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This study examined the effect of collaborative learning with a scientific approach (SA) on the learning achievement in mathematics viewed from the students’ multiple intelligences. This study compared two types of collaborative learning models, Three Steps Interview (TSI), and Think Pair Share (TPS). The participants of this study were grade 8 students of Secondary Schools in Sukoharjo, Central Java, Indonesia (N = 262). This study was a quasi-experimental study with a 3 × 3 factorial design. The results of the study can be concluded as follows. (1) TSI with a scientific approach got better math learning achievement than TPS with a scientific approach and classical with a scientific approach. Besides, TPS with a scientific approach got better learning achievement than classical with a scientific approach. (2) Students with logical-mathematical intelligence got better math learning achievement than students with linguistic intelligence and students with interpersonal intelligence, students with linguistic intelligence got better math learning achievement than students with interpersonal intelligence.
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A learning trajectory for probability: A case of game-based learning
This research is aimed to describe a learning trajectory for probability through game-based learning. The research employed design research consisting of three stages: preparing for the experiment, design experiment, and retrospective analysis. A hypothetical learning trajectory (HLT) using Sudoku and Snake-and-ladder games was developed by collecting data through documentation, interviews, and classroom observations. The HLT was implemented in the classroom to investigate students’ actual learning trajectory. The results of this research indicate that the games helped students understand the concept of probability. The learning trajectory for probability based on game-based learning is seen from the perspective of four levels of emergent modeling. In the first level –‘situational level’ –Sudoku and Ladder-and-Snake games were played by students. The second level is the ‘referential level’ where the rules of the games were used as a starting point to learn the concept of probability. Communication during game playing stimulated students’ knowledge about random events, sample spaces, sample points, and events. At the third level –‘general level’ –students used tree and table diagrams to generalize possible outcomes of an experiment and develop an understanding of sample spaces and sample points. Lastly, at the ‘formal level’ students developed their informal knowledge into formal concepts of probabilities.
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In the problem solving requires the ability to apply concepts and algorithms. Problems of particular concern in this regard are math problems related to everyday life. The abilities of each student are different and need to be analyzed. Therefore, a qualitative study with descriptive methods was carried out to determine the students’ problem-solving abilities in applying concepts and algorithms. But in this case, the research subjects were selected randomly and divided into two parts, namely students who applied offline and online learning with 5 discussion groups each. The research subjects were VII students of SMP RK Serdang Murni and SMP HKBP Lubuk Pakam. Based on problem solving on the student worksheet on the material of addition and subtraction of integers based on a realistic mathematics approach, it was obtained data that the ability to apply problem-solving concepts and algorithms in groups of students who applied offline learning tended to be better than the group of students who applied online learning. This was concluded based on results of problem solving carried out by the group of students. Therefore, it is hoped that the ability of teachers to design online learning will be further improved regarding the use of technology so that the results obtained are as good as the implementation of offline learning
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This study aimed to determine the geometry tasks in Laotian and Indonesian lower secondary school mathematics textbooks from the perspective of revised Bloom’s Taxonomy. The type of this study was textbook analysis. The data source of this study was the two selected mathematics textbooks from Laos and Indonesia. The Laotian mathematic is entitled lower secondary school mathematic textbook grade VII (Published by Ministry of Education and Sport), and The Indonesian mathematic textbook is entitled lower secondary school mathematic textbook grade VII (Published by Ministry of Education and Culture). The studied objects consist all of geometry tasks in Laotian and Indonesian mathematics textbooks from the perspective of revised Bloom’s Taxonomy. Data were collected through observation and recording techniques. The instruments used are the sheet analysis of geometry tasks from the perspective of revised Bloom’s Taxonomy in the six cognitive domain levels such as remembering (C1), understanding (C2), applying (C3), analyzing (C4), evaluating (C5) and creating (C6). The validity of the data is based on inter-rater reliability. Data analysis techniques are carried, namely unitizing, recording / coding, and inferring. The study results showed that there are some similarities between the geometry tasks in the two selected textbooks when comparing C2 and C3. The percentages of C2 and C3 in the Laotian mathematics textbook were 26.74% and 31.39%, respectively, versus 26.66% for C2 and 33.33% for C3, respectively, in the Indonesian textbook. In contrast, study results also showed some differences between the geometry tasks in the two selected textbooks such as C1, C4, C5, and C6. The study resulted revealed that the percentages of C1, C4, C5, and C6 were 9.30%, 22.09%. 10.46% and 0%, respectively in the Laotian textbook versus 2.22%, 29.62%, 5.18%, and 2.96% for C1, C4, C5, and C6 in the Indonesian textbook, respectively. Furthermore, the higher-order thinking skills (HOTS) consist of C4, C5, and C6 in the Indonesian mathematics textbook contain more geometry tasks than the Laotian mathematics textbook. Despite some differences between Laotian and Indonesian curricula, there are similar geometry topics in the Laotian and Indonesian mathematics textbooks. Based on the results, the researcher suggestions for the continuous revisions of Laotian mathematics textbook to include more tasks in HOTS similar to the Indonesian mathematics textbook to help educators develop higher order cognitive abilities in their students.
