Quality and change in higher education

There is increasing evidence that the pressures on British universities for greater quality and accountability, linked closely to funding, are leading to loss of quality. These governmental pressures, exerted through the Funding Councils, are wholly different from those applied in a quite separate way from another government source, the Employment Department. This article analyses the nature and effects of the two kinds of pressures in terms of change theory. This also demonstrates that the observed effects were not only largely predictable but to a substantial extent were predicted, and warns of the danger that the resulting deleterious effects may become irreversible.Lewis Elton obtained an M.A. in Mathematics at Cambridge University and a B.Sc. in Mathematics and a Ph.D. in Theoretical Physics at the University of London. He is a Further and Higher Education Adviser to the UK Employment Department and Emeritus Professor of Higher Education at the University of Surrey. His special interests are in the improvement of university teaching and learning; staff development; distance learning; and organizational change in higher education. Pat Cryer obtained a B.Sc. in Mathematics and Physics at the University of Exeter and a Ph.D. in Educational Development at the University of Surrey. She has recently resigned as Professional Adviser of the UK Universities' Staff Development Unit and is now a Consultant in Higher Education. Her special interests are in issues of quality; staff development; and teaching large classes.The opinions expressed in this paper are our own and do not commit the Employment Department.     

数学阅读教学中师生的角色定位及策略

数学阅读在数学教育中的重要性已经得到数学教育界的共识,如何才能提高学生的数学阅读能力,如何才能使数学阅读教学提高效率,这是困扰教育者的难题。本文就数学阅读的特殊性,数学阅读教学中师生的角色定位以及课堂教学对策等问题进行了论述。     

One and One is Sometimes Three in Small Group Mathematics Learning

In recent years, Mathematics teaching has been confronted by demands for higher standards and better pupil achievement in several parts of the world. Researchers have suggested the shift from teacher‐centred instruction towards more active participatory learning methods as one way to improve the quality of the teaching and learning process. The tension between whole‐class teaching versus small group learning in Mathematics has been particularly apparent in many education systems. This article analyses the development of Mathematics teaching by asking whether small group learning is an effective arrangement in teaching school Mathematics. We conclude that although there is no unanimity about the affects of small group learning on student achievement in school Mathematics, it seems that it produces at least equal academic outcomes among all students compared to more traditional methods of instruction. Working in pairs is a particularly effective form of learning Mathematics and that small groups are beneficial for developing mathematical problem‐solving skills. We also conclude that the present educational policies and increased quality assurance structures in many countries conflict, or are not consistent with scientific‐professional thinking and research on the teaching of Mathematics.     

Between the Academic Mathematics and the Mathematics Education Worlds

Change is always difficult, and there is no great doubt that teachers need time to come to terms with it. This fact is, however, too often forgotten. In the spirit of my earlier work, this paper is shaped by an action research perspective. It provides some insights into the learning experiences of a group of eleven experienced secondary mathematics teacher, who were enrolled in a Perspectives on Mathematics Education two semesters course, within the context of a Masters on Mathematics Teaching programme, held at a Department of Mathematics, in a Portuguese University. The first part of the paper highlights the conflicting pressures and stresses suffered, during the first semester course, by the participating teachers. Confrontation with new ideas about both mathematics and mathematics education, as well as work overload, had a damaging impact on the teachers’ self‐confidence and morale. The second part of the paper covers the second semester course by addressing three fundamental questions for teachers, which aimed at helping the students bridge the academic mathematics and the mathematics education worlds. Finally, brief scenarios of three participating teachers’ professional development throughout the course are discussed in order to illustrate the challenges they had to face and the possibilities the course (and the Masters programme) offered to promote individual change.     

关于函数最值问题的探讨

函数最值问题是中学数学的主要内容，首先对函数最值问题做了相关研究，总结归纳出了求解函数最值的一般方法，讨论了求解函数最值时应注意的问题，通过以上问题论述，培养学生的数学应用意识，提高学生的数学建模能力和解题能力．     

数学与文化

数学与文化有着密切关系,彼此之间的相互影响促进数学的发展。数学发展有其特殊的发展规律并有相对独立性所以可把数学看成文化系统即数学文化。数学文化有其自身的特征：层次性;稳定性;连续、传导性。     

新课程理念下的数学人文教育

数学既是一门科学，又是人类的一种重要文化；数学具有科学教育价值，又具有人文教育价值。数学课程是进行数学教育的载体，学科教育的目的应是人的健康和谐发展。因此，在数学课程的实施过程中除了发挥其科学教育功能外，更要注重人文教育的作用，培养学生的人文精神，使其成为一个具有健全人格的人，高尚的人。     

三思苏教版高中数学新教材

江苏高中数学课程改革已经进行了6年,有改革的欣喜,更有改革的阵痛.新教材的部分内容编排不尽合理;整体模块的顺序以及模块内个别教学内容的顺序需要调整;高中与初中,高中与大学以及数学与其它学科的衔接问题亟待解决;整个高中3年教学进度的现状更是令人担忧.     

Achieving mathematical excellence in Japan: Results and implications

This chapter describes how the Math Olympiad program operates in Japan. Mathematics achievement in Japan has been acknowledged around the world. Japan's success in the International Mathematics Olympiad (IMO) is documented and the reasons behind this success are examined. Finally, problems dealing with the mathematics curriculum are presented.     

关于"数学是什么"的哲学反思

数学家及数学哲学家对“数学是什么”做出了许多种阐释,但回头看去,没有一种令人完全满意的概括。究其原因,原因是多方面的,但主要还是数学、社会、教育的发展和认识的角度不同所致,换句话说,数学本质具有鲜明的时代特征。不可能也没有必要对“数学是什么”做出一个令所有人都完全满意的回答。     

Learners' Approaches to Solving Mathematical Tasks: Does Specialisation Matter?

