ON THE INSTRUMENTATION PROCESS OF A COMPUTATIONAL TOOL
Martha L. GarcĂa RodrĂguez
ESIME Cinvestav- IPN
## email not listed ##
Manuel Santos Trigo
Cinvestav – IPN, México
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This document analyzes the work of a group of university students in their attempts to
comprehend the concept of derivative. In particular, we focus on analyzing the type of students’
cognitive reorganization that they show as a result of using EXCEL as a problem solving tool.
The cognitive changes developed by the students are identified through the connections they
establish between systems of numeric, graphic and algebraic representations. The work of the
students was oriented trough the discussion of problems that involve phenomena of the rate of
change and linear approximation as fundamental ideas to the understanding the derivative
concept.
Introduction
The importance of employing different technological mediums in the learning of mathematics
has been sustained in the results obtained in different investigations (Santos, et al 2003), wherein
the student’s understanding of mathematical ideas seems to be tied to the relationships they are
able to establish among different representations. Recent curriculum proposals recognize that
symbolic calculators and computer software, as well as spreadsheets, can become powerful tools
for students to develop numeric, graphic and symbolic representations.
In order for technology to contribute to the exploration of connections, among different
representations and as a consequence to the construction of mathematics concepts for the
students, the activities in which the students take part in the classroom with the help of
technological mediums must be carefully designed and directed by the instructor. Thus, we
document the cognitive reorganization shown by first year university students when they were
asked to use EXCEL to solve a series of tasks that involved the concept of derivative. The tasks
selected in this report focus on the ideas of the rate of change and linear approximation for
approaching the derivative concept.
Conceptual Framework
In the process of learning mathematics student’s understanding can be enhanced when
working with activities that involve the use of different representations. The relationships that
students establish among different representation systems can be considered as indicators of
change in their cognition. One method of seeing the connections that a student establishes among
different representational systems is through the examination of external representations that the
subject produces in writing, in speaking or in the manipulation of symbols such as algebraic
symbols. By way of internal representations the individual constructs these external
representations. Between the internal and external systems of representation, the subject
establishes significant relationships, which can be modified throughout the development of the
learning activities.
By assuming that individual’s comprehension can be exhibited in terms of expressing
different representations, the activities implemented in the classroom, employing a cognitive tool
such as a Excel can help students in the construction of connections among representations.
The term cognitive tool is used here “as whatever medium that helps transcend the limitations
of the mind…in thought, learning and activities involved in the problem solving” (Pea, 1987 p.
91). In order for the students to utilize Excel as a cognitive tool, he or she should develop a
psychological construct. This construct is found to be determined by the actions that are realized
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Convention