10,047 research outputs found
Studentsâ Evolving Meaning About Tangent Line with the Mediation of a Dynamic Geometry Environment and an Instructional Example Space
In this paper I report a lengthy episode from a teaching experiment in which fifteen Year 12 Greek students negotiated their
definitions of tangent line to a function graph. The experiment was designed for the purpose of introducing students to the
notion of derivative and to the general case of tangent to a function graph. Its design was based on previous research results on
studentsâ perspectives on tangency, especially in their transition from Geometry to Analysis. In this experiment an instructional
example space of functions was used in an electronic environment utilising Dynamic Geometry software with Function
Grapher tools. Following the Vygotskian approach according to which studentsâ knowledge develops in specific social and
cultural contexts, studentsâ construction of the meaning of tangent line was observed in the classroom throughout the
experiment. The analysis of the classroom data collected during the experiment focused on the evolution of studentsâ personal
meanings about tangent line of function graph in relation to: the electronic environment; the pre-prepared as well as
spontaneous examples; studentsâ engagement in classroom discussion; and, the role of researcher as a teacher. The analysis
indicated that the evolution of studentsâ meanings towards a more sophisticated understanding of tangency was not linear. Also
it was interrelated with the evolution of the meaning they had about the inscriptions in the electronic environment; the
instructional example space; the classroom discussion; and, the role of the teacher
Using theoretical-computational conflicts to enrich the concept name of derivative
Recent literature has pointed out pedagogical obstacles associated with the use of computational environments in the learning of mathematics. In this paper, we focus on the pedagogical role of the computer's inherent limitations in the development of learners' concept images of derivative. In particular, we intend to discuss how the approach to this concept can be designed to prompt a positive conversion of those limitations for the enrichment of concept images. We present results of a case study with six undergraduate students in Brazil, dealing with situation of theoretical-computational conflict
Effective Approaches to Attention-based Neural Machine Translation
An attentional mechanism has lately been used to improve neural machine
translation (NMT) by selectively focusing on parts of the source sentence
during translation. However, there has been little work exploring useful
architectures for attention-based NMT. This paper examines two simple and
effective classes of attentional mechanism: a global approach which always
attends to all source words and a local one that only looks at a subset of
source words at a time. We demonstrate the effectiveness of both approaches
over the WMT translation tasks between English and German in both directions.
With local attention, we achieve a significant gain of 5.0 BLEU points over
non-attentional systems which already incorporate known techniques such as
dropout. Our ensemble model using different attention architectures has
established a new state-of-the-art result in the WMT'15 English to German
translation task with 25.9 BLEU points, an improvement of 1.0 BLEU points over
the existing best system backed by NMT and an n-gram reranker.Comment: 11 pages, 7 figures, EMNLP 2015 camera-ready version, more training
detail
Recurrent Models of Visual Attention
Applying convolutional neural networks to large images is computationally
expensive because the amount of computation scales linearly with the number of
image pixels. We present a novel recurrent neural network model that is capable
of extracting information from an image or video by adaptively selecting a
sequence of regions or locations and only processing the selected regions at
high resolution. Like convolutional neural networks, the proposed model has a
degree of translation invariance built-in, but the amount of computation it
performs can be controlled independently of the input image size. While the
model is non-differentiable, it can be trained using reinforcement learning
methods to learn task-specific policies. We evaluate our model on several image
classification tasks, where it significantly outperforms a convolutional neural
network baseline on cluttered images, and on a dynamic visual control problem,
where it learns to track a simple object without an explicit training signal
for doing so
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