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理论和它在数学教育里扮演的角色

(2011-04-30 16:30:03)
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分类: KFC学术文摘

 Theory and Its Role in Mathematics Education

理论和它在数学教育里扮演的角色

 

The increased recognition of theory in mathematics education is evident in numerous handbooks, journal articles, and other publications.

有关数学教育的理论认识出现在大量的手册、杂志或者其它出版物上。

 For example, Silver and Herbst (2007) examined “Theory in Mathematics Education Scholarship” in the Second Handbook of Research on Mathematics Teaching and Learning (Lester 2007) while Cobb (2007) addressed “Putting Philosophy toWork: Coping with Multiple Theoretical Perspectives” in the same handbook.

举个例子: Silver and Herbst(2007)在《数学的教与学研究的手册第2版》这本书中发表了关于“数学教育的学术性理论”方面的调查文章,而Cobb (2007)在同一本书里也发表了“让哲学起作用:对待多种理论视角”这篇文章。

And a central component of both the first and second editions of the Handbook of International Research in Mathematics Education (English 2002, 2008a, 2008b) was “advances in theory development.”

而《数学教育的国际研究手册》的第12版中的重要部分则是代表了理论发展中的进步。

Needless to say, the comprehensive second edition of the Handbook

of Educational Psychology (Alexander and Winne 2006) abounds with analyses of theoretical developments across a variety of disciplines and contexts.

不用说,全面的《教育心理学手册》第2(Alexander and Winne 2006)则在不同学科和背景下充分地分析了理论发展。

Numerous definitions of “theory” appear in the literature (e.g., see Silver andHerbst 2007).

众多不同定义的“理论”出现在文献里。

 It is not our intention to provide a “one-size-fits-all” definition of

theory per se as applied to our discipline; rather we consider multiple perspectives on theory and its many roles in improving the teaching and learning of mathematics in varied contexts.

我们并不想为我们学科的本质提供一个通用的理论概念;相反,我们考虑多种理论视角以及它在不同背景下的数学教学中所扮演的多种角色。

 At the 2008 International Congress on Mathematical Education, Assude et al.(2008) referred to theory in mathematics education research as dealing with the teaching and learning of mathematics from two perspectives: a structural and a functional perspective.

2008年“数学教育的国际会议”中Assude等人提出数学教育研究在处理数学教学时应从两个视角出发:“结构性”和“功能性”。

From a structural point of view, theory is “an organized

and coherent system of concepts and notions in the mathematics education field.”

从结构性角度来看:理论是数学领域里“有组织的、连贯的概念和观念”。

The “functional” perspective considers theory as “a system of tools that permit a ‘speculation’ about some reality.”

从功能性角度来看,则把理论当作“能推测现实的系统性的工具”。

When theory is used as a tool, it can serve to:

当理论被当作工具使用时,它可以服务于:

(a) conceive of ways to improve the teaching/learning environment including the curriculum,

(a) 有助于构思方法去改善教学环境,包括课程。

(b) develop methodology,

(b)形成原则

(c) describe, interpret, explain, and justify classroom observations of student and teacher activity,

(c)描述、理解、说明、证明在教室所观察到的学生和教师活动。

(d) transform practical problems into research problems,

(d)把实践问题转换为研究问题

(e) define different steps in the study of a research problem, and

(e)确定一个研究问题的不同的研究方式。

 (f) generate knowledge.

(f)再生知识。

When theory functions as an object, one of its goals can be the advancement of theory itself.

当理论的功能作为一个对象,它存在的其中一个目的就是理论自身的进步。

This can include testing a theory or some ideas or relations in the theory (e.g., in another context or) as a means to produce new theoretical developments.

理论的功能还可以包括测试功能,即对理论、一些想法、理论间联系的测试,这种功能可以作为发展新理论的方式。

Silver and Herbst (2007) identified similar roles but proposed the notion of theory as a mediator between problems, practices, and research.

Silver and Herbst(2007)赞同类似的理论角色,但是提出这样的看法:理论作为问题、实践、研究之间的调解人。

 For example, as a mediator between research and problems, theory is involved in, among others, generating a researchable problem, interpreting the results, analysing the data, and producing

and explaining the research findings.

例如,作为研究和问题之间的调解人,理论介入其中,形成一个可研究的问题,解释结果,分析数据,得出并且解释研究成果。

As a mediator between research and practice,theory can provide a norm against which to evaluate classroom practices as well as serve as a tool for research to understand (describe and explain) these practices.

作为研究和实践之间的调解人,理论可以提出一个行为模式用来评估课堂实践,同样这个行为模式也可以作为一个工具用来理解这些实践。

Theory that mediates connections between practice and problems can enable the identification of practices that pose problems, facilitate the development of researchable problems, help propose a solution to these problems, and provide critique on solutions proposed by others.

理论在调解实践与问题的联系时,能帮助认清出了问题的实践,促使研究性问题的发展,促成针对这些问题的解决方案,还可以提供对其它解决方案的评价。

Such theory can also play an important role in the development of new practices, such as technology enhanced learning environments.

这样的理论还可以在促进新实践的发展扮演重要角色,例如技术科学提升了学习环境。

What we need to do now is explore more ways to effectively harmonize theory,research, and practice (Silver and Herbst 2007; Malara and Zan 2008) in a coherent manner so as to push the field forward.

现在我们需要探索如何有效地将理论、研究与实践协调一致去推进这个领域的发展。

This leads to an examination of the extant theoretical paradigms and changes that have occurred over the last two decades.

这需要重新审视现存的理论的范式和最近20年来,它们所经历的变化。

This was briefly discussed at the outset of this chapter.

以上简单的讨论作为本章节的开端。

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