GEOMETRICAL THINKING
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هدف البحث إلى استكشاف فاعلية استخدام البرمجيات الديناميكية الهندسية في تدريس الهندسة الفراغية بالمرحلة الثانوية على التفكير الهندسي والاتجاه نحو الرياضيات، واستخدم البحث المنهج شبه التجريبي مع عينة من (50) طالب بالصف الثالث الثانوي قسموا... more
هدف البحث إلى استكشاف فاعلية استخدام البرمجيات الديناميكية الهندسية في تدريس الهندسة الفراغية بالمرحلة الثانوية على التفكير الهندسي والاتجاه نحو الرياضيات، واستخدم البحث المنهج شبه التجريبي مع عينة من (50) طالب بالصف الثالث الثانوي قسموا لمجموعتين، (25) تجريبية، و(25) ضابطة، حيث درست المجموعة التجريبية موضوعات (القطوع المخروطية) باستخدام برنامج كابري ثلاثي الأبعاد (Cabri 3D)، ودرست المجموعة الضابطة بالأسلوب التدريسي المعتاد، وطبق على العينة مقياس فان هايل للتفكير الهندسي، ومقياس اتجاه نحو الرياضيات، واختبار تحصيلي قبلياً وبعدياً، وأشارت النتائج إلى تحديد مستوى التفكير الهندسي لعينة البحث بالمستوى الثالث (مستوى الاستدلال غير الشكلي) وفق تصنيف مستويات فان هايل، ووجود فاعلية للبرمجيات الديناميكية في تدريس الهندسة الفراغية في المرحلة الثانوية على التحصيل الدراسي، ولم تكن هناك فاعلية على التفكير الهندسي والاتجاه نحو الرياضيات. وقدم البحث عدد من التوصيات والمقترحات.
The Efficacy of Dynamic Geometry Software (Cabri-3D) in Teaching Spatial Geometry at High School on Geometrical Thinking and Attitude towards Mathematics.
Abstract:
This research aim's to explorer the Efficacy of Dynamic Geometry Software (Cabri-3D) in Teaching Spatial Geometry at High School on Geometrical Thinking and Attitude towards Mathematics. The research used the quasi experimental methodology with sample (50) high school students that’s divided equally to experimental group and control group. The experimental group studied with (Cabri- 3D) and the control group studied with normal teaching strategies. With pretest - posttest for; (van Hiele test, Attitude toward mathematics scale, Achievement test). The result revealed that the geometric level of the sample was the third level of van Hiele levels, there are Efficacy of Dynamic Geometry Software (Cabri-3D) in Teaching Spatial Geometry at High School on Achievement Spatial geometry, but there are no Efficacy on Geometrical Thinking and Attitude towards Mathematics. Suggestion and proposal were presented.
Key Words: Dynamic Geometry Software, Geometrical Thinking, Attitude towards Mathematics, Geometrical Teaching, High School Mathematics.
The Efficacy of Dynamic Geometry Software (Cabri-3D) in Teaching Spatial Geometry at High School on Geometrical Thinking and Attitude towards Mathematics.
Abstract:
This research aim's to explorer the Efficacy of Dynamic Geometry Software (Cabri-3D) in Teaching Spatial Geometry at High School on Geometrical Thinking and Attitude towards Mathematics. The research used the quasi experimental methodology with sample (50) high school students that’s divided equally to experimental group and control group. The experimental group studied with (Cabri- 3D) and the control group studied with normal teaching strategies. With pretest - posttest for; (van Hiele test, Attitude toward mathematics scale, Achievement test). The result revealed that the geometric level of the sample was the third level of van Hiele levels, there are Efficacy of Dynamic Geometry Software (Cabri-3D) in Teaching Spatial Geometry at High School on Achievement Spatial geometry, but there are no Efficacy on Geometrical Thinking and Attitude towards Mathematics. Suggestion and proposal were presented.
Key Words: Dynamic Geometry Software, Geometrical Thinking, Attitude towards Mathematics, Geometrical Teaching, High School Mathematics.
