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Comparison of Modelling Tasks in Indonesian and Singaporean Mathematics Textbooks
The ability of students to apply mathematics has been regarded as an important goal of mathematics education in many countries, including Indonesia and Singapore. One of such abilities is the competence of mathematical modelling. Presenting students with mathematical modelling task is one of the efforts to improve their competence of mathematical modelling. This study aims to describe the characteristics of mathematical modelling task in Indonesian and Singaporean mathematics textbooks. This study used a qualitative approach with content analysis technique. The books analyzed in this study were an Indonesian mathematics textbook published by the government and a Singaporean mathematics textbook: Discovering Mathematics. Classification category for the modelling tasks is adapted from the classification made by Katja Maaβ (2010). The results of analysis showed that there is no significant difference between Indonesian and Singaporean mathematics textbooks. Indonesian mathematics textbook contains contexts that are still small as well as Singaporean mathematics textbook. Therefore, more comprehensive research is needed with regard to curriculum content and learning strategies in Indonesia and Singapore.
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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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Expanding hypothetical learning trajectory in mathematics instructional
The purpose of this article is to present a description of Hypothetical Learning Trajectory (HLT) which can be used as an instrument in mathematics learning activities in the classroom. More than 25 years, HLT has been introduced and developed in every learning especially mathematics learning. An HLT is developed based on the learning objectives, characteristics of students and the material to be taught. In HLT contains three important things that are: (1) learning objectives, (2) learning activities used in building students’ knowledge, and (3) allegations of the learning activities process. This article uses a literature review of previous theories. HLT can be developed with various learning methods that are adjusted to the characteristics of students and the material to be taught. However, this article only discusses important things that need to be considered in the development of HLT in mathematics learning. So that it is obtained that HLT can help students in building knowledge in a reflective manner.
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Developing Students’ Mathematical Literacy through Problem Based Learning
The modern era requires more than just conceptual and procedural knowledge. Many studies such as the Program for International Student Assessment (PISA) emphasize the importance of individual’s ability to apply their conceptual and procedural knowledge. Such competence in mathematics is referred to as mathematical literacy. With this respect, the present study is aimed to explore the possibility of Problem Based Learning (PBL) as a means to develop students’ mathematical literacy. For this aim, a literature review was used for which 11 research articles on the effectiveness of Problem Based Learning (PBL) in learning several mathematical competences were selected and reviewed. By focusing on the common characteristics between the mathematical competences reported in the 11 articles and the characteristics of mathematical literacy, the literature review show that PBL has a potential to develop students’ mathematical literacy. Variables in the 11 articles like critical thinking, creative thinking, students’ understanding, and mathematical communication are related to fundamental capabilities in mathematical literacy. The result of this studies prove that the use of PBL from elementary school to university level can improve students’ mathematical literacy skills.
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Comics are reading material that is generally more desirable than textbooks by children, especially teenagers. Based on its characteristics, comics contain stories in the form of pictures and text which is contained in the balloons of text and presented in the panels. If the comic is presented in line with the application of a realistic mathematical approach, especially in learning mathematics, it hopes to create an interesting learning atmosphere for students. However, in this case, the contents of the comic story presented are in the form of learning about integers that are connected with a realistic mathematical approach. Therefore, this study aims to determine the effect of learning with comic-based realistic mathematical approaches on learning motivation and students’ understanding of mathematical concepts. This research is a quasiexperimental study. The population in this study was all the students of class VII of Junior High School of RK Serdang Murni Lubuk Pakam in the Academic Year of 2019/2020. While the sample was the class VII-1 as a control class of 31 students and class VII-2 as an experimental class of 32 students. The instruments in this study were two tests of the ability to understand the mathematical concepts and a learning motivation questionnaire. The normality test uses Liliefors test and the homogeneity test uses the Levene’s test with significance. The data were analyzed using the Manova test. Based on the data analysis, the results show that there was a significant effect of comic-based realistic mathematical approaches on students’ learning motivation and conceptual understanding of integer’s material.
