Διερεύνηση γεωμετρικών γνώσεων μαθητών με ήπιες εκπαιδευτικές ανάγκες

Geometry is a structural component of mathematics, with increased spatial and design requirements that cannot be easily met by students with mild disabilities. Systematic investigation of the difficulties encountered by students with mild disabilities in their effort to learn Geometry is a prerequisite for the implementation of effective intervention programs. However, research on this issue is relatively scarce. The aim of the present study was to assess the geometric knowledge of 54 students with mild disabilities (learning disabilities or ADHD) who attended the two last classes of elementary school. Participants were asked to recognize, describe and categorize geometric shapes and solid bodies that were presented in tactile mode and through pictorial representations. Semi-structured clinical interviews were used for gathering the data in the context of Curriculum Based Assessment and the Van Hiele’s model of geometrical thinking. Participants of both categories of mild disabilities presented difficulties in distinguishing shapes and bodies, properly using the terminology, and formatting inductive geometrical reasoning. Participants with learning disabilities had higher achievement when dealing with haptic relative to pictorial representations of geometric shapes and bodies. Sixth graders performed better than fifth graders. Results are discussed in terms of the differences between the two categories of mild disabilities as well as with regard to the implementation of intervention programs.

PENGUASAAN KONSEP GEOMETRI PADA SISWA SMP KOTA PONTIANAK TAHUN 2020

This research was motivated by several reasons: (1) there was a misconception of some elementary school geometry materials that were considered essential; (2) the form of evaluation given was dominantly objective/multiple choice; (3) teachers' teaching methods tend not to be contextual; and (4) students' way of thinking simply to take the practical one. Through this research, it is expected to obtain information about: geometrical reasoning in elementary schools according to Bruner's theory, problem solving and mathematical representations. Theresearch was conducted in a descriptive analytic form, with the following steps: (1) giving questions for the geometry reasoning test for SMP; (2) analyzing answers according to the criteria of reasoning; and (3) mapping students' answers to the results of the analysis according to the profile criteria. The data obtained were analyzed, and the results were described to illustrate the condition of the geometric reasoning abilities of elementary school students. Theresults obtained in this study were: (1) The Mastery of the concept of geometry in each junior high school/equivalent. The target with the acquisition of an average score from all schools was 55, which was quite low because there were some students who did not master the concept of geometry and there were other mathematical concepts related to solving test questions; (2) There was no significant difference in the mastery of geometry concepts for male or femalestudents for each SMP/equivalent target, except for one school, namely SMP Negeri 17, which was because males are superior to females in three questions with a difference in the percentage of numbers of significantly correct; (3) The mastery of geometry concepts in each junior high school. The target of studying each geometry material was considered good, except for question number 1 with the subject of the Pythagorean Theorem, because students were dominant in not being able to use the relationship between concepts, especially the operation ofthe compounding form and the roots.

Structure Synthesis of a Class of Parallel Manipulators with Fully Decoupled Projective Motion

This paper describes the structure synthesis of a special class of parallel manipulators with fully decoupled motion, that is, a one-to-one correspondence between the instantaneous motion space of the end-effector and the joint space of the manipulator. A notable finding of this study is that a fully decoupled design can be achieved for parallel manipulators with any number of degrees of freedom (DOFs) when the rotational DOF of the end-effector is expressed in the form of a projective angle representation. On the basis of the geometrical reasoning of the projective motion interpreted by screw algebra, a systematic approach is developed for synthesizing the structures of f-DOF (f ≤ 6) parallel manipulators with fully decoupled projective motion. Several 2-, 3-, 4-, 5-, and 6-DOF parallel manipulators with fully decoupled projective motion were designed for illustrating the developed method.

Spatial diagrams and geometrical reasoning in the theater

This article offers an analysis of the cognitive role of diagrammatic movements in the theater. Based on the recognition of a theatrical work’s inherent ability to provide new insights concerning reality, the article concentrates on the way by which actors’ movements on stage create spatial diagrams that can provide new insights into the spectators’ world. The suggested model of theater’s epistemology results from a combination of Charles S. Peirce’s doctrine of diagrammatic reasoning and David Lewis’s theoretical account of the truth value of counterfactual conditionals. I argue that in several theatrical works – in particular those whose central image is dominated by movements – the relation of what Lewis names “comparative overall similarity” between the fictional and the actual world is based on diagrammatic homology. The cognitive process involved in deciphering them is, hence, based on diagrammatic reasoning. The main emphasis of the analysis is on the previously unnoticed but important cognitive role of observation in the theater: the idea that observation takes an active role in the reasoning process that enables the spectators to form new knowledge about their actual world. Samuel Beckett’s plays Quad and Come and Go serve here as case studies.

