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Creativity is often seen as one of the fundamental aspects of character education. As one of the 21st century skills, creativity has also been considered as an important goal of education across the world. This paper reports a study on promoting mathematical creativity through the use of open-ended mathematics problems. A total of 53 undergraduate students participated in the study. These students worked on open-ended problems in two types, i.e. bare mathematics problem and contextual problem. The contextual problem was presented in the form of paper-based and Geogebra-based. The students’ works were analysed qualitatively in order to describe how students’ mathematical creativity developed. It was found that the open-ended problems successfully promote students’ creativity as indicated by various solutions or strategies that were used by students to solve the problems. The analysis of students’ works show that students’ creativity developed through three kinds of exploration, i.e. (1) exploration of contexts, (2) exploration of software features, and (3) exploration of mathematics concepts. The use of metacognitive questioning was found to be helpful to develop the first two explorations into mathematical exploration.
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Teacher is an important component determining the success of education. In order to improve the quality of teachers, the Indonesian government has established a number of policies such as the Teacher and Lecturer Act of 2005 (UU Guru dan Dosen) and the Government Regulation No. 74/2008 that sets the academic qualification for teacher. Nevertheless, the results of the Competence Test for Teacher (Uji Kompetensi Guru) indicate the low competences of Indonesian teachers. Considering these facts, this study is aimed to develop instruments to assess the competences of prospective mathematics teachers participating in the Professional Education Program for Teacher (PPG). These instruments could provide early indication for improving the quality of teachers. This study employed a research and development approach; in particular the ADDIE model. The phases of this study comprised: (1) analysis phase for identifying the needs and content material; (2) design phase which dealt with constructing the indicators of the instrument; (3) development phase at which the indicators were elaborated into test items; (4) implementation of the prototype of instrument; and (5) evaluation that was aimed to evaluate the quality of the instrument. The subjects of this study were 70 students at Program PPG.
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The effectiveness of the realistic mathematics education approach for self-efficacy
The purpose of this study was to investigate the effectiveness of a realistic mathematics education (RME) approach for self-efficacy. The study was conducted with a quantitative methodology via a non-equivalent control group quasi-experimental design. The sample of 65 students enrolled in two eighth grade classes of a middle school in Indonesia, especially Bantul, was included in this study. One of these classes was randomly assigned to be the experimental group and instructed by means of RME, whereas the other class was assigned to be the control group and instructed by means of traditionally designed instruction. The instrument used in this study was self-efficacy questionnaires. Data analysis was done with the t test. The results of this study prove that RME is effective at developing self-efficacy.
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Designing hypothetical learning trajectory based on van Hiele theory: A case of geometry
This study is aimed to develop a hypothesis of learning trajectory based on the van Hieletheory which can assist students in comprehending the volume of cuboid. This study used design research to create a hypothetical learning trajectory for students to learn the volume of cuboid. Out of the three stages of design research, this study focused on the first stage, i.e. preliminary design because the main focus was to develop a sequence of learning activities to learn the volume of cuboid on the basis of van Hieletheory. The results of this study is a HLT on discovering the concept of volume of cuboid. This HLT consists of four stages of van Hiele, i.e. 1) visualization stage at which students discover the volume of cuboid by counting a number of unit cubes construct the solid; 2) analysis phase at which students identified the volume of cuboid by looking for the length of edges without counting unit cubes; 3) informal deduction stage at which students find out the volume of cuboid by looking at the length of the sides, 4) deduction phase at which the students discovered the general formula of volume for all types of cube, and cuboid.
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The Development of Student Worksheet Based on Realistic Mathematics Education
This study is aimed to develop student worksheet based on Realistic Mathematics Education for the topic of circle for the eighth-grade of junior high school. The study type was development research using the ADDIE model comprising analysis, design, development, implementation, and evaluation. The developed product was validated by experts and tested for its practicality by mathematics teachers and students. The product of this study is a set of students worksheets based on RME for the topic of circles. The worksheet has the following characteristics: using real-world context, facilitating mathematization process, facilitating interactivity and integrated learning. The results of validation and try out indicate that the worksheet was valid and practical.
