Search

This article aims to identify and understand the mathematics teachers' geometric knowledge, when addressing geometry concepts for students at Middle School. For this purpose, the theoretical tool Knowledge Quartet (KQ) is used to identify and analyze the dimensions of knowledge that are revealed in the actions triggered by two teachers in the classroom. The research context took place in a process of continuing education in geometry, in a group with collaborative characteristics. The data were produced through audio and video recording and later transcribed. Critical events were selected of the investigated environment. In addition to being a theoretical tool that identifies the teacher's mathematical and didactic knowledge in practice, according to the results, the KQ contributed to identify gaps associated with the teacher's difficulties in face of the contingencies that present themselves in the context of geometry teaching. [ABSTRACT FROM AUTHOR]

Proofs are attempts to conclusively demonstrate the validity of the claim for all cases indicated within its domain, which implies that proving should involve thoughtful consideration of the domain. This study analyzed the enactment of three general claim tasks, or tasks where the domain of the claim referred to an infinite number of cases, that were used during an introduction-to-proof teaching experiment with 10 ninth grade students. We analyzed the tasks in terms of the opportunities students experienced to engage in reasoning-and-proving and attend to the domain of the claims. The use of general claim tasks provided students with opportunities to engage in varied reasoning-and-proving activities, including forms not typically found in textbooks. Students’ attention to the domain of the claims increased over the course of study as a result of the teacherresearcher’s continued focus on this aspect of the tasks, although their attention did not always encompass all cases within the domain. By making the domain of mathematical claims a central focus, we emphasize its important role in the reasoning-and-proving opportunities afforded to students and contribute to an understanding of students’ early interpretations of this aspect of proof tasks. [ABSTRACT FROM AUTHOR]

The task of unsupervised image‐to‐image translation has seen substantial advancements in recent years through the use of deep neural networks. Typically, the proposed solutions learn the characterizing distribution of two large, unpaired collections of images, and are able to alter the appearance of a given image, while keeping its geometry intact. In this paper, we explore the capabilities of neural networks to understand image structure given only a single pair of images, A and B. We seek to generate images that are structurally aligned: that is, to generate an image that keeps the appearance and style of B, but has a structural arrangement that corresponds to A. The key idea is to map between image patches at different scales. This enables controlling the granularity at which analogies are produced, which determines the conceptual distinction between style and content. In addition to structural alignment, our method can be used to generate high quality imagery in other conditional generation tasks utilizing images A and B only: guided image synthesis, style and texture transfer, text translation as well as video translation. Our code and additional results are available in https://github.com/rmokady/structural-analogy/ [ABSTRACT FROM AUTHOR]

Copyright of German International Journal of Modern Science / Deutsche Internationale Zeitschrift für Zeitgenössische Wissenschaft is the property of Artmedia24 and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Paradigma is the property of Universidad Pedagogica Experimental Libertador and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This study investigates the impact of a dynamic geometry environment, GeoGebra, in enabling grade 9 students to explore a geometrical task related to the Euler's line. The research subjects were grade 9 students in India and Sweden who had no prior experience of using dynamic geometry. Their approach to geometrical reasoning, argumentation and conjecture making has been analysed using Marton's theory of variation, Pea's theory of technology as amplifier and reorganizer and with Marrades and Gutiérrez categorization of proofs. Results indicate that when students of both countries worked on geometrical tasks in GeoGebra, they arrived at similar conclusions. For both groups of students, GeoGebra played the role of amplifier and reorganiser in enabling their explorations. Further, in some of the construction and dragging episodes it was observed that the four functions of variation, namely, contrast, generalisation, separation and fusion played a significant role in developing students' geometrical thinking. Results further indicate that the dynamic geometry environment (DGE) facilitated the making of conjectures and developing empirical proof. However, when it came to developing a deductive proof, students required adequate scaffolding. In general, it concluded that students perform adequately when given investigatory problems in such an environment. They learn new mathematics and learn to handle the DGE at the same time. [ABSTRACT FROM AUTHOR]

In recent years, several extensions of the Hadoop system have been proposed for dealing with spatial data. SpatialHadoop belongs to this group of projects and includes some MapReduce implementations of spatial operators, like range queries and spatial join. the MapReduce paradigm is based on the fundamental principle that a task can be parallelized by partitioning data into chunks and performing the same operation on them, (map phase), eventually combining the partial results at the end (reduce phase). Thus, the applied partitioning technique can tremendously affect the performance of a parallel execution, since it is the key point for obtaining balanced map tasks and exploiting the parallelism as much as possible. When uniformly distributed datasets are considered, this goal can be easily obtained by using a regular grid covering the whole reference space for partitioning the geometries of the input dataset; conversely, with skewed distributed datasets, this might not be the right choice and other techniques have to be applied. for instance, SpatialHadoop can produce a global index also by means of a Quadtree-based grid or an Rtree-based grid, which in turn are more expensive index structures to build. This paper proposes a technique based on both a box counting function and a heuristic, rooted on theoretical properties and experimental observations, for detecting the degree of skewness of an input spatial dataset and then deciding which partitioning technique to apply in order to improve as much as possible the performance of subsequent operations. Experiments on both synthetic and real datasets are presented to confirm the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]