Combinatorial thinking is an important reasoning process in building one's knowledge and experience. The purpose of this study is to describe the characteristics of the level of combinatorial thinking in solving mathematical problems. The subjects of the study were 40 students of Elementary Teacher Education Department (PGSD): 20 students of the second semester and the others of the sixth semester. The reason for choosing subjects from these two levels is to meet all levels of combinatorial thinking. All research subjects were given test questions about combinatorial problems. From 40 subjects, five students were selected to be interviewed as they had fulfilled all five levels of combinatorial thinking. The data validity was conducted by triangulation through recording interview results and comparing it with data from students' written test results to ensure the validity and reliability of this research. The results show that there are five levels of combinatorial thinking in solving mathematical problems: investigating “some cases’, systematically checking cases, using the calculation order, systematically generating all cases, and changing the problem into another combinatorial problem. Level one is the identification of the possibility of students’ understanding the questions incorrectly, or vice versa, already can answer the questions with systematic procedures but the results are less precise. Level two is conducting systematic checking about students' understanding of the combination material. Besides, it also concerns about the ability to answer problems systematically using diagram trees. Level three is students are able to apply the calculation orders, which are addition and multiplication. Level four is systematically generating all cases about the ability to calculate possibilities without schematic, drawings, or diagrams. Level five is changing the problem into another combinatorial problem, it is the ability to calculate possibilities with complex problems Based on the research findings, it turns out there is another level of combinatorial thinking, which is using the calculation order and this is found between level two and level three. The researchers recommend further research to explore more on the application of calculation order.
This article describes gifted children’s mathematical reasoning abilities. They have a natural talent that must be facilitated, namely reasoning. In mathematics, problem-based learning, project-based learning literacy and Inquiry are learning models commonly used. Mathematics learning can improve the ability of mathematical reasoning because children are required to think logically. The research method was quantitative with the randomized pretest-posttest control group design. This research was conducted in three special classes of gifted children. The results showed that the reasoning of gifted children who obtained problem-based learning was better than gifted children who received other learning. It was caused by activities that always present problems contextually with everyday life. Then, gifted children were still required to be problem solvers by conducting in-depth investigations and collaborating with friends. Gifted children who get project-based learning literacy have good mathematical reasoning skills. It was because gifted children were required to make literacy work oriented to the mathematical problems presented. Furthermore, gifted children who obtain inquiry learning have a middle ability. Gifted children were asked to find mathematical concepts so that learning is meaningful.
This research was motivated by the variation of e-learning in 21st-century education used in elementary schools during the corona pandemic. The study aimed to determine the differences in the effectiveness of e-learning variations based on Google Classroom and Edulogy in elementary school students about Higher Order Thinking Skills (HOTS) in the corona pandemic. This type of research was quantitative, with quasi-experiment the Posttest-Only Control-Group design. The subjects in this study were 38 students of grade V elementary school in the even semester of the academic year 2019/2020. Data was collected using interviews and test instruments in the form of problem descriptions to test the ability to do HOTS questions. The results showed that the value of Sig. (2-tailed) = 0.011 was smaller than α = 0.05 which indicates that H0 is rejected and Ha is accepted. It was implied that there were differences in posttest results between e-learning based on Google Classroom and e-learning based on Edulogy that affect the effectiveness of e variations-learning. The features of Google Classroom such as assignment, grading, communication, time-cost, archive course, privacy, and mobile application facilitate the learning process of blended learning methods.
Mathematical communication is one of the important abilities for students to face the challenges in this era. The fact-based on the preliminary study conducted by researchers on students in elementary school showed that most students find difficulties in communicating mathematical ideas. The present study is aimed to describe whether the improvement of mathematical communication ability of students who learn through project-based learning using mind map technique is better than the improvement of mathematical communication ability of students who learn through project-based learning without mind map technique. This study used a quasi-experiment using a non-equivalent group design. Sixty-three students of one of the elementary schools in Bandung city were taken as subjects of this study. The instrument of this study used mathematical communication test. The data were analyzed using non-parametric statistics. The result showed that the improvement of mathematical communication ability of students who learn through project-based learning using mind map technique is better than the improvement of mathematical communication ability of students who learn through project-based learning without mind map technique.
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