Abstract:

The transition from Arithmetic to Algebra is one of the great difficulties of the students and there are errors that occur and persist over time. The curricular guidelines settled out in the Principles and Standards for School Mathematics (NCTM, 2000) suggest that students should significantly learn Mathematics based on their math skills that were previously acquired.

In Portugal, the Mathematics Program of Basic Education (MEC, 2013) considers that, in the 7th grade of basic school, students begin with formal study of algebra, when the students work with "letters" and points out that those students should understand the meaning of "letters", usually called variables and operations with them.

The chapter "Functions" awaken the algebraic thinking and leads, for example, to the generalization. In the case of the teaching process, there is a consensus that the issue of "Functions" must have a central place in algebra education, particularly at primary (elementary) level (Suh, 2007).

This paper explores the use of an applet, named Function Machine, which allows students to observe patterns and regularities from pairs of numbers and make generalizations using words and symbolic rules. As a specific purpose it was intended to show how an educational experience, based on the observation of numerical regularities, allows an expression of general and contributes to the development of algebraic thinking.

Methodologically, we opted for a qualitative and interpretative research approach, created on a case study. Data collection was done through direct observation of a lesson and written productions of students. An activity was drafted with two issues and applied to two classes of the 7th grade of basic school during a math class of fifty minutes, who answered individually to the data items and interacted with the computer at the same time. The teacher is an author and assumed the role of observer.

The results show that most of these students from the 7th grade of basic school are enabled to make generalizations, find an expression that translates the general structure of the displayed pattern and justify their answers using the current language, the language of mathematics, or a combination of both languages. Sometimes the Function Machine influenced the choice of the general expression of a pattern, because the student can confirm whether it is correct or not by viewing this dynamic form of information on the computer screen.
Overall, it is concluded that there was a significant improvement in student performance at the level of generalization.

References:
[1] Ministério da Educação e Ciência (MEC). (2013). Programa Metas curriculares Matemática - Ensino Básico. Lisboa: Ministério da Educação e Ciência.
[2] National Council of Teachers of Mathematics (NCTM). (2000). Principle and Standards for School Mathematics. Reston,VA: NCTM.
[3] Suh, J. M. (2007). Developing Algebra-‘Rithmetic in the Elementary Grades, Teaching Children Mathematics, 14(4), 246-253.

Keywords:

Pattern, Function, Function Machine, Algebraic thinking.