with the use of EXCEL during the problem solving process. The interaction of the student with
the tool (Excel), along with the combination of representations, knowledge and mental
operations, form what is known as instrumented action (Verillion in Guin and Trouche, 1999 p.
201). In this context, we can conclude that the use of Excel as a tool in mathematics learning
might be closely related to the students’ understanding of the mathematical concepts that underlie
the embedded procedures to represent and operate those concepts.
In order to interact with the instrument it is necessary for students to access to mathematical
knowledge to understand and employ the commands properly. At the same time it is the
instrument that permits the differentiation of mathematical objects from their different
representations, thereby promoting better understanding of the concepts.
However, the appropriation of an instrument is not accomplished naturally for all individuals.
It is the instructor who must be responsible for the design of learning activities that orient the
work of the students toward investigation and exploration by way of the interaction between
systems of graphic, algebraic or numerical representations. This then leads to the students’
cognitive reorganization (Dorfler 1993).
In activities that incorporate Excel as a tool, exploratory work seems necessary to promote
interaction among graphic constructions and numerical and algebraic calculations. The work of
the students in these activities must stimulate them to compare results and observe the differences
between the work with paper and pencil and that in which they use the tool (Guin & Trouche
1999).
Subject Methods and Procedures
In this study we document and analyze the work shown by university students who worked on
activities oriented towards the construction of the derivative concept integrated with the use of
Excel as a cognitive tool.
The use of different systems of representation permits us to approach a mathematical concept
such as the derivative. Our idea was that the study of the derivative concept can be developed
trough learning activities that involved infinitesimal, symbolical, definition, geometric
interpretation, physical interpretation and linear approximation approaches (Thurston 1994).
The integration of all of these ideas develops a more sophisticated thought process which
generates new concepts and new mathematics structures.
Tasks used in this study can be classified into two groups; a) those that relate quantities by
way of the mathematical model of a contextual situation; b) others wherein the mathematical
model is given in an activity to realize the interpolation by way of linear approximation.
In each activity the students have the opportunity to identify important mathematical ideas
that emerge in the proposed problems: functions, dependent and independent variable, linear
functions, the rate of change, the slope of a straight line and the derivative functions.
In order to document the distinct forms of understanding of the fundamental concepts
surrounding the derivative, activities were selected and designed so that they could be explored
by the students with different mathematical resources; utilizing different forms of representation,
these being the point between the mathematical activity of the student and the incorporation of
the tool (EXCEL).
The work of the students in the problems was organized in terms of problem solving phases
that involve:
Understanding of the problem
Analysis of the information
Identification and exploration of the function
Identification of the mathematical ideas
Convention