive style in solving the reproduction level were able to know basic facts, namely knowing and writing down any information that could be known in questions and determine the problem correctly, at the completion of the connection level students are able to integrate information, namely explaining the steps to solve the problem correctly and applying the right algorithm to solve the problem, at the completion of the analysis level students are able to mathematize situations, namely being able to change real problems into mathematical form by make equations and make generalizations, namely being able to find the correct answer.

A This study aims to determine: (1) the effect of Blended Learning models towards Mathematical Student’s Problem Solving Abilities and Self-Regulated, (2) the improvement of student’s mathematical problem solving and self regulated learning (3) the advantages of the advantages and disadvantages of blended learning model. This type of research includes descriptive qualitative research using library research methods. The data in this study were obtained from a collection of literature such as theses and journals that are relevant to the topic of discussion, namely Mathematical Student’s Problem Solving Abilities And Self-Regulated. The results show that, 1) Blended Learning Model has a great effect on students' problem solving abilities based on the overall effect size calculation which produces an average effect size of 1.56 where this number is included in the high category and Blended Learning Model has a great effect on student’s self-regulated based on the overall effect size calculation which produces an average effect size of 1.73  2) There is an increase in  mathematical the student's problem solving abilities and self-regulated learning that are taught through blended learning models. This can be seen from the achievement of N-Gain value and indicators in the experimental class in the literature which is generally better than the control class. 3) Based on the analysis, it was found that the advantages and disadvantages of blended learning. it can be obtained that the advantages of blended learning models as follows: (a) Learning is more effective and efficient, (b) Improve accessibility. with blended learning, it is easier for learning participants to access material learning. and disadvantages of blended learning is Not evenly distributed facilities owned by students, such as computers and internet access. Even though blended learning requires adequate internet access, if the network is inadequate it will make it difficult for participants to take part in independent learning via online.

Problem solving abilities can be used in everyday life to find solutions and solve mathematical problems. The ability to solve mathematical problems in class XI students at SMAN 55 Jakarta for the 2022/2023 academic year is the goal of this research. The research subjects were 36 class XI students consisting of 18 female students and 18 male students at SMAN 55 Jakarta. The research instruments used were interviews, observation, and documentation. The data analysis technique used is qualitative data analysis, namely data reduction, data presentation, drawing conclusions. The research results obtained show the importance of the teacher's role in helping students to solve problems in learning mathematics.

This study aims to describe students' mathematical problem solving skills in solving word problems.  The population in this study were all fourth grade students at SD 4 Dersalam with a total sample of 24 students.  The research method used is a qualitative approach with descriptive methods.  The research instrument used was in the form of test questions (essays) and interview for mathematical problem-solving abilities in diagrammatic material.  The data collection technique in this study has three stages of procedure namely;  1) preparation stage, 2) implementation stage, 3) final stage.  Based on the results of the tests that have been given, the ability to solve mathematical problems in the good category is 14 students (58.3%), the medium category is 4 students (16.6%) and the low category is 6 students (25%).  Based on the categories of mathematical problem solving abilities, namely good, sufficient and insufficient, it can be described as follows: 1. Students' Mathematical Problem Solving Ability in the Good Category 2. Students' Mathematical Problem Solving Ability in the Enough Category 3. Students' Mathematical Problem Solving Ability in the Poor Category.

This research was conducted with the aim of producing digital learning media using the Smart Apps Creator through a Realistic Mathematics Education approach that is valid, effective, and able to improve students' mathematical problem solving abilities in the matter of a system of two-variable linear equations. This type of research is Research and Development (R&D) with the ADDIE model. From the research results, it was obtained that the media and material validity values were 93.6% and 93% with very valid categories. The practicality of the media through the results of the teacher's response questionnaire obtained a practicality value of 97.3% in the very practical category and the results of the student response questionnaire for the small group test and large group test obtained values of 90.9% and 91.4% in the very practical category. Then the value of effectiveness is seen through the mastery of classical learning and the results of the student response questionnaire obtained percentages of 87.5% and 94.05% with very effective categories. Improving problem solving abilities in students, the results obtained are that the level of students' problem solving abilities is at a percentage of 92% with a very high category, while based on the N-Gain test the average value obtained by students is 0.6473 which means there is an increase in problem solving abilities in students medium category. So based on the results obtained it can be concluded that the learning media developed in this study are valid, practical, effective, and able to improve students' mathematical problem solving abilities.

This research aims to analyze mathematics learning, especially in number material, as well as classify students' mathematical problem solving abilities. , interviews and documentation. 12 students have no value, 5 students have moderate values and 3 students have very high scores, the questions given are 5 all description questions. In making mathematical problem solving questions we use indicators namely: 1.) Understanding new mathematical knowledge through problem solving, 2.) Designing mathematical models, 3.) implementing and adapting appropriate strategies to solve problems, 4.) completing models, 5.) monitor and reflect on the process of solving mathematical problems. Of the 5 questions, they are then assessed with an assessment rubik according to the points specified in the question grid used. The results of the assessment were categorized into 3 categories, namely high, medium category, and low category in class IV SD 1 Burikan.

