Creating an enjoyable atmosphere and fostering creativity are the two most required components in learning mathematics. Hence, creativity would enable students to formulate something new. In addition, creativity is one of the most important and highest competencies in Bloom's latest taxonomy. Furthermore, it is necessary to be possessed by everyone including prospective teachers. Not only for producing products in the form of objects, but the term creative also refers to problem solving in mathematic problems. This research is conducted to obtain a detail description regarding the impact of 3CM learning model among blended learning toward the enhancement of students' creative thinking skills in mathematical problem solving. To achieve this goal, a pre-experimental design with one group pre-test post-test design pattern is chosen. Creative thinking skills are measured by test techniques and are emulated with observation techniques. Observations were performed when students worked on the test. The impact of 3CM learning with blended learning seen from test results paired sample T tests with the help of SPSS program a that are acquired from close ended questionnaire techniques. The results show that the average of pre-test is 60.51 and the average of post-test is 75.96. As for the results of paired T tests is the test got sig value (2-tailed) 0.000, and hence there was a significant gap among the results of pre-test and post-test. All of these results imply that 3CM learning within blended learning is undoubtedly able to increase students' creativity in solving mathematical problems. This is due to the learning situation and activities which push students to do systematic thinking. It was started by criticizing the enchanting contextual problems, creating creative products based on particular mathematical concepts, and ended by having meaningful reflection.
The purpose of this research was to describe the positions and causes of students' errors in algebraic thinking based on the cognitive style. This study was qualitative research with subject consisting of twelve students. The results showed that (1) students with Field Independent type tended to make errors at the stage of comprehension, transformation, and process skills while students with Field Dependent type tended to make errors at the stage of comprehension, transformation, process skills, and encoding; and (2) the causes of errors were the students' incomprehension that related to the purpose of the problem, the lack of understanding that related to mathematical modelling, the lack of students' accuracy, the students' inaccuracy of using knowledge to convert an equations to the equivalent equation, student's inability to calculate the solution of an equations, students deviated from the formula that they used before and the students' incomprehension that related to the unit of measurement in mathematics.
AbstrakStrategi heuristik merupakan salah satu strategi pemecahan masalah matematika untuk mendapatkan hasil efektif. Penelitian ini bertujuan untuk menggali, mengelompokkan, dan menganalisis strategi heuristik berdasarkan modifikasi model Krulik dan Rudnik, sehingga dapat dijadikan dasar untuk memberikan pendampingan dalam pembelajaran. Penelitian ini merupakan penelitian kualitatif yang melibatkan 32 siswa SMP Muhammadiyah 4 Yogyakarta sebagai subjek penelitian. Variabel penelitian ini adalah indikator-indikator penggunaan heuristik model Krulik dan Rudnik, meliputi: read and think, explore and plan, select a strategy, find and answer, serta reflect and extend. Penelitian ini menggunakan metode kuesioner dan wawancara. Hasil penelitian menunjukkan bahwa: 2 siswa (6,25%) berada pada kategori baik dengan lebih sering melakukan semua strategi heuristik; 21 siswa (65,62%) berada pada kategori cukup dengan melakukan sebagian strategi heuristik; dan 9 siswa (28,13%) berada pada kategori kurang menunjukkan penggunaan strategi heuristik. Pada semua kategori, indikator find and answer lebih sering dilakukan siswa sedangkan indikator explore and plan masih jarang dilakukan.Kata Kunci: pemecahan masalah matematika, strategi heuristik, model Krulik dan Rudnik Abstract Heuristic strategy is one of the mathematics problem solving strategies to gain effective results. This research aimed to analyze the use of the heuristic strategies based on the modification of the Krulik and Rudnik model. This research discovered and classified the students' heuristic strategies which can be used as a basis to provide assistance in the learning. This research was a qualitative research involving 32 students of SMP Muhammadiyah 4 Yogyakarta as its subjects. The research variables are the indicators of the Krulik and Rudnik heuristic models which the students performed including: read and think, explore and plan, select a strategy, find and answer, as well as reflect and extend. The data was taken through questionnaire and interview methods. The result suggested that: 2 students (6.25%) were in the good category as they did all of the heuristic strategies more often; 21 students (65.62%) were in the fair category since they implemented some indicators of the heuristic strategies; and 9 students (28.13%) were in the poor category since they were lack in implementing the heuristic strategies. In all categories, indicator of find and answer was more oftenly done by the students while the indicator of explore and plan was less done.
Purpose This study aims to describe how creative thinking ability could be improved through correcting the thinking schemata using cool-critical-creative-meaningful (3CM) learning model. Design/methodology/approach This study implemented mixed methods with explanatory sequential, which means a study that was conducted by collecting quantitative and qualitative data, consecutively. The creative thinking ability was measured through tests and then triangulated with the student teachers answers in the interviews. The qualitative data consisted of creative thinking schemata that were collected with task analysis and think aloud method. The data were analyzed in two stages. Quantitative data analysis was used to identify the effectiveness of 3CM learning. Qualitative data analysis was conducted using Miles and Huberman’s analysis. Findings The findings presented that 3CM learning model is significantly effective to improve the creative thinking ability of pre-service primary teacher; students with formal, content and linguistic schemata that are good and complete will also have good mathematical creative thinking ability; the mathematical creative thinking ability of student is determined by the completeness of their schemata; and a good and complete schemata (formal, content and linguistic) will help the students to produce several problem-solving alternatives. Research limitations/implications Because of the chosen research approach, the research results may lack generalizability. Therefore, researchers are encouraged to test the proposed propositions further. Practical implications The results of this study suggest lecturers to give their students a great opportunity to develop their creativity in solving mathematical problems. Lecturers could give the students the opportunity to think systematically by beginning by criticizing the interesting contextual problems and ending with meaningful reflection with adequate learning resources. Originality/value 3CM learning model is a model that is proven to be effective in helping the students in shaping the thinking schemata well and able to improve the creative thinking ability of the students.
This study aims to describe and test the effectiveness of 3CM learning model with blended learning to improve students' creative thinking ability in solving mathematic problems. A pre experimental design with one group pre-test post-test design pattern was applied in this study. Creative thinking ability is measured by test technique and then in triangulation with observation and interview. Students were given a test, observed when solving the problem, and interviewed based on the answers given. To see the effectiveness of 3CM learning with blended learning done with paired T test with assisted with SPSS program then triangulated with observation and interview. Based on the test results, it obtained the average pre-test 60.51 and post-test 75.96. Result of paired T tests, test got sig value. (2-tailed) 0.000 means there was a significant difference between pre-test and post-test results. It indicated that 3CM learning with blended learning effectively improves students' creative thinking ability in solving problems. This happened because learning gives students the opportunity to think systematically by beginning by criticizing the interesting contextual problems and ending with meaningful reflection with adequate learning resources both when face-to-face and online.
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