Researching the net-work of school (mathematics) education practices Paola Valero PhD course “Designing social learning systems in a globalized world: At the crossroads of cultural diversity and technological development” Sæby, November 5-8, 2007

A dialectic relationship in research Theoretical perspective Research object

Broadening my perspective in Colombia Context: Educational policy changes and demands for change in school subjects. Emphasis on the quality of education seen in terms of students’ “mathematical power” Question: What is it needed in order to make education improve in quality? Principles: People are the motor of change. Change should involve the school community as a whole.

Institutional System of Mathematics Education (ISME)

Lessons: –Understanding school change demands understanding the dynamics of mathematics education in the school organization. –The school system is embedded in larger systems and they influence its functioning Many “disruptions” in school functioning Assumption: We can recognize the influence, though we can’t act on it and therefore it is worth studying only the dynamics on which we can have influence.

in Denmark My study: Reform Democracy (Socio- political approach) Institutional System of Mathematics Education

Starting point: Reformulation of the notion of ISME –Empirical work Three exemplary cases in three different countries (Nyspor, Rajas, Esperanza) A “theory-case contrast” design An information collection strategy that covered the areas of the ISME with a variety of techniques: –classroom interaction observation, video and audio taped –students with one-time cameras –significant pieces of work for students and teachers –interviews –informal conversations –policy documents at different levels –Information materials Analysis of information and construction of data through the construction of “vivid images” (episodes)

–Theoretical work Episodes as triggers of reflection Search for possible and plausible interpretations Discourse analysis of existing literature (school reform, organizational theory, mathematics education) The process: Development of a language of interpretation to talk about reform in the ISME from a socio-political perspective

Issues that emerged from the analysis –The problem of context and complexity How to account for the “external factors” that evidently influence education reform in schools? Which is the dominant way in which “context” is dealt with in the field of study in which the study is located? How to conceptualize context so that the “research objects” can be interpreted in relation to their surrounding?

–The problem of an analysis that goes beyond initial research focus If context is important, how does one builds an analysis that connects the elements of the ISME to layers of context? –The problem of theory Which kinds of concepts are helpful in such analysis? (Perspective) What do these concepts imply for the construction of research objects? –The problem of methodology What do theoretical perspectives and research objects imply for the process of knowing in the research? How do I act as a researcher?

–A focal point on the continuum Agency Structure –Reduction of complexity –Empirical research

In the field of educational research –Sociology of education –Organizational learning –Social theory of learning –General didactics –Subject matter didactics (Mathematics education) Focus on mathematical learning as an individual cognitive process Individuals are a privileged unit of analysis Research objects dominantly defined in term of the “didactic triad”

Linking micro and macro is a challenge: “This switching between the smallest and widest units of observation is the normal and necessary procedure of the sociologist; it is one of the most characteristic traits of the field of sociological study and at the same time constitutes one of its greatest difficulties. For the sociologist there is no break in continuity between the microsociological and macrosociological planes, but rather interpenetration and complementarity of two levels of social reality and two levels of analysis. From Rocher, G. (1972). A general introduction to sociology. A theoretical perspective. New York: St. Martin Press, p. 6)

What is involved in the challenge? –Acknowledgement of social complexity –Contextualization –Historicity –Interpenetration and complementarity of levels

A post-rationalization A socio-political perspective Mathematics education studies the historically-situated, social processes through which concrete human being get involved in the creation and re-creation of diverse forms of knowledge and ways of reasoning related to mathematics

Mathematics education is seen as a net-work of social practices The meaning of learning and teaching mathematics is constructed in the relationship between: Actors Social, political, economic, cultural arenas Teachers Students Parents Leaders Politicians Employers Classroom School Family Educational policy Labor market Meaning

T E M Classroom School Nation International arena Leaders Colleagues Employers Teacher educators Parents International organizations Policy makers Friends

T E M Classroom practice School Nation International arena Working practice Teacher education practices International comparison practices Leadership practice International policy practice Family practice Policy-making practice Youth practice Staff prof. practice Technology development practice Research practice