Identification of Graph Thinking in Solving Mathematical Problems Naturally

This research is motivated by the lack of interest of teachers in the use of props in the process of learning mathematics in elementary school. In accordance with the demands of the curriculum in 2013 and supported by the developed learning theory, learning mathematics is abstract object of study, students need an intermediary that props math-ematics, so that students can more easily understand the concepts that will be pre-sented, and in the end it can deliver students to solve mathematical problems, not only that proposed by the teacher but also the problems in life. The purpose of this study was to determine the interest of prospective elementary teachers on the use of props mathematics after getting lectures media and elementary mathematics learning model. By knowing the interest of prospective elementary teachers will be developed further realization of the state of the subject being studied. The method used is descriptive research, then the instruments used were questionnaires and interviews. The results of this study stated that the interest of prospective elementary teachers on the use of props after attending lectures media and elementary mathematics learning model is high over-all with a percentage of 76.70%.Keywords : Interest, Props Mathematics

Self-efficacy of students plays a role in determining student success in learning, including learning mathematics. Affective aspects such as self-efficacy, play a major role when students work and use mathematics, because to be able to solve mathematical problems is not enough just to know how to do it, but must be accompanied by self-efficacy about the truth of the concepts and procedures they have. This research was conducted in two groups of students using an instrument in the form of a questionnaire to measure students' self-efficacy. Observation data collection techniques were also conducted to determine the learning process of the two groups. The results showed that groups of students who used active and cooperative learning had higher self-efficacy. Keywords: self-efficacy, mathematics, cooperative learning.

The knowledge on geometry are of great importance for the understanding of reality. Spatial notion and geometrical concepts, graphical skills and habits are an important part of the study of geometrical knowledge in elementary school as propedeutics of the system course on geometry in the next school levels. In the recent years, education in Bulgaria follows the trends imposed by the European Union related to the acquiring of some basic key competencies. They promote to the improvement of knowledge, skills, abilities and attitudes of students and their more successful social development. From the school year 2016/2017, the education in the Bulgarian schools is in accordance with the new Law on pre-school and school education. Under this law, students are teached under new curriculum and teaching kits for the corresponding class. According to the new curriculum, the general education of the students of I-IV grade, covers basic groups of key competencies. Here, much more attention is paid also to the results of international researches on the students’ performance in mathematics. Primary school students participate in international competitions and Olympiads, which lead to the need of working on more mathematical problems with geometric content of the relevant specific types. This allows to study and use author’s various mathematical problems for teaching geometry. Their purpose is to contribute to the expansion of space notions of the students, to develop their thinking and imagination. This article is dedicated to the application of author’s various mathematical problems and exercises for teaching students from the third grade through which the geometrical knowledge and skills of the students develop and build. The solving of the mathematical problems is realized on a rich visual-practical basis, providing conditions for inclusion of the students in various activities. The proposed various mathematical problems are developed by themes including fully geometric problems and exercises for teaching mathematics to third grade students. Teaching by using the various mathematical problems was held with 149 students from third grade, from five schools - three in Sofia and two in smaller towns, in the school year 2016/2017.

The aim of learning mathematics in universities is to improve students' mathematical abilities. One of the important mathematical abilities of students is understanding the concept. With an understanding of the concept, students will easily solve mathematical problems. This research is an experimental research design with One Group Pretest-Posttest Design. In the design of this study, researchers used one class as the subject of research. Before being given treatment, the pretest is first performed, then given treatment within a certain period, then given a posttest. The results showed that there was an increase in students' understanding of the concept after being given the application of the expository method.

Before children learn to use language, they learn about the world in action and by imitation. This learning provides the basis for language acquisition. Learning by imitation and thinking in action continue to be significant throughout life. Mathematical concepts are grounded in children’s schemas of action, which are action patterns that represent a logical organization that can be applied to different objects. This chapter describes some of the conditions that allow deaf or hard-of-hearing (DHH) children to learn by imitation and use schemas of action successfully to solve mathematical problems. Three examples of concepts that can be taught by observation and thinking in action are presented: the inverse relation between addition and subtraction, the concepts necessary for learning to write numbers, and multiplicative reasoning. There is sufficient knowledge for the use of teaching approaches that can prevent DHH children from falling behind before they start school.