Epistemology of Geometry

From Euclid to Einstein, geometry has continually shown itself to be a remarkably rich area of philosophical inquiry. Major geometrical traditions find their roots in the Āryabhatīya of Āryabhata from the classical age of Indian mathematics, the Nine Chapters on the Mathematical Art from Han dynasty China, and in Euclid’s Elements of ancient Greece, conveyed via the Arabic textual tradition to medieval scholars. Ancient reasoning methods—characteristically relying on pictures or diagrams—have found a renaissance in the scholarship of the last few decades and are now seen as far more rigorous than has often been supposed. Much contemporary geometry traces back to the development of algebraic methods (spurred in the Western tradition through philosophers such as Descartes and Leibniz), and geometry today overlaps with many other areas of mathematics (including set theory, category theory, and homotopy type theory). In the interim, a number of traditions have risen to prominence. Kant regarded geometry as the paradigm example of the synthetic a priori, and Hilbert’s work on geometry set a new standard for the axiomatization of a mathematical theory. Having always been admired as a paradigm of science, there is a long-standing tradition of seeking out “geometrical formulations” of physical theories (including classical mechanics, electromagnetism, and quantum physics). The emergence of a plurality of non-Euclidean geometries—sending shock waves through mathematics, physics and philosophy—led in particular to the 19th-century “problem of space,” which then fed into Einstein’s theories of special and general relativity, radically transforming the physical application of geometrical notions. This article is organized into three major areas of the epistemology of geometry. The first, Geometrical Reasoning, concerns the epistemology of geometrical practice itself. The second, Geometry and Philosophy, concerns the various pathways between geometry and philosophical theorizing more generally, including the historical engagement between the two. And the third, Geometry and Physics, concerns the intimate connections between geometry and physics, especially (of course) the physics of space. The bibliography begins with a selection of general overviews and textbooks that can serve as entry points into more specific areas.

Analysis of the Difficulty of Mathematical Education Students in Completing the Geometric Running Problem Based on Van Hiele Theory in Geometry Transformation

The purpose of this study was to: (1) finding out the difficulties experienced by mathematics education students in solving geometric reasoning problems based on van Hiele's theory; (2) identifying the factors causing difficulties experienced by students in solving geometric problems based on van Hiele’s theory; and (3) determining the steps that need to be taken to overcome the students' difficulties in solving geometric reasoning problems based on van Hiele's theory in the Transformation Geometry Course. The students' difficulties in solving geometric reasoning problems based on van Hiele's levels will give an idea of the indicators of geometrical reasoning abilities that are still low, so that the right alternative solutions are obtained. This type of research is descriptive research with a qualitative approach. The research subjects were 28 students who programed geometry transformation courses. The instrument in this study was a test instrument, namely geometric reasoning abilities of students as many as 5 questions consisting of 5 levels of ability, namely visualization, analysis, abstraction, formal deduction, and rigor. While the data analysis techniques in this study used descriptive analysis. Collecting data in this study used interview techniques and written tests. The results showed that from the five indicators of geometric reasoning ability, for the visualization level, there were 26 people who achieved the optimal score with a percentage of 92.9. Seen at the level of analysis still not reached optimally with a percentage of 21.4 or only 6 people who achieved the optimal score, while the level of abstraction, formal deduction, and rigor has not been achieved. Difficulties experienced by students at the level of analysis, abstraction, formal deduction, and rigor. The causal factors experienced by students based on the results of interviews obtained information that students have difficulty answering questions due to several things including; students have forgotten about the material being taught, when they learn they understand but are less interested in developing, feel unsatisfied so they expect concrete media, need to be trained in many questions, and follow up to students. From this information, an appropriate alternative is needed, for example using van Hiele's theory to familiarize students with reasoning skills.