The evolved system for conceptual understanding: Implications for mathematical development

It has been observed that Asian, in particular Chinese students frequently outperform their Western counterparts in international academic comparisons. However, it is still open to doubt as to whether they actually possess a deeper conceptual understanding than their Western counterparts and as to whether they would perform as well in non-routine mathematical problems (such as open-ended problems). The reason for such queries owes as much to the students' as to teachers' conceptions of mathematics. When mathematics is regarded as an absolute truth or a set of rules governing symbols, students tend to consider doing mathematics as the memorisation of algorithms and learning mathematics as a process of transmission. We posed certain hypothetical situations to students in Hong Kong and China and found that they possess a relatively restricted conception of mathematics. Later, we investigated this phenomenon at greater depth by the use of open-ended problems. We found that students usually approached a mathematical problem by searching for a rule that identifies what is given, what is being asked and the category of topic for the problem. Evidence has also shown that this approach to mathematical problems is largely shaped by the way they experience learning, their response to task demands, and the classroom environment. In other words, such a restricted conception of mathematics which exists both within the students and in the classroom culture has led students to tackle mathematical problems by searching for rules rather than approaching them through a conceptual understanding of the context. It is well known that students' conception of mathematics is closely related to their problem-solving behaviour. This conception is shaped by a number of factors, in particular, by the space of learning in which they 'live'. Of particular significance is the finding that the teachers' conception of mathematics could contribute to the shaping of this 'lived space'. These inter-relationships are the focus of a series of studies which will be reported in the present paper.

The lived space of mathematics learning

This research is motivated by the lack of student learning activity that affects the understanding of student concepts in mathematics learning in class XI F 4.2 SMA Veteran 1 Sukoharjo. The importance of student activity in learning needs to be done so that learning becomes interesting and students have the curiosity to learn more deeply related to the knowledge taught by the teacher, in addition, understanding the concept is one of the important factors that supports student activity in the learning process. This study aims to improve the activity and understanding of student concepts in mathematics learning using PBL based on lesson study. The subjects in this study were 27 students of class XI F4.2 majoring in social sciences. The study results showed that using the PBL learning model based on lesson study can improve the activity and understanding of student concepts in learning. Based on the study's results, the percentage of student activity increased from pre-cycle 15% and cycle 1 by 59% then cycle 2 by 100%. This is the same as the increase in student's conceptual understanding from the pre-cycle stage with a percentage of 37%, then cycle 1 by 59% to cycle 2 by 100%, so it can be concluded that using the lesson study-based PBL learning model can increase students' activeness and conceptual understanding.

Understanding mathematical concepts is the ablitiy of students to accept material in the form of mathematical concepts and then can restate the concept, can use, utilize, an choose certain procedurs or operations in determaining a concept, and apply the concept in solving mathematical problems. Trigonometry is one of the subjects in mathematics that students’ understanding of concepts is still low. The process of understanding mathematical concepts can be seen from the learning styles that each student has. Grasha Riechman's learning style is the tendency of students to think and interact with each other in various learning environments and various experiences in the process of gaining new knowledge. The purpose of this study is to describe the profile of students’ understanding of mathematical concepts in trigonometry based on Grasha-Riechman’s learning style. Grasha-Reichman learning style consist of independent, dependent, collaborative, competitive, contributive/participant, and avoidant. This study uses qualitative approach and this type of this study in descriptive qualitative. Data collection techniques used in this study were written test and interviews. Data analysis techniques used are data reduction, data presentation, and conclusions.. The subject of this study were each one student from the existing Grasha Riechmann’s learning style type. The results show that Students who have a dependent and competitive learning style have ability to restate a concept, present concept in various mathematical representations, use or choose certain procedures in determining a concept, and apply concepts in completing mathematical problems. Students who have independent and collaborative learning style have the ability to restate a concept, present concepts in various mathematical representations, and use or choose certain procedures in determining a concept, but the have not been able to apply the concept to solving mathematical problems. Student who have avoidant learning style have the ability to present concept in various mathematical representations and use or choose procedures in determining a concept, but this student have not been able to restate a concept and apply the concept to solving mathematical problems. Student who have participant learning style only have the ability to present concepts in various mathematical representations, this student have not been able to restate a concept, use or choose procedures in determining a concepts, and apply the concept in solving mathematical problems.Keywords: Understanding mathematical concept, Trigonometry, Grasha Riechman's learning style

