In this paper, the method of understanding of visual objects is presented. The main novelty of the presented method is that the process of understanding is related to the visual concept represented ...as a symbolic name of the possible classes of shapes. The possible classes of shapes, viewed as hierarchical structures, are incorporated into the shape model. At each stage of the reasoning process that led to assigning an examined object to one of the possible classes, novel processing methods are used. An understanding is based on interpretation of the visual object as a meaningful unit. A big advantage of the proposed method of understanding of the visual objects is that it can explain many problems connected with understanding visual forms. In this paper, the selected concept of the method of understanding of the visual objects is discussed in the context of the psychological and philosophical research. This method is implemented as a module of the shape understanding system (SUS) and tested on the broad classes of shapes.
In this paper the new method of understanding of the curve-polygon object is presented. The method of understanding of the curve-polygon object is part of the research aimed at developing a shape ...understanding method able to perform complex visual tasks connected with visual thinking. The shape understanding method is implemented as the shape understanding system (SUS). Understanding includes, among others, obtaining the visual concept in process of the visual reasoning, naming and visual explanation by generation an object from a required class. In this paper generation of the object from the selected well defined class, the curve-polygon class, as well as assigning the visual object into one of the shape classes is presented. The generation of the visual objects is used in SUS during learning of the visual concept, explanatory process and self-correcting process. The visual object is assigned into one of the shape classes during the visual reasoning process. The visual reasoning, presented in this paper, in contrast to other forms of reasoning depends on the type of objects which are analysed. In this paper visual reasoning that assigns an object to the curve-polygon class is presented. The shape understanding system consists of different types of experts that perform different processing and reasoning tasks. The self-correcting expert, that implements the new method of testing and reasoning, is invoked to test ability of the system to understand the concept of the curve-polygon shape.
This study identifies characteristics of polygon class learning opportunities for 8–9-year-old children during the whole-class instruction. We consider the interplay between the geometrical tasks ...demanding different ways of reasoning, features of children’s geometrical thinking, and the teacher’s moves to identify characteristics of learning opportunities. We identified 3 types of learning opportunities during whole-class instruction: (a) recognizing (initiating the deconstruction dimensional), (b) supporting children’s analytical reasoning, and (c) encouraging children to establish relations between attributes of the figures. Our findings highlight the holistic facet of the learning opportunities of geometry in primary education that connect the students’ geometrical arguments generated by solving enriching geometrical tasks and the teacher’s moves drawing on children’s geometrical thinking during the whole-class instruction. We conjectured that weaving these 3 aspects together supported the emergence of relevant geometric learning opportunities for children.
This paper reports sophistication levels in third grade children’s understanding of polygon concept and polygon classes. We consider how children endow mathematical meaning to parts of figures and ...reason to identify relationships between polygons. We describe four levels of sophistication in children’s thinking as they consider a figure as an example of a polygon class through spatial structuring (the mental operation of building an organization for a set of figures). These levels are: (i) partial structuring of polygon concept; (ii) global structuring of polygon concept; (iii) partial structuring of polygon classes; and (iv) global structuring of polygon classes. These levels detail how cognitive apprehensions, dimensional deconstruction, and the use of mathematical language intervene in the mental process of spatial structuring in the understanding of the classes of polygons.
PDF