This study aims to determine the effect of the Thinking Aloud Pair Problem Solving (TAPPS) method on students' mathematical communication abilities. The type of research used is a Quasi-Experimental type (pseudo-experimental) and uses the True Experimental Design research design with the Posttest-Only Controll form. The research was conducted at SMP Ikhlasiyah Palembang with a population of all students of class VII consisting of 2 classes. The sample were taken from all members of all population so that class VII.1 as the experimental class was given treatment, namely the Thinking Aloud Pair Problem Solving (TAPPS) method and class VII.2 as the control class which was not given treatment, namely the conventional method. Research data was collected through tests. Based on the analysis of the test results, it shows that the students' mathematical communication skills in the experimental class are higher than those in the control class. This means that the class that was treated with the TAPPS method affected students' mathematical communication skills. Statistical calculations obtained from the test results yield tcount = 2.944 and ttable = 2.013, so that tcount > ttable which causes H0 to be rejected and H1 to be accepted. Thus, it can be concluded that there is an influence of the Thinking Aloud Pair Problem Solving (TAPPS) method on the mathematical communication abilities of class VII students of SMP Ikhlasiyah Palembang.    

This study aims to describe the improvement of mathematical problem-solving skills after applying the realistik mathematics learning assisted by digital media of class VIII students of SMP Dharma Patra Sei Lepan for the 2022/2023 academic year. The subjects in this study were 32 class VIII-A students of Dharma Patra Private Middle School. Data collection techniques used were teacher observation sheets, tests of mathematical problem-solving skills, and documentation. This research is a classroom action research (PTK) which consists of 2 cycles, each cycle consisting of 2 meetings. Before taking action, first given the initial test and at the end of each cycle is given a test of students' mathematical problem-solving abilities. The test results of students' mathematical problem-solving abilities increased from the initial test, cycle I, and cycle II. In the classical pre-test, 3 students (9.38%) passed and the average pre-test ability was 49.12% with a very low level of ability. In the first cycle test, there was an increase classically, 17 students (53.13%) completed and the average ability test obtained 69.01% with the ability level in the medium category. Then the second cycle test also experienced an increase in classically obtained 28 students (87.5%) completed and an average ability obtained 81.05% with a high level of ability category. Thus it can be concluded that the application of realistik mathematics learning assisted by digital media can improve the mathematical problem-solving skills of class VIII students of SMP Dharma Patra Sei Lepan.

This research focuses on developing a game-based learning model to improve students' mathematical problem-solving abilities of class XI students at SMK Pratidina Makassar. This model was designed to make the learning process more interesting and interactive while increasing students' understanding of mathematical concepts. Through a game approach, students are invited to think critically and analytically in solving mathematical problems, so that their problem-solving abilities can develop. The research results show that this game-based learning model is effective in improving students' mathematical problem-solving abilities. Apart from that, this model also succeeds in creating a more enjoyable learning atmosphere and students' learning motivation is higher. Therefore, this research recommends implementing a game-based learning model in teaching mathematics.

This study aims to determine the application of problem based learning learning models with lottery game media in improving junior high school students' problem solving abilities. This research is an experimental research in the form of Pre-Experimental Designs. The design used is One Group Pretest-Postest Design. The population in this study were class VIII A and class VIII B. The sample in this study was students of class VIII B consisting of 20 students with the selection of subjects based on the cluster random sampling technique. The data collection technique used is a measurement technique with a data collection tool in the form of test questions in essay form. The data analysis technique used was anava one line of dissimilar cells, with further testing using the Scheffe method. The research results obtained were that there was a significant increase in students' mathematical problem solving abilities before and after being given treatment through the problem based learning model using lottery media with high categories.  

This study aims to obtain teaching materials based on a valid, practical, and effective realistic mathematical approach, so as to improve students' mathematical reasoning abilities on the material of a three-variable linear equation system. The research instruments used were questionnaire validation sheets, lesson plans validation sheets, teaching material validation sheets, test instrument validation sheets, mathematical reasoning ability tests, and teacher and student response questionnaires to teaching materials. After all instruments, lesson plans, and teaching materials were declared valid by the validator, then readability tests and field trials were carried out. The results showed that: (1) the teaching materials based on the realistic mathematical approach developed had met the criteria of validity based on the validator's assessment with the average validity of the teaching materials for the material being 3.13 and 3.29 for media with a very feasible category; (2) the teaching materials based on the realistic mathematical approach that have been developed have met the practicality criteria through: a) the results of the questionnaire student responses to teaching materials show the percentage of practicality of 81.19% with a very practical category, b) the results of the questionnaire responses of teachers to teaching materials show the percentage of practicality 88.75% with very practical category; (3) The teaching materials based on the realistic mathematics approach developed meet the effective criteria with: a) classical student learning mastery of 88%, b) more than 65% of students have achieved 75% of learning objectives for each indicator, c) increased mathematical reasoning ability students after using teaching materials seen through the average score of students increased from 50 in the pretest to 85.33 in the posttest and the results of the N-Gain analysis which showed students' mathematical problem solving abilities increased by 0.712, meaning in the high category.