A Comparative Study Of Directional Connections In Popular U.S. And Chinese High School Mathematics Textbook Problems

Mathematical connection has received increasing attention and become one major goal in mathematics education. Two types of connections are distinguished: (a) between-concept connection, which cuts across two concepts; and (b) within-concept connection, which links two representations of one concept. For example, from the theoretical probability to experimental probability is a between-concept connection; generate a graph of a circle from its equation is a within-concept connection. Based on the directionality, unidirectional and bidirectional connections are discerned. Bidirectional connection portrays a pair of a typical and a reverse connection. The benefits of connections, especially bidirectional connections, are widely endorsed. However, researchers indicated that students and even teachers usually make unidirectional connections, and underlying reasons may be the curriculum and cognitive aspects. Previous studies have reported differences in learning opportunities for bidirectional connections in U.S. and Chinese textbook problems, but few have explored the high school level. This study addressed this issue by comparing the directionality of mathematical connections and textbook-problem features in popular U.S. (the UCSMP series) and Chinese (the PEP-A series) high school mathematics textbook problems. The results indicated that the between-concept condition and unidirectional connections dominated textbook problems. Mathematical topic, contextual feature, and visual feature were most likely to contribute to different conditions of connections. Overall, problems dealing with quadratic relations from Chinese textbooks presented a vigorous network of more unique and total between-concept connections with balanced typical and reverse directions than the U.S. counterparts. Problems from U.S. textbooks showed a denser network of (a) within-concept connections in two topics and (b) between-concept connections in probability and combinatorics than the Chinese counterparts, but still exhibited an emphasis on specific concepts, representations, and directionality. The study reached a generalized statement that the new-to-prior knowledge direction was largely overlooked in textbook problems. The results have implications for adopting graph theory and Social Network Analysis to visualize and evaluate mathematical connections and informing mathematics teachers and textbook authors to pay attention to the new-to-prior knowledge connection

The Euclidean Space is Evil: Hyperbolic Attribute Editing for Few-shot Image Generation

Few-shot image generation is a challenging task since it aims to generate diverse new images for an unseen category with only a few images. Existing methods suffer from the trade-off between the quality and diversity of generated images. To tackle this problem, we propose Hyperbolic Attribute Editing (HAE), a simple yet effective method. Unlike other methods that work in Euclidean space, HAE captures the hierarchy among images using data from seen categories in hyperbolic space. Given a well-trained HAE, images of unseen categories can be generated by moving the latent code of a given image toward any meaningful directions in the Poincar\'e disk with a fixing radius. Most importantly, the hyperbolic space allows us to control the semantic diversity of the generated images by setting different radii in the disk. Extensive experiments and visualizations demonstrate that HAE is capable of not only generating images with promising quality and diversity using limited data but achieving a highly controllable and interpretable editing process

An improvement of a recent closed graph theorem

AbstractWe obtain a new closed graph theorem which is a substantial improvement of a recent result

Hidden Markov Model with Information Criteria Clustering and Extreme Learning Machine Regression for Wind Forecasting

This paper proposes a procedural pipeline for wind forecasting based on clustering and regression. First, the data are clustered into groups sharing similar dynamic properties. Then, data in the same cluster are used to train the neural network that predicts wind speed. For clustering, a hidden Markov model (HMM) and the modified Bayesian information criteria (BIC) are incorporated in a new method of clustering time series data. to forecast wind, a new method for wind time series data forecasting is developed based on the extreme learning machine (ELM). the clustering results improve the accuracy of the proposed method of wind forecasting. Experiments on a real dataset collected from various locations confirm the method\u27s accuracy and capacity in the handling of a large amount of data

Demi-linear Analysis III---Demi-distributions with Compact Support

A series of detailed quantitative results is established for the family of demi-distributions which is a large extension of the family of usual distributions

Atmospheric hydroxyl radical (OH) abundances from ground-based ultraviolet solar spectra: an improved retrieval method

The Fourier Transform Ultraviolet Spectrometer (FTUVS) instrument has recorded a long-term data record of the atmospheric column abundance of the hydroxyl radical (OH) using the technique of high resolution solar absorption spectroscopy. We report new efforts in improving the precision of the OH measurements in order to better model the diurnal, seasonal, and interannual variability of odd hydrogen (HOx) chemistry in the stratosphere, which, in turn, will improve our understanding of ozone chemistry and its long-term changes. Until the present, the retrieval method has used a single strong OH absorption line P1(1) in the near-ultraviolet at 32,341 cm−1. We describe a new method that uses an average based on spectral fits to multiple lines weighted by line strength and fitting precision. We have also made a number of improvements in the ability to fit a model to the spectral feature, which substantially reduces the scatter in the measurements of OH abundances