Content knowledge and pedagogical content knowledge in Taiwanese and German mathematics teachers

In comparing content knowledge (CK) and pedagogical content knowledge (PCK) of Taiwanese and German inservice mathematics teachers, the present study examines whether the two-dimensional structure of teachers' subject matter knowledge is cross-culturally invariant and whether differences in teacher education and in teacher selection are reflected in teachers' subject matter knowledge. The results confirm that CK and PCK represent two distinct, but correlated dimensions, even in teachers from completely different backgrounds. Taiwanese inservice teachers showed considerably higher CK and also higher PCK scores than German teachers. Teacher education and teacher selection should be considered important levers for reform in mathematics education.     

相空间中二阶非完整力学系统的形式不变性

研究相空间中二阶非完整力学系统的形式不变性．给出相空间中二阶非完整力学系统形式不变性的定义和判据,得到形式不变性的结构方程和守恒量形式,并举例说明结果的应用．     

Comparisons of Three Empirical Methods for Partial Factorial Invariance: Forward,Backward, and Factor-Ratio Tests

When factorial invariance is violated, a possible first step in locating the source of violation(s) might be to pursue partial factorial invariance (PFI). Two commonly used methods for PFI are sequential use of the modification index (backward MI method) and the factor-ratio test. In this study, we propose a simple forward method using the confidence interval (forward CI method). We compare the performances of the aforementioned 3 methods under various simulated PFI conditions. Results indicate that the forward CI method using 99% CIs has the highest perfect recovery rates and the lowest Type I error rates. A performance that is competitive with this is that produced by the backward method with the more conservative criterion (MI = 6.635). Consistently delivering the poorest performance, regardless of the chosen confidence level, was the factor-ratio test. Also discussed are the work’s contribution, implications, and limitations.     

WebQuest教学模式评价问题研究

WebQuest作为一种基于网络的探究式教学模式,其评价环节是至关重要而又难度较大的部分。针对WebQuest教学模式应用过程中出现的问题,参考圣地亚哥州立大学WebQuest研究中心提出的评价量规,结合教学实际,该文提出明确评价目的、制定评价原则、制定量规的评价策略,并对评价量规所测数据的效度与信度进行检验。     

Psychometric properties of Science Motivation Questionnaire II-Chinese version in two waves of longitudinal data

Science motivation is an important factor that directly influences students’ science learning. Numerous studies have been undertaken to develop and validate questionnaire items for measuring students’ motivation in science learning. This study is the first longitudinal examination of the Chinese version of Science Motivation Questionnaire II (SMQ II-C) in a Chinese cultural context. Using two waves of surveys, we evaluated its internal structure validity and criterion-related validity. Results showed that at each time point, scores were internally consistent and the hypothesized five-factor model was confirmed as the best model fit for the data. Results of multigroup invariance revealed the structure of the SMQ II-C was equivalent within gender subgroups. Furthermore, the present study added longitudinal invariance evidence of the SMQ II-C by sampling two-time points. Overall, this study suggests the SMQ II-C is a robust instrument for evaluating Chinese high school students’ motivation to learn science. Furthermore, boys yielded higher scores than girls among all five subscales of science motivation and significant gender differences were observed in both waves. Implications and limitations of these results are discussed.     

梯度特征向量法的性质及在新元素导入下强保序的充要条件

讨论了梯度特征向量法的四个性质,即相容性、协调性、置换不变性、对称性,并且用梯度特征向量法推导和证明了判断矩阵在新元素导入下强保序的充要条件．     

有关规范场与纤维丛关系问题的三次阐释

20世纪末期,先后有四位学者论述了规范场与纤维丛的关系：数学物理学家陆启铿的研究最早发表,它表明抽象数学世界的纤维丛在物理世界获得了规范场这一对应物,纤维丛的客观实在性得到了体现;物理学家昊大峻与杨振宁的研究影响深远,它体现了纤维丛为规范场提供了基础性支持这一思想;数学家陈省身给出了一个本质性的总结：一维纤维的几何表示就是麦克斯韦方程（电磁场）,它向二维推广就是杨一米尔斯方程（规范场）。     

谈极限保号性的教与学

极限保号性是极限理论中的重要性质,对这一性质的教与学,本文提出比现行教材更全面,更简捷明确,更便于学习者掌握其实质的阐述方法。     

Improving the Measurement of School Climate Using Item Response Theory

The U.S. government has become increasingly focused on school climate, as recently evidenced by its inclusion as an accountability indicator in the Every Student Succeeds Act. Yet, there remains considerable variability in both conceptualizing and measuring school climate. To better inform the research and practice related to school climate and its measurement, we leveraged item response theory (IRT), a commonly used psychometric approach for the design of achievement assessments, to create a parsimonious measure of school climate that operates across varying individual characteristics. Students (n = 69,513) in 111 secondary schools completed a school climate assessment focused on three domains of climate (i.e., safety, engagement, and environment), as defined by the U.S. Department of Education. Item and test characteristics were estimated using the mirt package in R using unidimensional IRT. Analyses revealed measurement difficulties that resulted in a greater ability to assess less favorable perspectives on school climate. Differential item functioning analyses indicated measurement differences based on student academic success. These findings support the development of a broad measure of school climate but also highlight the importance of work to ensure precision in measuring school climate, particularly when considering use as an accountability measure.     

Factor structure of character strengths in youth: Consistency across ages and measures

The VIA Classification of Strengths and Virtues attempts to provide a comprehensive model of character based on 24 character strengths. The present study is the largest study to date exploring the structure of the 24 strengths in youth. One sample (N = 23,850) completed the VIA-Youth, a teen measure of the VIA Classification. Based on a random subsample, it was determined the data were best modeled using four factors. The remainder of the sample was used to demonstrate measurement invariance for the four-factor model across ages 10–17 and country. Comparison with 471 English academy school students who completed two alternate measures of the VIA Classification also demonstrated measurement invariance. The results suggest a four-factor model that includes two primarily interpersonal factors, one reflecting general engagement, the second other-directedness. Other factors involved intellectual and self-control strengths. Implications for the understanding of character strengths in youth versus adults are discussed.