Efforts to overcome students’ learning difficulties in geometry: A didactic design of creative thinking skills through metacognitive approaches

Developing students' creative mathematical thinking skills is essential for problem-solving and innovation in mathematics education. GeoGebra, as a dynamic geometry software, has been widely used to support conceptual understanding and visualization. However, limited studies have explored its impact on creative mathematical thinking in schools with different characteristics. This study aims to analyze and provide an overview of the improvement in students’ creative mathematical thinking skills using GeoGebra software in schools with different characteristics. This research uses a quasi-experimental method with a pre-test and post-test design without a control group. The sample consists of 90 eleventh-grade students from three high schools in Padang City. Data were collected through tests of creative mathematical thinking skills and classroom observations. Statistical analyses, including Wilcoxon and t-tests, were conducted to measure the significance of changes in students' creative thinking skills. The results indicate that most aspects of creative thinking skills showed significant improvement, particularly in originality and flexibility, although there was a decline in some aspects, namely fluency and elaboration, in these schools. The Wilcoxon and t-test analyses showed a significant difference (p < 0.05) between students' pre-test and post-test creative mathematical thinking scores. Therefore, there is an improvement in students’ creative mathematical thinking skills after learning using GeoGebra. This study demonstrates that integrating GeoGebra into mathematics instruction enhances students’ creative mathematical thinking. The results suggest that GeoGebra can be an effective tool for fostering creativity in mathematics education. Future research should focus on addressing the decline in fluency and elaboration to optimize its implementation.

High self-confidence and creative mathematical thinking skills will change students from having difficulty with mathematics to active learners who can solve mathematical problems. But the facts show that the achievement of both abilities is still quite low. The purpose of this research is to analyze how students' creative mathematical thinking skills are viewed from the perspective of self-confidence in social arithmetic material. Social arithmetic material is used because it allows them to abstract mathematical processes into their daily lives, thereby developing their creativity. The research method is descriptive qualitative. The sample was 3 people, namely 1 person for each level of self-confidence (high, medium, and low). They are selected through purposive sampling. The data collection techniques used include questionnaires, tests, interviews, and field notes. The data analysis techniques employed are data reduction, data presentation, and conclusion drawing. The results indicate that students' self-confidence levels in social arithmetic material affect their creative mathematical thinking skills. It was found that students with high self-confidence were able to meet three indicators of creative mathematical thinking skills: fluency, flexibility, and elaboration. However, students with high self-confidence were not able to meet the originality indicator. Students with moderate self-confidence were able to meet one indicator of creative mathematical thinking skills, namely fluency, but were not able to meet the flexibility and elaboration indicators. Meanwhile, students with low self-confidence were not able to meet any indicators of creative mathematical thinking skills. Thus, self-confidence can be increased to improve mathematical creative thinking skills.

Creative thinking and problem-solving skills are needed to face the 21st century of 4.0 industrial revolution. Improving the quality of human resources to face the era of the industrial revolution 4.0 must be developed in education. Biology as one of the subjects in high school, especially in plant growth and development matters, allows to develop creative thinking and problem-solving skills because in it there is a student project on plant growth and development. It takes the right instrument to measure the achievement of creative thinking skills and problem solving skills in Biology learning, especially on the topic of plant growth and development. Two instrument questions have been developed, namely the instrument for creative thinking skills and problem solving skills. The development of this instrument was carried out through the stages of Research and Development Borg and Gall 1983. It produced 10 essay questions measuring creative thinking skills and 8 questions measuring problem solving skills. The question gets very decent expert validation criteria with a score of 91% - 97%. The results of the validation test based on the Pearson Product Moment formula show that the ten items of creative thinking skills are valid with a significance level of 0.05. The reliability test of the two instruments has a result of 0.82, above Cronbach's Alpha coefficient, which is reliable for creative thinking skills instruments. Meanwhile, the instrument of problem solving skills showed very reliable results with Cronbach's Alpha value of 0.95.

