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Students' mental manipulation of a shape at the early educational level

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Swoboda E., Zambrowska M.
Didactica Mathematicae
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2019
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tom 41
EN
In this article we present results of research aiming at describing the strategies used by 10-year-old children while solving one geometric task. The research was lead through three different stages. In May 2015 the Educational Research Institute in Poland carried out a survey titled Competences Of Third Grades. One task, related to the domain "the geometric imagination", solved by 199 361 students, achieved a low degree of solvability, also among students achieving good results in other educational domains. To identify the strategy for solving this task, about 3000 submitted solutions were reviewed. One of them was based on imagination of action. We were interested to which extent such dynamic thinking is present in children's solutions, therefore, in the next stage, individual observations of a child working on this task were carried out. 35 children aged 10 years participated in this stage. The results of all stages are briefly presented in this study, with particular attention to the result of the third stage. This last stage supports our opinion that dynamic reasoning is possible to trigger, but requires special teaching methodology and specially designed tasks.
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Analysis of students’ solutions to geometry questions forming a bundle

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Czajkowska M., Zambrowska M.
Didactica Mathematicae
|
2016
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tom 38
EN
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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