本科毕业设计（论文）
外文翻译
Teaching Mathematics: Ritual, Principle and Practice
作者：YVETTE SOLOMON
国籍：America
出处：Journal of Philosophy of Education, Vol. 32, No. 3, 1998
原文正文：
One of the criticisms of standard teaching practices is that they support merely lsquo;ritualrsquo; as opposed to lsquo;principledrsquo; knowledge, that is, knowledge which is procedural rather than being founded on principled explanation. This paper addresses issues and assumptions in current debate concerning the nature of mathematical knowledge, focusing on the ritual/principle distinction. Taking a discussion of centralism in logic and mathematics as its start-point, it seeks to resolve these issues through an examination of mathematics as a community of practice and the teachers role as epistemological authority in inducting pupils into such practices.
Piagets developmental theory remains the dominant informing ideology of current teaching practices, particularly those associated with primary mathematics. However, one of the criticisms levelled at standard teaching practices is that they support merely ritual as opposed to principled knowledge (Edwards and Mercer, 1987), syntax but not semantics (Hull, 1985) or, similarly, semantically-debased or pseudo-structural conceptions rather than meaningful constructions (Cobb and Yackel,1993). Using the appropriation metaphor, Ernest (1989) makes a comparable distinction between knowledge owned by the teacher and knowledge owned by the pupil: while the ideal might be knowledge owned by the pupil, the reality frequently is ownership by the teacher. In Lave and Wengers (1992) analysis, standard didactic instruction creates unintended practices which are not those of the practice supposedly being reproduced in the classroom. Bound as we have been by a Piagetian image of learning as an individual pursuit of the child-scientist, our explanations of childrens failure to learn mathematics have inevitably invoked individual failure (cognitive immaturity on the part of the child, inadequate teaching on the part of the teacher); more recent recognition of mathematics as a social practice means, however, that we have no grounds for assuming that a child whose ordinary activity concerns immediate and real problems about quantities, say, will discover formal mathematical principles in the mathematics classroom without reference to the social context in which they find themselves.
Thus Vygotskian and neo-Vygotskian approaches to the classroom construction of knowledge such as Edwards and Mercers (1987) and Mercers later work (1994, 1995) maintain that the shaping of principled knowledge relies on the continuous production of shared mental contexts or frames of reference culminating in a handover of competence from guide to apprentice (cf. Rogoff, 1990). Context, by this definition, is a property of the understanding of a situation which is jointly negotiated or constructed by the participants. There are several assumptions about knowledge contained within such analyses and criticisms which raise the questions which form the basis of this paper. what are teachers doing when they teach children to do mathematics, and what is the role of social context—both in terms of relations between teacher and pupil, and in terms of the mathematical activity itself—in that situation? The answers which I will offer all cluster around issues of what it is to understand mathematics and what mathematical activity actually constitutes and, therefore, what the mechanisms—both individual and social—of arriving at that understanding must be.
1.THE PRIORITY OF PRACTICE
For Edwards and Mercer and many others, principled knowledge is something to be aimed at as quality knowledge versus the empty
syntactic rule-following of—to take an extreme example—stimulus—
response pairs. Edwards and Mercers most illuminating example comes from their demonstration of a group of secondary school students failure in a lesson on pendulums to grasp, among other issues in scientific method, that of controlling variables (i.e. allowing only one at a time to vary) and their acquisition instead of knowledge which is embedded in the trappings of the lesson (You couldnt have us all doing the same thing, so we/there was three of us and there was really three things to change on the pendulum so we done one each). Within mathematics, Hulls (1985) consideration of the problems encountered by children in dealing with concepts such as right-angle, parallel and triangle argues that their definitions are frequently incomplete or erroneous, based as they are on a limited range of referents used in textbooks. Pimm (1987) makes similar observations about the concept diagonal which, together with many mathematical terms which have ordinary language parallels, is likely to invoke everyday meaning in making sense of a task because mathematical meaning is absent. Piaget (1952, 1966, 1968, 1972a, b) can be included in this group despite being the target of much neo-Vygotskian criticism; Indeed a primary aim of his genetic epistemology is to account for the acquisition of the necessary knowledge which underlies logical principles and which is differentiated from mere learning by association. But while there is a useful distinction to be made in the contrast between ritual knowledge and what might be called principled knowledge, it is not of the nature presupposed by Edwards and Mercer and Piaget. We can agree that a knower has principled knowledge when she shows power to project from what has been learned in the past to appropriate and correct behavior in a variety of new and previo
剩余内容已隐藏，支付完成后下载完整资料
本科毕业设计（论文）
Teaching Mathematics: Ritual, Principle and Practice
作者：YVETTE SOLOMON
国籍：America
出处：Journal of Philosophy of Education, Vol. 32, No. 3, 1998
原文正文：
One of the criticisms of standard teaching practices is that they support merely lsquo;ritualrsquo; as opposed to lsquo;principledrsquo; knowledge, that is, knowledge which is procedural rather than being founded on principled explanation. This paper addresses issues and assumptions in current debate concerning the nature of mathematical knowledge, focusing on the ritual/principle distinction. Taking a discussion of centralism in logic and mathematics as its start-point, it seeks to resolve these issues through an examination of mathematics as a community of practice and the teachers role as epistemological authority in inducting pupils into such practices.
