1. TEACHERS LEARNING HOW TO TEACH MATHEMATICS

2. THE RESEARCH’S CONTEXT  This research is inserted in a wider project (Observatório da Educação/Capes).  The two focuses are: - Literacy practices in school  practices related to mathematics. - Mathematics teachers’ education practices.  It is carried out through a cooperative work with elementary school teachers.

3.  3 professors  7 teachers from public schools in the State of São Paulo/Brazil (aged: 6 – 9).  2 post-graduation students (Master’s degree).

4.  The group meets every 15 days: - To perform studies about literacy - To analyze documents that are sent to the school (from diferent teaching systems) - To plan tasks for the classes. - To analyze teachers’ practices which are reported to the group (orally or in writing).

5.  The research of the teachers in their classes  their practices are systematized in narratives.  The academic research is carried out by the Master’s degree students and coordinating professors.  Materials for the research consist of: - narrative documents from teachers - audio/video recordings from the group meetings.

6.  The research has a qualitative approach.  Theoretically grounded on historical- cultural perspectives focused on the concepts of: - Literacy - Learning - Conceptual elaboration - Pedagogical mediation.

7.  B. Street (2003)  ideological literacy (social practice)  We are using the concept in the plural: literacies  practices produced in school: school literacy (mathematical literacy) and teacher literacy.  Smagorinsk (2011)  literacy in a historical-cultural perspective.

8. Comprehension of the teachers’ and students’ writing and reading practices: - specific social practices - historically shaped by pedagogic traditions - spheres of human activity in which multiple texts and significances appear, emerging from the texts used in school and the texts produced by teachers and students. OUR FOCUS

9. We advocate that teaching activities should:  Foster the conceptual construction process, and become common in the school environment;  Are intentional activities, directed by goals, and shaped by different literacy practices:  Reading; writing; drawing; registering; questioning; using measuring and calculation tools; using computing tools, etc.  In short, being in contact with multiple languages.

10. TEACHERS EVALUATE THE STUDENTS’ PROCESS OF CONCEPTUAL CONSTRUCTION As educators: - We intend to promote the ‘transition’ between what the teachers bring from stories of reading and writing, and the concepts we present, with the intention of instigating reflection and raising awareness regarding their knowledge and practices.

11. We believe that the historical-cultural perspective, and a few of its concepts (integration, mediation, means, learning, development, significance and language) may optimize the organization of pedagogic work, and the role of the teacher as promoter of both the learning and development of students.

12.  Pedagogic action must be intentional  the choice of the tasks for students.  Ideally, classroom activities must take the form of a partnership – pairs or small groups (ZPD). “The children were separated in pairs of similar learning levels, so one can contribute to the development of the other” (Narrative, Elizangela, October 2013).

13.  Everyday concepts are transformed into cientific concepts, through systematic work.  When teachers give voice to students and listen to what they have to say, they may incorporate the social context, in which the students are inserted in their literacy practices.

14. During the elaboration process, the teacher’s mediation is essential: T 01 – Marcelo: Ms. are we supposed to count only the ties? T02 – Teacher: What does the problem want you to find out? T 03 – Leandro: The total amount of ties he has. T 04 – Teacher: Do you think you are supposed to count only the ties or ties and scarfs? T 05 – Leandro: Ties and Scarfs. T 06 – Teacher: And what do you think, Marcelo? T 07 – Marcelo: The same! T 08 – Teacher: But, what answer does the problem ask for? T 09 – Marcelo: How many ties does he have? T 10 – Teacher: So what are you going to count? T 11 – Leandro: We’ll count like this: 21, 22, 23, 24 (to add 21 to 15, and so on). (Narrative, Elizangela, October 2013).

15. The different ways through which students have reported their experiences are valuable to our group, and the teachers have also used them very often in their classes. Through writing, students show their mathematic ideas, and the teachers may evaluate the level of development of each student, identify the ways they develop reasoning, and identify conceptual problems and mistakes.

16. Teachers use the records to promote group discussions in the classroom. The pedagogic practice is based on dialogue and interactions among actors (teacher and students, students among themselves). The central role the teacher as a mediator in the teaching/learning process is also clear, both in the negotiation established in the classroom, and in the dialogical relation among the participants.

17. Using both educational actions and pedagogical mediation, as central elements in the students’ processes of conceptual construction, teachers learn and validate new ways of teaching mathematics. When teachers analyze the different mathematic reasoning that students express in the interactive dynamics of classroom, or in written texts, they are able to produce new meanings, and bring new possibilities to school mathematics.

18.  Teachers learn with narrated practices  the narratives are socialized in the group.  The debates among participants, as well as the sharing of oral or written narratives, have enabled all of them to increase their knowledge about school mathematics and learning.

19.  We are witnessing a cooperative knowledge building process to teach mathematics, in conceptual, pedagogical and curricular terms.  Teachers’ reflections are based on:  methodological and conceptual aspects of the practices narrated,  In the ways to organize pedagogic work,  Kinds of texts which circulate among students and types of texts that they produce,  literacy practices used in classroom, etc.

20.  When teachers analyze what their colleagues report, they raises aspects considered significant.  The fact they can make these analyses is a sign of learning with their own practices, and that of their colleagues.  When they agree with the way the colleague do their work, they validate this knowledge produced in classroom context. This kind of knowledge is invaluable for the professional development of teachers.

21.  The teachers learn with their colleagues and with the reflections produced collectively.  They also learn with the professors, who contribute to their development, through a new appreciation of the movement of construction of mathematical concepts, through records and literacy practices.

22. When reflecting and analyzing the narrated practices, the professors also learn with their elementary school colleagues. They understand the complexity of the school routine, and the constraints teachers face when they wish to do an activity with students, but several factors prevent its success. Or new demands for which they were unprepared arise, and they have to postpone their plans.

23. We have started to understand:  the importance of dialogue and of the use of mathematical discourse in the classroom.  the need to organize pairs of students at similar levels of development, so both of them can further develop.  the need to evaluate and reflect about our actions in the classroom.  And that, when we share the things we learn we develop ourselves as professionals.

24. Góes, M. C. R. de (1997). As relações intersubjetivas na construção de conhecimentos. In: Góes, M.C. R.de; Smolka, A.L. B. (Org.). A significação nos espaços educacionais: interação social e subjetivação (pp. 11-28). Campinas, SP: Papirus. Nacarato, A.M. (2013). A sala de aula de matemática dos anos iniciais como objeto de investigação de professoras-pesquisadoras. [The mathematics lesson in the initial years as an object of investigation for teachers-researches]. Educação Matemática Pesquisa. São Paulo, v.15. Número especial, pp. 837-855. Prestes, Z. (2012). Quando não é quase a mesma coisa: traduções de Lev Semionovitch Vigotski no Brasil. Campinas, SP: Autores Associados. Smagorinsky, P. (2011). Vygotski and literacy research: a methodological framework. The Netherlands: Sense Publisher. Street, B.V. (2013). Políticas e práticas de letramento na Inglaterra: uma perspectiva de letramentos sociais como base para uma comparação com o Brasil. Caderno Cedes, Campinas, v. 33, n. 89, p. 51-71, jan.-abr. 2013. Disponível em. Acesso em agosto de 2013. Vigotski, Lev S. (2001). A construção do pensamento e da linguagem. Tradução de Paulo Bezerra. São Paulo: Martins Fontes.