Saberes e práticas de docentes que atuam no 5º ano do ensino fundamental sobre as operações de adição e subtração à luz da cifranavização

Abstract

The ability to perform calculations is necessary for solving many everyday situations, as well as for learning various Sciences. The term ciphernavaring indicates the process by which the subject learns numerical notation, as well as performing fundamental operations. Many children still complete the 5th year of Elementary School without correctly solving simple addition and subtraction maths. This scenario is related to inadequate practices, among which, the teaching centered on the algorithm stands out with explanations based on “go one” and “borrow”, without students understanding them, as they are related to the characteristics of the so-called System. of Decimal Numbering – SND, especially to the place value. Given the above, we ask: how does the teacher explain the addition and subtraction algorithms? How do teachers interpret the resolutions of numerical representations of addition and subtraction accounts of students from the 5th year of Elementary School; What are the contributions of reflection provided by continuing education on practice to expand teaching knowledge about teaching and learning the operations of addition and subtraction? The objectives of this research are: General – To analyze the contribution of formative meetings to the expansion of knowledge of teachers of the 5th year of Elementary School in the teaching of addition and subtraction operations. Specific: i) To analyze the teaching strategies of teachers of the 5th year of Elementary School in the teaching of addition and subtraction operations; ii) Interpret the resolutions of numerical representations of addition and subtraction accounts of students of the 5th year of Elementary School; iii) Analyze how teachers interpret the resolutions of numerical representations of addition and subtraction accounts of students in the 5th year of Elementary School; and iv) Evaluate the pedagogical contributions of the diagnosis of student knowledge in the professional practice of teachers in the 5th year of Elementary School in the teaching of addition and subtraction operations. The resources and techniques used in the data collection of this qualitative research were: training meetings, class observation, field diary, diagnosis of student knowledge and interview. The research had 4 stages: i) formative meetings and class observation; ii) diagnosis of students' knowledge; iii) training meetings, via internet, with professors to analyze and interpret the results of the students' diagnosis; and iv) interview. During the observed classes, we found that the teaching strategies in teaching addition and subtraction had aspects of traditional mathematics teaching, which had the blackboard, brush and textbook as the only resources. We witness mistakes during the explanation of addition and subtraction operations. A diagnostic instrument with 8 beads (4 addition and 4 subtraction), with numerals from 2 to 5 orders and involving grouping and ungrouping, was applied at the beginning of the school year, and answered by 83 students from the 5th year of Elementary School of 3 classes. The percentage of correct answers in the addition accounts was 58.1% and in the subtraction accounts it was 13.3%. The most frequent error in the resolution of the numerical representations of the addition accounts was Error in counting the digits, either without grouping or with grouping. The most frequent error in solving the numerical representations of the subtraction accounts was Error in the operation of the digits, with the student subtracting the (smallest) digit of the subtrahend from the (larger) digit of the minuend. The 3 (three) teachers participating in the research reported that the students' difficulties in solving problems stem from the lack of understanding of the SC characteristics and that the use of the Place Value Table (QVL) can help them to overcome many of the mistakes made, notably regarding the understanding of place value. Teachers also stated that a careful analysis of the diagnosis of student knowledge, quantitatively and qualitatively mapping errors, guiding the proposition of pedagogical interventions appropriate to reality, favoring student learning. We conclude that the formative meetings contributed to the expansion of teaching knowledge, especially concepts related to learning and teaching addition and subtraction.