一种求摄动矩阵的逆矩阵的方法

应用矩阵的运算法则和逆矩阵的定义，对摄动矩阵（A＋δuv^T）和它的更一般形式（A＋UBV）给出了具体的求逆矩阵公式。     

用特殊分块法求逆矩阵的一个充要条件及相关的结果

本文给出了用特殊分块法求逆矩阵的充要条件及一些推导结果和应用．     

求循环矩阵的两种简便方法

探讨循环矩阵的求逆问题,提出求解循环矩阵的逆矩阵的两种方法,线性方程组法,伴随矩阵法。     

托普勒兹矩阵的若干性质

托普勒兹矩阵「１」在系统理论中有着十分重要的作用。本文要讨论了主对角线上的元素是任意数的情况,因此也就推广了文「２」的结论。     

对矩阵的迹的性质研究

对矩阵的迹作了较深入的研究，地其性质给予归纳。     

介绍求循环矩阵与反循环矩阵的逆矩阵的一种简便方法

循环矩阵和反循环矩阵是一种特殊的矩阵,其逆矩阵可用一般方法求得.文章介绍求循环矩阵和反循环矩阵的逆矩阵的一种较为实用而简便的方法.     

初等矩阵与次初等矩阵

初等矩阵是高等代数的一个重要概念，它在求矩阵的秩及求逆矩阵方面有着重要作用，给出了初等矩阵的几个新的性质，初等矩阵与它的转置矩阵，伴随矩阵，幂矩阵之间的关系，丰富了初等矩阵的性质，同时给出了次初等矩阵的概念以及初等矩阵与次初等矩阵的关系定理等一系列结果。     

广义正定矩阵与稳定矩阵、M-矩阵的关系

本文证明了一类广义正定矩阵类Psn+与负稳定矩阵类-Sn相同，指出了它们与M-矩阵类的关系；最后给出了一个广义正定矩阵的有效判定定理。     

伴随矩阵的若干性质及其解题中的应用

伴随矩阵在教材中是作为公式法求逆矩阵的一个工具而提出的,有关它的性质及其运用在教材中出现很少.但伴随矩阵的性质及其应用是历届考研的重点内容之一.本文归纳了伴随矩阵的重要性质,以及讨论了其在解题中的方法和技巧.     

分块矩阵和广义初等矩阵

主要介绍了分块矩阵的初等变换与广义初等矩阵（又称分块初等矩阵）的关系,从而获得一些新的解题方法     

初等变换在矩阵运算中的应用

总结了初等变换在矩阵运算中的几种应用：求逆矩阵、求解矩阵方程、求矩阵的秩和求解线性方程组,并且通过实例加以说明。     

线性代数教学中对初等变换的一点注记

主要介绍了矩阵的初等变换不改变矩阵的可逆性和矩阵的秩,初等行变换不改变线性方程组的解的结构和向量之间的线性相关性.同时,通过几个例子介绍了初等变换在求矩阵的逆等方面的应用.     

正交化的一种简便方法

文[1]给出了求标准正交基的一种简便方法,但仅适用于R~n,本文加强了文[1]引理2,给出了一个改进的正交化方法,适用于任意实内积空间。     

Fostering Third-Grade Students’ Use of Scientific Models with the Water Cycle: Elementary teachers’ conceptions and practices

Elementary teachers play a crucial role in supporting and scaffolding students’ model-based reasoning about natural phenomena, particularly complex systems such as the water cycle. However, little research exists to inform efforts in supporting elementary teachers’ learning to foster model-centered, science learning environments. To address this need, we conducted an exploratory multiple-case study using qualitative research methods to investigate six 3rd-grade teachers’ pedagogical reasoning and classroom instruction around modeling practices (construct, use, evaluate, and revise) and epistemic considerations of scientific modeling (generality/abstraction, evidence, mechanism, and audience). Study findings show that all teachers emphasized a subset of modeling practices—construction and use—and the epistemic consideration of generality/abstraction. There was observable consistency between teachers’ articulated conceptions of scientific modeling and their classroom practices. Results also show a subset of the teachers more strongly emphasized additional epistemic considerations and, as a result, better supported students to use models as sense-making tools as well as representations. These findings provide important evidence for developing elementary teacher supports to scaffold students’ engagement in scientific modeling.     

Teaching Scientific Measurement and Uncertainty in Elementary School

The concept of measurement is fundamental in science. In order to be meaningful, the value of a measurement must be given with a certain level of uncertainty. In this paper we try to identify and develop the reasoning of young French pupils about measurement variability. In France, official instructions for elementary school thus argue for having students do activities of measurement, followed by treatments and analysis of the data. The notion of measurement ‘uncertainty’ appears in fourth and fifth grades. A similar approach is proposed in the USA. We present a teaching sequence divided into two parts: the first part in grade 4, the second one in grade 5, the following year, with the same students. The main sources of data were field notes, videotapes, as well as the intermediate written traces produced, individual written tests given each year and clinical interview. We showed that the pupils were capable of entertaining all three possible causes of uncertainty (the quantity being measured, the measuring instrument, and the measurer). Concerning data organization and handling, we found that after teaching, most of them were able to construct a frequency table and a bar chart from a list of N measures of the same quantity. When interpreting this type of chart, some of them were able to argue in terms of a confidence interval. We have also shown that the proposed instructional units allowed pupils to become aware of the need to repeat measurements.     

Science centers in Australia provide valuable training for preservice teachers

This paper describes an innovation in teacher education designed to increase the confidence of preservice teachers in their ability to instruct elementary children in hands-on science. The program relied on small group teaching experiences at an on-campus interactive science center to provide preservice teachers with controlled instructional experiences. The findings showed that the program at the science center achieved its aims and benefitted the preservice teachers involved. Interview data suggest that working in peer groups was also a significant factor and supports previous research conducted at the San Francisco Exploratorium. Follow-up research is now needed to determine if supportive peer groups of preservice teachers are needed in order to achieve desirable outcomes.     

Understanding pedagogical design capacity through teachers’ narratives

Teachers need to develop the ability to adapt curriculum materials. Two elementary teachers, Maggie and Catie, were asked to write narratives about their use of and changes to particular reform-oriented science lesson plans. Maggie drew on her knowledge of and experiences with students, as well as other knowledge, experiences, and resources, to make productive changes to account for her students’ prior knowledge and abilities. Catie based her curricular adaptations on her learning goals—but these were not aligned with the learning goals of the curriculum materials. The paper discusses implications for teacher education, professional development, and educative curriculum materials.     

小学作文教学要虚实并举

课标要求学生写作要贴近实际，表达真情实感，“说真话、实话、心里话，不说假话、空话、套话”．笔者将“作文自由”还给学生，鼓励学生写真实、讲真话，自由选材、自由立意，展开合理想象，培养创新精神．