This study aims to investigate how PjBL via traditional games impact students’ critical thinking, creative thinking, and collaborative skills. The research sample is a local school in Semarang. The research design was a quantitative study using the pre-experimental design type one group pretest-posttest method. There is only one predetermined group in this design. The theme of the game that the project will create was revealed following the pre-test. The research results show students’ creative thinking skills in applying the PjBL model via game techniques are 61.53% in high criteria and 38.46% in medium criteria. The study results also show a fair increase in the N-Gain value for the four indicators of creative thinking skills: improvisation, elaboration, creativity, vision, effectiveness, and efficiency. The results show it is effective for six students (25%), fairly effective for 13 students (54.16%), and less effective for five students (20.83%). The study’s results also show that the Mann-Whitney U statistical test is 69. It means that the PjBL model impacts students’ collaborative skills. This research has a big impact on increasing students’ creative thinking skills and collaboration.

One important aspect of education in the 21st century is developing students' creative thinking skills. The development of creative ideas is usually related to a person's socio-cultural. One of the cultural heritages in Lamongan is batik Sendang. Batik Sendang motifs can make students to explore, so that students can grow their creativity. Therefore, ethnomathematics plays an important role in connecting culture with mathematics learning to foster student creativity. This research aims to analyze and describe students' creative mathematical thinking skills in solving problems designed with the application ethnomathematics batik Sendang. The subjects of this research consisted of four students in class IX at MTs Tarbiyatus Shibyan Lamongan who were classified according to the criteria for creative thinking skills, namely low, medium, high, and very high. The results of this research show impressive things. That is 70.59% of students show high to very high creative thinking skills. Meanwhile 29.41% of students show low and medium creative thinking skills. It is hoped that the results of this research can help researchers and teachers to determine measuring tools or methods to improve students' creative thinking skills, one of which is ethnomathematics of batik Sendang.

Facts in the field show the low creative thinking skills of students. Students' difficulties in understanding the material lead to low creative thinking skills. The background of this research in the era of the Industrial Revolution 4.0, students are expected to have creative and solution-oriented thinking skills, so they are able to solve various everyday problems intelligently and productively. The purpose of this research is to develop an electronic module based on Science, Technology, Engineering, and Mathematics (STEM) to improve students' creative thinking skills in motorcycle electrical systems in State Vocational High Schools. The research method used is development research with the ADDIE model. The research subjects were grade XI students in State Vocational High Schools. Data analysis techniques in this study used qualitative and quantitative methods. The results of the creative thinking skills improvement test showed an N-Gain score of 0.45, which is included in the moderate category. Media expert validation results 86.25%, material expert validation 87.50%. The conclusion of this study is that the STEM-based motorcycle electric E-module is feasible to use and can improve creative thinking skills in State Vocational High Schools. This research provides implications that the development of an electronic module based on Science, Technology, Engineering, and Mathematics (STEM) in motorcycle electrical systems can be a reference for teachers in improving creative thinking skills in terms of content, strategies, methods, and teaching approaches.

This study examined the effectiveness of using project-based learning (PBL) for the teaching of home economics and determine its impact on the development of students’ creative thinking and problem-solving skills. To achieve the objectives of the study, the researchers used the quasi-experimental approach. Pre- and post-intervention tests were conducted with two (experimental and control) groups of third-grade intermediate female students. Two tests were administered: one to test the students’ creative thinking skills, and the other to test their problem-solving skills. The control group were taught a home economics unit by conventional teaching methods; the experimental group were taught using the PBL approach. The following materials and tools have been prepared by the researchers: a proposed educational program based on project-based learning (PBL), a test of creative thinking skills, and a test of problem-solving skills. The findings revealed that there were statistical differences (0.05) between the mean scores for the pre-PBL and post-PBL tests, indicating that PBL significantly improved the students’ creative thinking and problem-solving skills. Several recommendations and suggestions are offered based on the findings.

