Pensamento algébrico e os significados do sinal de igualdade: o uso da oralidade e da narrativa nas aulas de matemática - Cruz, Patrícia de Souza Ferreira da (2016)
This study aims to understand and analyze how the communication, the student explaining how thought to solve the activity in math class you will be able to contribute to the development of algebraic thinking. To this end, we look for evidence of the development of some elements of algebraic thinking that can be attributed to the understanding of the equal sign with the sense of equivalence. To guide this study have formulated the following research question: how communication in math class you will be able to contribute to the construction of algebraic thinking? To perform this qualitative interpretive research, developed a string of activities based on the assumptions of the theory of Didactic Situations and records of Semiotic Representation, with 7th grade students of a State school, located in a traditional neighbourhood in the city of São Paulo. The students were placed in a situation of communication so that they could act, formulate their conjectures and validate their hypotheses. At first, the students in pairs decided activities producing a collective sense the equal sign and communicated their ideas through writing and orality. After that first time, the teams were swapped so that they could validate their responses or produce a new sense to the equal sign. The data were collected by means of audio recordings, video and some written observations in field journal. For the analysis, the transcript of some of the students ' dialogues in order to identify: (i) the different meanings of equal sign presented by the students and how it can interfere in the development of algebraic thinking; (ii) contributions to the development of algebraic thought attributed to interaction, communication, with fellow; (iii) the record of the natural language, as a first record of semiotics of equal representation and liaison with the other records of semiotic representation. From these analyses, we have seen the development of relational thinking and algebraic thinking, which were facilitated by communication between the students and the negotiation of meanings. Most of the students, at first, the meaning of the equal sign as an operator, that is, immediately after the equal sign should be writing the result of the operation, before the equal sign. Students who showed the significance of the sign as an operator, presented difficulty to address activities and, at times, were not knowing how to complete the proposed activity. In some cases, we observe that students, at first, showed the operational meaning, but, with the interaction with the partner and with the activity, managed to mobilise the expertise to assign a new sense to the equal sign as equivalence. The latter has overcome the activities so as to leave the sentences true. Communication in math class can help students produce sense of equivalence of the equal sign by facilitating the development of algebraic thinking, emphasizing the important role of the teacher, as a mediator of this interaction