# the notion of convergence of number sequences with

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 [&lt;(variable, expression)&gt;, &lt;variable&gt;,
&lt;starting value&gt;, &lt; final value &gt;]
These commands were used
Sequence [(expression, 0), &lt;variable&gt;, &lt;starting
value&gt;, &lt; final value &gt;]
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 &quot;points&quot; 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