Claudete Cargnin –UTFPR-CM/UEM Rui Marcos de Oliveira Barros - UEM

 To study construction of the concept of definite integral using concept maps  was created a didactic sequence in which the concept of convergence was one of the target concepts

 Data were collected in a short course offered to first year students of undergraduate courses, who voluntarily enrolled (total 14) and were, on occasion, studying Calculus I for the second or third time, or already attending Calculus II.

 we used the software Geogebra and wxMaxima as support for research students.  The analysis of the convergence of numerical sequences supported by graphical representations in R and R2 were requested for the students, as well as the writing of convergence using the notation of limits. The records of the analyzes both in natural and algebraic language were required.

 Sequence [,,, ]  These commands were used  Sequence [(expression, 0),,, ]  Both representations allow students to associate convergence with proximity  Students have to describe the sequences’ behavior using natural language and notation of limits

 We observed that is not natural, to students, to register the behavior of the sequences using the natural language.  which indicates the need for activities in the classroom, where students can describe, in their own words, what is being done, and to convert the mathematical language to natural language, and vice versa

 the graphical representation of sequences in R and R2 allowed the understanding of the notion of convergence by the students, which could record their observations in natural language, but not in algebraic language.

 At first, the students did not understand the meaning of "points" on the x-axis, and many resorted to representation in R2 to compare the behavior of the sequences.  The use of software wxMaxima corroborated this understanding and enabled students to attribute meaning to expressions like f(n).

 The students’ facility in understanding the convergence of a numerical sequence from the graphical representation and collective discussions, allows us to concluded that the exhaustive exploration of these factors, before the formal presentation of a concept or definition, can provide a better understanding of mathematics on screen, reducing rejection and aversion of mathematical symbols, which become educational obstacles for teaching math concepts.

 Activities related to the concept of convergence also allowed students to assign meaning to theoretical calculations presented in the course of Calculus, when discussing the limits at infinity. This information was used to create a convergent sequence.

 the didactic sequence applied to the concept of convergence possible with the support of software Geogebra and wxMaxima, the collective discussions, and varying forms of semiotic register, understanding the notation of limits, provided greater familiarization with the mathematical registration form and encouraged participants to write more and better about their observations of mathematical facts.

Thank you!