The definition of creativity among professional mathematicians and the definition of mathematical creativity in the classroom context are significantly different. The purpose of this study was to investigate the relationship between students’ mathematical creativity (i.e., cognitive flexibility) and figure apprehension when solving geometric problems with novel auxiliary features such as straight lines and curved lines. In other words, this study determined if geometry knowledge influenced mathematical creativity (cognitive flexibility) in problem-solving. Grade-12 students participated in the intervention. The high school that is the research topic attempts to equip students with academic abilities and is, except for vocational schools, the most popular form of high school among all other types. Such a school was chosen for the study so that a significant proportion of students in Makassar could be represented. In this study, we discovered a relationship between cognitive flexibility and the geometric ability of pupils while solving problems involving auxiliary lines. This indicates that the usage of auxiliary lines as a reference for developing pupils’ creative thinking skills must be advocated. In addition, good geometric abilities (e.g., visual thinking, geometrical reasoning) will encourage pupils to generate various problem-solving concepts. This finding contributes significantly to future research by focusing on auxiliary lines.

The purpose of this study was to compile and statistically analyze the results of research studies that examined students' problem-solving skills in worksheets. The research method used was a meta-analysis. The study search was conducted from 2013 to 2022 in Google Scholar and the Garuda portal databases. The search yielded 40 studies that met the inclusion criteria for extraction from research and development, experimental, and quasi-experimental. From the extracted results, 45 comparisons of data were examined. Microsoft Excel was used to calculate the effect size of the problem-solving worksheet. This study yielded a value of 1.281 for the entire study, indicating that the worksheet had a significant and positive impact on students' problem-solving skills. The results indicate the need to develop worksheets to improve students' problem-solving skills.

The implementation of learning activities in schools has not provided opportunities or encouragement for students in developing their procedural knowledge. This research aimed to test the effectiveness of developing Bloom’s Taxonomy revision-oriented learning activities to grade IV elementary learners’ procedural knowledge capabilities and learning outcomes. This research used quasi-experiment with a quasi-experimental design which consisted of a posttest-only control design. The population of this study was sixth-grade students of 9 schools with an overall number of 229 students. The sample in the study was 50 students, there were 26 students from the experimental class and 24 students from the control class. A test method with 10 question items was used as a data collection method. The data analysis methods and techniques used were quantitative descriptive analysis and inferential statistical analysis. Then the data were analyzed using the MANOVA test assisted by the IBM SPSS Statistics 21.0 program. The hypothesis test results showed a significance value of .000 (Sig<.05). It can be concluded in procedural capabilities and learning outcomes between groups of students there is a significant difference from following learning by implementing Bloom's Taxonomy Revision oriented learning activities with the experimental and control group.

Teacher knowledge is one of the main factors in the quality of mathematics learning. Many mathematics teachers have difficulty using proportional reasoning. Proportional reasoning is one of the essential aspects of the middle school mathematics curriculum to develop students' mathematical thinking. Teachers should realize that developing proportional reasoning is not an easy task. In this study, we investigated how teachers give proportional reasoning about the concept of proportional and non-proportional situations, especially in making sense of them. The research subjects were mathematics teachers who had taught proportional-related material. Data was collected using task-based interviews outside the teacher's working hours. Data analysis and interpretation were completed using a framework meaning-based approach. The results of the data analysis showed that the teacher is careful in understanding information, is aware of multiple meanings, and knows key information in understanding the contextual structure of proportional and non-proportional situations. Furthermore, they are also able to identify additive and multiplication relationships, have flexibility in understanding proportional and non-proportional situations separately or collectively, and understand problem-solving systematics in detail.

