Applications of Tulip Motif in Turkish Art with Geometer’s Sketchpad Program

In the 21st century we live in, technology is developing rapidly. Inevitably, the technologies used in almost every area of daily life will also reflect in the field of education. Educational technologies, which enable students to grasp abstract concepts more easily and facilitate the teaching process for teachers, have increased their impact in schools. The effects of dynamic geometry software on course success, attractiveness, and concretization in mind have been the subject of different studies. Dynamic geometry software that can visualize algebraic expressions with graphics creates an interdisciplinary working environment with its drawing features. Thanks to Geometer’s Sketchpad (GSP), one of this software, students can dynamically create very different patterns and shapes. Students can realize higher-level cognitive learning thanks to the relationships and inferences they make on these shapes. These and similar patterns that emerged thanks to GSP can increase students’ awareness in different fields by combining different disciplines such as history, mathematics and art. In this study, the drawing stages of the tulip motif, which we come across in important architectural works in the Ottoman and Anatolian Seljuk history, which have been the subject of ornament art, are shown via GSP using both the transformation geometry and functions.

Mapping pre-service teachers’ faulty reasoning in geometric translations to the design of Van Hiele phase-based instruction

Background: Pre-service teachers (PSTs) training does not equip students with adequate skills and knowledge of geometry to enable them to teach this section of mathematics competently. Inadequate teacher knowledge of transformation geometry, in particular, requires intervention that targets PSTs’ faulty reasoning displayed in errors they make.Aim: The aim of this study was to explore the use of Bachelor of Education (BEd) students’ faulty reasoning in geometric translations, in designing a Van Hiele phase-based instructional programme that could address such faulty reasoning.Setting: The setting for the study was a newly established rural university in South Africa.Methods: Tests on geometric translations were administered to BEd Foundation Phase students, followed up by interviews to explore errors made when responding to the test items. The errors were then mapped to the design of a Van Hiele phase-based instructional programme.Results: The results revealed that the students had several misconceptions with geometric translations. The misconceptions were delineated into the errors that the students displayed and these were classified under two themes. The first theme was incorrect properties of transformation and under this theme, the errors were coded as confusing translation with rotation, wrong translation method, incorrect interpretation of coordinates and confusing the x and y axis. The second theme was errors involving basic mathematics operations including wrong diagrammatic representation of coordinates and incorrect calculations.Conclusion: The study showed that if the students’ misconceptions and the resulting errors are mapped to specific instructional approaches, their faulty reasoning in geometric transformations is addressed and effective learning is enhanced.

Performing Sacral Spaces – Spatializing Sacral Performance

Spaces are closely connected with actions. By implementing an artistic-phenomenological approach, the existing interplay between sacral space and performance (highlighted bodily actions) can be found in the idea of cultural performance, which integrates the interdependance of movement and lively space, the origin of one in another. As space is something in motion, something that is created, in sacral spaces human beings experience an impact of space on the body and vice versa the eThects of movement creating space. Performing „Artists in Church“ encounter a space characterized by actions generating knowledge and "nally intermediate: the idea of transformation, geometry, places, absence, threshold and transcending. Performance Art provokes and leads syntopically and sympathetically to an aesthetic way of understanding space and action.

Ethnomathematics Exploration of The Masjid Raya Bandung Ornaments in Transformation Geometry Materials

The mosque is the result of acculturation between Islamic culture and local culture. Many mosque ornaments use geometric motifs. This research is an ethnomathematics study that aims to explore the ethnomathematics aspects of mosque ornament, especially the material of geometric transformation Ethnomathematics research is part of qualitative research, so this research uses qualitative research. The purpose of ethnomathematics research is to study the mathematical ideas contained in a culture, so the method used is ethnographic. The research location is Masjid Raya Bandung which was selected by purposive sampling. The researcher acts as an instrument that collects data through observation, documentation, and literature review. The research data were analyzed through data condensation, data display, and concluding. The results showed that there are ethnomathematics aspects of Masjid Raya Bandung ornaments in the material of transformation geometry, namely translation, reflection, rotation, and dilation. The mosque ornaments can be used as an alternative source of learning in mathematics learning, especially transformation geometry material. Keywords: ethnomathematics, transformation geometry, mosque ornament.

Hypothetical learning trajectory in student’s spatial abilities to learn geometric transformation

The relationship between spatial conceptions and students' spatial abilities is still rarely studied specifically, even though this is the basis for students to think in learning geometry. This paper aims to explore spatial abilities and the development of spatial ability theory, discusses the relationship between spatial conceptions in students' understanding, and how to develop HLT (Hypothetical Learning Trajectory)in transformation geometry learning. HLT design consists of three stages: initial design, experimental, and retrospective analysis. The results of HLT are then refined into LIT (Local Instructional Trajectory). Then this paper present the empirical results of the perceptions of twenty 9th grade students in one of Islamic private school in Kabupaten Kuningan, West Java, Indonesia, towards the corresponding geometric and math questions. Literature review analysis was used to analyze the retrieved articles. At the end of the paper, we explain and discuss how to apply mathematical conceptions in learning geometry. This research is expected to be a guidance for teachers to develop learning in accordance with the students' spatial thinking process in studying geometry.