This is a study that has applied descriptive survey model. Descriptive survey model is a research approach which aims at describing a past or present phenomenon, an object or a person as realistically as it is. Convenient sampling was... more
This is a study that has applied descriptive survey model. Descriptive survey model is a research approach which aims at describing a past or present phenomenon, an object or a person as realistically as it is. Convenient sampling was applied to specify the study group. Within the scope of the study, 56 pre-school children from Turkey (28) and the UK (28) were reached. A Geometric Shape Form was used by the researchers as an instrument to collect data. In accordance with the focus questions, the children’s oral responses and the geometric shapes they drew were analyzed by the researchers. The analysis of data, which included percentages, frequency values and q-square tests, was conducted through SPSS 15 for Windows. The results showed that Turkish and English pre-school children both had similar characteristics in drawing and perceiving geometric shapes, in general. However, in recognizing rectangles and shape-corner perceptions, there was statistically significant difference.
El objetivo de esta investigación es evidenciar relaciones entre la identificación de configuraciones que inician el razonamiento configural y la trayectoria de resolución de problemas de probar en geometría. Los resultados indican que la... more
El objetivo de esta investigación es evidenciar relaciones entre la identificación de configuraciones que inician el razonamiento configural y la trayectoria de resolución de problemas de probar en geometría. Los resultados indican que la identificación de una figura prototípica en la configuración inicial activa determinados conocimientos de geometría determinando la trayectoria de resolución. Estos resultados sugieren la necesidad de potenciar en la enseñanza de la geometría el reconocimiento explícito de la relación entre la identificación de sub-configuraciones y la generación de determinadas trayectorias de resolución.
The goal of this research is to establish the relationships between the identification of configurations that initiate configural reasoning and the trajectory of the resolution of geometry proof problems. The results show that the identification of a prototypical figure in the initial configuration activates certain knowledge of geometry and determining a trajectory of resolution. These results suggest the need to enhance the teaching of geometry explicit recognition of the
relationship between the identification of sub-configurations and generating certain trajectories resolution.
Keywords: learning of geometry
The goal of this research is to establish the relationships between the identification of configurations that initiate configural reasoning and the trajectory of the resolution of geometry proof problems. The results show that the identification of a prototypical figure in the initial configuration activates certain knowledge of geometry and determining a trajectory of resolution. These results suggest the need to enhance the teaching of geometry explicit recognition of the
relationship between the identification of sub-configurations and generating certain trajectories resolution.
Keywords: learning of geometry
The paper defines a special type of problem tasks and considers its didactic potential, as well as the success of students in solving the selected problem. The research instrument used is a geometrical task from the National Secondary... more
The paper defines a special type of problem tasks and considers its didactic potential, as well as the success of students in solving the selected problem. The research instrument used is a geometrical task from the National Secondary School Leaving Exam in Croatia (State Matura). The geometrical task is presented in three versions: as a verbal problem, as a verbal problem with a corresponding image and as a problem in context. The material analysed in the present paper was collected from 182 students in 7 th and 8 th grade of Croatian urban elementary schools. The didactic potential is considered from the aspect of use of mathematical concepts and connections. The success of students in problem-solving is considered from the aspect of implementation of the problem-solving process and producing correct answers, depending on the manner in which the tasks are set up. The results show that the stand-alone problem, as a special type of problem task, has considerable didactic potential. However, the students' skills of discovering and connecting mathematical concepts and their properties are underdeveloped. In addition, the manner in which the tasks are set up considerably affects the process of solving the task and consequently the success of that process. Based on the results of the research, proposals are given for application of stand-alone problems in teaching mathematics.
Geometry is an integral part of the curriculum on a global scale as it is a learning object where students can engage in inquiry learning process and develop skills and competences. The teaching of geometry in secondary education is an... more
Geometry is an integral part of the curriculum on a global scale as it is a learning object where students can engage in inquiry learning process and develop skills and competences. The teaching of geometry in secondary education is an active field of reflection between teachers, editors of curricula, as well as among researchers and there is a strong interest in enriching learning and teaching strategies where they will improve understanding of the basic concepts of geometry that will help cultivate and develop the geometric reasoning of students, But, what is the way that students learn geometrical concepts and in which way they construct and transform geometrical concepts? What are the basic frameworks of teaching and learning geometry that could be used of educational and research community as base for assessment the level of students' geometrical thinking? In what ways can we explain the difficulties faced by students in reasoning geometrical problems? What is the cognitive learning progression in learning geometry? This paper replies to above research questions and presents the art objects (paintings) as research tools under the theoretical frameworks of learning process of geometry. In other words, this research work attempts qualitative analysis of cognitive processes for the construction a theoretical model of cognitive progression in geometrical thinking based on art objects. This approach focus on understand and interpret the potential of students and the processes that follow in learning geometry. In this case, theory is not the basis for research planning but is used as a tool to explain the situations and results that provided by students worksheets under the terms of art objects.
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