Salinas, P. (2010). - Repositorio Digital - Instituto Politécnico Nacional

ABSTRACT
This research is part of a collegial working on the conceptualization of a proposal for what
to teach and how to teach Calculus. The proposal seeks to promote in the classroom, the
emergence and development of procedures and basic concepts of calculus in such a way
as to fairly assess the formation of Calculus as a conceptual system structured logically.
This proposal responds to a broad vision of mathematics according to which its role as
human activity to solve problems makes this science of crucial importance for the study of
other areas of knowledge. The proposal is developed for higher level of education,
particularly for an institution in northern Mexico, and responds to the instrumental nature
of the courses in the curriculum of Mathematics for the different university programs
offered. In its design intends to integrate, educationally speaking, a Newtonian approach
with a Leibnizian approach to the genesis of Calculus, in the belief that a discourse of this
kind offers greater opportunities for the student to take ownership of the ideas behind
the construction of notions and procedures of Calculus in their role as tools to solve real
problems related to the study of change.
The purpose of this paper is to consolidate the implementation of the proposal at its first
part, one in which the practice of predicting the value of a quantity that is changing with
respect to other works as a prelude to introducing the Newtonian approach in school
discourse. In this introduction plays a key role incorporating a numerical procedure to
approximate the value of magnitude. Euler's method, the name which finally identifies
this procedure in the classroom, has been introduced in the calculation of the school
discourse allowing simultaneous incorporation of the notions of rate of change and
cumulative change, thereby fostering the notions of derivative and integral being involved
from the beginning of a first course in Calculus. The effect of early and simultaneous
incorporation of these notions raises new questions to be addressed in an effort to
strengthen the proposal.
The inquiring about the conditions affecting the student ownership of the numerical
procedure to approximate the value of the quantity that is changing becomes a research
problem. The interest on further analysis of this problem lies in the very stage where the
interaction takes place between teachers, students and mathematical content, in the
classroom. The aim of this work consists of: 1) design activities for the introduction of the
Newtonian paradigm through numerical procedure known as Euler's method, 2) carry out
a sequence of performances that include such activities in the first course of Mathematics
for Engineering careers, 3) capture data to assess the effectiveness of the acquisition of
this procedure in each staging and to suggest items for improvement and 4) strengthen
the establishment of a teaching sequence that functions as the epistemology of the
notions of rate of change and cumulative change.
Both, the aforementioned proposal and this work are framed within the
Socioepistemological approach to research in Mathematics Education in responding to an
epistemology of practice rather than concepts. Consistent with this approach is
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