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BETWEEN CURRENT TEACHER TRAINING AND THAT WE WISH TO HAVE: POSSIBLE PATHS
Regina Maria Pavanello
Cllia Maria Ignatius Nogueira
Universidade Estadual de Maring, Maring PR Brazil
Although different variables may be associated to and, to a certain extent, may have produced the Mathematic difficulties experienced by many students, none is so deep as that which refers to teacher training. In fact, most problems on the teaching process and the learning of Math may be overcome through the teacher mediation.
In Brazil training is undertaken in Pedagogy Courses since the 1990s and more recently in the Teachers Training Colleges. This work deals with the initial training of teachers who teach Math in the first years of the primary school and the situations in which this contributes for they to successfully put into practice such mediation.
Teachers Training: current issues
Several researches have shown that students who attended these courses have had difficulties with Mathematics during their former schooling. This fact may have influenced their choice for a type of training which apparently has no special requirements in mathematical knowledge. Actually class load given to Math in these courses is highly reduced and the disciplines, Methodology for the Teaching of Math or Fundamentals of Math, are always given in a single semester.
Teachers of these disciplines are either professors capacitated in Mathematics who do not have any experience in primary classes or any interest for methodological discussions or they are pedagogues with not enough mathematical knowledge. Anyway, the professors take for granted that students already know the elementary concepts of Mathematics. They thus have in mind that the warrant to be a future teacher would be limited to the methodology of the teaching of Mathematics in the case of the Pedagogy teacher or would provide him/her with a broader aspect of this field in human knowledge in the case of the Math teacher.
However, both concepts are at fault. Mere methodological discussions do not capacitate the future teacher for the day-to-day teaching practice. The fact that they, as students, have already been in contact with these concepts is not a guarantee of knowledge since the latter may have been limited to techniques and procedures without the understanding of concepts and contents involved. In other words, knowing how to do things is insufficient for teaching the what, the how and the why of doing. The study of more complex mathematical themes does not guarantee a better understanding of the most elementary ones. According to Franchi,
teachers must have a comprehensive knowledge at their hands reach that illuminates their activities. It should not be limited to contents and tools with which they work in the classroom. Perhaps the most important thing is to make sure that the teachers have a knowledge which is highly different from that which predominates in the practices and contents that are proposed to them in their teacher training courses. In simple terms, the teachers should not merely know what they are teaching as if the quality of their lessons depends on being a carbon copy of the teaching they received. On the contrary, teaching quality depends on a broader knowledge system so that the teachers should better understand what gives meaning and function to their teaching (1995, p. 66).
According to the above, it is not surprising that teachers of the first initial years of the primary school acknowledge that their initial training did not provide them with the knowledge of Mathematics required during their teaching practice. This occurs not merely with the contents but also with the pedagogical approach in the classroom. They actually reported that this fact has made difficult their teaching practice and explains their dependence on text books and their incapacity to evaluate their quality. They complain that the course is highly theoretical and that theory is distant from practice. This is not only due to the fact that theory and practice are given separately within the curriculum but mainly because theory does not seem to be articulated to the concrete problems of the classroom, the school and teaching (Freitas, 1996, p.90). They also state that, although the political dimension of Education and the need for change in pedagogical practice are discussed during courses, such discussions do not provide teachers with the essential theoretical and practical knowledge inherent to these changes.
[It] may be taken for granted that future teachers finish their training courses without any knowledge of mathematical concepts with which they will work, including concepts, procedures and the very language they will use in their teaching practice. In other words, it seems that a general view exists that it is not required for the polyvalent teacher the knowledge of Math and that it suffices to know how to teach it (CURI, 2005, p. 69-70).
Teachers Training: a possible solution
We agree with Campos (1999) that teachers training should take the professional preparation and the future exercise of the profession as a point of reference and that
nobody facilitates the development of that which one did not have the opportunity to make better. No one improves the learning of contents which are unknown, or the constitution of meanings that are not understood, or the autonomy that is unable to be built (CAMPOS, 1999, p. 7).
It is pure ingenuity to believe that a student fresh from a teachers training course, even if it is the best course possible, is completely and definitively prepared to exercise his/her professional activity. All training is necessarily provisional in a non-static society which transforms itself through human activities and the evolution of knowledge.
