The concept of function and the student´s knowledge of High School
This dissertation presents an investigation that aimed to investigate the practice of the teacher who teaches mathematics from the use of tasks on the concept of function in High School. For this, we used theoretical references that dealt with the learning of students of Basic Education and the practice of the teacher who teaches mathematics from the systematic literature review to legitimize the units of analysis chosen for each axis. For the systematic literature review on the students' learning axis, three units of analysis were used: didactic resources, technological resources and tasks. The units of analysis for the practical axis of the teacher who teaches mathematics were used two units of analysis: didactic resources and technological resources, where the mathematical tasks were represented between them. Especially regarding the communication of typologies of the concept of function. The research has a qualitative nature and had as participants the researcher himself, who seeks to reflect on his professional practice in the classroom in the development of tasks and students in the 1st grade of regular high school in a public school in the state of São Paulo. The multipaper format of this dissertation provides the reader with guidance on the developed subjects: student learning, the practice of the teacher teaching mathematics and the development of the mathematical task. Data production was developed based on three aspects: (1) the elaboration of tasks on the concept of function; (2) the development of tasks by students in the classroom; and (3) reflection on protocols and audios on teacher and student knowledge. The research results showed how tasks favor the communication of the concept of function, highlighting the dimensions of teacher knowledge and student learning.