The mathematical literacy ability of Indonesian pupils is still relatively low, as indicated by Indonesia's score of 379 for mathematical literacy in PISA 2018. Paying attention to the learning process such as the teaching materials used in learning, is one of ways to increase mathematical literacy skills. To strengthen students' mathematical literacy skills, it is great for building qualified mathematics teaching materials with the nuances of science, technology, engineering, and mathematics (STEM) which are supported by the information and communication technology (ICT)-assisted Preprospec (Prepare, Problem Solving, Presentation and Conclusion) Learning Model. The research method used in this study is research and development (R&D), with the main reference of 4D-model development by Thiagarajan, whose stages are limited to define, design, and develop. The results showed that the feasibility test on teaching materials obtained the total average percentage of validator I to validator V, respectively, 90.19, 95.45, 93.90, 91.95, and 97.95 with very eligible criteria. It is easy to understand by students with a readability score of ρ = .109 > α = .05 or Cochran's Q = 13.091, and it can improve students' mathematical literacy skills, as evidenced by the Wilcoxon test and a gain normalization result of 485.

This exploratory and descriptive study aims to theoretically promote the schema of pseudo-thinking processes in mathematical problem-solving by students. The participants in this study were 36 eighth graders and one math teacher. The researchers collected the data using tests and interviews. The results showed that the structure of pseudo-thinking based on the processes of assimilation and accommodation is theoretically composed of five hierarchical components, namely (a) the structure of the problem, (b) the structure of the subject's thinking, (c) the analytic process, (d) the integration of structures or substructures, and (e) the complete integration of structures. When the subject integrates incomplete substructures into existing thinking schemes, assimilation or accommodation becomes imperfect, resulting in cognitive disequilibrium. The results of such a thought process are called pseudo-thinking. Pseudo-thinking processes can be refined and improved into actual thinking processes through reflection and scaffolding. Assimilation and accommodation occur through defragmentation or organization to rearrange the internal schema so that full structural integration occurs. In the end, the subject experiences cognitive equilibrium so that it becomes an actual student thought process.

Active learning (AL) techniques invite students to participate actively, either physically or mentally, in the learning process so that they can change their behavior efficiently to achieve great achievement. Still, there is insufficient knowledge concerning the dimensions of AL techniques for business subjects of secondary school students in Malaysia. Thus, the research’s goal is to assist in the determination of the instruments’ reliability to measure the AL techniques measurement scale for business subjects’ students using exploratory factor analysis (EFA) as well as reliability analysis. Moreover, this research conducted a self-administered survey among secondary school students who have taken business subjects as their elective subjects. From secondary schools in Negeri Sembilan, Malaysia, 123 respondents were randomly chosen for the sample. To measure the AL constructs, the study retained 30 items developed because no items have been omitted since the factor loading turned out higher than the 0.50 cut-off point and was used as a tool for data collection. Essentially, this research empirically validates the dimension which helps lead to AL techniques in business subjects that are improved, and the findings are particularly beneficial to secondary school students in Malaysia.

Many education and learning experts currently recommend the flipped classroom model as an alternative to learning after the COVID-19 pandemic. This study aims to explore the impact of the flipped classroom model on social skills and problem-solving skills for cadets. This research used a sequential mix method involving 50 maritime students in semester 7 of the Engineering Study Program at the Maritime Sciences Polytechnic Makassar, South Sulawesi, Indonesia. Researchers used two main instruments, namely problem-solving skill tests and interviews. Furthermore, in the quantitative analysis, the researcher ran paired sample t-tests and one-way Multivariate Analysis of Covariance (MANCOVA) using the SPSS 25.00 program. In addition, researchers also analysed qualitative data from interviews using thematic analysis techniques. The results showed that the flipped classroom model proved to have a positive effect on the problem-solving skills of maritime students. Other findings state that the cadets also respond positively to the flipped classroom model. Researchers recommend that teachers use the flipped classroom model, especially in dealing with learning in the post-pandemic era, like today.

