Creating Design Principles of a Learning Environment for Teaching Vector Spaces

In this study, determining the design principles of a technology-supported learning environment for teaching vector spaces by taking into account the representation languages defined by Hillel (2000), Harel's (2000) pedagogical principles and Sierpinska's (2000) thinking modes on Linear Algebra teaching were intended to be established. The research is a design-based research and three cycles were conducted to determine the design principles for the learning environment. The study group of the first cycle consists of 51, the second cycle's working group was 44, and the third cycle's study group consisted of 11 teacher candidates. The data of the research were obtained by field notes and video recordings. By analyzing the field notes and video recordings, design principles for the learning environment were determined after the first two cycles in light of the literature. The third cycle was carried out with the determined design principles, and the design principles were revised in line with the opinions of the teacher candidates and the course teacher after the application with the reports obtained during the application process. Design principles in the light of the results obtained from the research are as follows ; the use of technology, usage of modes of description, tasks, worksheets, the role of the teacher and group work. It is thought that a learning environment that will be created by paying attention to these design principles will contribute to the pre-service teachers' differentiation and use of different languages, the development of thinking styles, and to meet the principles of concreteness, necessity and generalizability

A General Analytical Model for Problem Solving Teaching: BoS

In this study, a general analytical model called Bag of Solution (BOS) was developed to help students understand and solve mathematical problems. The model is based on graph theory, a topic under discrete mathematics. The types of problems to be modelled for BoS were determined by looking at densities of the problems in the central placement examinations and exam preparation books. As a result, three types of problems were selected; namely Mixture, Worker and Motion problems. In order to develop a common model for solution of the three types of problems, a total of 1509 mixture, worker and movement problems were examined. After the analysis, the problem types were taken together, and variable relations were determined, and a common graph model was created. Since it is an algorithmic model, it allows solving problems both by paper and pencil and computer. This study proves that different types of problems (with different scenarios, objects and object relations) can be solved using a single model. It is expected that the BoS developed in this study will offer two benefits. It is hoped to both provide an algorithmic basis for computer-aided instructional materials, adaptive systems and intelligent tutoring systems to be developed for problem solving and also help students to develop a new understanding of the problem-solving process. A common graph structure that can covers the entirety of a problem can allow students to construct their own learning while solving the problem step by step

The Effect of 4MAT Instructional Model on Teaching of Geometric Subjects

The main purpose of this study was to examine the effect of the learning environment designed for teaching geometric subjects according to the 4MAT model on permanent learning. The study used a quasi-experimental design with control group and was carried out with 86 students (41 students in experimental and 45 students in control group) at a lower secondary school located in Trabzon. The data were collected with The Pre-test (ÖBT), The Achievement Test (BT) and The Retention Test (KT) which were developed by researchers and The Learning Style Inventory (ÖSE) which was developed by Kolb. The results of the study showed that the courses conducted according to the 4MAT teaching model were more effective on students' achievement and more permanent learning. It also showed that the common effect of teaching method and learning style on students' academic achievement was not significant. In this context, it was suggested that teachers who use different methods, techniques and strategies in their lessons should primarily determine their students’ learning styles

The Potential of GeoGebra Dynamic Mathematics Software in Teaching Analytic Geometry: The Opinion of Pre-service Mathematics Teachers

The potential of GeoGebra in teaching analytic geometry concepts was investigated in this paper. The study carried out with case study methodology and the participants were 6 pre-service mathematics teachers at 3rd grade of elementary mathematics education. All of the participants had the skill of well self-expression and they were volunteers for interview. Two participants were at high achievement levels, two participants were at medium achievement levels and two participants were low achievement levels. While carrying out each lesson, participants used worksheets which were prepared by the researchers. The data were obtained by semi-structured interviews which were carried out at the end of the courses and the data were analyzed with content analysis method. Research results showed that using dynamic mathematics software while studying on analytic geometry provides convenience for the participants and they felt more active while they were using software in the learning environment

