On the Integration of Digital Technologies into Mathematics Classrooms

Trouche’s [Third Computer Algebra in Mathematics Education Symposiums, Reims, France, June 2003] presentation at the Third Computer Algebra in Mathematics Education Symposium focused on the notions of instrumental genesis and of orchestration: the former concerning the mutual transformation of learner and artefact in the course of constructing knowledge with technology; the latter concerning the problem of integrating technology into classroom practice. At the Symposium, there was considerable discussion of the idea of situated abstraction, which the current authors have been developing over the last decade. In this paper, we summarise the theory of instrumental genesis and attempt to link it with situated abstraction. We then seek to broaden Trouche’s discussion of orchestration to elaborate the role of artefacts in the process, and describe how the notion of situated abstraction could be used to make sense of the evolving mathematical knowledge of a community as well as an individual. We conclude by elaborating the ways in which technological artefacts can provide shared means of mathematical expression, and discuss the need to recognise the diversity of student’s emergent meanings for mathematics, and the legitimacy of mathematical expression that may be initially divergent from institutionalised mathematics.     

A Challenge: Can Mathematics Aid Development of the Process of Operational Research?

Some of the structures developed by operational researchersto help clients explore a problem-situation and design a wayforward are described briefly. The difficulty of getting appropriatemathematical support for the analysis, interpretation, and developmentof these structures is discussed.     

人文社科领域开展高等数学教学的研究与实践

本文根据高等数学教学大纲的要求 ,紧密结合作者自身多年的教学实践经验 ,从教育目标、教材内容、教学原则与教学质量考评等方面深刻全面地阐述了人文社科领域开展高等数学教学值得研究与探讨的一些带根本性的问题 .它不论是在实践方面 ,还是在理论上皆有一定的意义     

Digital Mathematics Libraries: The Good,the Bad,the Ugly

The idea of a World digital mathematics library (DML) has been around since the turn of the 21th century. We feel that it is time to make it a reality, starting in a modest way from successful bricks that have already been built, but with an ambitious goal in mind. After a brief historical overview of publishing mathematics, an estimate of the size and a characterisation of the bulk of documents to be included in the DML, we turn to proposing a model for a Reference Digital Mathematics Library—a network of institutions where the digital documents would be physically archived. This pattern based rather on the bottom-up strategy seems to be more practicable and consistent with the digital nature of the DML. After describing the model we summarise what can and should be done in order to accomplish the vision. The current state of some of the local libraries that could contribute to the global views are described with more details.     

Joining the World The Challenge of Internationalizing Undergraduate Education

Abstract

In 1858, John Henry Cardinal Newman wrote The Idea of a University. His ideal was a residential community of students and teachers devoted to the intellect. To him, a college was “an alma mater, knowing her children one by one, not a foundry, or a mint, or a treadmill.” Given a choice between an institution that dispensed with “residence and tutorial superintendence and gave its degrees to any person who passed an examination in a wide range of subjects” or “a university which … merely brought a number of young men together for three or four years,” he chose the latter.     

将素质教育贯穿于数学教学的始终

数学作为打开科学大门的钥匙,在素质教育中有着举足轻重的地位．本文通过几个典型案例,介绍了我们如何在数学教学的过程中贯彻素质教育的思想,以开发学员的学习潜能,启发学员的科学思维,调动学员的创造精神．     

中美大学数学教育研究之比较

论证了大学数学教育是高等教育的核心,数学教育本质上是一种素质教育,数学的应用遍及自然科学和社会科学.数学是大学理工科各专业知识的基础;探讨了大学数学教育研究的重要性,对中美大学数学教育的研究进行了对比,指出我们在研究大学数学教育方面的不足之处,提出了我们在大学数学教育研究方面的任务和目标.