This research is motivated by the lack of understanding of students' mathematical concepts in mathematics which is caused by a lack of motivation to learn in students and the lack of material connection with everyday life. Mathematics learning really needs to be learned by students because Mathematics has an important purpose to meet practical needs related to the development of students' abilities to use mathematics in everyday life, such as counting which is often experienced by students and can develop the ability to calculate weight. and content. Although Mathematics is considered important to learn, not a few students feel that Mathematics is difficult to master, so it is considered boring and makes students' interest in learning in Mathematics considered low. Based on the PISA annual study survey, the Indonesian Mathematics competency has decreased from 386 points in 2015 to 379 points in 2018 with an OECD average of 489. The benefits of studying Mathematics are used to make transactions in trade. One way to make mathematics more understandable is to use the Realistic Mathematics Education (RME) approach so that students can learn more realistically. The purpose of this study was to determine the increase in students' understanding of mathematical concepts using the Realistic Mathematics Education (RME) approach and whether there were changes that occurred after the treatment using this approach. This research was conducted with quantitative research methods and the research design of One Groups Pretest-Posttest Design. The subject of this research is class IV with a total of 28 students at SDN Curugrendeng II. The instrument used is a written test with a total of 10 questions. Calculation of data processing using Microsoft Office Excel 2007 and using IBM SPSS Statistics 22 with a significance level of 0.05. The results of this study indicate that there is an increase in students' understanding of mathematical concepts with an average value of 0.691 which is included in the medium category. Thus, the understanding of mathematical concepts of students using the Realistic Mathematics Education (RME) approach changes from before the action to the final score after the action. done. And there is an effect of the Realistic Mathematics Education (RME) approach on students' understanding of mathematical concepts by showing the results of sig.(2-tailed) 0.000 <0.05, which means H_1 is accepted so that this Realistic Mathematics Education (RME) approach can be applied to learning Mathematics in Primary school.

Problems in the class X MIPA 3 of SMA Negeri 1 Badegan is student have not been able to apply concepts, classify objects, and make good use of operating procedures. This shows that students' understanding in mathematical concepts is still low. This study aims to describe the application of problem based learning model assisted by game mazelabirin and puzzle to improve students understanding of the mathematical concept of class X MIPA 3 students in SMA Negeri 1 Badegan. This type of research was Classroom Action Research (CAR). The subjects of this study were 34 students of Class MIPA 3 of SMA Negeri 1 Badegan. The students consisted of 9 male students and 25 female students. The analytic data understanding of students' mathematical concepts were taken from the results of tests understanding mathematical concepts and learning management data were taken from the learning management observation sheet. The instrument used was a matter of concept comprehension test and observation management learning sheet. The results of this study were the application of Problem Based Learning models assisted by Game Mazelabirin and Puzzle cauld improve students' understanding of the concepts. This application started from the teacher who gove problems, students in groups, then discussing to solve problems with puzzle games or mazelabirin, then the results of the discussion were delivered in front of the class, the teacher provided reinforcement and drews in conclusions with students. The researchers made improvements with the first thing students were taught the importance of understanding the material and the spirit of learning. Provide column completion steps on the LKS answer sheet. Give questions that require understanding to be constructed in the form of mathematics.    Keywords: Problem Based Learning (PBL) Model; Game Mazelabirin and puzzle; Understanding Mathematical Concepts

The concept of mathematics education reflects people's understanding and expectation of the purpose, process and value of mathematics education, and is an important factor affecting the development of mathematics and the cultivation of social talents. STEAM education is an interdisciplinary integrated education based on real problems. It emphasizes the participation process of students, focuses on solving practical problems through interdisciplinary knowledge based on mathematical knowledge and skills, and cultivates students' comprehensive quality including discipline quality and comprehensive practical ability. STEAM education plays an important role in cultivating compound social talents with innovative consciousness and ability. Therefore, STEAM education, its interdisciplinary, situational, rational and artistic educational concept, and the practical essence of mathematical knowledge as the tool basis, has triggered and guided the discussion of our mathematical education concept. On the basis of in-depth understanding and analysis of the original mathematical education concept, based on the perspective of STEAM education, this paper attempts to re understand the mathematical education concept, In the view of STEAM education, this paper re understands the view of mathematics education, that is, mathematics education has the educational purpose of coordinated development of tool literacy and humanistic literacy, the educational process of learning based on real problems, and the educational value of the unity of education and mathematics, with a view to providing a new perspective for the development of mathematical education concept and the reform of mathematical education.

