Darbe analizuojamos dvimačių ir trimačių objektų geometrinės transformacijos. Yra sistemų, kurios pateikia priemones demonstruoti ir atlikti užduotis. Yra galimybė sukurti ir transformuoti figūrą. Bet tokiose sistemose nėra galimybės atlikti kontrolinę užduotį, kurią vėliau galima peržiūrėti ir spręsti apie studento žinias. Analizuojamose sistemose nėra galimybės išsaugoti užduotį. Kuriama sistema turi galimybę sukurti, įtraukti ir išsaugoti naują užduotį. Sistema skirta dviejų tipų vartotojams - paprasti vartotojai ir administratoriai. Paprastas vartotojas gali mokintis transformacijų valdymo ir atlikti kontrolinę užduotį. Administratorius be šių galimybių dar gali kurti naujas užduotis ir valdyti duomenų bazę. / I am analysing the system for two-dimentional and three-dimentional objects transformation in this work. There is the system that serves the purpose to demonstrate and control exercised worksheets. Available systems allows to create and transform the shape. But there is no condition of worksheet, that after accomplished, we could conclude about students‘ knowledge. There is no possibility to save created worksheet in the analysed systems, so there is no chance to resume its data base. My demonstrated system has the tools for creating, saving and including new worksheet to the data base. There are two types of users using the system – ordinary user and administrating user. Administrator has all privilege to control the program. Ordinary user can study or make worksheet.

This text discusses final results from empirical studies, scientific articles and literature from the period 1990-2023, concerning teachers’ knowledge, students’ misconceptions and various teaching methods related to geometric objects. The results highlight challenges for both teachers and students in understanding and defining geometric shapes and figures. The work elucidates students in grade 4-6 difficulties and knowledge in identifying geometric objects in varied positions, as well as their understanding of the properties of geometric shapes and figures. The teacher’s understanding is crucial för imparting accurate information to students in instruction. Therefore, effective teaching methods such as practical activities, everyday connection and Van Hiele’s instructional model are suitable to apply in practice. This instructional model has been effective in students education and is therefore a good example for a teaching method.  In summary, the results are based on the abilities of teachers and students and their abilities can be enhanced by adapting teaching methods related to geometric objects, and how misconceptions are something that should be taken seriously and be prevented.

This thesis is an investigation into the phenomenon which Shozo Ohmori (1921-1997) considered “a peculiar manner of awareness”, and to which he attributed the term ‘fancy’. The objective is to achieve an approximate understanding of Ohmori’s theory of ‘fancy’, as it relates to awareness of entities in three-dimensional space, and the extensions mentioned in his only publication in English: “Beyond Hume’s Fancy” (1974). This objective will be realized by asking three questions. The first question is how we are to understand the demarcation of the different phenomena of awareness which Ohmori identifies. The second question that this thesis asks is what applications that the phenomenon ‘fancy’ mentioned in Ohmori’s account have, as Ohmori saw it. Having answered these questions, I will then make an assessment of another salient consideration: how does Ohmori’s employment of the term ‘fancy’ relate to Hume’s employment of the same term (seeing as the name of Ohmori’s article makes such a reference). As we shall see, Ohmori is attempting to identify a more specific phenomenon than the widely discussed issue of thinking about something that is not currently perceivable in our perceptual field. The third and final question that this thesis asks is whether there are any salient issues with Ohmori’s theory of ‘fancy’ and, if so, whether those issues can be resolved. When we are aware of entities in three-dimensional space, we are subject to various mental processes. Our awareness, seemingly, uses different modes of interpretation and orientation. In other words, our ‘point of view’ (which is something that not only pertains to the use of our visual sensory organs) determines both our place and relation towards other entities. One salient issue when considering the notion of awareness is how and by which order awareness emerges. Impressions, as David Hume would call them, seemingly precede our ideas. Sense-data, as Shozo Ohmori phrased it, is unquestionably inseparable from conceptions. Our conceptions, in turn, seem to inform our perceptions with expectations and predictions of how things are. When we perceive an entity, we are ready to make judgements about its being at this moment. When we see the front of a desk, we are ready to claim awareness of said desk-front as part of a desk (which entails the ontology of a desk, namely, being a three-dimensional construction of a particular variety). In everyday situations we simply speak of such an awareness as ‘perception’ when in actuality, all we see (which constitutes the sense-data or content of a perception) is the front of a desk. It seems we cannot regard our awareness of a desk (a three-dimensional entity) as a perception simpliciter. Of course, by having a notion of what a desk is, our awareness is pregnant with a ‘conception’ in the form of an idea that is informing our awareness of said desk. But our conceptual understanding of the notion of something being a desk is not enough to explain what our awareness of a desk-at-this-moment is. At least, that is what Ohmori thought.