关于可逆矩阵定义的注记

本文就矩阵可逆性的定义进行讨论,给出矩阵可逆的另一定义形式,并利用这一定义,证明了逆矩阵的存在性和唯一性．说明新定义与传统定义是一致的,不过新的定义在使用上要简单一些。     

关于“矩阵的直积”一文的注记

本文指出文[1]的定义及性质均是矩阵论中已有定义及已知性质,并进一步探讨了矩阵的直积的一些新的性质。     

"三角的"Cartan矩阵的Coxeter矩阵为周期矩阵的充要条件

对一类阿廷环上"三角的"Cartan矩阵的Coxeter矩阵的周期性进行了研究,给出了其为周期矩阵的1个充要条件,并由此给出了文[2]中的猜想的1种特殊情形的证明.     

标准形在矩阵秩证明题教学中的应用

如何处理好习题课是当前形势下线性代数教学中值得关注的一个方面。矩阵的秩是线性代数的一个重要概念。与矩阵的秩相关的证明题是非常难的,掌握它们的证明能很好地培养学生数学思维能力。本文将重点介绍在习题课教学中,矩阵标准形的概念在矩阵秩的相关证明题中的应用。通过推导矩阵秩的分解定理来引导学生对基础知识的应用,加深概念的理解。     

对HSK部分等级的验证性研究

中国汉语水平考试(HSK)的作用之一是界定留学生进入中国大学入系学习时所应具备的汉语能力。根据有关规定,HSK三级和六级分别是进入中国大学理工西医类和文史中医类入系学习的最低标准。本文采用安哥夫、边缘组及对照组三种方法对此标准进行了验证性研究。     

分层抽样下多项选择敏感问题随机抽样调查方法及应用

目的是为多项选择敏感性问题提供科学的、精度更高的随机抽样调查方法及其统计量的计算公式,设计出多项选择敏感问题分层抽样下的随机抽样调查模型,并推导出在此模型下总体比例的估计量及其估计方差的计算公式,计算出敏感属性比例95％的置信区间。并在湖南城市学院本科学生考试作弊情况的实例调查中取得了信誉度较高的应用效果。     

A Comparison of Angoff and Bookmark Standard Setting Methods

This article presents a comparison of simplified variations on two prevalent methods, Angoff and Bookmark, for setting cut scores on educational assessments. The comparison is presented through an application with a Grade 7 Mathematics Assessment in a midwestem school district. Training and operational methods and procedures for each method are described in detail along with comparative results for the application. An alternative item ordering strategy for the Bookmark method that may increase its usability is also introduced. Although the Angoff method is more widely used, the Bookmark method has some promising features, specifically in educational settings. Teachers are able to focus on the expected performance of the barely proficient student without the additional challenge of estimating absolute item dificulty.     

A Short Note on the Relationship Between Pass Rate and Multiple Attempts

For a certification, licensure, or placement exam, allowing examinees to take multiple attempts at the test could effectively change the pass rate. Change in the pass rate can occur without any change in the underlying latent trait, and can be an artifact of multiple attempts and imperfect reliability of the test. By deriving formulae to compute the pass rate under two definitions, this article provides tools for testing practitioners to compute and evaluate the change in the expected pass rate when a certain (maximum) number of attempts are allowed without any change in the latent trait. This article also includes a simulation study that considers change in ability and differential motivation of examinees to retake the test. Results indicate that the general trend shown by the analytical results is maintained—that is, the marginal expected pass rate increases with more attempts when the testing volume is defined as the total number of test takers, and decreases with more attempts when the testing volume is defined as the total number of test attempts.     

