Uma base de conhecimentos para o ensino de taxa de variação na Educação Básica - Silva, Edson Rodrigues da (2017)
The present research aims to build a knowledge base for the teaching of rate of change in Basic Education. For this, and in order to guide our research, we have established the following research question: What knowledge base is required for the teaching of rate of change in Basic Education? To answer this question, we used a bibliographical study as a methodological contribution, in which the sources of investigation consisted of researches that deal with the processes of teaching and learning of the rate of change in Basic Education, of the official documents that guide and organize the teaching of Mathematics in Brazil and in most Brazilian states, of the didactic materials used in different periods in Basic Education and scientific articles. The theoretical framework was based on the Knowledge Base Theory for Teaching, specifically in the conceptions of Shulman, Mishra and Koehler, Lima and Silva and Ball, Thames and Phelps and in the Anthropological Theory of Didactics of Chevallard. These theories helped us to compose a scenario that evidences the know that, when studied, conditions the construction of the necessary knowledge for the teaching of rate of change in Basic Education. There are four categories of teaching knowledge of fundamental and for the teaching of rate of change in Basic Education mediated by technologies: content knowledge, didactic knowledge, technological knowledge and pedagogical knowledge, in which their different interactions meet the conception of knowledge as a network of meanings and that, for us, constitute a knowledge base for the teaching of rate of change in this level of schooling. The construction of an Epistemological Model of Reference for the teaching of rate of change in Basic Education evidenced a Mathematical Organization that includes the know that, when studied, condition the construction of content knowledge for this teaching. The didactic knowledge for the teaching of rate of change includes the range of knowledge concerning the Theory of Didactical Situations, the Theory of Registers of Semiotic Representation, the Theory of Conceptual Fields, the Anthropological Theory of the Didactics, Didactic Engineering, the notion of Didactic Contract And the notion of Obstacle. The technological knowledge for the teaching of rate of change comprises the knowledge about the interface, functionality and characteristics of dynamic mathematical software that can be used in favor of the teaching and learning of this notion. The pedagogical knowledge for rate of change teaching comprises the range of knowledge that the teacher needs to mobilize to prepare, structure and assess tasks, to motivate and support student autonomy, to organize the different materials available, to manage the classroom, to deal with subjectivity and heterogeneity in the classroom, with the cognitive time of each student, with diverse groups, etc