Pengembangan E-Modul Berbasis Contextual Teaching and Learning (CTL) pada Materi Geometri Transformasi dengan Berbantuan Flipbook Maker

The purpose of this research is to produce an E-module based on Contextual Teaching and Learning in Geometry Transformation material that is valid and practical so that it can be used as one of the mathematics learning resources, especially the material of transformation geometry. The type of research used is research and development. The model used is the Plomp model. The stages used in this development model only phase 1 to phase 4, namely is a preliminary investigation, design, realization/construction, evaluation, and revision. The types of questionnaires used were expert validation and a student response questionnaire. Based on the results of expert validation the results of the material and the language expert validation percentage were 83.08% (very feasible category), design experts 86.11% (very feasible category) so that the overall material and language validation results and design were 84.56 % (very decent category). The results of the small group trials obtained from the student questionnaire responses to the mathematics E-Module were 88.6% (very practical category). Based on the results, it can be concluded that the E-Module mathematics based on Contextual Teaching and Learning (CTL) on the transformation geometry material assisted by Flipbook Maker is very feasible and very practical to be used as one of the sources of mathematics learning, especially on geometry material transformation.

PENGEMBANGAN MODUL BERBASIS PENEMUAN TERBIMBING PADA MATA KULIAH GEOMETRI TRANSFORMASI

Based on the results of observations, the learning process still uses conventional methods and the textbooks used in the lecture process have not been able to lead to finding a concept. The aim of the study was to design a guided discovery-based module in the transformation geometry course at STKIP PGRI West Sumatra. This type of research is development research using the Plomp model which consists of 3 phases, namely preliminary research, prototyping phase, and assessment phase (Plomp, 2013: 19). The preliminary research stage consists of interviews with students and teachers, syllabus analysis, and textbook analysis. The prototyping phase is designing systematics and module structures, developing prototypes, and expert reviews. The results obtained at the preliminary research stage were based on interviews with lecturers and students who did not understand the basic concepts of geometry and were less able to prove the proposition. In the analysis of the syllabus and literature that was carried out was that the material taught was in accordance with the syllabus. The results of the module validity from the experts show that the guided discovery-based module is quite valid in the category.

Student Approaches Resulting from Integration of Cultural Context into Transformation Geometry

The purpose of this study is to investigate how students’ in senior grade of the high school participate in and interpret the transformational geometry activities integrated with cultural context. 5 students in senior grade participated in this study, all of whom live in Aydın district of Turkey. The main design of the study is qualitative. Participant students of the study involved in 9 different rotational geometry and culture integrated activities, 7 of which were performed as student activity sheets, 2 of which were performed as cultural games. 2 of the activities were constructed as a result of pilot study applied to 28 senior students by their math teacher. To collect data about how students participated in and made interpretations about the activities; various data collection tools such as observation, field notes, interview, audio recording and student activity sheets were used. The collected data were analyzed by qualitative descriptive analysis techniques. The results were presented as tables, figures constructed by students and direct quotations. Lastly, at the end of this study students were said to recognize the hidden mathematics in the objects from daily life, games with cultural background and history, and both in Turkish culture and other cultures.

Transformation Geometry in Toraja Carving

Ukiran Toraja (passura’) merupakan hasil budaya Toraja yang tetap dilestarikan dan memuat berbagai nilai kehidupan. Selain itu, pada ukiran Toraja juga kaya dengan konsep matematika, khususnya bangun geometri. Penelitian ini bertujuan untuk mengidentifikasi konsep-konsep geometri transformasi apa saja yang terdapat pada ukiran Toraja. Penelitian ini merupakan penelitian kualitatif dengan pendekatan etnografi, dan dilakukan dalam 3 tahapan. Informan (sumber data) dalam penelitian ini adalah orang yang paham tentang seluk beluk budaya Toraja. Data dalam penelitian ini diperoleh dari data hasil wawancara dengan informan, catatan lapangan yang dibuat selama penelitian berlangsung dan hasil dokumentasi berupa foto ukiran dan saat mengukir. Untuk memperoleh data yang valid maka peneliti menggunakan triangulasi teori. Hasil dari penelitian menunjukkan bahwa pada ukiran tongkonan dan lumbung Toraja terdapat konsep-konsep geometri transformasi yaitu refleksi baik terhadap garis x, y, y = x, y = -x, dan terhadap titik 0 (0,0), translasi, rotasi dan dilatasi.