This research examined the impact of gamification techniques on math proficiency among students in Rwandan public secondary schools. In particular, to look at how gamification techniques affect math performance in Rwandan public secondary schools, to gauge how much math performance is attributable to gamification techniques in Rwandan public secondary schools, and to analyse the connection between gamification techniques and math academic achievement in Rwandan public secondary schools. 503 pupils, 52 headteachers, and 115 instructors made up the study's population ; there were 670 responders in all, and 251 kids from 20 schools in the Muhanga District made up the sample size. Results were analysed using SPSS version 21. According to the results for the first objective, 57.4% strongly agreed and 19.1 % agreed that assigning points, badges, or other rewards for completing math problems or achieving specific milestones can encourage them to engage more deeply with the material. 58.5% strongly agreed and 18.1% agreed that displaying a leaderboard that shows my progress and rankings compared to my peers can foster healthy competition and motivate them to improve. 68.1% strongly agreed that introducing virtual currencies or tokens that students can earn for completing math tasks can add an element of fun and encourage students to participate more actively. 66.0% strongly agreed and 21.3% agreed that designing math challenges or quests that students can complete to earn rewards or advance through a game-like progression system can make learning math more engaging and enjoyable and 74.5% strongly agreed and 21.3% that using interactive simulations or math games that allow students to visualise and interact with mathematical concepts can help students better understand and retain mathematical concepts. To the second aim, 53.5% strongly agreed and 16.3 % agreed that their ability to accurately solve math problems and complete assignments can indicate their understanding of mathematical concepts and my ability to apply them to real-world scenarios, while 53.5% agreed and 20.9% that their fluency and speed in performing math operations, such as addition, subtraction, multiplication, and division, can indicate their comfort and proficiency with basic arithmetic. 65.1% strongly agreed and 18.6% that their ability to solve complex math problems and demonstrate critical thinking skills can indicate their understanding of mathematical concepts and their ability to apply them to novel situations, and finally, 60.5% strongly agreed and 18.6% Agreed that their ability to explain and demonstrate their understanding of mathematical concepts, such as fractions, decimals, or algebra, can indicate their grasp of the subject matter. The correlation matrix between independent variables (problem-based learning, displaying leaderboards, using projectors in teaching math, and assigning badges instead of grades) and dependent variables (improved student mathematics score from tests and exams, exam and test results, engagements and participation, and improved class participation) Finally, they indicate positive significance since the p-value is smaller than 0.05. The study recommended that Incorporating game-like elements, interactive tools, and collaboration into the math curriculum can make learning more engaging and motivate students. These tools can help students understand complex concepts in a fun and engaging way. Providing immediate feedback on performance, setting clear goals, and creating a positive learning environment can also help students stay focused and motivated. These gamification practices can lead to improved academic performance in math in public secondary schools in Rwanda.

The background to this research is the low understanding of concepts experienced by students, and the lack of student interest in learning mathematics. For this reason, teachers must choose the right learning media so that they can increase students' understanding of concepts, as was done by the teacher in class IV MI Darul Ulum 02. This research was conducted at MI Darul Ulum 02 for the 2023/2024 academic year. This research aims to analyze the increase in understanding of mathematical concepts regarding fractions in class IV using folded paper learning media. The method used in this research is observation, directly observing the mathematics learning process and interviews with class IV teachers. The results of this research show that the use of folded paper media increases students' understanding of concepts in mathematics regarding fractions. This is shown when the teacher asks students questions, and the students can answer correctly.

The urgency or main issue in this study lies in the low problem-solving skills of students, particularly in understanding and solving story problems based on real-life contexts in algebra learning. This study aims to analyze the needs and impact of the contextual Problem-Based Learning (PBL) model on students' ability to analyze mathematical problem concepts. This research is a descriptive qualitative study, designed to deeply explore students' experiences, perceptions, and abilities in addressing mathematical problems through the PBL approach. This study employs survey and quasi-experimental methods to measure the impact of the application of this learning model, as well as to identify factors influencing its success in the context of mathematics education. The study was conducted at the Sekolah Indonesia Kuala Lumpur over one semester of learning, involving 88 seventh-grade students as the research subjects. The selection of subjects was purposive, choosing students who participated in mathematics learning with the contextual PBL approach, with the aim of exploring the needs and impact of applying this learning model. The main instruments used to collect data in this study were observation, essay tests, and questionnaires. Analysis was carried out using descriptive qualitative methods. The results of the study showed that the application of the contextual Problem-Based Learning (PBL) model played a significant role in improving students' ability to analyze mathematical concepts, particularly in algebra learning. Contextual PBL allows students to connect abstract mathematical concepts with real-life situations, which strengthens their conceptual understanding and encourages their active involvement in solving problems. This approach not only improves students' academic understanding but also develops critical thinking and problem-solving skills useful in everyday life. Therefore, the application of contextual PBL should be expanded, as it supports meaningful learning and prepares students to face complex challenges.

Mathematics learning that occurred in SMP Negeri 5 Kerinci still centered on the teacher. Teachers tend to give concepts and formulas and how to use them, resulting in low student learning outcomes. This study aims to improve understanding of concept and problem solving ability of mathematics through cooperative type model of TPS. The research is classroom action research with 2 cycles.The subjects of this study are the students of class IX C SMP Negeri 5 Kerinci amounted to 21. This class is chosen as the subject of research because the researchers teach the class, the concept understanding and solving the mathematical problems of students are still low, the lack of attention of students in learning mathematics, and viewing the learning of mathematics is a difficult lesson and the activity of students in the classroom is limited to listening, recording and working on the problem The results showed the application of cooperative learning model type Think-Pair-Share can improve concept understanding and mathematical problem solving and based on the result of questionnaire and the interview given can improve the motivation of studying student of class IX C SMP Negeri 5 Kerinci.

