Understanding Linear Function in Secondary School Students: A Comparative Study between England and Shanghai

How to facilitate students’ understanding of mathematics is a major concern for the mathematics education community as well as education authorities, especially in England, UK and Shanghai, China. However, research into such understanding in these two regions is still in its infancy. The aim of this thesis is to contribute to this research area by investigating how well students understand a particular mathematical concept, linear function, and describe how their understanding has been shaped. A model of understanding function is defined in terms of six levels: Variable Perspective, Dependent Relationship, Connecting Representations, Property Noticing, Object Analysis, and Inventising. These six levels are developed by examining the most prominent theories from existing Western and Eastern literature on understanding function. Using this model, three perspectives around understanding linear function are investigated: what the official documents expect; what students actually achieve; and teachers’ views of how students’ understanding of linear function develops. Mixed methods are adopted to portray a holistic view of understanding function in the two regions. The quantitative data analysis includes three curricula and seven selected textbooks to identify their characteristics and requirements. The main study also analyses student tests from 403 Year 10 Higher Level English students and 907 Grade 8 Shanghai students. Findings demonstrate that the Shanghai students have more abstract understanding than the English Higher Level students, and are more comfortable with algebraic expression, which is emphasised heavily in the Shanghai curriculum and textbook. The graphic representation dominates the Higher Level English students’ solution approaches, which is again emphasised in their textbooks. This study recommends that the more emphasis should be on algebraic expression for understanding linear function in England and graphic representation in Shanghai

Reviving the Forgotten Scholarly Discipline of Commonplacing to Enhance Teaching & Learning in Higher Education

This paper explains how the forgotten scholarly discipline of commonplacing can be revived and deployed as a technique for enhancing learning and teaching. It presents a case study of a recent third year undergraduate Business School module to demonstrate how reviving the practice of commonplacing can lead to remarkable learner achievements. The paper also provides some advice for teachers and points to opportunities for further development

Exploration of Famille-rose porcelain painting art form

Modern People's understanding of beauty, the exploration and innovation of materials, for our innovation provides infi nite possibilities.Through the understanding of the high-temperature glaze, as well as the exploratory understanding, the rich and variable color glaze characteristics of the kiln change and Famille-rose painting characteristics of the combination, this is based on the understanding of new materials and the improvement of fi ring technology, for the powder porcelain provides a material basis for innovation.Therefore, the combination of high-temperature color glaze and pastel porcelain is an innovative model, which provides a new era contribution to the historical development of pastel. With the further development of ceramic artists, new techniques and techniques of pastel-colored porcelain painting will constantly emerge, and then make the traditional pastel art bloom a new luster

Learning Raw Image Denoising with Bayer Pattern Unification and Bayer Preserving Augmentation

In this paper, we present new data pre-processing and augmentation techniques for DNN-based raw image denoising. Compared with traditional RGB image denoising, performing this task on direct camera sensor readings presents new challenges such as how to effectively handle various Bayer patterns from different data sources, and subsequently how to perform valid data augmentation with raw images. To address the first problem, we propose a Bayer pattern unification (BayerUnify) method to unify different Bayer patterns. This allows us to fully utilize a heterogeneous dataset to train a single denoising model instead of training one model for each pattern. Furthermore, while it is essential to augment the dataset to improve model generalization and performance, we discovered that it is error-prone to modify raw images by adapting augmentation methods designed for RGB images. Towards this end, we present a Bayer preserving augmentation (BayerAug) method as an effective approach for raw image augmentation. Combining these data processing technqiues with a modified U-Net, our method achieves a PSNR of 52.11 and a SSIM of 0.9969 in NTIRE 2019 Real Image Denoising Challenge, demonstrating the state-of-the-art performance. Our code is available at https://github.com/Jiaming-Liu/BayerUnifyAug.Comment: Accepted by CVPRW 201

THE EFFECTS OF STATIC STRETCHING AFTER STRENUOUS TRAINING ON ULTRASTRUCTURE AND FLEXIBILITY OF RATS' GASTROCNEMIUS

The purpose of the present study was to investigate effects of static stretching after strenuous training on the ultrastructure and flexibility of rats' gastrocnemius. 24 male Sprague-Dawley rats were randomly divided into three groups: normal control (NC), training control(TC) and stretching group(ST). The results were as follows: 1) The myofilaments became supercontracted and Z discs were obscure in TC. On the contrary, the myofilaments arranged orderly and the Z lines were clear and the mitochondrial cristas were manifolded in ST. 2) Compared with NC, the ultimate tensile strength of gastrocnemius was increased in TC, while the Max. deformation of gastorcnemius was decreased. However, the Max. deformation in ST was increased than that of NC. The conclusion was that the ultrastructure of muscle was resumed and the ability of distortion and flexibility was improved by static stretching, which decreased the risk of injury