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理论发展

(2011-04-29 22:02:06)
标签:

杂谈

分类: KFC学术文摘

Theory Development

理论发展

Our arguments on the relevance of Lakatos for mathematics education comes more from the view of doing research and being practitioners, both of which have to rest on an underlying philosophy and an associated theory of learning.

关于拉卡托斯与数学教育的相关性的讨论大多来自于做研究和成为实践者这两个观点, 这两个观点都建立在基础性哲学和与学习相关的理论基础上。

The present diversity in the number of new theories used in mathematics education from domains like cognitive science, sociology, anthropology and neurosciences are both natural and necessary given the added complexity in teaching and learning processes/situations in mathematics.

目前数量众多的应用于数学教育的新理论来自的领域有:认知科学、社会学、人类学和神经科学。这些理论必然为数学的教学过程增加了复杂性。

Even though theory development is essential for any field mathematics education has often been accused of “faltering” in theories (Steen 1999).

尽管如此,理论发展对于任何一个领域来说都是必不可少的,数学教育总是被指责在理论上步履蹒跚。

The development of “universal” theoretical frameworks has been problematic for mathematics education.

在“普遍性”的理论框架的发展上数学教育存在着疑问。

A research forum on this topic was organized by us at the 29th Annual meeting of the International Group for the Psychology of Mathematics Education (PME29) in Melbourne, which led to the two ZDM issues on theories that eventually became a basis for the present book.

我们在墨尔本举行的每年一届的第29届国际数学教育心理学研讨会上,组织过与这个问题有关的论坛。这次论坛产生了两本与理论相关的ZDM杂志,而这两本杂志最终成为现在这本书的基础。

 In one of the extended papers emanating from this research forum, Lester elaborated on the effect of one’s philosophical stance in research:

Cobb puts philosophy to work by drawing on the analyses of a number of thinkers who have grappled with the thorny problem of making reasoned decisions about competing theoretical perspectives.”

在从研讨会后一篇扩展性的文章中,Lester详细分析了一个人的哲学立场会对研究产生什么影响:Cobb分析一些哲学家是如何使理论更符合逻辑的,以此确认哲学的作用。

He uses the work of noted philosophers such as (alphabetically) John Dewey, Paul Feyerabend, Thomas Kuhn, Imre Lakatos, Stephen Pepper, Michael Polanyi,Karl Popper, Hilary Putnam, W.V. Quine, Richard Rorty, Ernst von Glasersfeld, and several others to build a convincing case for considering the various theoretical perspectives being used today “as sources of ideas to be appropriated and adapted to our purposes as mathematics educators. (Lester 2005, p. 461)

他利用了许多著名哲学家的著作,诸如:约翰·杜威保尔·费耶阿本德、托马斯·库恩、伊姆雷·拉卡托斯、斯蒂芬·佩珀迈克尔·波兰尼、卡尔·波普尔、希拉里.普特南、奎因、理查德·罗蒂、冯.格拉斯菲尔德和其它的几个,由此分析了不同的理论视角,这些理论视角可以很好地成现今数学教育者的思想资源。

Having addressed some of the debates that dominated the theoretical underpinning of the field for nearly two decades, we now focus on alternative conceptions of theory development.

在论述了一些这个领域内近20年来有关理论基础的争论后,我们将聚焦于理论发展中一些非主流的概念。

As stated earlier, we have seen a significant increase in the conceptual complexity of our discipline, where we need to address myriad factors within a matrix comprising of people, content, context, and time (Alexander and Winne 2006; Sriraman 2009a).

如前所述,我们学科概念的复杂性显著增加,我们需要论述众多的因素,被交织于人、主题、语境、时代。(Alexander and Winne 2006; Sriraman 2009a).

 This complexity is further increased by ontological and epistemological issues that continue to confront both mathematics education and education in general, which unfortunately have not been directly addressed.

由于在数学教育和一般性教育的本体论和认识论的问题,还没有被直接地进行论述,这种概念的复杂性进一步增加了。

Instead a utilitarian mix-and-match culture pervades the field given the fact that mathematics education researchers have at their disposal a range of theories and models of learning and teaching.

然而一种实用主义的“混搭”文化遍及这个领域,说明数学教育研究者还是支配了许多学习和教授方面的理论和模型。

Choosing the most appropriate of these, singly or in combination, to address empirical issues is increasingly challenging.

单独地或者结合地选择其中最适合的理论和模型,来论述经验主义的问题,越来越具有挑战性。

The current political intrusion, at least in the USA, into what mathematics should be taught, how  it should be assessed, and how it should be researched further complicates matters (e.g., Boaler 2008).

如今政治的介入——至少在美国的情况是这样的,对于什么样的数学应该被教,应如何评价,应如何研究,——使问题更加复杂化。

Indeed, Lester (2005) claimed that the role of theory and philosophical bases of mathematics education has been missing in recent times, largely due to the current obsession with studying “what works”—such studies channel researchers along pathways that limit theoretical and philosophical advancement(p. 457).

