This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden.

<p>Previous studies have shown that students, who have high levels of metacognitive awareness, perform better achievement levels than other students.<strong> </strong>Besides,<strong> </strong>it can be said that learning styles may affect metacognitive awareness of students. In the literature, studies about metacognition focused on problem solving and learners’ mathematical achievement, improvement in metacognition, and supporting some learning environments with metacognition. Therefore, in this study, relationship between metacognitive differences, learning styles, genders and mathematics grades of the fifth grade students are examined. This study was designed as descriptive study and conducted by using relational screening model. The participants consist of 330 fifth grade students from public middle schools. Data collection tools of this study are “Metacognitive Awareness Scale for Children” and “Learning Styles Scale”. The data gathered through these scales were analyzed by using Statistical Package for Social Science (SPSS) 21.0. As a result, there is no statistically significant relationship between learning styles and gender. But, there is statistically significant relationship between learning styles-mathematics grades, metacognitive awareness levels<strong> </strong>(MAL)—grade levels in mathematics, MAL-gender and MAL-learning styles. Learning styles may affect individuals’ way of thinking in every moment of the life. Thus, this result has a significant part in education. In fact, parents, teachers and administrators should know metacognitive awareness and learning styles. Thus, knowing these terms can be helpful to understand how the problematic and unsuccessful students show undesirable behaviors since those students’ learning styles and metacognitive awareness levels are not considered.</p>

No abstract

A real life problem was created in this study and ellipse equations and integral concept were used in the solution of this problem. As a real life problem, the change in the surface area of the water in a cylinder half of which was full of water and situated vertically was examined in a process in which it was tilted until it became parallel to the floor. In the study, piecewise function which gave the surface area of the water for the angle that the floor and the cylinder built was constructed. This process was visualized as two and three dimensional using GeoGebra which is a dynamic mathematics software program. As this problem situation overlaps with the principles of Realistic Mathematics Education approaches, it is believed that it will guide the teachers in classroom activities.

Technological Pedagogical Content Knowledge (TPACK) is a model that explains how teachers use technology more effectively in the context of technological, pedagogical, and content knowledge. Teachers' TPACK competencies play great importance in this regard. Lesson study has also been playing significant roles in the development of teachers' professional trainings. When the researches on TPACK and lesson study have been analyzed, the research is expected to provide significant contributions to the literature. This study aims to present reflections from a lesson study practice that carried out to urge techno-pedagogical competencies of the secondary school mathematics teachers and to reveal the development of teachers' progress. The study used case study method, and it was conducted with three in-service teachers. The research data were collected through semi-structured interviews, voice recorder, and observation notes. To analyze the collected data, descriptive analysis method was used. The results have revealed that teachers have made much more progress in designing, implementing, and problem solving in terms of TPACK competencies. It has also been determined that teachers' development of openness to the innovations was limited. This limitation appeared to emerge as a result of teachers' time anxiety and insufficient knowledge regarding the use of technology.