자연주의적 탐구조사(Naturalistic Inquiry)

How to ... be a reflective practitioner.

Note on Translation Introduction by Michael Holquist Response to a Question from the Novy Mir Editorial Staff The Bildungsroman and Its Significance in the History of Realism (Toward a Historical Typology of the Novel) The Problem of Speech Genres The Problem of the Text in Linguistics, Philology, and the Human Sciences: An Experiment in Philosophical Analysis From Notes Made in 1970-71 Toward a Methodology for the Human Sciences Index

Speech Genres and Other Late Essays

National Science Education Standards

미국의 “전국 수학 교사 협의회”(National Council of Teachers of Mathematics, NCTM)는 1989년부터 〈학교 수학의 교육과정과 평가 규준〉(1989), 〈수학 가르침(교수)의 전문성 규준〉(1991), 〈학교 수학의 평가(시험) 규준〉(NCTM, 1995), 〈학교 수학의 원리와 규준〉(2000)을 출판하여 미국의 수학 교육 의 전망(목표, 나아갈 길)과 규준(실행 지침)을 제시하였다. 수학 교사들로 구성된 미국의 NCTM은 학생, 학부모, 학교 행정가 등 많은 사람들과 힘을 합하여 모든 학생들에게 수준 높은 수학 교육을 받을 수 있는 여건(환경, 기회)을 조성하는 데 구심점의 역할을 하였다. 한편 많은 관련 단체들은 여러 배경과 능력을 가진 학생들이 전문성을 지닌 교사(특수 교사를 일컫는 밀이 아니다. 수학 교과를 이해하고 수학의 전문성과 특수성을 가르칠 수 있는 일반 교사를 일컫는 말이다.)로부터 미래를 대비해 평등하고, 진취적이며, 지원이 잘 이루어지고, 공학 도구(IT)가 잘 갖춰진 환경에서 중요한 수학적 아이디어를 이해하면서 학습할 수 있는 수학 교실(미국에서는 우리나라처럼 수학 교사가 수학 시간에 학생의 방(교실: Homeroom)에 찾아가지 않고 학생들이 선생의 방(수학 교실: Classroom)을 찾아온다. 전형적인 수학 교실의 사진은 2쪽에 나와 있다.)을 만들기 위해 함께 힘썼다. NCTM에서 출간한 여러 규준들은 우리나라의 제6차와 제7차 교육과정에도 큰 영향을 미쳤다. 이 글에서는 NCTM(2000)에서 제시한 학습 원리를 간단히 살펴본 다음 이를 중심으로 현재 미국 수학 교육의 교수ㆍ학습 이론의 동향을 살펴본다.

미국 NCTM의 Principles and Standards for School Mathematics에 나타난 수학과 교수,학습의 이론

In this paper we synthesize the theoretical model about mathematical cognition and instruction that we have been developing in the past years, which provides conceptual and methodological tools to pose and deal with research problems in mathematics education. Following Steiner’s Theory of Mathematics Education Programme, this theoretical framework is based on elements taken from diverse disciplines such as anthropology, semiotics and ecology. We also assume complementary elements from different theoretical models used in mathematics education to develop a unified approach to didactic phenomena that takes into account their epistemological, cognitive, socio cultural and instructional dimensions.

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The onto-semiotic approach to research in mathematics education

The nature of mathematical objects, their various types, the way in which they are formed, and how they participate in mathematical activity are all questions of interest for philosophy and mathematics education. Teaching in schools is usually based, implicitly or explicitly, on a descriptive/realist view of mathematics, an approach which is not free from potential conflicts. After analysing why this view is so often taken and pointing out the problems raised by realism in mathematics this paper discusses a number of philosophical alternatives in relation to the nature of mathematical objects. Having briefly described the educational and philosophical problem regarding the origin and nature of these objects we then present the main characteristics of a pragmatic and anthropological semiotic approach to them, one which may serve as the outline of a philosophy of mathematics developed from the point of view of mathematics education. This approach is able to explain from a non-realist position how mathematical objects emerge from mathematical practices.

The Emergence of Objects from Mathematical Practices.

Resumen Diversos marcos teoricos proponen sistemas de categorias del conocimiento matematico para la ensenanza que ayudan a describir la practica docente y a elaborar planes de formacion de profesores. En este articulo se describe uno de estos sistemas, que incluye tanto los conocimientos como las competencias del profesor de matematicas y esta basado en el Enfoque ontosemiotico del conocimiento y la instruccion matematicos. Las nociones de sistema de practicas, configuracion ontosemiotica, configuracion didactica, dimension normativa e idoneidad didactica, introducidas en dicho sistema teorico, son consideradas como herramientas de analisis de las practicas matematicas y didacticas. Se utilizan estas nociones como base para delimitar sub-competencias de la competencia general de analisis e intervencion didactica, propia del profesor de matematicas. Las investigaciones que se vienen realizando usando este modelo teorico de articulacion de los conocimientos y las competencias, apoyan la pertinencia y posibilidad de que el profesor conozca, comprenda y este capacitado para aplicar las herramientas de analisis propuestas en su propia practica profesional. Se incluye tambien la descripcion sucinta de acciones formativas para lograr el desarrollo de los conocimientos didactico-matematicos y la competencia de analisis e intervencion didactica de los profesores de matematicas.

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Enfoque ontosemiótico de los conocimientos y competencias del profesor de matemáticas

The viability of a theoretical model to analyse teaching and learning mathematical processes is presented in the paper. It is a model with five levels of analysis that are jointly applied to a classroom episode. We have constructed the model in order to describe (what has happened here?), explain (why has it happened?) and evaluate (what could be improved?) instruction processes in the mathematics classroom. Our work is based on a theoretical synthesis of aspects of the onto-semiotic approach applied to mathematical knowledge and instruction. Although some parts of the model are specific to mathematical activity, researchers from other educational areas can adapt them so that they can be used effectively to analyse other types of educational practices. The application of the model primarily seeks to provide a solid evaluation of the educational suitability of mathematics instruction processes.

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Modelo para el análisis didáctico en educación matemática

Background:The objective of this study is to demonstrate that the criteria of didactical suitability, proposed by the theoretical framework known as the Onto-Semiotic Approach (OSA) of mathematical knowledge and instruction, are powerful tools for organizing the reflection and assessment of instruction processes carried out by mathematics teachers.Material and methods:To this aim, the results of a multiple case study are presentedResults:which prove that when teachers are faced with the task of evaluating processes of instruction, they employ-either implicitly or explicitly- the OSA criteria of didactical suitability (epistemic, cognitive, affective, mediational, interactional and ecological).Conclusions:Therefore, the explicit application of said criteria in teachers’ education cycles contributes to the development of the didactic analysis competence that is necessary for teachers to be able to reflect on their own practices.

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Papers

The onto-semiotic approach to research in mathematics education

The Emergence of Objects from Mathematical Practices.

Enfoque ontosemiótico de los conocimientos y competencias del profesor de matemáticas

Modelo para el análisis didáctico en educación matemática

Meta Didactic-Mathematical Knowledge of Teachers: Criteria for The Reflection and Assessment on Teaching Practice