Реално окружење у почетној настави геометрије /Realistic Mathematics Education in Teaching and Learning Elementary Geometry (original) (raw)

2017, Realistic Mathematics Education in Teaching and Learning Elementary Geometry. Space as a source for modeling geometric concepts - methodical aspects

The main aim of teaching elementary mathematics is to make students mathematically literate. This is why we advocate the view that aims, apart from the stated ones, are, as well, creating the states of curiosity, tendency towards crating researching minds of students and the sense for creating connections between formal Mathematics on one side and appearances from real environment on the other side. This has led us to Realistic Mathematics Eduction as one of the possible teaching approaches towards creating such a connection. There are four basic chapters and many sub-chapters. We have done both theoretical and experimental research and studying effects of the teaching approach to realistic mathematics in teaching elementary geometry based on the theory of Realistic Mathematical Education supported by the additional innovative model of the textbook. We have selected three aims of the paper. The first refers to studying theoretical bases (geometrical and didactic-methodological) by using the method of theoretical analysis. We have pointed at some international and domestic projects, which in their concepts of mathematical education, use Realistic Mathematics Education for their starting point. The second aim refers to presenting results of the experimental part of our research which is aimed at the examining ways in which realistic mathematics in geometry contents of the fourth grade of teaching elementary Mathematics influences the students’ achievements (according to the levels of knowledge) and reasoning, as well as students’ motivation for learning. We have used the experiential method here. Finally, the third aim refers to referring the innovative model of the textbook as practical implementation, which supports constructivist approach in teaching realistic mathematics, and we pointed at key results and their methodological implications on teaching elementary Mathematics gained according to experiential research. Our research is directed to revealing to the way, which leads the students to concepts with meaning, from, on one side, visual concepts to, on the other side spatial reasoning, emphasizing visual and verbal association process as the subtle shaping of reasoning as significant in students' work and to build mathematical concepts.On this basis, we followed the ideas of building up and elaborating the existing intuition about space, developing, unconditionally geometrical intuition. Adding constructivist approach, in the research we have dealt with development of geometrical concepts and geometrical thinking in realistic mathematics in which students learn. We have studies development of students’ knowledge in realistic mathematics, as well as how teachers use this from learning and how this process occurs. We are stating results of the research with significant explanations and conclusions. Innovative model of a textbook, which supports realistic mathematics approach, by models and actions, we have tended to make teaching more efficient and to improve the levels of students’ achievements. Results confirm the general hypothesis that introducing the realistic mathematics, additional innovative textbook, positively influences achievements, and motivation of students of the 4th grade in Geometry and in this way, we confirm the effect of teaching approach into realistic mathematics. Students who learned according to the experimental programme are more successful in factual tasks from the control group students, but these are at the same level in the tasks of knowledge application, and the students of the control group showed much worse results and in this way partially confirmed one of the stated additional hypotheses. Students of the experimental group, in the tasks of knowledge application, have significantly better results in mathematical context, but this is not the case in the realistic one. However, application of the chosen approach created better motivation of students for learning geometrical contents in elementary teaching and one of the additional hypotheses was approved. Attitudes of both teachers and students about the chosen teaching approach is positive, and students recognized the very textbook as an encouraging tool for learning and created pleasant atmosphere and provoked better motivation and readiness for doing problem solving tasks and some additional hypotheses were approved. Our belief is that in a long-term approach, this will prove a greater effect of experimental programme. Explicit and systematically leading the conversation is the characteristic of future in creating cultural and social construction of knowledge, which enables active application of knowledge. In the classroom, the experiment encourages early adoption of geometrical skills, creating simulation of the real world. This process illustrates knowledge, which creates the need for imaginative pictures and results crating geometrical tools. Developing significant cognitive process of intuition, hypothetical reasoning and work with different hypotheses and strategies, students become involved into ‘realistic activities’. This is why it is justifiable to introduce changes into the existing mathematical curriculum, in the teaching praxis to support the teaching process in realistic mathematics (as one of the several possible ones), supported by the quality innovative textbook. The observed lessons have given us a clear picture that teachers should be trained for systematically leading a conversation and classroom discourse, and offer methodologically well created and activated programmed activities. We have opened some issues for further research in teaching geometry, which more directed to development of abilities and spatial reasoning and improving experience when measuring length, area and volume, particularly in elementary teaching. Key words: space, spatial reasoning, RME, geometry, guided reinvention, textbook for elementary Mathematics, levels of knowledge, task type, motivation for learning, Serbia.