The Potential of GeoGebra Dynamic Mathematics Software in Teaching Analytic Geometry: The Opinion of Pre-service Mathematics Teachers

Öz: Bu çalışmada, analitik geometri kavramlarının öğretiminde GeoGebra’ nın potansiyeli incelenmiştir. Özel durum çalışması yöntemiyle yürütülen bu araştırmanın katılımcılarını, ilköğretim matematik öğretmenliğisınıfa devam eden 6 öğretmen adayı oluşturmaktadır. Katılımcılar kendini ifade etme becerisi yüksek, mülakata gönüllü ve farklı başarı düzeyinde (yüksek, orta, düşük) olan ikişer öğretmen adayından oluşmaktadır. Çalışmada analitik geometri dersleri, araştırmacılar tarafından geliştirilen çalışma yaprakları kullanılarak yürütülmüştür. Araştırmanın verileri derslerin sonunda yapılan yarı yapılandırılmış mülakatlarla toplanmıştır. Araştırmadan elde edilen veriler, içerik analizi yöntemi ile analiz edilmiştir. Araştırma sonuçları öğretmen adaylarının analitik geometri kavramlarını öğrenmede yazılımı kullanmalarının onlara kolaylık sağladığını, yazılımı kullandıkları öğrenme ortamında kendilerini daha aktif hissettiklerini göstermiştir. 3.Abstract: The potential of GeoGebra in teaching analytic geometry concepts was investigated in this paper. The study carried out with case study methodology and the participants were 6 pre-service mathematics teachers3rd grade of elementary mathematics education. All of the participants had the skill of well self-expression and they were volunteers for interview. Two participants were at high achievement levels, two participants weremedium achievement levels and two participants were low achievement levels. While carrying out each lesson, participants used worksheets which were prepared by the researchers. The data were obtained by semi-structured interviews which were carried out at the end of the courses and the data were analyzed with content analysis method. Research results showed that using dynamic mathematics software while studying on analytic geometry provides convenience for the participants and they felt more active while they were using software in the learning environment. at a

The Potential of GeoGebra Dynamic Mathematics Software in Teaching Analytic Geometry: The Opinion of Pre-service Mathematics Teachers

Öz: Bu çalışmada, analitik geometri kavramlarının öğretiminde GeoGebra’ nın potansiyeli incelenmiştir. Özel durum çalışması yöntemiyle yürütülen bu araştırmanın katılımcılarını, ilköğretim matematik öğretmenliğisınıfa devam eden 6 öğretmen adayı oluşturmaktadır. Katılımcılar kendini ifade etme becerisi yüksek, mülakata gönüllü ve farklı başarı düzeyinde (yüksek, orta, düşük) olan ikişer öğretmen adayından oluşmaktadır. Çalışmada analitik geometri dersleri, araştırmacılar tarafından geliştirilen çalışma yaprakları kullanılarak yürütülmüştür. Araştırmanın verileri derslerin sonunda yapılan yarı yapılandırılmış mülakatlarla toplanmıştır. Araştırmadan elde edilen veriler, içerik analizi yöntemi ile analiz edilmiştir. Araştırma sonuçları öğretmen adaylarının analitik geometri kavramlarını öğrenmede yazılımı kullanmalarının onlara kolaylık sağladığını, yazılımı kullandıkları öğrenme ortamında kendilerini daha aktif hissettiklerini göstermiştir. 3.Abstract: The potential of GeoGebra in teaching analytic geometry concepts was investigated in this paper. The study carried out with case study methodology and the participants were 6 pre-service mathematics teachers3rd grade of elementary mathematics education. All of the participants had the skill of well self-expression and they were volunteers for interview. Two participants were at high achievement levels, two participants weremedium achievement levels and two participants were low achievement levels. While carrying out each lesson, participants used worksheets which were prepared by the researchers. The data were obtained by semi-structured interviews which were carried out at the end of the courses and the data were analyzed with content analysis method. Research results showed that using dynamic mathematics software while studying on analytic geometry provides convenience for the participants and they felt more active while they were using software in the learning environment. at a