Creativity and creative thinking are considered as innate skills developed under positive environmental conditions, stagnating or dulling under negative environmental conditions. Creativity and creative thinking skills, which can be improved with education, have taken their place among the general aims of education in our country. Many factors especially such as family and social and physical environ-ment, school, curriculum, teacher etc. affect the development of individuals' creativity and creative thinking skills. This review study was conducted in order to compile and present the basic information in the literature about creativity and creative thinking. First of all, definitions related to creativity concept were given and the approaches that originated from these definitions were examined in the scope of the study. Then, features of creative individual, misunderstandings about creativity, dimensi-ons and stages of creativity were given. The factors that prevent creativity were discussed after mentio-ning the relationship between the concepts of intelligence, age, brain, divergent thinking and imagina-tion. On the other hand, definitions of thinking and thought concepts are given and information about creative thinking which is one of the high level thinking skills is presented. In addition, the ways of facilitating the development of creative thinking, learning-teaching environments, teacher characteris-tics are mentioned, and the duties of parents and the environment to develop and support creativity are explained. It is hoped that this study which can be considered as “a brief handbook of creativity and creative thinking” will contribute to the literature, the creativity of individuals and the development of creative thinking skills.

This study aims to analyze the effect of applying problem-based learning with a STEM approach integrated with local culture (STEM-PBL-local culture) on improving creative thinking and problem-solving skills and determine the relationship between creative thinking and problem-solving skills. This research is an experimental study with a pretest-posttest non-equivalent control group design. A total of 72 prospective teachers who attended introductory chemistry courses at teacher education institutions were selected by purposive sampling. The test instrument is validated open-ended questions. Data analysis used an independent t-test. Pearson's product-moment correlation test is used to determine the relationship between problem-solving and creative thinking skills. The results show significant differences between the experimental and control groups. Students in the experimental group who received STEM-PBL-local culture experienced an improvement in creative thinking and problem-solving skills in the medium category, while the control group experienced an improvement in the low category. The Pearson product-moment correlation test shows that creative thinking and problem-solving skills have a significant relationship with a high level of correlation.

Science learning in elementary schools using the PBL learning model can grow students' higher-order thinking skills, such as problem-solving and creative thinking skills. The purpose of correlational research was to analyze the relationship between problem-solving and creative thinking skills of elementary school students through the implementation of PBL. The predictor variables and criteria in the research were in the form of problem-solving and creative thinking skills, respectively. The population of this study was the fifth-grade elementary school students, totaling 120 students. This study’s sample was 33 students. The data retrieval used problem-solving and creative thinking skills tests on the concept of the human circulatory system. The data analysis was performed by linear regression. The results showed a correlation between creative thinking and problem-solving skills in learning with PBL. There is a strong relationship between problem-solving and creative thinking skills through PBL. The predictor variable contributed 37.8% to the criterion variable. This study recommends that it is essential to familiarize PBL in elementary schools learning to improve students' higher-order thinking skills.

Metacognition is influenced the creative thinking process in Computational Physics courses. The Computational Physics is needed in the business and industrial. However, Computational Physics courses are less attractive for students. The challenge in learning Computational Physics is how to help students effectively develop creative and computational thinking skills. Based on the above, the purpose of this study is to determine the effectiveness of the PGOC3ARE learning model to create the students’ creative thinking skills in Computational Physics learning and to determine the effect of using the PGOC3ARE learning model on metacognitive-based creative thinking skills, especially in Computational Physics courses. The research method used was an explanatory sequential design research method. The research sample was taken through simple random sampling, where the sample was divided into an experimental class and a control class. The sampling technique for collecting qualitative data was purposive sampling. Data analysis using comparative test statistics. The result of the research is that the PGOC3ARE model is effective in shaping students’ creative thinking skills, especially in the Computational Physics course. Furthermore, the PGOC3ARE learning model has a significant positive effect on the development of students’ creative thinking skills in the Computational Physics course with base on metacognition.