In spite of the above and based on the above-mentioned Campos (1999) and on our previous research and analysis, we insist that the Math formation of the polyvalent teacher, who will trigger the initiation to Mathematics in the primary school in the context of a pedagogical practice that would contribute towards the building of mathematical knowledge by pupils, should include:
Knowledge of school Mathematics. Teachers should know to a profound degree the concepts and properties of the contents with which they work, coupled to their history, so that they would go beyond the paradigm of knowledge transmission that gives priority to language instead of thought, that emphasizes learning of terms, definitions and algorithms instead of stimulating the establishment of relationships, or rather, a search for similarities and differences, of rules and patterns which, among other things, constitute the core of mathematical thought. Such knowledge is essential so that the teacher may be aware of and lead the pupils to perceive Mathematics as a dynamic and an open field of knowledge.
The historical construction of knowledge. Knowledge of the history of Mathematics is important so that teachers understand that mathematical knowledge has not been constructed once for all and within a short period of time. On the contrary, many concepts took a great deal of time to be understood and systematized. This fact involves their complexity and difficulty to be understood. The knowledge of obstacles involved in the process of concept construction helps the teacher to better understand some aspects of his/her own learning and that of the pupils. Consequently, the mediation between the formal Mathematics given at school and the Mathematics as a daily activity may be better organized.
In-depth knowledge of the principles that govern the development, learning and the construction process of mathematical knowledge. Such knowledge warrants the future teacher: a significant and applied learning of these principles; the ability to respect differences (cognitive style, learning rhythm, forms of expression); the possibility of choosing a theory of learning to uphold his/her pedagogical activities so that the lack of nexus between discourse and pedagogical activity could be avoided.
Didactic and methodological knowledge. The future teacher should know and analyze different didactic and methodological alternatives (electronic resources; different languages and materials) to understand their possibilities or limitations, their adequacy or lack of it with regard to the aims that should be reached by them, such as the comprehension of mathematical notions, concepts, processes and phenomena. In other words, the future teacher must have the opportunity to participate in a mathematical learning process based on a personal construction which, in its turn, results from an experiential process in which possibilities exist to compare, analyze and relate the mathematical concepts under different forms (hearing, visual and kinesthetic) and to attribute a personal meaning to the new acquisitions.
Knowledge on possible interrelationship of different mathematical themes, among themselves and with other fields of knowledge. This fact will make the future teacher aware that certain specific contents in a determined field facilitate acquisitions or help overcoming difficulties in another field.
The permanent and continuous integration between theory and practice from the start of the undergraduate course, in all the disciplines of the professional training curriculum, so that situations of significant learning are provided to future teachers in the fields of specific contents and in the field of fundamentals in Education. The curricular training period comprise school internment with an effective participation, observation in the classroom, management of pedagogical time and space and of other support didactic resources during the required time to face differentiated and unforeseen situations, under the supervision of the school where training occurs. School supervisions should participate in the final evaluation of the future teacher.
Development of studies and researches. It is highly important that in the course of the different stages in professional development the teacher should be in contact with researches in the field. This activity is important so that teachers should better understand the educational phenomena in all its different aspects and reflect in which direction and with what limits these investigations may help them in the professional practice. Undertaking studies and research is required so that the future teacher may experiment a new educational paradigm based on investigation and discussion in which contradictions are not avoided, doubts are natural, mistakes normal and conflicts are faced as improvements for new steps in knowledge.
Teachers training: the challenge to face
Although current teachers training courses are incapable of providing the required knowledge for the mathematical learning of pupils, we cannot state that these teachers are inevitably destined to develop an inefficient practice in spite of the fact that their past training in the school certainly leaves its mark which may only be overcome by a great deal of interest, study and dedication.
According to Curi (2005), the publication of books and didactic material for the training of the polyvalent teacher is highly undeveloped. Consequently the opportunities for teachers to supplement their initial training and develop competences that would help them to reflect on their practice and analyze their pupils difficulties are impaired.
The publication of such material is currently the main challenge that Brazilian researchers in mathematical education have to face.
References
CAMPOS, M. M. (1999) A formao de professores para crianas de 0 a 10 anos: modelos em debate. Educao e Sociedade, v.20, n. 68.
CURI, E. (2005) A matemtica e os professores dos anos iniciais. So Paulo: Musa.
FRANCHI, E. P. (1995) A insatisfao dos professores: conseqncias para a profissionalizao. In FRANCHI, E. P. (org.) A causa dos professores. Campinas: Papirus.
FREITAS, H. C. L de. (1996) O trabalho como princpio articulador na prtica de ensino e nos estgios. Campinas: Papirus.
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