The Effect of Various Factors on Standard Setting

This paper reports two studies of standard setting using Angoff's method. Results of the first study suggest that specialization within broad content areas does not affect an expert's estimates of the performance of the borderline group. This is reassuring because the knowledge base of many professions is so large that no individual can be considered an expert in all aspects of it. Results of the second study support the recommendation that performance data be provided during the standard-setting process. They are frequently used by experts, but will not have an impact on the standard unless the distribution of item difficulties is skewed markedly. It also increases the correspondence between p-values and estimates of borderline group performance, thereby reducing errors in pass/fail decisions. Overall, the results support recommendations often made in standard-setting literature, but they need to be replicated with other groups of experts     

实对称矩阵正交相似变换标准形的应用

通过实例探讨了实对称矩阵的正交相似变换标准形在矩阵问题中的应用。     

全港性系统评估:水平参照分数报告和水平厘定技术在香港的实践

本文以小学数学科为例,介绍了香港全港性系统评估应用项目反应理论中的Rasch模型进行测验设计和数据分析,以及用改进的Angoff方法和书签法进行水平厘定,获得水平参照分数报告的过程。     

A Conceptual Framework for a Psychometric Theory for Standard Setting with Examples of Its Use for Evaluating the Functioning of Two Standard Setting Methods

A conceptual framework is proposed for a psychometric theory of standard setting. The framework suggests that participants in a standard setting process (panelists) develop an internal, intended standard as a result of training and the participant's background. The goal of a standard setting process is to convert panelists' intended standards to points on a test's score scale. Psychometrics is involved in this process because the points on the score scale are estimated from ratings provided by participants. The conceptual framework is used to derive three criteria for evaluating standard setting processes. The use of these criteria is demonstrated by applying them to variations of bookmark and modified Angoff standard setting methods.     

正定矩阵标准型的子式阵

利用一般的正定矩阵的标准形的子式阵讨论正定矩阵的子式阵的正定性是研究正定性的基础，本文给出了一般公式及具体算法。     

关于“广义正定矩阵与稳定矩阵的关系”的注记

指出广义正定矩阵与稳定矩阵的关系;介绍文[2]的定理1的证明依赖于文[2]的引理1,而文[1]指出文[2]引理1的证明是错误的,证明文[1]的定理1是正确的。     

Using Diagnostic Profiles to Describe Borderline Performance in Standard Setting

In test-centered standard-setting methods, borderline performance can be represented by many different profiles of strengths and weaknesses. As a result, asking panelists to estimate item or test performance for a hypothetical group study of borderline examinees, or a typical borderline examinee, may be an extremely difficult task and one that can lead to questionable results in setting cut scores. In this study, data collected from a previous standard-setting study are used to deduce panelists’ conceptions of profiles of borderline performance. These profiles are then used to predict cut scores on a test of algebra readiness. The results indicate that these profiles can predict a very wide range of cut scores both within and between panelists. Modifications are proposed to existing training procedures for test-centered methods that can account for the variation in borderline profiles.     

制定幼儿园评估标准需要澄清的几个问题

对幼儿园进行等级评估是各省市教育行政部门对幼儿园进行业务管理的重要手段,很多省市相继出台或修订了幼儿园评估标准。竖于我国地域广阔,各地自然状况与社会文化经济发展水平差异显著,各地确实需要因地制宜,制定地区性的标准,但逐步实现省域范围内标准的统一还是比较适宜的,这不仅便于分级管理,而且利于横向比较,也是符合国内外评估体系建构与使用趋势的。评估标准应始终体现当前幼儿教育的主流价值观,以消除幼儿教育市场化产生的各种不良影响,如可对办园规模、所用教材、课程等进行明确规定与限制,以消除幼儿园小学化倾向及其商业化行为。评估标准应主要围绕教师、设施、课程、儿童四个教育基本要素,建构能够真实反映幼儿园教育质量的指标体系,包括各结构性指标与过程性指标,并科学考虑各指标的权重。在此,要特别强调设施设备等物质为教育教学服务的理念,有关办学条件和设施的指标所占分量应恰当,以避免幼儿园之间在环境创设上的无意义攀比。同时,还应考虑哪些指标是在短暂的评价期间就能观察和了解到的,特别应将幼儿园在幼儿发展评价方面所做的工作列为评价内容,将对班级教育工作的评价作为重点,将幼儿在教育过程中可观察的行为表现列入评价指标。在最终的评价结果上,宜采取先...