Algoritmos das operações de adição e subtração no 4º ano do ensino fundamental à luz da cifranavização: saberes docentes, práticas pedagógicas e conhecimentos discentes

Abstract

Even before starting school life, we build a relationship with Mathematics based on the needs we encounter in our daily lives and one of them is performing calculations. The Curricular Documents emphasize the importance of this skill when they propose that students are able to solve problems, which consider the reality they experience. Despite the guidelines on Mathematics Education in Basic Education contained in those texts, the learning of fundamental operations (Cyphernavaring) is unsatisfactory according to several studies. One of the main factors for this scenario is that teachers do not have enough knowledge to teach such content, which is related to the Decimal Number System (Ciphernavic System). Given the above, this research sought to answer the following questions: What are the teaching strategies that a 4th year elementary school teacher uses to teach the operations of addition and subtraction? What is the teaching knowledge of a teacher who teaches Mathematics in the 4th year of Elementary School about the Ciphernavic System? What knowledge do students in the 4th year of Elementary School have about addition and subtraction algorithms? The general objective of this research was to analyze the knowledge and practices of a teacher who works in the 4th year of Elementary School on addition and subtraction algorithms. The specific objectives were: i) Identify the teaching strategies used by the teacher in teaching addition and subtraction operations; ii) Discuss the teaching knowledge of a teacher who teaches Mathematics in the 4th year of Elementary School on the Ciphernavic System; and iii) Interpret the knowledge of students in the 4th year of Elementary School about addition and subtraction algorithms. The qualitative research was carried out in a 4th year elementary school class at a public school in the municipality of Eusébio, in which the teacher and 21 students from the class participated. To collect data, observations of Mathematics classes were carried out, in order to understand the practices carried out by the teacher; semi-structured interview, to identify the teacher's content, pedagogical and existential knowledge about the Cifranavic System; and a diagnosis of student knowledge about addition and subtraction algorithms, with 4 addition accounts and 4 subtraction accounts. It was concluded that the practices carried out by the teacher, rooted in a mechanical methodology, centered on the textbook and carrying out activities copied on the board, match the gaps in teaching knowledge related to the Ciphernavic System and fundamental operations, directly impacting the learning of students about these algorithms. This is manifested in the percentage of correct answers in the addition (69.6%) and subtraction (26.8%) calculations, as well as in the different types of errors made by students when diagnosing student knowledge. Student errors when performing calculations need to be interpreted by teachers so that pedagogical interventions increase student learning.