事实上,Lester (2005)宣称现今理论所扮演的角色和数学教育的哲学基础正在迷失,而很大程度上归咎于对“什么有效”的研究——这样的研究路径限制了理论的和哲学的发展。

On the other hand, if we compare the presence of theory in mathematics education scholarship today with its occurrence in past decades, it is clear that theory has become more prominent.

在另一个方面,如果我们把理论出现在数学教育学术性研究上的机会和过去几十年来比,会清楚地发现理论变得更加显著了。

Herein lies an anomaly, though. The elevation of theory in mathematics education scholarship could be considered somewhat contradictory to the growing concerns for enhancing the relevance and usefulness of research in mathematics education (Silver and Herbst 2007).

这里有一个不正常的现象。在数学教育的学术性理论的发展和与数学教育实践研究中对相关性和应用性的关注存在一些矛盾。

These concerns reflect an apparent scepticism that theory-driven research can be relevant to and improve the teaching and learning of mathematics in the classroom.

这些关注明显存在着这样一种怀疑:从理论出发的研究能否提高课堂中的数学教学。

Such scepticism is not surprising, given that we have been criticized for inadequacy in our theoretical frameworks to improve classroom teaching (e.g.,King and McLeod 1999; Eisenberg and Fried 2008; Lesh and Sriraman 2005;Lester 2005; Steen 1999).

考虑到我们已经因为在提高课堂教学方面的理论性框架不充分而受到批评,对这么些怀疑也不应感到惊讶(e.g.,King and McLeod 1999; Eisenberg and Fried 2008; Lesh and Sriraman 2005;Lester 2005; Steen 1999).

Claims that theoretical considerations have limited application in the reality of the classroom or other learning contexts have been numerous,both in mathematics education and in other fields (Alexander and Winne 2006;Sfard 1991).

众多的观点认为理论上考虑的问题在课堂实际或者其它学习环境下的应用非常有限,不仅数学教育如此,其它教育领域也如此(Alexander and Winne 2006;Sfard 1991)

But we concur with Alexander and Winne (2006) that “principles in

theory necessarily have a practical application” (p. xii); it remains one of our many challenges to clearly demonstrate how theoretical considerations can enhance the teaching and learning of mathematics in the classroom and beyond.

但是我们赞同Alexander and Winne的观点:“理论的原则需要体现在实践的应用上” (p. xii);而要论证理论观点如何使起到提升课堂上的数学教学,依然是众多挑战之一。

One source of difficulty here lies in the language barriers that so many theories display—how can others interpret and apply our theoretical messages if the intended meaning is lost in a world of jargon?

一个重要的困难存在于众多理论显现出来的语言性壁垒——如果我们想表达的意思受困于理论性的术语,其它非理论人事如何运用我们的理论信息。

We explore the following but do not claim to have covered all

that needs examining:

Is there such a thing as theory in mathematics education?

What are the changes in theory in recent decades and the impact on mathematics education?

What are some European schools of thought on theory development, particularly the French School?

What are the future directions and possibilities?

我们需要探索以下或者还有更多的问题:在数学教育里存在着理论吗?在最近的几十年里理论有什么变化,对数学教育的影响又有哪些?欧洲的思想流派,特别是法国在理论上的发展如何?将来的方向和可能性有哪些?

Many commentaries have been written on theory and mathematics education,including why researchers shift their dominant paradigms so often, whether we develop our own theories or borrow or adapt from other disciplines, whether we need theory at all, how we cope with multiple and often conflicting theories,why different nations ignore one another’s theories, and so on (e.g., Cobb 2007;King and McLeod 1999; Steiner 1985; Steiner and Vermandel 1988).

在数学教育和理论方面有很多的评论:包括为什么研究者会如此频繁转换他们主导性理论;我们是发展自己的理论,还是借助或者改造别的学科理论;是否我们真的需要理论;我们如何应付多样性的和相互冲突的理论;为什么不同的国家会忽视其它国家的理论等等。

Steen’s (1999)concerns about the state of mathematics education in his critique of the ICMI study on Mathematics Education as a Research Domain: A search for Identity (Sierpinska and Kilpatrick 1998) were reflected a decade later in Eisenberg and Fried’s (2009)

commentary on Norma Presmeg’s reflections on the state of our field (see Presmeg 2009).

Steen1999)在1999年把他对数学教育的关注体现在他的评论性文章——《ICMI(国际数学教育委员会)关于数学教育作为一个研究领域的研究:寻找身份》上,这样关注也表现在十年后Eisenberg and Fried(2009)对于Norma Presmeg作出的对我们领域的反思所进行的评论上。

Eisenberg and Fried (2009) claimed that, “Our field seems to be going through a new phase of self-definition, a crisis from which we shall have to decide who we are and what direction we are going.” (p. 143).

Eisenberg and Fried (2009)断言到:“我们的领域似乎进入一个自我定义的时期,一个需要确定我们自身和走向的关键期。”

 It thus seems an appropriate time to reassess theory in mathematics education, the roles it has played and can play in shaping the future of our discipline.

现在似乎是一个合适的时间来重新评估数学教育理论在形成我们学科的未来时已经扮演的角色和它所能扮演的角色。

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