Understanding mathematical concepts is a basis for students in understanding mathematic lesson. By a good understanding of mathematical concepts, students are able to solve problems, especially mathematic problem. Unfortunately, there are still many students who do not understand the important of understanding mathematical concepts. The purpose of this study is to determine 1) The effect of independence and learning creativity on understanding mathematical concepts simultaneously, 2) The effect of learning independence on understanding mathematical concepts, 3) The influence of learning creativity on understanding of mathematical concepts. The number of samples in this study was as many as 89 students at North Jakarta Junior High School in academic year 2021/2022 with proportional random sampling. Based on the results of the hypothesis, it can be concluded that 1) There was a significant effect of independence and learning creativity on understanding mathematical concepts together. This was evidenced by the Sig value of 0,000 <0,05 and Fcount of 62,542. 2) There was a significant effect of learning independence on the understanding of mathematical concepts. This was evidenced by the Sig value of 0,000 <0,05 and tcount of 4,307. 3) There was a significant effect of learning creativity on understanding mathematical concepts. This was evidenced by the Sig value of 0,000 <0,05 and tcount of 3,837.

Visual Representations in Mathematical Word Problem Solving Among Form Four Students in Malacca

Lack of understanding of students' mathematical concepts in restating a concept, classifying objects according to specific properties according to the concept, giving examples and not examples of a concept, presenting concepts in various forms of mathematical representation, developing the necessary and sufficient conditions of a concept, and applying the concept or logarithm of problem-solving is a problem that is often encountered in students. This study aims to improve the understanding of the concept of the Pythagorean theorem of class VIII D even semester in SMP Negeri 1 Pleret, Bantul Regency. This type of research is Classroom Action Research (CAR). The research setting was class VIII D in the even semester of SMP Negeri 1 Pleret, Bantul Regency in the academic year 2019/2020, with 31 students. Data collection methods: observation, tests, interviews, and field notes. Research instruments: observation sheets, Pythagorean concept understanding test questions, interview guidelines, and field notes. The test instrument used was the content validity test. Data analysis using descriptive qualitative. The results showed that learning mathematics using the Jigsaw cooperative learning model could improve students' understanding of concepts. The average percentage of understanding concepts can show this: (1) the average percentage of understanding of concepts based on observations in the first cycle was 87.50% with moderate criteria, then increased cycle II to 93.75% high category. (2) the average percentage of concept understanding based on concept understanding tests in the first cycle was 59.34%, and then it increased in cycle II to 74.13%. The results of interviews with students showed that students enjoyed learning using the Jigsaw cooperative learning model.

This journal is motivated by students who still find it difficult to solve mathematical problems in the form of problems that lead to an understanding of the concept of a certain subject, so that students cannot answer the questions perfectly. The students' difficulties can be seen from the answers of students working on the concept of understanding problems given. Another situation that is also still happening in the field is the lack of awareness of students about the importance of learning mathematics, for example, there are still some students who when learning mathematics are just sitting in class without taking notes on the material. This is due to a lack of confidence, a sense of responsibility and initiative from students during the teaching and learning process. To overcome the above problems, and to improve students' understanding of concepts and Self-Regulated Learning, various efforts can be made by using a learning model that can actively involve students in learning. One of the learning models that can be used is the jigsaw-type cooperative learning model. Related to this, the researcher tried to conduct research on the influence of the jigsaw-type cooperative learning model on the understanding of mathematical concepts and Self-Regulated Learning of grade students. This type of research is a type of pre-experimental research. This study uses the research design of The Static Group Comparison. The population of this study is all grade VIII students of SMP Negeri 1 Bukittinggi in 2023/2024. The sampling technique used is random sampling first carried out normality tests, homogeneity tests, and average similarity tests of population data. The samples in this study are class VIII.A as the experimental class and class VIII.B as the control class. The research instruments used are Self-Regulated Learning questionnaires and tests for understanding mathematical concepts. The data analysis technique used is the t-test. The results of the study found that bakaghu religious activities have a deep meaning Based on the analysis of the data of the research results, it was obtained that the understanding of mathematical skills and Self-Regulated Learning of students who participated in learning with the jigsaw method was better than students who participated in learning with conventional methods in grade. The average score of the experimental class was 3.31 and the control class was 2.26. Meanwhile, the overall final average score in the experimental class was 57,54 and the control class was 45,04.