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Facilitating pedagogical content knowledge development through professional development intervention
Teacher has main responsibility to accommodate all students and their learning needs in dynamic classroom situations. This goal can be accomplished if teacher can organize high quality teaching practice to support student’s success. So that teachers must be equipped with wide range of knowledge about how particular mathematics topics, problems, or issues are organized, represented, and adapted to the diverse interests and abilities of learners. Such knowledge is known as Pedagogical Content Knowledge (PCK). Many studies have proven PCK as professional knowledge that should be acquired by teacher to make effective teaching. Considering its importance, there must be systematic effort to develop pedagogical content knowledge through professional development. Teacher professional development has been used as the most effective approach to promote teacher change. Accordingly, the purpose of this paper is to explore ways to develop PCK in professional development intervention. The method used in this study is literature review. The review revealed that professional development intervention with collaborative-reflective situation such as: lesson study, analysing student’s work, analysing video of classroom practices, or construction of Content of Representation (CoRe) and Pedagogical and Professional Experience Repertoires (PapeRs) – based program, has positive impact to develop teacher’s pedagogical content knowledge.
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The aim of this research was to investigate the effectiveness of Inquiry-Based Learning (IBL) on computational thinking skills and self-efficacy of 11th grade students with derivative as the learning topic. The type of this research was quasi experimental research. The population of this research was 191 of 11th grade students in a public high school in Yogyakarta. The sample was 42 students from class XI Natural Science 1 and XI Natural Science 3 which were chosen by random sampling. The data were collected from pre-test and post-test for computational thinking skills and survey for self-efficacy. The results showed that: (1) IBL was effective toward computational thinking skills, (2) IBL was effective toward selfefficacy, (3) scientific learning was effective toward computational thinking skills, (4) scientific learning was effective toward self-efficacy, (5) IBL was not more effective than Scientific Learning toward computational thinking skills, (6) IBL was more effective than Scientific Learning toward self-efficacy. IBL failed to become learning model that was more effective than scientific learning toward computational thinking skills because of the failure in developing asking skills, but succeed to be more effective than scientific learning on improving self-efficacy because IBL provided more diverse sources of self-efficacy.
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The role of mathematics teacher in the digital era
The complex characteristics of the digital era requires more than just conceptual knowledge. In addition to a so called 21st century skills, ‘digital literacy’ has been raised to highlight a set of important competencies to cope with the demands of the future era. Digital literacy comprises practical and functional skills, critical thinking and evaluation, creativity, esafety, proficient communication, collaboration, cultural and social understanding, and information processing. Developing such competencies since early education requires a big role of teacher. By putting the idea of technological pedagogical content knowledge (TPACK) into practice, there are three important areas of consideration. First, preparation stage for which teacher should design or prepare technology-based or technology-assisted tasks that focus on exploratory activities. Second, during the implementation stage teachers needs to give proper scaffolding to bring from technical exploration to mathematical exploration. Lastly, the assessment stage for which teachers could use technology to improve efficiency and accessibility.
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This study is aimed to investigate the pedagogical content knowledge of prospective professional teachers who participated in the In-service Teacher Professional Program (Program Profesi Guru Dalam Jabatan or PPG Daljab) for the topic of Derivative. The investigation into teachers’ knowledge was conducted during the phase of developing lesson plan. For this purpose, 24 in-service teachers were observed during their participation in the PPG program. The data analysis was performed for the interview results, the teachers’ lesson plan (RPP), and observation note from the peer teaching activities. The data analysis reveal that the teachers already possessed a correct conceptual understanding of derivative as indicated from their lesson plan. Nevertheless, the concepts that teachers presented in the lesson plan was still partial and did not represent a comprehensive conceptual understanding. This partial conceptual understanding was also observed during peer teaching activities. When performed a teaching simulation, teachers tended to deliver the concept in a procedural way so that the classroom activities did not fully support the development of students’ higher order thinking skills.
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Mapping of mathematics topics that can be integrated their learning utilizing calculator
Calculator is one of technology product that can be integrated with mathematics learning. However, mathematics topics that require calculator in teaching and learning process haven’t been identified. This research was revealed to map the school mathematics topics that can be integrated into learning using calculator. This research was a qualitative study, with a content analysis approach. Initially, a focus group discussion (FGD) was held regarding the format of mapping mathematical material. The FGD participants were officials from the education office at the Ministry of Education and Culture, staff from Casio Education Singapore, and reviewers from various universities that had mathematics education study program in Yogyakarta Indonesia. The mathematics topics from elementary school, junior high school, high school and vocational school were mapped, which basic competencies can use a calculator in learning. The results showed that most of the basic competencies in elementary, junior high, high school, and vocational school could integrate their learning using calculator. These uses were categorized into exploration, representation, computation and affirmation. The dominant features of scientific calculator were also mapped at each school level.