Artificial ANNs (ANNs) are relatively new computational tools used in the development of intelligent systems, some of which are inspired by biological ANNs, and have found widespread application in the solving of a variety of complex real-world problems. It boasts enticing features as well as remarkable data processing capabilities. In this paper, a comprehensive overview of the backpropagation algorithm for digital image denoising was discussed. Then, we presented a probabilistic analysis of how different algorithms address this challenge, arguing that small ANNs can denoise small-scale texture patterns almost as effectively as their larger equivalents. The results also show that self-similarity and ANNs are complementary paradigms for patch denoising, as demonstrated by an algorithm that effectively complements BM3D with small ANNs, surpassing BM3D at a low cost. Here, one of the most significant advantages of this learning technique is that, once taught, digital images may be recovered without prior knowledge of the degradation model (noise/blurring) that caused the digital image to become distorted.

The current study aims to explore the impact of the two-column format in writing simple mathematical arguments. That is to say, a structured method of presenting a mathematical proof or argument by using a tabular layout with two columns. The underlying goal of the research reported in this paper is to inform understanding of how to effectively assess students’ proof construction, particularly online. In this paper, we report the results of an experiment designed to test the hypothesis that students provide more justifications when using the two-column format in writing mathematical proofs. The participants were 80 first year undergraduate mathematics students at the University of Edinburgh who were enrolled in a calculus course. The findings supported this hypothesis: overall frequency of justification were higher in the two-column condition compared with the traditional condition. This is due to the format structure where students are expected to justify each line in the statements’ column with a corresponding explanation in the justification column. However, as a side effect of increasing the amount of justifications, students in the two-column group generated more non-explanation statements which we classed as paraphrasing. A secondary outcome was our use and further development of the coding scheme.

The STACK system is a computer aided assessment package for mathematics. STACK questions include full algebraic input with validation. Feedback is provided to students using "potential response trees", written by the teacher for each question. In this research, we are updating STACK potential response tree based on students' concerns in learning induction proofs. We have identified a specific misconception in learning mathematical induction from prior educational research, designed STACK question to test if students exhibit this misconception, and then illustrated how we updated STACK potential response tree based on this misconception. One main goal of separating concerns is to understand students’ responses and evaluate the question itself from an academic prospective and ultimately to improve the questions for future years. In addition, one of the contributions of this study is to improve our general understanding of how to design and use STACK potential response trees.