薹草属广义菱形果薹草组（莎草科）的叶表皮微形态特征及其分类学意义

利用光学显微镜,对薹草属广义菱形果薹草组Carexsect.Rhomboidales s.l.(莎草科)54种、2亚种、8变种,共76个样品进行了叶片表皮形态特征的观察研究.结果表明:表皮细胞形状和垂周壁式样在大多数种中表现出稳定性,上、下表皮细胞大多为长方形,少数为近方形、近圆形或长条形,其垂周壁式样多为深波状,少数为波状;气孔器在下表皮脉间呈列或随机分布,气孔的大小、气孔指数及密度在种内有差异;有些种具硅质乳突,而表皮附属物分为刺突和刺毛2种,刺突常出现在sect.Rhomboidales s.str.的成员中.根据表皮的各项性状尚无法区分sect.Rhomboidales s.str.和sect.Careyanae,叶表皮性状近缘种之间存在显著区别,可以作为区分种或种下类群的依据.     

核心素养背景下化学教材中人文意蕴的分析与启示*——以美国教科书《化学:概念与应用》为例

针对当代核心素养背景下学科核心素养中人文向度的部分缺失,以美国主流理科教科书《化学:概念与应用》作为研究对象,选取了4则人文意蕴特征明显、内涵丰富的“跨学科”栏目典型案例,通过对其人文意蕴向度的结构性与教学价值分析,获得学科人文智性及其教育的启示:以科学与人文的对话推动2个世界的沟通;以科学的革命性突跃弘扬科学精神的人文光辉;倡导自然与艺术和谐统一的人文审美意向;肩负社会责任与维护和平正义的进步人文思想。 为学科教学中人文教学资源的研究开发提供认识导向;为完善当前学科核心素养内容提供参考;并从选材理念、教学准备、课程教学、目标达成4个方面为该类资源的教学应用提供策略建议。     

Pedagogical alternatives for triple integrals: moving towards more inclusive and personalized learning

This paper is based on the presumption that teaching multiple ways to solve the same problem has academic and social value. In particular, we argue that such a multifaceted approach to pedagogy moves towards an environment of more inclusive and personalized learning. From a mathematics education perspective, our discussion is framed around pedagogical approaches to triple integrals seen in a standard multivariable calculus curriculum. We present some critical perspectives regarding the dominant and long-standing approach to the teaching of triple integrals currently seen in hegemonic calculus textbooks; and we illustrate the need for more diverse pedagogical methods. Finally, we take a constructive position by introducing a new and alternate pedagogical approach to solve some of the classical problems involving triple integrals from the literature through a simple application of integration by parts. This pedagogical alternative for triple integrals is designed to question the dominant one-size-fits-all approach of rearranging the order of integration and the privileging of graphical methods; and to enable a shift towards a more inclusive, enhanced and personalized learning experience.     

基于L~*-格值逻辑上的BCK-代数中直觉不分明化理想

在L~*-格值逻辑的语义框架下,以L~*-格值上的Lukasiewicz蕴涵算子为工具定义了L~*-格值逻辑上的直觉不分明化BCK-代数的概念,将用集论所刻画的BCK-代数中理想、正定蕴涵理想和蕴涵理想等概念在L~*-格值谓词演算下给予了新的刻画,讨论了它们的性质及其关系,研究了这些理想与其同态象、同态原象之间关系,获得了同类理想之积仍为该类理想.     

How well prepared are the teachers of tomorrow? An examination of prospective mathematics teachers' pedagogical content knowledge

There is a growing emphasis in the teaching profession on pedagogical content knowledge (PCK) as an important knowledge component. The study reported in this article investigates Turkish prospective mathematics teachers’ mathematics teaching knowledge in the numbers content domain. A series of 10 open-ended scenario-type questions were adopted to challenge 83 prospective mathematics teachers’ knowledge of the learner and presentation of content in the context of PCK. The participants’ responses were analysed by means of rubrics and scoring guides developed by the researchers. The results showed that many of the future teachers performed well in determining what misconceptions students might express in the given scenarios. However, a majority of the participants performed poorly on presentation of content in terms of instructional strategies. In line with these results, the authors offer some suggestions for teacher training programmes.     

关于格蕴涵代数公理的一个注记

设在一个非空集合L上有一个二元运算→和两个零元运算O与I，除此之外没有其它已知的代数结构，利用这三个运算可以在L上定义一个一元运算′和两个二元运算∨和∧（定义2．1）。本文证明了只要这些运算满足格蕴涵代数的公理（不包括有余格的公理），（L，∨，∧，′）就是一个有泛界O，I的有余格（定理2．2）。因此在定义格蕴涵代数时可以在一个没有任何代数结构的非空集合上定义蕴含运算而不必在一个有泛界的有余格上定义蕴含运算，而且在这两种定义方式中蕴含运算所满足的条件是相同的。     

HEYTING代数与FUZZY蕴涵代数

Heyting代数是作为直觉主义命题逻辑的代数模型而引进的Fuzzy蕴涵代数是 [0 ,1]值逻辑的蕴函联结词的一种代数抽象 .本文给出Heyting代数的若干基本性质 ,并证明了Heyting代数是Fuzzy蕴涵代数 ,也是Heyting型Fuzzy蕴涵代数。     

Ultra LI-ideals in lattice implication algebras

We define an ultra LI-ideal of a lattice implication algebra and give equivalent conditions for an LI-ideal to be ultra. We show that every subset of a lattice implication algebra which has the finite additive property can be extended to an ultra LI-ideal.     

A case study of pedagogy of mathematics support tutors without a background in mathematics education

This study investigates the pedagogical skills and knowledge of three tertiary-level mathematics support tutors in a large group classroom setting. This is achieved through the use of video analysis and a theoretical framework comprising Rowland's Knowledge Quartet and general pedagogical knowledge. The study reports on the findings in relation to these tutors’ provision of mathematics support to first and second year undergraduate engineering students and second year undergraduate science students. It was found that tutors are lacking in various pedagogical skills which are needed for high-quality learning amongst service mathematics students (e.g. engineering/science/technology students), a demographic which have low levels of mathematics upon entering university. Tutors teach their support classes in a very fast didactic way with minimal opportunities for students to ask questions or to attempt problems. It was also found that this teaching method is even more so exaggerated in mandatory departmental mathematics tutorials that students take as part of their mathematics studies at tertiary level. The implications of the findings on mathematics tutor training at tertiary level are also discussed.     

Zariski‐type topology for implication algebras

In this work we provide a new topological representation for implication algebras in such a way that its one‐point compactification is the topological space given in [1]. Some applications are given thereof (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)