This study aimed to determine whether there is a simultaneous difference in students' creative thinking and collaboration skills when using the Problem-Based Learning (PBL) model integrated with Team Assisted Individualization (TAI). The research employed a quasi-experimental design with a posttest-only control group design. The study population comprised tenth-grade students at SMA N 7 Surakarta during the 2023/2024 academic year. The sample included control and experimental classes selected through cluster random sampling. Data were collected using a creative thinking skills posttest, collaboration observation sheets, and documentation. The hypothesis was tested using MANOVA. The data analysis revealed that the creative thinking and collaboration skills of students in the experimental class were higher than those in the control class. The hypothesis test results indicated that the significance value was 0.021 (sig = 0.021 0.05), leading to the rejection of H0. This finding signifies that there is a simultaneous difference in creative thinking and collaboration skills when applying the PBL model integrated with TAI. It is concluded that the PBL model integrated with TAI creates a significant difference compared to the PBL model alone in fostering students' creative thinking and collaboration skills.

The ability of creative thinking and mathematical communication is important in learning mathematics. However, in fact mathematics learning in schools today has not shown an optimal effort to help students develop creative thinking skills and mathematical communication skills. The purpose of this study is to examine the use of open-ended questions in mathematics learning and in the evaluation of mathematics learning to support the ability of creative thinking and mathematical communication skills of students, this will be implemented in the perspective of literature review. The type of research used is a systematic and structured literature review, where researchers synthesize relevant study results from international and national literature through Google Scholar, Eric, DOAJ, Scopus and ScienceDirect. Based on the analysis results obtained that mathematical learning using open-ended questions is effectively used to support the ability of creative thinking and mathematical communication skills of students; the provision of open-ended questions can be familiarized with providing learning methods leading to an open-ended approach; the test in the form of open-ended questions can be used as a tool to measure the ability of creative thinking and mathematical communication skills of students; the use of open-ended question can be applied to all levels of education; and the need for high creativity from teachers to prepare learning by applying open-ended questions.

Atoms, ions and molecules are considered as abstract concepts that often lead to students’ learning difficulties. Th is study aimed at providing description of pre-service science teachers (PSTs)’ creative thinking skills on atoms, elements and compounds digital media creation. Qualitative descriptive method were employed to acquire data. Instruments used were rubric of PSTs’ digital teaching media, open ended question related to PSTs’ technological knowledge and pre-test about atoms, ions and molecules that were given to eighteen PSTs. The study reveals that PSTs’ creative thinking skills were still low and inadequate to create qualified teaching media of atoms, ions and molecules. PSTs’ content and technological knowledge in regard with atoms, ions and molecules are the most contributing factors. This finding support the necessity of developing pre-service and in-service science teachers’ creative thinking skill in digital media that is embedded to development of technological content knowledge.

Education is a major component in national development that functions as a means of developing human resources. In the 21st century, technological advances facilitate access to education, but there are still challenges in improving students' knowledge and skills. The modern learning paradigm emphasizes creative, analytical, cooperative and collaborative thinking skills. Students' creative thinking skills in Indonesia are still lacking. Many factors hinder students' creative thinking abilities, including conventional or teacher-centered learning methods. The Treffinger learning model is proposed as a solution to improve students' creative thinking skills with three important elements: independent learning, idea generation, and creativity. This study aims to analyze the urgency of improving creative thinking skills through treffinger learning. This study uses a qualitative method through a systematic review with data obtained from a literature review. To achieve the research objectives, relevant sources are needed to answer the research questions and other related references are collected through the search process. Furthermore, the analysis is carried out by collecting various scientific journals and books related to the research variables. The results of the literature review study indicate that treffinger is independent learning, the main key is finding concepts or information through events experienced by students during teaching and learning activities. From the results of the analysis of several references obtained, it is known that this treffinger learning makes the subject matter easier to understand and remember the material. In its application, the treffinger learning model integrates cognitive dimensions and effectively finds the direction of problem solving to be taken. The results of the analysis can be concluded that Treffinger learning is effective in improving creative thinking skills in all subjects and can be applied to students and college students.