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Diagnosing students’ learning difficulties in the eyes of Indonesian mathematics teachers
Teachers’ diagnostic practice on students-difficulties is one of the important steps in designing and managing classroom lessons. The purpose of this study was to explore teachers’ perception and practices regarding diagnosing students’ learning difficulties. The participants of the study were 28 Indonesian mathematics teachers of Junior High School. The data was collected through a Focus Group Discussion and a teacher questionnaire. The data were analyzed qualitatively to describe how the teachers perceive learning difficulties and how the teachers diagnosed students’ learning difficulties. The results of the analysis reveal that the teachers do not yet perform an in-depth diagnosis of students’ difficulties in learning mathematics. The teachers only focus on the mathematics topics and non-mathematical issues, instead of on students’ thinking process. The teachers also do not differentiate the diagnosis, evaluation, and prediction test. With regard to the strategies used by the teachers to diagnose students’ difficulties, analyzing students’ responses to tests was the majority. In this respect, observing students’ learning process during classroom activities is rarely done by the teachers in the purpose of diagnosing students’ learning difficulties. The results of the diagnosis are mainly used as the basis for remedial and drill and practices. The results imply that more support is needed for teachers to improve their competences particularly in diagnosing students’ thinking process difficulties when learning mathematics.
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Student worksheet based on realistic mathematics education: How the effect toward reasoning ability?
The aim of this research is to know the effectiveness of students’ worksheet based on Realistic Mathematics Education toward reasoning ability. The research was conducted with a quantitative methodology via non-equivalent control group quasi-experimental design. The population is the eight grade students of middle school in Pangkalpinang, Indonesia. The experimental class is treated by using students’ worksheet based on RME and the control class is treated by using the conventional students’ worksheet. The instrument used in this research is reasoning ability test. Data analysis is done with t test. The results of this research proves that students’ worksheet based on Realistic Mathematics Education is effective toward reasoning ability. RME has the characteristics that are starting learning by using real-world context, construct student knowledge, using mathematization process, the existence of student interactivity and integrated learning.
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Mathematical thinking is an important aspect of mathematics education , also needs to be understood by prospective teachers. Prospective teachers should have the ability to analyze and interpret students’ mathematical thinking. Comparing model is one of the interpretation models from Wilson, Lee, and Hollebrands. This article will describe the prospective teacher used the model of the building process in interpretation students’ mathematical thinking. Subjects selected by considering them in following the students’ strategies in solving the Building Construction Problem. Comparing model is a model of interpretation in which a person interprets student thinking based on student work. There are two types comparing model building process prospective teacher use in interpreting students’ mathematical thinking ie. comparing work and comparing knowledge. In comparing works, prospective teachers use an external representation rubric. This is used to analyze student activities in order to provide an interpretation that is comparing the work of students with their own work. In comparing knowledge, prospective teachers use internal representation rubrics to provide interpretation by comparing the students’ work with their knowledge or thought.
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Mathematical creativity is very important in this 21st century competition. This skill can be taught and facilitated through a supported textbook. There is a relationship between textbooks used and mathematics achievement of the students. To what extent students’ creative thinking can be seen in the tasks of the textbooks. This study compared the mathematical creativity for the topic of probability in Junior High School (JHS) Indonesian and Singaporean mathematics textbooks. Textbooks will be analyzed from the perspectives of originality, fluency, flexibility, and elaboration aspects. Indonesian mathematics textbooks and Singaporean mathematics textbooks both facilitate mathematical creativity. Indonesian textbooks can facilitate three of four aspect creativity and Singaporean mathematics textbooks two of four aspect creativity. There are many tasks that supported more than one aspect of mathematical creativity but all mathematics textbook were analyzed doesn’t support fluency aspect. Singaporean textbook has 18% task that facilitated mathematical creativity and Indonesian mathematics textbook has 10%. The finding showed that Singaporean textbooks more facilitate thinking of students’ mathematical creativity.
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Textbook is considered as a potentially implemented curriculum because it mediates between the intended curriculum and teachers’ classroom practices. Textbooks heavily influence the teaching and learning process that, consequently, implies students’ achievement. A number of studies show the relationships between students’ mathematics achievement and the textbooks they use during the learning processes. The present study reports a comparative analysis of Indonesian and Singaporean textbooks for the topic of the Pythagorean Theorem. An Indonesian mathematics textbook and a Singaporean mathematics textbook for junior high schools were analyzed. The results of the textbook analysis show that both textbooks used activities-based and context-related explanation section. Although Indonesian and Singaporean textbooks included context, the purpose of context in both textbooks were different.