Comparing example generation with classification in the learning of new mathematics concepts

Prompting learners to generate examples has been proposed as an effective way of developing understanding of a new concept. However, empirical support for this approach is lacking. This article presents two empirical studies on the use of example-generation tasks in an online course in introductory university mathematics. The first study compares the effectiveness of a task prompting learners to generate examples of increasing and decreasing sequences, with a task inviting them to classify given examples; it also investigates the effectiveness of different sequences of generation and classification tasks. The second study replicates the investigation of interactions between generation and classification tasks. The findings suggest that there is little difference between the two types of task, in terms of students' ability to answer later questions about the concept.

Research on an Adaptive Neural Network K-Pixel Adversarial Example Generation Algorithm

Neural network technology has achieved good results in many tasks, such as image classification. However, for some input examples of neural networks, after the addition of designed and imperceptible perturbations to the examples, these adversarial examples can change the output results of the original examples. For image classification problems, we derive low-dimensional attack perturbation solutions on multidimensional linear classifiers and extend them to multidimensional nonlinear neural networks. Based on this, a new adversarial example generation algorithm is designed to modify a specified number of pixels. The algorithm adopts a greedy iterative strategy, and gradually iteratively determines the importance and attack range of pixel points. Finally, experiments demonstrate that the algorithm-generated adversarial example is of good quality, and the effects of key parameters in the algorithm are also analyzed.