Piagets developmental theory remains the dominant informing ideology of current teaching practices, particularly those associated with primary mathematics. However, one of the criticisms levelled at standard teaching practices is that they support merely ritual as opposed to principled knowledge (Edwards and Mercer, 1987), syntax but not semantics (Hull, 1985) or, similarly, semantically-debased or pseudo-structural conceptions rather than meaningful constructions (Cobb and Yackel,1993). Using the appropriation metaphor, Ernest (1989) makes a comparable distinction between knowledge owned by the teacher and knowledge owned by the pupil: while the ideal might be knowledge owned by the pupil, the reality frequently is ownership by the teacher. In Lave and Wengers (1992) analysis, standard didactic instruction creates unintended practices which are not those of the practice supposedly being reproduced in the classroom. Bound as we have been by a Piagetian image of learning as an individual pursuit of the child-scientist, our explanations of childrens failure to learn mathematics have inevitably invoked individual failure (cognitive immaturity on the part of the child, inadequate teaching on the part of the teacher); more recent recognition of mathematics as a social practice means, however, that we have no grounds for assuming that a child whose ordinary activity concerns immediate and real problems about quantities, say, will discover formal mathematical principles in the mathematics classroom without reference to the social context in which they find themselves.
Thus Vygotskian and neo-Vygotskian approaches to the classroom construction of knowledge such as Edwards and Mercers (1987) and Mercers later work (1994, 1995) maintain that the shaping of principled knowledge relies on the continuous production of shared mental contexts or frames of reference culminating in a handover of competence from guide to apprentice (cf. Rogoff, 1990). Context, by this definition, is a property of the understanding of a situation which is jointly negotiated or constructed by the participants. There are several assumptions about knowledge contained within such analyses and criticisms which raise the questions which form the basis of this paper. what are teachers doing when they teach children to do mathematics, and what is the role of social context—both in terms of relations between teacher and pupil, and in terms of the mathematical activity itself—in that situation? The answers which I will offer all cluster around issues of what it is to understand mathematics and what mathematical activity actually constitutes and, therefore, what the mechanisms—both individual and social—of arriving at that understanding must be.
1.THE PRIORITY OF PRACTICE
For Edwards and Mercer and many others, principled knowledge is something to be aimed at as quality knowledge versus the empty
syntactic rule-following of—to take an extreme example—stimulus—
response pairs. Edwards and Mercers most illuminating example comes from their demonstration of a group of secondary school students failure in a lesson on pendulums to grasp, among other issues in scientific method, that of controlling variables (i.e. allowing only one at a time to vary) and their acquisition instead of knowledge which is embedded in the trappings of the lesson (You couldnt have us all doing the same thing, so we/there was three of us and there was really three things to change on the pendulum so we done one each). Within mathematics, Hulls (1985) consideration of the problems encountered by children in dealing with concepts such as right-angle, parallel and triangle argues that their definitions are frequently incomplete or erroneous, based as they are on a limited range of referents used in textbooks. Pimm (1987) makes similar observations about the concept diagonal which, together with many mathematical terms which have ordinary language parallels, is likely to invoke everyday meaning in making sense of a task because mathematical meaning is absent. Piaget (1952, 1966, 1968, 1972a, b) can be included in this group despite being the target of much neo-Vygotskian criticism; Indeed a primary aim of his genetic epistemology is to account for the acquisition of the necessary knowledge which underlies logical principles and which is differentiated from mere learning by association. But while there is a useful distinction to be made in the contrast between ritual knowledge and what might be called principled knowledge, it is not of the nature presupposed by Edwards and Mercer and Piaget. We can agree that a knower has principled knowledge when she shows power to project from what has been learned in the past to appropriate and correct behavior in a variety of new and previ
剩余内容已隐藏，支付完成后下载完整资料
资料编号：[276385]，资料为PDF文档或Word文档，PDF文档可免费转换为Word
以上是毕业论文外文翻译，课题毕业论文、任务书、文献综述、开题报告、程序设计、图纸设计等资料可联系客服协助查找。