The incorporation of Computer Science teaching in educational systems has increased in recent years. Given international interest, Chile has promoted projects to promote the development of students' digital skills. Focusing on this new educational context, this research reports the results regarding the identification of computational concepts and practices that can be articulated with the contents and skills of the curriculum. of Chilean mathematics. for first grade of primary school based on the use of the Bee-Bot robot. For this, the study followed a qualitative approach, developing a case study of the Chilean study program with the content analysis technique and using, as analysis categories, computational concepts and practices from the field of educational computing. In total, 30 learning objectives of the study program were analyzed. The results indicate that, although there is little articulation between computational concepts and first grade content proposed in the curriculum, there is greater articulation between computational practices and mathematical skills suggested in the Chilean curriculum. It is concluded that Computational Thinking can be developed from the earliest school levels using the Bee-Bot robot (or similar), and this is demonstrated by the structure of the Chilean primary mathematics curricular program.

Mathematical modeling offers a promising approach to improving mathematics education. This study aims to determine if the concept of metacognitive awareness in the learning process is associated with mathematical modeling. This study also considers the interaction effect of sex and academic year level on both variables. Focusing the study on preservice elementary teachers might address potential issues and targeted intervention in their preparation program concerning their ability to teach and guide young learners in modeling activities. The research sample includes 140 preservice elementary teachers at Central Luzon State University, Philippines. Data collection used an adapted metacognitive awareness inventory and a validated researcher-made mathematical modeling competency test aligned with the K-12 mathematics curriculum in the Philippines. Results revealed that the preservice elementary teachers had a high metacognitive awareness and mathematical modeling competency, ranging from 22 to 31 out of 36 points. Besides, Factorial ANOVA indicates that academic year level positively affects both variables regardless of sex, and stepwise regression analysis unveiled that information management, declarative knowledge, and planning significantly predict 41.4% of the mathematical modeling competency variance. This suggests that developing metacognitive awareness supports preservice elementary teachers in performing modeling tasks that improve their competency level in mathematics.

This study examines the impact of digital tools on fraction comprehension among 5th-grade students with learning difficulties in mathematics. It assesses the effectiveness of three teaching methods: educational software, video tutorials, and their combination. The research involved 252 students from 8 state-funded elementary schools, employing a quantitative experimental design with pre- and post-test assessments. Grounded in Constructivist Learning Theory and Technological Pedagogical Content Knowledge (TPACK), this research explored how technology can enhance mathematical understanding. Results indicated that the combined method achieved the highest improvement (58%, p < .001, Cohen’s d = 3.03), significantly outperforming educational software alone (33%, p = .015, Cohen’s d = 2.52) and video tutorials alone (7%, p = .987, Cohen’s d = 0.14). These findings highlight the substantial benefits of integrating diverse digital tools to effectively support mathematics learning among students facing additional educational challenges.

This study aims to address students' low mathematical problem-solving skills and self-regulated learning by developing website-based mathematics learning media using the problem-based learning model. Learning that integrates website-based media allows for more independent learning activities in solving mathematical problems. This study uses the ADDIE model to test the validity, practicality, and effectiveness of the product. Website-based media met the validity criteria based on expert assessments with an average score of 137 from subject matter experts and 78.5 from media experts, and the research instruments were declared valid with an Aiken index ranging from 0.9 to 0.99. Website-based media meet the criteria for practicality based on an average teacher assessment of 90.5, an average student assessment of 50.1, and a learning implementation rate of 93%. Website-based media are proven to be effective through four indicators: (1) students who pass exceed the threshold of 80%. (2) One sample t-test results p-value <.05 and t-value >1.69, so that H_0 is rejected. This proves that website-based mathematics learning media are effective in improving students' mathematical problem-solving skills and self-regulated learning. (3) The results of the paired sample t-test show p-value <.05 and t-value >1.69, so that H_0 is rejected. This proves that there is a significant improvement in students' mathematical problem-solving and self-regulated learning abilities after using website-based mathematical learning media. This study is able to facilitate students' problem-solving and self-regulated learning abilities simultaneously in mathematics education.