Contributions from cultural-historical theory to research in mathematics education: Research Guiding Activity

Author(s):

Elaine Araujo(presenting / submitting)

Conference:

ECER 2016

Network:

10. Teacher Education Research

Format:

Poster

Session Information

10 SES 04.5 PS, General Poster Session

General Poster Session

Time:

2016-08-24

12:00-13:30

Room:

NM-Concourse Area

Chair:

Rachel Shanks

Contribution

The considerable bibliographic production in decades on concepts such as mediation and Zone of Proximal Development, allows us to afirm, without exaggeration, that Vygotsky has become an obligatory name not only in psychology but also in pedagogy and even in mathematics education. However, this intense movement, reflected in such productions and research does not necessarily mean a due appropriation of the foundations and methods of historical-cultural theory to which they are linked. The risk of vulgarization, the convenient interpretation of the theory, seems pronounced in the case of Marxist psychology, particularly in its interface with education. This is why the aim is to demonstrate how the foundations of cultural-historical theory, in content and form, can guide research in mathematics education within the teacher education. So it starts from the thesis of Vygotsky (2000), that a "new method" also defines "a new phenomenon", ie, the method is closely linked to the phenomenon in the same way that the phenomenon is "revealed" by the method.

In this work we demonstrate how the fundamentals of cultural-historical theory, in content and form, can guide research in mathematics education in teachers’ formation. In the case of research conducted the aim has meant to understand the teacher learning in the context of Teaching Guiding Activity (TGA) math. We develop the Research Guiding Activity (RGA) which, like the TGA, contains the synthesis of an educational project, has a collective need, must be the subject; have a coordinated plan of action; motive coincides with the object. We organize Research Guiding Activity that could, on the one hand, promote learning and teacher development and, secondly, to enable the researcher to understand the formation of teachers’ theoretical thought. The RGA thereby constituted as a unit formative research and teacher learning, acting as mediation between the researcher (research objectives) and the teacher (formative objectives).

Method

In this work we present the realized research process (2009 - 2011), to explain the constitution of the research, its genesis and development, highlighting the procedures and instruments adopted. The effort is to demonstrate how was permeated the state "fossilized" of the research, that has as its object the teaching learning, having as context the teaching of mathematics in childhood. The first question that arises is to overcome the understanding of research as an extension activity which usually sets it up as a situation in a non-scientific level. The activity conformed as a research project was initially considered as an extension project, requested in 2007 by teachers of the public network of São Paulo, Brazil, "in order to promote the curriculum mathematics organization in Childhood". For this purpose, it was constituted a study group that initially had eleven participants, including teachers, educational technicians and managers. In this group it was developed teaching activities considering the theoretical and methodological support of the Guidance Education Activity (MOURA, 2000). This meant observe, on the one hand, some of the main mathematical content for the first stage of basic education: geometric language, measurements, algebraic and stochastic language and, on the other, methodological features such as virtual history, game, emergent situations and graphic activities. From the understanding that the formative research involves collaboration, reflection, action, transformation and mediation, the formative dynamic was accomplished through systematic meetings in which mathematics activities took the configuration of the main object analysis. With this, it was intended also to ensure conditions to observe the phenomenon in the process of change (Vygotsky, 1995), in this case, the formation of theoretical thinking. Related to the research subjects, the group was formed by four teachers of early childhood education and the early grades of elementary education in publics schools of a country city in São Paulo, Brazil and three students of the Faculty of Education of University public of the state of São Paulo and an investigator.

Expected Outcomes

The development of this research became possible to analyze and reflect on the instruments (collection, analysis and presentation of data) we have adopted and how they directly relate to a particular course of action that competes for the demarcation of our work as an extension activity and as research activity. It's not enough to have a clear research problem and well-defined objectives, much less a collection of facts to ensure the investigative nature of the work. Overall, we can say that RGA as an activity has two dimensions, orientation and execution. Although inseparable, the first relates to the motive and subject and the object of research and the other to the actions and operations to achieve the object. In this sense, the general RGA which, in terms of guidance, had as motive to understand the training of teaching theoretical thinking. In terms of execution, each new developed action is equivalent to certain objectives (formative and investigative) and operations (necessary materials and resources). The RGA was constituted thus as a formative unity of research and teaching learning, acting as a mediator between the researcher (research purposes) and the teacher (training objectives). When we consider that the concepts are historical creations, in which knowledge is objectified on the mental plane, their ownership at the same time, structure and reveals a way of thinking. That meant overcoming a kind of reflection mediated only by the phenomenon of appearance. Therefore, it was necessary to conduct a series of actions: study of theoretical frameworks geared to the fundamental concepts in mathematics and didactic principles of organization of teaching in cultural-historical perspective; development, implementation, and activities production.

References

DAVIDOV, V. (1988) La enseñanza escolar y el desarrollo psíquico. Moscou: Progresso. ________. (2002) El aporte de A N. Leontiev al desarollo de la psicologia. In: GOLDER, M. Angustia por la utopía. Buenos Aires: Ateneo Vigotskiano de la Argentina. KOPNIN, P. (1978) A dialética como lógica e teoria do conhecimento. Rio de Janeiro: Civilização Brasileira. LEONTIEV, A. (1983) Actividad, Consciencia, Personalidad. Habana: Editorial Pueblo yEducación. MOURA, M. O. (1996) A atividade de ensino como unidade formadora. BOLEMA, v. 12, p. 29-43, Rio Claro: UNESP. ________. (2001) A Atividade de Ensino como Ação Formadora. In: CASTRO, A. D. E CARVALHO, A.M P. Ensinar a Ensinar. São Paulo: Pioneira. MYNAYO, M.C.S, (2005) O desafio do conhecimento.São Paulo: Hucitec. VIGOTSKI, L. S. (2000) A Formação social da mente. São Paulo: Martins Fontes. VYGOTSKI, L.S (1995) Obras Escogidas, V. III. Madri: Visor.

Author Information

Elaine Araujo (presenting / submitting)

Universidade de São Paulo

DEDIC

Ribeirao Preto

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