Practice proves that students tend to face difficulties in learninggeometry. This observation is partially confirmed by the results of educationalresearch as well as external exams. It happens repeatedly that studentsget lower marks in arithmetic or algebra tasks. The causes of such situationare complex. One of the reasons is that teaching geometry requires specialteaching skills characteristic for this specific teaching branch as well as theneed for “specific vision”. Therefore, I decided to study the geometric skillsof mathematics teachers more carefully. For this purpose, I made use of tworesearch results: international research TEDS-M 2008 as well as nationwideresearch The research of needs the elementary education teachers as well asmathematics teachers have in the scope of their professional development.This article presents the results of the analysis together with my personalthoughts on education and improvement of teachers’ skills in the area of geometry.
W ostatnich latach w wielu krajach, tym również Polsce, w centrum uwagi znalazło się kształcenie przyszłych kadr nauczycielskich i kompetencje czynnych nauczycieli zajmujących się edukacją matematyczną. Zaczęto prowadzić badania, których celem było m.in. określenie związku między kompetencjami nauczyciela a wiedzą i umiejętnościami uczniów. Niniejszy artykuł stanowi przegląd badań w tym zakresie, prowadzonych w różnych krajach europejskich.
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In many countries, including Poland, attention has been focussed on teacher training and in-service training for the teaching of mathematics over recent years. Research has been initiated to identify the relationship between teacher competence and knowledge and skills of their students. This article reviews research conducted in different European countries.
One of the main goals of mathematical education is to develop the skills for problem solving as well as skills that help carry out mathematical reasoning and argumentation.Geometric problems play here a special role. These require the person solving them to act with an inquiry attitude and a ‘specific vision’. The ‘specific vision’ is the ability one can manipulate with geometric objects in ones’ mind and perceive, separate and focus on the important information only. However, it is not enough to “see” it is also necessary to know how to interpret what is being seen. Although many researchers have dealt with the problem and many establishments have been made in this scope, the question of how to develop the skills of the “specific vision” stays still open.Herein article presents the research results which aimed at, among others, verification to what degree the combination of geometry problems formed into a bundle helps the secondary school students ‘notice’ and understand the presented situation and as a consequence to find the answer to few questions about this situation. We wanted to establish whether such an organised educational environment entails students natural thinking over the subsequent bundle of problems solved, or maybe makes them return to questions already solved, or by the usage of knowledge acquired helps students to find the problem solution for the next question or a correction for the committed mistakes. The analysis was based on some results coming from the survey School of Independent Thinking conducted by the Institute for Educational Research in 2011.
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The language of school mathematics is specific as it combines the elements of natural language and the language of mathematics. Practice shows that sometimes the language, instead of becoming a tool for communication of information, may be an obstacle in the way of communication between the speaker and the listener. Frequently during mathematical education classes there is no proper communication between the teacher and the learners. The students do not understand what the teacher says, and the teacher does not try to understand the meaning of the students’ utterances. For the last decade there has been a new source of information in the lesson – a computer, thus a new way of communication. In the paper we will present and discuss some of the difficulties associated with communication between teacher – students and computer – students, illustrating them with examples from the school practice.