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Ethnomathematics: Exploration of transformation geometry elements in Troso weaving motifs
Troso weaving is one of original cultural product from Jepara, Indonesia. Similarly with batik, weaving has various motif as well, such as flora, fauna and geometry. Weaving Troso are not only fabrics with the different motif, but also relate with mathematics aspect such as transformation geometry. This study aims to explore the elements of transformation geometry in Troso weaving motifs. The type of this research is qualitative research. This study used a semi-structured interview that focused on two questions: are there mathematical concepts in this jaran motif? Are there geometric transformation concept in jaran motif? Interviews were conducted with four mathematic teachers via video call using WhatsApp (WA).The data were analyzed qualitatively, followed by the concept given by Miles and Huberman. The result showed that weaving Troso motifs contains the concept of geometry such as rhombus, parallel line and rectangle while the geometry transformation concept includes reflection, translation, rotation, dilation. The study implies that Trowo weaving motif then be used as learning media in schools by introducing existing cultures in Indonesia.
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Comparison of Indonesia and Singapore middle school mathematics material mapping
A curriculum is a fundamental element of a country’s education. Learning material is one of the important parts of the curriculum that can affect the quality of education. Indonesia and Singapore are countries with close geographical location. However, both have differences and similarities in mapping mathematics learning material. This study aims to compare Indonesia and Singapore middle school mathematics material mapping. This study is a comparative study with qualitative approaches methodologically, and document analysis is the methodological technique to be utilized. Therefore, an in-depth analysis of curriculum documents from both countries will be carried out to find the comparability of the mathematics material mapping of the two countries. The analysis showed that the materials taught in both countries are at the same grade for numbers, percentage, indices, perimeter and area of triangles and polygons, angles, Pythagoras’ theorem, probability, cartesian coordinate, linear equations in two variables, and quadratic equations. The differences in material mapping found in terms of the number of materials, distribution of materials, the depth of materials, and the order of materials.
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Mathematical epistemology in mathematics learning: Its definition, role and implementation
Epistemology is one of the important aspects in mathematics education. The individual’s view of epistemology may affect how his attitude towards knowledge and his achievement to acquire knowledge. In fact, epistemology is only seen as a theory of truth of mathematical knowledge, mathematical proof, and the history of mathematical knowledge in its implementation. Most students do not understand that epistemology is actually ‘knowing what they believe’ rather than simply accepting mathematics as a ‘finished product’. Therefore, it is very necessary to conduct a study on the importance of epistemology in mathematics learning which aims to find out what and how the epistemology of mathematics and its implementation in mathematics learning. This literature review article aimed to add to the study of mathematical epistemology, focusing on explaining the definition, rules and implementation of mathematical epistemology in mathematics learning.
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The effect of contextual approach on students’ mathematical problem solving ability
In its implementation, mathematical problem solving ability (MPSA) has not been developed well and is expected to be increased through a contextual approach (CA). The study is a quasi-experiment with pretest and posttest control group design that aims to (1) determine the significance of the increase in MPSA students who are taught through CA and conventional learning (CL), (2) determine the difference of increase MPSA students who are taught through CA and CL, and (3) the achievement of MPSA students indicators through CA. The research sample consisted of two classes, VII-5 as the experimental class and VII-8 as the control class. Data were analyzed through the Kolmogorov-Smirnov test, Levene test, and t-test. The results showed that (1) there was significant increased MPSA student that was learned through CA and CL, (2) increased MPSA of students who were taught through CA higher than who were taught through CL, (3) increased student MPSA through CA was categorized as high, while through CL was categorized as moderate, and (4) the achievement of “understand the problem” indicator was highest in the achieving MPSA students who were taught through CA.