This article emerged from an analysis of learners’ responses to a task presented to learners studying Mathematics and Mathematical Literacy (ML) in Gauteng, South Africa. Officially, Mathematics and ML are two separate learning areas. Learners from Grade 10 onwards are supposed to take either one or the other, but not both. This means that by Grade 11, learners would have acquired different kinds of knowledge and problem solving skills depending on which of these they take. The article demonstrates that this possibility may not necessarily happen. Grade 11 learners from both learning areas appeared to have acquired sufficient knowledge and skills and were able to solve similar Mathematics tasks in similar ways, with similar adequacy. We argue that, contrary to common perceptions in the field of Mathematics education (particularly in South Africa), engaging in ML does not and should not make one less mathematically advanced than engagement in pure Mathematics.     

Secondary School Mathematics Teacher's Professional Knowledge: A case from the teaching of the concept of function

This study examines the relationships between a secondary Mathematics teacher's pedagogical content knowledge and the dilemmas posed when teaching the concept of function. Alternative tools and procedures for analysing these relationships are used. The results illustrate the flexibility of her knowledge use in Mathematics teaching and how it is related to her knowledge of the pupils as Mathematics learners. In addition, it highlights the central role played by the teacher's knowledge about pupil comprehension in the content and organisation of her teaching agenda. The difference that the teacher establishes between exercise and problem shows her struggle with the two-fold understanding-memorisation of procedures as the content of a teaching dilemma. The results obtained suggest the need for secondary Mathematics teacher education programmes to adopt approaches that take into account the central role played by teacher knowledge about Mathematics learning, and the dilemmas generated when teachers have to reconcile objectives that are apparently contradictory during their teaching practice.     

数学教学中渗透社会主义核心价值观教育的思考

高校数学教育是科学素质教育的重要部分,在数学教学中如何抓住数学学科特点,开展社会主义核心价值观教育呢？文章从数学教学内容蕴含着丰富的德育素材,是开展核心价值观教育的重要资源;在渗透社会主义核心价值观教育的过程要坚持“以人为本”,要发挥教师的主导作用展开了分析和讨论。指出只要我们抓住数学教学特点,注意路径和方法,脚踏实地、持之以恒地在数学教学中渗透社会主义核心价值观教育,一定能够起到事半功倍的作用。     

激发自觉学习兴趣强化课堂教学目标

教师应该培养学生良好的自觉学习能力,必须让学生用积极的态度和旺盛的精力、自觉、主动地去探索知识,知道数学知识在实际中的实用性和重要性,始终有一种对学好数学的极大兴趣,从而获得预期课堂目标.     

高职数学教学的研究实践及思考

数学教学在高职人才培养中有着十分重要的地位,传统的教学方式已不适应高职教育的发展要求。在高职数学课程教学中教师应通过转变教学理念、融入建模思想、引入数学实验、整合教学内容等方面的创新来推进高职数学教学改革．充分发挥数学在高职技能人才培养中的促进作用。     

类比思维在高等数学中的应用

类比法是指一类事物所具有的某种属性,可以推测与其类似的事物也具有这种属性的推理方法。类比法是数学研究中最基本的创新思维形式。在数学中,采用类比法有助于学生对基本知识的理解和掌握,用已学知识和新知识进行类比,更容易地接受新知识巩固旧知识,并且无形中培养了学生的类比思维。     

重现度与理解度关系应用研究

理解度是衡量学习成绩的重要指标,理解并驾驭重现度与理解度之间的关系规律直接影响数学教学策略是否有效地实施。本文立足数学学科,以不同研究对象获得的重现度和理解度关系规律是否相同为出发点,得出他们之间的显性关系表达式,进而通过对比分析,提出教材编写与教师教学中普适的教学策略,以期为其他学科教学研究提供借鉴。     

谈维果茨基概念发展理论对高职数学概念教学的启示

前苏联杰出的教育心理学家Vygotsky（维果茨基）对学生的科学概念的形成作了特定视角的研究，提出了独到的见解，对我们认识数学概念的教学有着重要的启示。随着我国高等职业教育教学改革的不断推进，这一理论也必将在新的背景下不断充实、丰富，为未来我国的高等职业数学教育教学改革提供更有益的启迪。     

60年来初中数学教材编写的历史沿革与启示——以人教版为例

初中数学教材在基础教育课程教材中有着举足轻重的地位.人教社成立60年来,编写初中数学教材经历了初创、探索、停滞、恢复、发展等时期.从人教社初中数学教材编写的历史沿革中,可以得到如下启示:教材编写要结合国情、与时俱进;改革要谨小慎微,试验过程需通盘考虑;需加强层次性与多样性;把握好数学本身的内在逻辑;处理好各学段之间的衔接.     

逻辑数学悖论及其解决

逻辑--数学悖论是指仅借助于逻辑和数学的符号而得以构造的悖论.从历史发展看,其主要是指布拉里--福蒂(Burali-Forti) 悖论,康托悖论和罗素悖论,它们分别是在1897、1899及1902年提出的.逻辑--数学悖论的出现,明确地表明素朴集合论中包含有逻辑矛盾.解决逻辑--数学悖论,必须对康托的素朴集合论加以限制,特别是必须抛弃前面所提到的概括原则.按策梅罗的研究成果,只须对公理适当地加以选择,就可做到既能使新建立的集合论能成为数学的基础,同时又能确保新的理论不会导致悖论.