全日制化学教育硕士的PCK水平调查研究*

以美国埃里克森学院PCK量化工具为研究基础设计调查问卷,选取离子反应第1课时的电离概念教学片断,以河北某高校学科教学(化学)专业37名教育硕士为研究对象,要求被试者在对视频片断进行观摩的基础上作答9个开放性问题。研究发现:全日制化学教育硕士PCK整体和各维度知识处于“基本的”水平,在教学内容知识维度表现最佳,在学生知识、教学策略知识维度稍差一些,在把握概念关系、调整教学策略等能力活动上的表现有待发展。针对研究发现,结合化学教育硕士的专业属性及培养过程中的问题,提出构建“教师专业学习共同体”,干预化学教育硕士PCK结构的改善;依托教学案例情境载体功能,帮助化学教育硕士进行PCK的深度建构;开展基于研究性反思的教学实践,促进化学教育硕士PCK螺旋式提升等3条建议。     

中学化学骨干教师PCK的实证研究*——以“析氢腐蚀和吸氧腐蚀”主题为例

使用本土化的教学内容表征(CoRe)工具调查了46名接受“国培计划”的中学化学骨干教师关于“析氢腐蚀和吸氧腐蚀”主题的PCK,结果表明:(1)骨干教师的PCK包含5个相互联系的组分,其中课程知识、学生知识以及策略知识均较为丰富。骨干教师能有针对性地选取化学学科专属的教学策略;(2)在教学取向方面,骨干教师在教学中发展与评价学生化学基本观念与学科核心素养的意识有待加强,引导学生自主建构学习的落实程度有待提高;(3)在评价知识方面,评价方式较为多元,但骨干教师对于形成性评价的重视程度不够。文末据此对我国化学教师教育以及化学PCK研究提出相关建议。     

On the Product and Factorization of Lattice Implication Algebras

In this paper,the concepts of product and factorization of lattice implication algebra areproposed,the relation between lattice implication product algebra and its factors and some properties oflattice implication product algebras are discussed.     

On Some Properties of L Type Intuitionistic Fuzzy Family

ＯｎＳｏｍｅＰｒｏｐｅｒｔｉｅｓｏｆＬＴｙｐｅＩｎｔｕｉｔｉｏｎｉｓｔｉｃＦｕｚｚｙＦａｍｉｌｙＹｕｅＳｈｕｓｏｎｇ；（岳树松）ＷａｎｇＪｉａｎｐｉｎｇ（王建平）（ＨｅｎａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ）（ＨｅｎａｎＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔ...     

允许卖空的资本市场中存在非负均衡价格向量的充要条件

For the capital market satisfying standard assumptions that are widely adopted in the equilibrium analysis,a necessary and sufficient condition for the existence and uniqueness of a nonnegative equilibrium price vector that clears the mean-variance capital market with short sale allowed is derived. Moreover, the given explicit formula for the equilibrium price shows clearly the relationship between prices of assets and statistical properties of the rate of return on assets, the desired rates of return of individual investors as well as other economic quantities.The economic implication of the derived condition is briefly discussed. These results improve the available results about the equilibrium analysis of the mean-variance market.     

The influence of some fuzzy implication operators on the accuracy of a fuzzy model-part II

The influence of fuzzy implication operators and the connective Also on the accuracy of a fuzzy model of a d.c. series motor is considered. Some typical fuzzy implication operators are applied to the construction of a fuzzy model of a d.c. series motor. A root-mean-square error is used as the criterion of the fuzzy model's adequacy to the real system. A number of mathematical operations necessary for the implementation of the fuzzy model are used as the criterion by which the fuzzy model's applicability if estimated from the point of view of computing techniques. The best types of fuzzy relations, representing fuzzy models of a real system, are chosen in order to secure the least root-mean-square error with minimal number of mathematical operations necessary for computer implementation.     

Prime Space of Lattice Implication Algebras

1.IntroductionPeoplehavepaidmoreattentiontolathcevaluedlogicsystem,whichwillbecomemuchbetterlogicalsystemforintelligentcomputer.InreferenceL1JXuYangpresentanalgebrastructure-latticeimplicationalgebrabycomblngthelatticewithimplicationalgebraastruevaluefieldoflatticevaluedlogicaIsystem.Afterthat,westudytheimplicationhomomor-phism,congruencerelationsandalgebraicstructureoflatticeimplicationalgebraanddiscussthefirstorderlogicalsystemFMbasedonlatticeimplicationalgebras,andobtainedseveralimpor-ta…     

ICT integration in mathematics initial teacher training and its impact on visualization: the case of GeoGebra

This case study investigates the impact of the integration of information and communications technology (ICT) in mathematics visualization skills and initial teacher education programmes. It reports on the influence GeoGebra dynamic software use has on promoting mathematical learning at secondary school and on its impact on teachers’ conceptions about teaching and learning mathematics. This paper describes how GeoGebra-based dynamic applets – designed and used in an exploratory manner – promote mathematical processes such as conjectures. It also refers to the changes prospective teachers experience regarding the relevance visual dynamic representations acquire in teaching mathematics. This study observes a shift in school routines when incorporating technology into the mathematics classroom. Visualization appears as a basic competence associated to key mathematical processes. Implications of an early integration of ICT in mathematics initial teacher training and its impact on developing technological pedagogical content knowledge (TPCK) are drawn.     

Loop invariants,exploration of regularities,and mathematical games

Loop invariants are assertions of regularities that characterize the loop components of algorithms. They are fundamental components of computerprograms verification, but their relevance goes beyond verification—they can be significantly utilized for algorithm design and analysis. Unfortunately, they are only modestly introduced in the teaching of programming and algorithms. One reason for this is an unjustified notion that loop invariants are ‘tied to formality’, hard to illustrate, and difficult to comprehend. In this paper a novel approach is presented for illustrating on a rather intuitive level the significance of loop invariants. The illustration is based on mathematical games, which are attractive examples that require the exploration of regularities via problemsolving heuristics. Throughout the paper students' application of heuristics is described and emphasis is placed on the links between loop invariants, heuristic search activities, recognition of regularities and design and analysis of algorithms.     

Closure-based constraints in formal concept analysis

We present a method of imposing constraints in extracting formal concepts (equivalently, closed itemsets or fixpoints of Galois connections) from a binary relation. The constraints are represented by closure operators and their purpose is to mimic background knowledge a user may have of the data. The idea is to consider and extract only these itemsets that are compatible with the background knowledge. As a result, the method extracts less clusters, those that are interesting from the user point of view, in a shorter time. The method makes it also possible to extract minimal bases of attribute dependencies in the input data that are compatible with the background knowledge. We provide examples of several particular types of constraints including those that appeared in the literature in the past and present algorithms to compute the constrained formal concepts and attribute implications.