Developing pedagogic theory: the case of geometry proof teaching

This paper compares the teaching of proof in geometry at the lower secondary school level in the East (China, Japan) and in the West (UK). The aim is to seek to identify teaching strategies that might inform new pedagogic approaches for teaching deductive proof and proving. In the West, much theory focuses on examining the nature of classroom tasks. In the East, the heuristic nature of teaching and the theory of variation are useful as they focus on the dynamic role of the teacher. The paper suggests that the main need is for deeper thinking on the relationship between teachers’ instructional practices and the development of students’ mathematical reasoning

The Application of Two-level Attention Models in Deep Convolutional Neural Network for Fine-grained Image Classification

Fine-grained classification is challenging because categories can only be discriminated by subtle and local differences. Variances in the pose, scale or rotation usually make the problem more difficult. Most fine-grained classification systems follow the pipeline of finding foreground object or object parts (where) to extract discriminative features (what). In this paper, we propose to apply visual attention to fine-grained classification task using deep neural network. Our pipeline integrates three types of attention: the bottom-up attention that propose candidate patches, the object-level top-down attention that selects relevant patches to a certain object, and the part-level top-down attention that localizes discriminative parts. We combine these attentions to train domain-specific deep nets, then use it to improve both the what and where aspects. Importantly, we avoid using expensive annotations like bounding box or part information from end-to-end. The weak supervision constraint makes our work easier to generalize. We have verified the effectiveness of the method on the subsets of ILSVRC2012 dataset and CUB200_2011 dataset. Our pipeline delivered significant improvements and achieved the best accuracy under the weakest supervision condition. The performance is competitive against other methods that rely on additional annotations