Golden material in teaching fundamental arithmetic operations for teachers in the Teacher Training Course

Abstract

The present work aims to present a report on the implementation of a Thematic Workshop on the fundamental operations of arithmetic with the aid of the golden material. The workshop was carried out with future teachers of the Teacher Training Technical Course at a public school in the municipality of Paranavaí. Forty-four future teachers participated, distributed into three groups with an average of 15 participants per group. Each workshop lasted approximately 1 hour and 45 minutes. According to Grando (1995, p. 35), games play a pedagogical role in the application of concepts in mathematical learning. In the first part of the workshop, we explained, based on historical materials, the origin of the golden material, its creator, and the meaning of each piece that composes the material. In the second part, a game was carried out with the future teachers with the intention that they could apply their knowledge about the transformations that can be made between the place values in the golden material, that is, between units and tens, and between tens and hundreds, respectively. Afterwards, the addition and subtraction algorithms were explained on the board, with practical examples followed by the mathematical definition. Furthermore, the concept of the decimal number system, its classes, and its place values were explored and systematized. Next, some practical examples were given so that the future teachers could practice the addition and subtraction algorithms using the golden material, according to the class and place value of the given numbers. The same process was repeated for the multiplication and division operations, with the game being played, followed by the explanation and systematization of the algorithms of these respective operations, and the practice using the golden material. This game made it possible to explore the algorithms of addition and subtraction between integers, as well as to lead discussions about the algorithms of multiplication and division. During the implementation of the workshop, it was observed that, with the help of the manipulable material, the students had the opportunity to understand the meaning of each operation and the transformations that occur in each. The future teachers had more difficulty when they needed to place the numbers in their respective places on the positional value board during the multiplication operation using the golden material. This doubt was addressed during the workshop, with explanations through the review of the addition and subtraction operations and through practical examples, in which the future teachers were able to continue solving the exercises. We conclude that the use of the golden material can contribute to and provide opportunities for understanding the fundamental operations of Mathematics, since, in addition to generating greater interest in the content through the applied game, there were explanations about common expressions used when performing fundamental operations, such as “carry one” or “borrow one.” We hope that this workshop can contribute to the development of investigations regarding signs and meanings in Mathematics teaching, highlighting communication and interpretation in the learning process of Mathematics.