STUDY OF SOLVING STRATEGIES AND PROPOSAL FOR THE TEACHING OF RATIO AND PROPORTION
Elena Fabiola Ruiz Ledesma
CINVESTAV-IPN
This document reports an investigation in process, which approaches the
topics of ratio and proportion, whose importance and current interest have been
shown in studies done in several countries and during various decades. The research problem consists of identifying
the strategies employed by students who are finishing their primary education
as they solve problems involving ratio and simple and direct proportions, in
order to identify qualitative and quantitative components linked to these
topics and their diverse modes of representation. These strategies will be the basis on which a proposal for
teaching these topics will be designed and applied. The strategies used by the subjects are important because they
permit the recovery of certain passages of thought, they exhibit a wide
diversity of resources as well as different modes of representation, all of
which are fundamental for the design and application of the teaching proposal
to be carried out.
The theoretical background consists of work by researchers from
different countries in different epochs, beginning with the theory of Piaget
(1972, 1978) and culminating with the recent tasks Lesh (in press) has designed
to teach ratio and proportion. The
authors mentioned in the theoretical framework are mostly constructivists like
Hart (1988), and the rest have basic coincidences with constructivism. These have attempted to create consistency
in the conjunction of didactics with mathematical reflection on ratio and
proportion.
The research instruments establish a relationship with the
objectives. In terms of the sequence of
the application of these instruments, first direct observations have been done
in the classroom, following this are indirect observation of the activities
carried out by the students in their notebooks. After that, a questionnaire has been given to the students on
their form of work when dealing with ratio and proportion problems to look more
closely at the students. In order to
confront the situations lived by the student in this framework, a series of sessions
have been conducted by the researcher and have been observed by people involved
in the field of mathematics education, as she gives students ratio and
proportion problems to be solved by the students. Once the work sessions were concluded, a second questionnaire was
given to the students in order, in this case, to check the progress the
students might have made. To look more deeply into this progress and into the
strategies that can be identified through the teaching process put into
practice by this researcher, “semi-structured” interviews will be used.
References
Hart, K. (1988). Ratio and proportion. In: J. Hiebert & M. Behr (Eds.), Concepts and operations in the Middle Grades, 2. Reston, Virginia: National Council of Teachers of Mathematics.
Lesh, R. & Doerr, H. (in press). Modeling and Local Conceptual Development. In: A. Kelly & R. Lesh (Eds.), Research design in mathemathics and science
education. Hillsdale, NJ: Lawrence
Earlbaum.
Piaget, J. & Inhelder, B. (1978). Las operaciones intelectuales y su desarrollo. In J. Delval (Ed.), Lecturas en Psicología del Niño, I (pp. 70-119). Madrid: Alianza Editorial.